# Taming the Electromagnetic Boundaries via Metasurfaces: From Theory and Fabrication to Functional Devices

Authors: Xiangang Luo; Mingbo Pu; Xiaoliang Ma; Xiong Li
Journal: International Journal of Antennas and Propagation
 (2015)

---

## Abstract

As two-dimensional metamaterials, metasurfaces have received rapidly increasing attention from researchers all over the world. Unlike three-dimensional metamaterials, metasurfaces can be utilized to control the electromagnetic waves within one infinitely thin layer, permitting substantial advantages, such as easy fabrication, low cost, and high degree of integration. This paper reviews the history and recent development of metasurfaces, with particular emphasis on the theory and applications relating to the frequency response, phase shift, and polarization state control. Based on the current status of various applications, the challenges and future trends of metasurfaces are discussed.


---

## Body

## 1. Historical Remarks

Metasurface is a two-dimensional (2D) analogy of metamaterials [1, 2], which are artificial three-dimensional (3D) structures with subwavelength inclusions as well as effective constitutive parameters not occurring in natural materials. In the last years, metamaterials with negative, zero-refractive-index, and other exotic phenomena have enabled novel functionalities, such as invisibility cloaking [3] and perfect imaging [4]. Although metamaterials have achieved great success in the entire spectrum, great challenges still exist in the large-scale fabrication and the design of devices with broadband response, especially in the visible frequency range [5]. As alternatives, metasurfaces were proposed to tune the behavior of electromagnetic wave within one infinitely thin layer. Since metasurfaces are extremely thin and much easier to be fabricated than metamaterials, they have become one of the most promising researching areas in electromagnetics and optics [5]. As noted by Holloway et al., current optical metamaterials are actually often limited to construction of metasurfaces as a result of the huge fabrication obstacles [6].Since James Clark Maxwell formulated his famous equations in 1863, it has been known that all electromagnetic problems can be solved if one knows the constitutive parameters, initial and boundary conditions [7]. Actually, the essence of metamaterials is the precise design of constitutive parameters, whereas metasurfaces can be treated as a modification of boundary condition since they possess theoretically vanishing thickness. From this point of view, one can conclude that both metamaterials and metasurfaces can provide complete control over the electromagnetic fields. As illustrated in Figure 1, metasurface could replace traditional metamaterials in many conditions, such as invisibility cloak, perfect lens, and high-efficiency radiators [3, 4, 8, 9]. It should be noted that the interface between metamaterials and normal materials can be also regarded as a novel metasurface boundary condition, where many optical properties can be engineered without resorting to the bulk properties of the metamaterials [10]. In particular, exotic surface waves at these metasurfaces have also attracted great attention.Figure 1
Comparison of metamaterials with metasurfaces. (a) Metasurface cloak. (b) Perfect metasurface lens. (c) Conformal metasurface versus traditional zero index metamaterial. Figures are reproduced from [2].
(a)
(b)
(c)Although the upsurge in attention has been paid to metasurfaces only recently, the actual concept of metasurface is far from new. In fact, the electromagnetic theory of metasurface can be dated back to 1902, when Wood reported his notable anomaly [11] and Levi-Civita gave the boundary relations for a metallic sheet with vanishing thickness [12]. The discoveries of Wood and Levi-Civita have promoted the development of two areas, which are long treated as independent of each other. One research area of metasurface is about the surface plasmon polariton (SPP), which is a particular solution of surface wave at metal-dielectric surface; the other includes frequency selective surface (FSS), impedance sheet, and various types of planar antenna arrays. In the optical regime, the two areas begin to overlap with each other [13], since most of the metals in the metasurfaces become plasmonic at this particular frequency range. Indeed, it will be shown that the SPP and ordinary electromagnetic wave in metasurfaces can be deduced from a unified theory.In recent years, there are a lot of research articles and review papers regarding the topic of metasurfaces. As an attempt to distinguish the concept of metasurface from previous FSS, Holloway et al. suggested that the different concepts can be classified according to the length scales [6]. Nevertheless, it is difficult to separate FSS and metasurface from the perspective of electromagnetic interactions, since both of them can be well described by effective impedance, although FSS is only intended to modify the frequency dependent transmission/reflection.In this review, we attempt to give a unified perspective to the development of metasurfaces. The mechanism and applications of these metasurfaces are discussed in detail with an outlook for future development. As shown in Figure2, there are many categories in the applications of metasurfaces: spectrum filters (including FSS [14–16], color filters [17], Fano resonances [18–25], and modulators [26–29]), plasmonic components for near-field optics [30–34], amplitude manipulation devices (absorbers [35–38] and antireflection coatings [39–42]), phase shifters (geometric phase [43, 44] and impedance-induced [19, 45] and plasmon-induced [2, 46] phase shifter), antennas, and other electromagnetic devices [47–50].Figure 2
History and applications of metasurfaces.


## 2. Overview of Theoretical Approach

As implied by its name, metamaterial can be treated as an effective medium with complex permittivityε and permeability μ. In the last several years, the effective medium theory (EMT) has been successfully applied in the analysis of metamaterials. Various methods, such as field averaging and S-parameters retrieving, have been proposed to obtain these effective parameters [51]. Although metasurface is an analogy of metamaterials with reduced dimensionality, the effective medium theory turns out to be less useful since the thickness of metasurface is approaching zero [6]. Indeed, the definition of permittivity and permeability is ambiguous in such a thin layer [52].In this section, we would like to give an overview of the impedance theory for simple metasurfaces [2]. Instead of the susceptibilities, the electric impedance and magnetic impedance are adopted to connect the electric and magnetic fields at the boundaries of metasurfaces. For simplicity of discussion, the discussion in this paper is confined in uniaxial metasurfaces. First, the impedance boundary condition for metasurface is deduced from a general slab with given constitutive parameters and thickness. Second, some possible applications are discussed based on the properties of metasurfaces.As depicted in Figure3, the electromagnetic boundary condition requires that the tangent components of both electric fields E and magnetic fields H are continuous across the interface between two dielectric media. For both the transverse electric (TE) polarization and the transverse magnetic (TM) polarization, the boundary conditions can be written as(1)
1
+
r
=
t
,
Y
1
1
-
r
=
Y
2
t
,where r
=
E
y
r
/
E
y
i and t
=
E
y
t
/
E
y
i for TE polarization and r
=
E
x
r
/
E
x
i and t
=
E
x
t
/
E
x
i for TM polarization. The horizontal admittance for each medium is defined as Y
i
=
H
x
i
/
E
y
i for TE polarization and Y
i
=
H
y
i
/
E
x
i for TM polarization (here i is the index of layer). From Maxwell equations, one can obtain(2)
∇
×
E
=
-
μ
μ
0
∂
H
∂
t
,
∇
×
H
=
ε
ε
0
∂
E
∂
t
.Figure 3
Boundary conditions at the interface between (a) two media and (b) a slab embedded in the two half spaces. Figures are reproduced from [2].
(a)
(b)Appling (2) to (1), the admittance can be obtained as(3)
Y
i
=
k
z
i
μ
i
μ
0
ω
=
ε
i
μ
i
k
0
2
-
k
x
2
μ
i
μ
0
ω
,
for TE
,
ε
i
ε
0
ω
k
z
i
=
ε
i
ε
0
ω
ε
i
μ
i
k
0
2
-
k
x
2
,
for TM
.Here,k
x is the horizontal wave vector in this system, which is continuous for all planar multilayers. If light is illuminated from the air side, the incidence angle is θ
i
=
arcsin
⁡
k
x
/
k
0. From (1) and (3), the reflection and transmission coefficients can be then expressed as follows:(4)
t
=
2
Y
1
Y
1
+
Y
2
,
r
=
Y
1
-
Y
2
Y
1
+
Y
2
.It should be noted that (3) and (4) are identical to the traditional Fresnel equations, except that the horizontal wave vector instead of the ambiguous incidence angle is used here. Our approach has also an advantage of simplicity since the reflection and transmission coefficients for both of the two polarization states keep the same.As shown in Figure3(b), for a thin slab sandwiched by two different media, the boundary conditions are(5)
1
+
r
=
a
+
b
,
Y
1
1
-
r
=
Y
2
a
-
b
,
c
+
d
=
t
,
Y
2
c
-
d
=
Y
3
t
,where 1, 2, and 3 denote the three layers and a, b, c, and d are the coefficients for the counter-propagating waves inside the slab. By definition, there is(6)
a
=
c
exp
⁡
-
i
k
z
2
h
,
b
=
d
exp
⁡
i
k
z
2
h
.For extremely thin metasurface wherek
z
h
≪
1, it follows that(7)
a
=
c
1
-
i
k
z
2
h
,
b
=
d
1
+
i
k
z
2
h
.From (7), one can derive that(8)
a
+
b
=
c
1
-
i
k
z
2
h
+
d
1
+
i
k
z
2
h
=
c
+
d
+
i
k
z
2
h
c
-
d
,
a
-
b
=
c
1
-
i
k
z
2
h
-
d
1
+
i
k
z
2
h
=
c
-
d
-
i
k
z
2
h
c
+
d
.Here, we focus on the case when the permittivity and/or permeability of the middle layer is larger than that of the surrounding space. For nonmagnetic layer,Y
2
≫
Y
3; thus, c
-
d
≪
c
+
d, so (8) approximates as(9)
a
+
b
=
c
+
d
,
a
-
b
=
Y
3
Y
2
t
-
i
k
z
2
h
t
.Inserting (9) into (5), there is(10)
1
+
r
=
t
,
Y
1
1
-
r
=
Y
3
t
-
i
Y
2
k
z
h
t
.Comparing with the electric impedance boundary conditions(11)
1
+
r
=
t
,
Y
1
1
-
r
=
Y
3
t
+
Y
e
t
,one can derive the electric admittance for this slab:(12)
Y
e
=
-
i
Y
2
k
z
2
h
=
-
i
ε
2
k
0
2
-
k
x
2
μ
0
ω
h
≈
-
i
ω
ε
2
ε
0
h
-
i
ω
ε
2
ε
0
h
.When the permeabilityμ is much larger than ε, Y
2
≪
Y
3; thus, c
-
d
≫
c
+
d, so (8) approximates as(13)
a
+
b
=
c
+
d
-
i
k
z
2
h
c
-
d
,
a
-
b
=
c
-
d
.As a result, there is(14)
1
+
r
=
t
-
i
k
z
2
h
Y
3
Y
2
t
,
Y
1
1
-
r
=
Y
3
t
.Since the magnetic impedance boundary conditions can be written as(15)
1
+
r
=
t
+
Z
m
Y
3
t
,
Y
1
1
-
r
=
Y
3
t
,thus the magnetic impedance could be derived as(16)
Z
m
=
-
i
k
z
2
h
Y
2
=
-
i
ω
μ
2
μ
0
h
-
i
ε
2
μ
2
k
0
2
-
k
x
2
ε
2
ε
0
ω
h
≈
-
i
ω
μ
2
μ
0
h
.Clearly, the above assumption is valid even for oblique incidence as long ask
z
h is much smaller than unit and the constitutive parameters are much larger than unit. The expressions in (12) and (16) are similar to the previous results obtained from radiation problem [53].In the following, we will only discuss the case of thin structures without magnetic response. From (11), the reflection and transmission coefficients are(17)
r
=
Y
1
-
Y
3
-
Y
e
Y
1
+
Y
3
+
Y
e
,
t
=
2
Y
1
Y
1
+
Y
3
+
Y
e
.These equations can be considered as therevised Fresnel equations for metasurfaces. In principle, there are two kinds of waves: one with k
∥
<
k
0 and the other with k
∥
>
k
0. When k
x
<
k
0, waves will transmit from the upper space to the lower one. There is an abrupt change in the phase and amplitude in the reflection and transmission coefficients.Whenk
x
>
k
0, the surface plasmon modes can be derived by enforcing the reflection and transmission coefficients simultaneously to be infinite. For a single interface between dielectric and metal, this condition for (4) becomes Y
1
+
Y
2
=
0, leading to a propagation constant for TM polarization:(18)
β
=
k
x
=
k
0
ε
1
ε
2
ε
1
+
ε
2
.Since the discussion is confined to the case of nonmagnetic response, there is no solution for TE polarization.For an electric layer embedded in an infinite dielectric medium (insulator-metal-insulator, IMI), the guiding wave can be obtained similarly asY
1
+
Y
3
+
Y
e
=
0. It follows that the propagation constant can be derived from(19)
ε
1
ε
1
k
0
2
-
β
2
+
ε
3
ε
3
k
0
2
-
β
2
+
Y
e
ε
0
ω
=
0
.If one assumesε
1
=
ε
3, there is [54](20)
β
=
k
0
ε
1
-
2
Y
1
Y
e
2
.Considering the fact thatY
e
=
-
i
ω
ε
2
ε
0
h, there is(21)
β
=
ε
1
k
0
2
+
2
ε
1
ε
2
h
2
.According to (21), the wavelength of the coupled SPP approaches zero along with the decrease of the thickness [55].For metal-insulator-metal (MIM) structure, the above approximation is not valid anymore. The accurate propagation constant should be derived by directly solving Maxwell’s equations with boundary conditions:(22)
tanh
⁡
β
2
-
ε
d
k
0
2
h
2
=
-
ε
d
β
2
-
ε
m
k
0
2
ε
m
β
2
-
ε
d
k
0
2
.In the microwave frequencies, many metals behave as nearly perfect conductors, so that no SPP can be found in ideal planar metal surfaces. Instead, if the metal surface is perforated by subwavelength holes, the effective permittivity can be arbitrarily tuned to sustain spoof SPP [56], where(23)
μ
x
=
μ
y
=
8
α
2
μ
h
π
2
p
2
,
ε
x
=
ε
y
=
π
2
p
2
ε
h
8
a
2
1
-
π
2
c
2
a
2
ω
2
ε
h
μ
h
.The plasmon frequency is the cutoff frequency:(24)
ω
p
l
=
π
c
ε
h
μ
h
.As will be shown in Section3.6, spoof SPPs have been successfully utilized in the design of groove antennas in the microwave frequencies.


## 3. Applications of Metasurfaces

As shown in the previous discussion, the waves in metasurfaces have many exotic properties, including the extremely short wavelength, abrupt phase change, and strong achromatic dispersion. Based on these properties, traditional electromagnetic laws and theory, such as the theory of diffraction limit, laws of reflection and refraction, the Fresnel equation, and absorption theory, should be revised correspondingly [2]. Practically, the revised theorem could find many applications as follows.


### 3.1. Frequency Selective Surfaces

Frequency selective surfaces (FSSs) are planar, periodic arrays of conducting patches on a substrate or a periodic array of apertures in a conducting sheet, which are used to filter electromagnetic waves [14]. The spectral responses of these structures are affected by various physical and electrical parameters, including the shape and type of their constituting elements. These FSSs can be designed to demonstrate low-pass, high-pass, band-pass, or band-stop behavior. Over the years, they have been extensively used in a variety of applications ranging between radar radomes, radar absorbers, and so on [14].Early in 1919, Marconi and Franklin granted a patent that the contribution of a parabolic reflector was mimicked by using half-wavelength metallic wires [14]. Owing to the great potential military applications, FSSs have been the subject of intensive study since the 1960s.The performance of FSS can be interpreted by the impedance and equivalent circuit theory, combined with the boundary condition. For a nonmagnetic freestanding metasurface, the band-pass and band-stop FSSs correspond to parallel and series type LC circuits, respectively. One common feature of the traditional FSSs is that the size of the resonant elements and their spacing are comparable to half a wavelength at the desired frequency of operation [58]. Since the electromagnetic response is a collective effect, the finite surface must include a large number of the constituting elements and be illuminated by a planar phase front to obtain the desired frequency response. At some conditions, such as radomes at lower frequencies, FSSs of relatively small electrical dimensions that are less sensitive to incidence angle and can operate for nonplanar phase fronts are highly desirable. In order to achieve this purpose, Sarabandi and Behdad proposed a new type of FSS. The structure consists of a periodic array of small metallic patches printed on one side of a dielectric substrate and a wire grid structure printed on the other side, both with the same period. The periodicity of the printed patterns is much smaller than the wavelength of the operating wavelength. The validity of this concept was demonstrated by numerical simulations and experiments.One of the recent challenges for FSS is to optimize the frequency spectra with respect to angle of incidence and polarization of the waves impinging on it. In principle, multilayered FSS can improve these performances, but with oversized profiles. By using cavity mode whose resonant frequency is angle-independent, it was recently demonstrated that annular apertures array can show angle and polarization-independent transmission properties [15].Ideal FSSs require that the transmission/reflection at the band edge changes sharply, which cannot be satisfied by most single-layer FSSs. In 2011, we proposed a novel plasmonic FSS with sharp band edges. By making use of plasmon hybridization, the bandwidth of the filter is tunable over a large range from 56.6 to 182.2 THz with magnetic and electric couplings between adjacent unit cells, as shown in Figures4(c)–4(f).Figure 4
(a) Sketch of the large-angle FSS. (b) Evolution of the transmission efficiency as a function of the angle of incidence and incident wavelength. (c, d) Top and side views for the tunable band-stop FSS. (e, f) Evolution of the transmission spectra with different geometric parameters. Figures are reproduced from (a, b) [15] and (c)–(f) [57].
(a)
(b)
(c)
(d)
(e)
(f)More recently, the unique spectral properties of FSS were utilized to mimic many quantum phenomena, such as electromagnetically induced transparency (EIT) [59–61] and Fano resonance [19, 20, 62]. The interactions of different modes in the metasurfaces were tuned independently to achieve the desired spectral distribution of reflection and transmission. In 2007, Fedotov et al. reported a resonance response with a very high quality factor in a planar metasurface with symmetry breaking in the shape of its structural elements [20]. It was shown that this symmetry breaking enabled the excitation of trapped modes, that is, modes that are weakly coupled to free space. The interference of trapped mode and normal mode makes the transmission spectrum be of the famous Fano shape.In order to give a rigorous theory of Fano resonance in metasurface, we studied the electric and magnetic responses of a planar metasurface with perturbed periodicity [19]. Rigorous sheet impedance theory was given to analyze the electric-magnetic and magnetic-magnetic coupling effect. Interestingly, perturbation of the widths of wire pairs makes the adjacent metallic particles couple with each other. Q-factor as large as 100 has been theoretically obtained accompanying huge field enhancement, as described in Figure 5. It was believed that this kind of periodicity perturbation can provide a general approach for Fano resonance with ultrastrong local field enhancement.Figure 5
(a) Transmission coefficients for the symmetric and asymmetric metasurface slabs. Region I shows typical asymmetric line shape of Fano resonance. Region II demonstrates the ultrasharp resonance peak induced by interelement coupling. (b) Normalized magnetic fields (Hz) at the center of these resonators. The inset shows the unit cell and the points where the magnetic fields are extracted. (c) Quality factor of a cylinder array. (d) Scattering parameters of this array. Inset shows the distribution of the electric fields at resonant frequency. Figures are reproduced from (a, b) [19] and (c, d) [63].
(a)
(b)
(c)
(d)Since there are three resonant peaks, the magnetic impedance can be written as a combination of individual magnetic resonances, as described by equivalent LC circuit model:(25)
Z
m
=
∑
n
=
1
3
Z
m
n
=
∑
n
=
1
3
i
ω
L
n
1
-
ω
2
L
n
C
n
.Here,L
1, L
2, L
3, C
1, C
2, and C
3 are the corresponding inductances and capacitances. By fitting (25) with the retrieved magnetic sheet impedance, the LC parameters can be obtained as L
1
=
0.295 nH, L
2
=
0.273 nH, L
3
=
0.27 nH, C
1
=
0.896 pF, C
2
=
0.8 pF, and C
3
=
0.794 pF. The corresponding resonance frequencies are 9.79 GHz, 10.77 GHz, and 10.87 GHz.Similar to the magnetic sheet impedance, the magnetic sheet current is also a summation of all the individual sheet currents:(26)
j
m
=
∑
n
=
1
3
j
m
n
,where (27)
j
m
n
=
2
Z
0
Z
m
n
Z
m
+
2
Z
0
H
,
n
=
1,2
,
3
.Using (25), (26), and (27), the sheet currents for different resonators can be easily calculated. The current of the first resonator dominates at frequencies around 9.79 GHz. On the contrary, the second and third resonators dominate the frequency region around 10.8 GHz. Besides, one can find that the first resonator is out of phase with the other two resonators for 9.79 GHz < f < 10.77 GHz. Also, for 10.77 GHz < f < 10.87 GHz, the third one is out of phase with the others.In fact, theπ phase shift between these resonators is the key of resonant enhancement of sheet current. As an example, at frequency 10.82 GHz, there are Z
m
1
≪
Z
m
2
≈
Z
m
3 and Z
m
1
≪
Z
m. Thus, we have(28)
j
m
1
≪
Z
0
H
i
,
j
m
2
=
i
L
2
L
3
L
2
+
L
3
C
2
+
C
3
L
3
C
3
-
L
2
C
2
H
i
,
j
m
3
=
-
j
m
2
=
i
L
2
L
3
L
2
+
L
3
C
2
+
C
3
L
2
C
2
-
L
3
C
3
H
i
.It is interesting that the second and third sheet currents in (28) are out of phase. As a result, even higher enhancement factor and narrower bandwidth can be achieved by decreasing the difference between ω
2 and ω
3.Up to date, a great deal of previously proposed or demonstrated metasurfaces and nanostructures require the use of metallic inclusions, leading to large ohmic loss, a serious limitation to obtain ultrahigh Q-factor and huge field enhancement when Fano resonance occurs. In 2014, a new type of Fano resonance in silicon rods array was reported, and the maximum Q-factor was achieved at a rather large gap width between adjacent rods [63]. It was also different from the previously reported Fano resonance in photonics crystal slab [64], where the maximum Q-factor corresponds to a vanishing hole diameter.In the optical regime, FSS can be utilized to realize color filtering [17, 65]. Xu et al. demonstrated plasmonic MIM nanoresonator structures to filter white light into individual colors [17]. The key concept of their method is to use the linear dispersion of plasmon to realize the photon-plasmon-photon conversion efficiently at specific resonant wavelengths (Figure 6). Compared with the aforementioned color-filtering methods, the new design significantly improved the absolute transmission, pass bandwidth, and compactness. In addition, the filtered light is naturally polarized, making it attractive for direct integration in liquid crystal displays (LCDs) without a separate polarizer layer.Figure 6
(a) Schematic diagram of the proposed plasmonic nanoresonators. Inset is the scanning electron microscopy (SEM) image of the fabricated device. Scale bar, 1μm. (b) Plasmon dispersions in MIM stack array. The shaded region indicates the visible range. (c) Simulated transmission spectra for the RGB filters. The solid and dash curves correspond to TM and TE illuminations, respectively. (d) Cross section of the time-average magnetic field intensity and electric displacement distribution (red arrow) inside the MIM stack at a wavelength of 650 nm with 360 nm stack period. (e) SEM image of the fabricated 1D plasmonic spectroscope with gradually changing periods from 400 to 200 nm (from left to right). Scale bar, 2 μm. (f) Optical microscopy image of the plasmonic spectroscope illuminated with white light. Figures are reproduced from [17].
(a)
(b)
(c)
(d)
(e)
(f)FSS can be also utilized in selective solar absorbers to suppress infrared reradiation. Owing to the frequency-independent absorption, the equilibrium temperature of an irradiated blackbody in vacuum is only 80°C. In order to realize frequency selective transmission and absorption, multilayered films were utilized. Nevertheless, high-temperature instability limits the highest operating temperatures. In 1974, Horwitz used an array of deep holes in a metal to realize selective solar absorbers with ratios of solar absorbance to thermal emittance of 30 : 1 at temperatures of about 200°C [66]. Recently, we proposed a multilayered pyramidal array made of tungsten to demonstrate the selective solar absorption [67]. The broadband absorber is made up of a periodic array of multilayered truncated pyramids. The absorbance is about 99% from 0.28 μm to 1.5 μm for both TE polarization and TM polarization at room temperature or high temperature (966 K).


### 3.2. Polarization-Manipulating Metasurfaces

Polarization plays an important role in electromagnetic waves since a majority of phenomena are polarization sensitive. Manipulation of polarization has been a hot topic for quite a long time. Traditional birefringent and chiral medium have the ability of polarization modulation. However, these traditional media need large thickness to accumulate enough phase shift between the perpendicular components of the incident electric fields. Thus, the optical systems involving polarization applications have become complex and bulky.With the help of metasurface-assisted law of polarization conversion (MLPC), one can greatly improve the performance and enable high conversion efficiency and ultrathin thickness [2]. In general, metasurfaces for polarization manipulation include transmissive and reflective types and can be classified into anisotropic and chiral ones from the viewpoint of the structure properties.


#### 3.2.1. Transmissive Anisotropic Metasurface Polarizer

It is well known that polarization states of light can be changed by naturally occurring anisotropic media as the two axes possess different refractive indexes (n
+ and n
-), leading to a relative phase shift between the two axes. However, as the difference between n
+ and n
- is typically small, the thickness of traditional polarizers is required to be much larger than the operational wavelength. Moreover, the working bandwidth is narrow because the phase shift is frequency dependent.As an alternative, metasurfaces provide new opportunities to achieve polarization manipulation with ultrathin artificial structures, including strip gratings and meander lines [68, 69]. In particular, Wang et al. utilized a single-layer metasurface with asymmetric cross-shaped apertures and demonstrated an ultrathin (0.29
λ) terahertz quarter-wave plate [70].The physical foundation of the polarization control with metasurface is the metasurface-assisted polarization conversion (MLPC), that is, the revised Fresnel equations [2], which can also be written as(29)
r
x
=
Y
1
-
Y
3
-
Y
e
x
Y
1
+
Y
3
+
Y
e
x
,
t
x
=
2
Y
1
Y
1
+
Y
3
+
Y
e
x
,
r
y
=
Y
1
-
Y
3
-
Y
e
y
Y
1
+
Y
3
+
Y
e
y
,
t
y
=
2
Y
1
Y
1
+
Y
3
+
Y
e
y
.Based on (29), we can control the reflection and transmission for both polarization states. One particular simple example of this kind of anisotropic metasurface is shown in Figure 7, where the gaps between the parallel strips can be taken as capacitance and the strips can effectively be equal to inductance. Therefore, the electromagnetic wave with electric perpendicular (E
⊥) or parallel (E
∥) components to the strips would be modulated by the effective capacitance and inductance. Hence, the transmitted phases of E
⊥ and E
∥ would also be, respectively, retarded and advanced. When the differential phase shift equals ±90°, circular polarized wave would emerge.Figure 7
(a) Schematic of the anisotropic polarizer based on meander lines. (b) Decomposition of the incident fields along the two main axes. (c) Equivalent circuits for the two polarized waves. (d) Phase shifts for the two orthogonal polarization types. Figures are reproduced from [68].
(a)
(b)
(c)
(d)In 2010, Euler et al. [71] designed a single-layer circularly polarized convertor using periodic split slot ring structure, and this polarization convertor can realize relative 3 dB axial ratio (AR) bandwidth of 11.75%. In 2011, a λ
/
20 thick metasurface was employed to manipulate EM wave polarization with near 100% efficiency in transmission geometry [72].Recently, Ma et al. reported a single-layer metasurface to convert the incident linearly polarized wave into circularly polarized one in a broadband [45], as shown in Figure 8. This polarizer is composed of metallic periodic structures. Two basic patterns are the metallic annular ring and 135° orientated strip. When a linearly polarized plane wave with E field along the x-axis or y-axis normally irradiates onto the polarizer, it can be converted into the circularly polarized wave. The simulated and measured results show that this polarizer can transform the incident linearly polarized light into circularly polarized one in the frequency range from 13.5 to 15.3 GHz, where the AR is less than 3 dB. The relative bandwidth of this polarizer is 17%, and its thickness is only λ
/
40 (λ is the central working wavelength).Figure 8
Photograph of the (a) fabricated polarizer and (b) high-gain circularly polarized patch antenna. (c, d) Measured and simulated AR for the polarizer and the antenna, respectively. Figures are reproduced from [45].
(a)
(b)
(c)
(d)As depicted in Figures8(b) and 8(d), the circular polarizer was integrated into a conventional linearly polarized patch antenna to realize high gain and circular polarized radiation. The gain of conventional patch antenna is sharply increased from 7 dB to about 11 dB at 13.9 GHz. In addition, near-perfect circularly polarized radiation pattern is realized in the frequency band ranging from 13.55 GHz to 13.9 GHz. This metasurface-based circularly polarized antenna solved the difficulty problem of antenna design, and the radiation character was greatly improved.The above mentioned anisotropic metasurfaces modulate the phase shift in two perpendicular directions, in a way similar to the traditional dielectric polarizers. However, this kind of single-layer metasurface suffers the half power loss; namely, the incident power is 50% reflected by the metasurface, and only half of the incident linearly polarized wave can be converted into the circularly polarized wave. To solve this problem, more layers of metallic structures are needed according to the theory proposed by Markovich et al. [73]. It is proved that the efficiency can reach 100% in the two layered metasurfaces. However, the perfect polarization transformation is limited to a single frequency, and the transformation effect deteriorates drastically away from the central frequency.


#### 3.2.2. Reflective Anisotropic Metasurface Polarizer

In order to increase the polarization conversion efficiency and working bandwidth of the metasurfaces, reflective metasurfaces (or metamirrors) have been proposed by various groups [74–79]. In 2007, Hao et al. [75] proposed a circular polarizer based on an ultrathin metasurface reflector. Hao et al. [80] and Pors et al. [74] also obtained similar phenomenon at optical frequencies using orthogonally oriented electrical dipoles. Compared to the transmissive polarization transformers, the metamirrors have much smaller thickness due to the large anisotropy as well as higher energy efficiency since no complicated antireflection technique is applied.Owing to the intrinsic resonance, metamirrors are often realized in narrow frequency band. In order to overcome this problem, we designed a dispersive ultrathin metamirror to extend the bandwidth [81]. In general, the impedance sheet for both the x- and y-directions can be frequency dependent. As a first attempt, we set Z
x as being constant (Z
x
=
∞) and Z
y as being highly dispersive. Since the dielectric spacer is chosen as air (n
=
1), the reflected phase shift can be calculated directly from the well-established transfer matrix method [81]:(30)
Φ
x
=
π
+
2
k
d
,
Φ
y
=
arg
⁡
-
Z
0
/
Z
y
-
2
-
Z
0
/
Z
y
exp
⁡
i
2
k
d
2
+
Z
0
/
Z
y
-
Z
0
/
Z
y
exp
⁡
i
2
k
d
,where k is the wave vector in free space and d is the thickness of dielectric spacer. The optimal impedance for a certain relative phase shift Δ
Ф can be calculated as(31)
Z
y
Z
0
=
-
1
2
A
-
A
B
+
1
-
B
A
+
B
,where A
=
e
x
p
(
i
(
Δ
Ф
+
2
k
d
+
π
)
) and B
=
e
x
p
(
i
2
k
d
). Subsequently, the optimal impedance required for the perfect polarization control can be obtained. The optimal impedance for Δ
Ф
=
π
/
2, that for π, and that for 3
π
/
2 were calculated, which vary slightly with working frequency. In particular, the required impedance for Δ
Ф
=
π
/
2 is mainly capacitive within the whole frequency range. For Δ
Ф
=
π, however, the curve is separated to one capacitive region and the other inductive region at the two sides of the central frequency f
=
0.25
c
/
d, where c is the speed of light. For Δ
Ф
=
3
π
/
2, the requirement of dispersion becomes mainly inductive within the entire frequency range.Using anisotropic metasurface, the optimal impedance can be approximated. Then, metamirror with I-shaped unit cell was constructed, as shown in Figure9. The geometrical parameters were optimized using finite element method (FEM) at near normal incidence. In order to prove the above numerical results experimentally, a sample with 40 × 40 unit cells was fabricated using PCB technology. The measured reflection coefficient was below −15 dB in the frequency range between 5.5 and 16.5 GHz. This large relative bandwidth further confirmed the design of broadband polarization convertor. The reflective metasurface ensures the energy efficiency.Figure 9
(a) Schematic of the anisotropic metamirror inx- and y-directions. (b) Schematic of polarization transformation for a p polarization incident wave. (c) Reflection coefficients for copolarized and cross-polarized components. Inset is the photograph of the fabricated sample, which is comprised of I-shaped resonators. (d) Reflectance of copolarization and cross-polarization for dipole array. Figures are reproduced from (a)–(c) [81] and (d) [77].
(a)
(b)
(c)
(d)Based on the theory of broadband polarization conversion, Guo et al. [82] improved the performance of the broadband polarization convertor. In the design, it was proposed that the operation bandwidth and frequency selectivity of metasurfaces can be increased significantly with fully released dispersion management capability in two dimensions. Multiple resonance mechanism was employed to match the effective impedance of the metamirror with the ideal impedance and significantly broaden the operating bandwidth. Experimental results demonstrated that this metamirror worked well from 3.2 to 16.4 GHz with polarization conversion efficiency higher than 85%. This converter was also superior to the previous devices in the frequency band selectivity because the operation band approximates an ideal rectangle. The rectangular coefficient, defined as the bandwidth ratio between high (>80%) and low (<20%) conversion efficiency, was high up to 0.94.In 2013, Grady et al. experimentally demonstrated a reflective metasurface-based terahertz polarization converter that is capable of rotating a linear polarization state into its orthogonal one [77]. As depicted in Figure 9(d), the device is able to rotate the linear polarization by 90°, with a conversion efficiency exceeding 50% from 0.52 to 1.82 THz, with the highest efficiency of 80% at 1.04 THz. They also created multilayered structures capable of realizing near-perfect anomalous refraction.More recently, Jiang et al. proposed an equivalent theoretical description of metasurface polarizer [78]. As examples to apply this concept, a broadband quarter-wave plate and a half-wave plate were demonstrated. Once again, this approach validated the importance of chromatic dispersion in metasurface polarization control. In a similar work, broadband metasurface polarizers were demonstrated in the visible frequencies with high-efficiency, angle-insensitive polarization transformation over an octave-spanning bandwidth [79]. Nanofabricated reflective half-wave and quarter-wave plates designed using this approach have measured polarization conversion ratios and reflection magnitudes greater than 92% over a broad wavelength range from 640 to 1290 nm and a wide field of view up to ±40°.


#### 3.2.3. Chiral Metasurface Polarizer

Beside the anisotropic polarizers, there is another type of material suitable for polarization manipulation, which is called chiral material. Chirality refers to the materials or structures that cannot superpose with their mirror structures by only transferring or rotating the materials or structures. As depicted in Figure10, chirality can be observed in naturally occurring media, including aminophenol, DNA molecule, and crystals.Figure 10
Classical naturally occurring chiral materials including (a) aminophenol, (b) DNA molecule, and (c) crystals. The chiral materials present (d) circular dichroism and (e) optical rotation character when illuminated by electromagnetic waves.
(a)
(b)
(c)
(d)
(e)Due to the lack of mirror symmetry, the cross-coupling between electric field and magnetic field exists in chiral materials, which is the physical original of these special electromagnetic properties. The strength of the coupling can be represented by the chirality parameterκ, and thus the constitutive relation in the chiral materials can be stated as(32)
D
B
=
ε
0
ε
i
k
ε
0
μ
0
i
k
ε
0
μ
0
μ
0
μ
E
H
,where ε
0 and μ
0 are the permittivity and permeability of vacuum, ε and μ are the relative permittivity and permeability, and κ is the strength of the coupling between the electric and magnetic fields. Negative refraction index can be obtained in chiral metamaterials while it is not necessary to realize negative permittivity and negative permeability at the same time. Chiral materials have attracted great attention for their special electromagnetic properties such as circular dichroism and optical activity. Right circularly polarized (RCP) wave and left circularly polarized (LCP) wave would encounter different transmission coefficients at the resonances and exhibit polarization manipulation property, such as circular dichroism (CD) and optical rotation (OR). The refraction indices of the LCP wave (n
-) and RCP wave (n
+) are related to the chiral parameter κ and can be stated as n
±
=
ε
μ
±
κ. Therefore, negative refraction index can be obtained if the chiral parameter κ is large enough. As analyzed above, chiral materials can act as a kind of polarizer for their selection of circularly polarized waves. However, the cross-coupling between the electric and magnetic fields is rather weak in these natural materials, and very thick materials are often needed to produce useful CD and OR properties.The appearance of artificial chiral structures makes it possible to realize giant CD and OR with the thickness of ~λ
/
10 at the operating frequency. Thus, due to their unique properties, chiral metamaterials promise to tailor the polarization state of electromagnetic wave and be functionalized as polarization rotators, circular polarizers, and polarization spectrum filters with ripple-free isolated transmission peaks. Furthermore, chiral metamaterials are more suitable to achieve multiband and multipolarization conversion compared to anisotropic ones.In the extreme case, chiral material can be used to achieve circular polarization selective surface (CPSS), which was thought to be an important polarizer [83]. The ideal CPSS should have thickness much larger than the working wavelength; thus, it cannot be approximated as metasurface. In 2009, Gansel et al. [84] designed a broadband CPSS based on the periodic gold helix structure, which splits the incident circularly polarized waves in an octave bandwidth at mid-infrared frequency. Later, this helix shaped chiral metamaterial was scaled to other frequencies [85, 86].To obtain chiral metasurfaces, the bandwidth needs to be compromised. In recent years, a great number of chiral metasurfaces have been reported in the form of twisted U-shape [87] and L-shape [88], and so forth. Ma et al. proposed chiral metasurfaces based on planar spiral structures to achieve multiband and multipolarization conversion [89].Firstly, a multiband circular polarizer was proposed by using three layered planar spiral metasurface structure in analogy with classic spiral antenna [86]. At three distinct resonant frequencies, as shown in Figures 11(a) and 11(b), the incident linearly polarized wave with electric field parallel to one specific direction was transformed into the left-/right-handed circularly polarized waves.Figure 11
Geometry and the performance of the helix chiral metamaterial. (a) Focused-ion-beam (FIB) cut of a polymer structure partially filled with gold by electroplating. (b) Oblique view of a left-handed helix structure after removal of the polymer by plasma etching. (c) Top-view image revealing the circular cross section of the helices and the homogeneity on a larger scale. (d, e) Normal-incidence measured transmittance spectra for (d) two pitches of left-handed helices and (e) two pitches of right-handed helices. Figures are reproduced from [84].
(a)
(b)
(c)
(d)
(e)Subsequently, a dual-band asymmetric chiral metasurface was constructed by using two pairs of planar spiral structures with a certain twisted angle [89], as shown in Figure 11(c). Two planar spiral structures with different radii in each layer were adopted to achieve more resonant frequencies. The incident linearly polarized wave can be converted into the circularly polarized waves with different rotation directions at four distinct resonances. This multiband chiral metasurface greatly decreased the loss of chiral metamaterials, compared to the results reported before by combining the chiral and anisotropic properties in the unit cells. This design of multiband response by putting together structures with different size into one unit cell can also be extended to other metasurfaces and metamaterials.In order to extend the operational bandwidth, Huang et al. [91] proposed a dual-band wideband polarization rotator which is proposed by using chiral metasurface composed of two pairs of two layered twisted split ring resonators (SRRs) in each unit. This chiral metasurface transformed the incident linearly polarized wave into its cross-polarized one at two distinct frequencies with high efficiency.In some satellite communication systems, different circular polarization types are required, that is, LCP wave for the up-link and RCP wave for the down-link at Ku band. The usual method for the above requirement is to design two antennas with different circular polarization types as transmitter and receiver, respectively. Another solution is integrating dielectric polarizers or orthomode transducers (OMT) into the horn antennas. Though broadband polarization splitting can be realized, these methods may increase the size of the antennas.Owing to the giant polarization conversion efficiency, the chiral metasurfaces are suitable for the construction of high performance circularly polarized antennas with multipolarization and multiband performance. As shown in Figure12(e), a dual-band dual circularly polarized horn antenna was designed [92] based on the planar spiral chiral metamaterial. The chiral metasurface converts the incident linearly polarized wave into the LCP and RCP waves at two resonance frequencies, with insertion loss less than 0.6 dB. The measured 3 dB AR bandwidths of the antenna were, respectively, 0.8% (12.4 GHz–12.5 GHz) and 1.4% (14.2 GHz–14.4 GHz). The radiation patterns of the proposed antenna for the LCP and RCP wave depicted great cross-polarization ratio, which confirmed that the dominant circular polarization was left-handed at the lower frequency and was right-handed at the higher resonance. The gain of the antenna composite was only degraded by 0.6 dB around these two resonant frequencies, in comparison with the horn antenna without the chiral metasurface. The designed antenna has the advantages of low cost and simple structure and thus could be utilized in satellite communication systems.Figure 12
Schematic configuration of the (a) triple-band circular polarizer, (c) four-band chiral metasurface, and (e) dual-band circularly polarized horn antenna based on chiral metasurface. (b, d) Simulated and measured circular transmission for the chiral metasurface of (a) and (c). (f) Radiation patterns in LCP and RCP of the antenna at 14.35 GHz. Figures are reproduced from [86, 89, 90].
(a)
(b)
(c)
(d)
(e)
(f)In order to extend the operational bandwidth, Huang et al. [91] proposed a dual-band wideband polarization rotator by using chiral metasurface composed of two pairs of two layered twisted split ring resonators (SRRs) in each unit, as shown in Figures 13(a) and 13(b). The sizes of the two pairs of SRRs are different. Therefore, this chiral metasurface transformed the incident linearly polarized wave into its cross-polarized one at two distinct frequencies with high efficiency. Pure optical activity was observed at two distinct resonant frequencies. The designed planar polarization rotator had a high transmission in the polarization rotation frequency bands and can be also easily extended for transforming polarization state at the multiple-frequency bands, which may have many potential applications in the microwave domain.Figure 13
(a) Unit cell and (b) photograph of the dual-band wideband polarization rotator. (c) Transmission spectra of (b). (d) The photograph of the twisted Y-shape chiral metasurface and transmission spectra for (e) linear polarization and (f) circular polarization. Figures are reproduced from [91, 93].
(a)
(b)
(c)
(d)
(e)
(f)Lately, Ma et al. proposed a double-layer twisted Y-shape structure to achieve obvious circular dichroism and giant optical rotation at different frequencies [93]. The schematic geometry of the proposed metasurface is depicted in Figure 13(d). The unit cell is composed of two Y-shaped metallic structures at a certain twisted angle printed on two sides of a dielectric lamina. The angle between the neighboring two branches of this Y-shaped structure is designed to be 120°. When a y-polarized wave is incident to this chiral metamaterial, circular dichroism with a great difference of 25 dB between the transmission coefficients for the circularly polarized waves is obtained at 12.28 GHz. Meanwhile, 90° optical rotation is observed at 12.70 GHz, where the incident y-polarized wave is transformed into its cross-polarization with a transmission coefficient of −1.15 dB.


### 3.3. Antireflection Metasurfaces

In many optical devices and electrooptical equipment, the efficiency of light transmission determines to a large extent the overall performance. For example, it was reported that a normal solar panel absorbs and reflects approximately 25% and 33% of the incident solar radiation, respectively. For lens systems, the reflection would seriously reduce the imaging quality.The first theoretical frame for analyzing antireflection coating (ARC) is Fresnel equation, which was developed in 1823 by Augustin-Jean Fresnel. Before this time, some antireflection phenomena have been already discovered by Lord Rayleigh and Joseph Von Fraunhofer [94].In general, there are two ways to create broadband antireflection surfaces, which are based on either coating multilayer thin films or texturing the substrate surfaces with subwavelength structures. The first method is based on multilayer material with gradient refractive indices, and the latter needs only a single-layer material but gradient morphology. Due to the scarcity of optical materials with refractive indices close to air, multilayer thin films for broadband antireflection surfaces were not realizable until recently [95]. However, the mismatch in thermal properties of different materials hinders multilayer thin film applications.One of the inspirations of ARC design comes from the natural worlds. In the eyes of some moths, broadband antireflection was observed and the physical mechanism is attributed to the effective gradient refractive index distribution. However, it was found that, in moth-eye-like structures, high-reflection frequency bands alternate with low-reflection frequency bands. It is of great interest for us to see if these high-reflection bands can be suppressed and hence obtain a broadband reflection approaching 0.1%. As an effort to achieve this object, it was proposed that a hybrid moth-eye structure could be used to enhance broadband antireflection properties. An ultralow average reflectance down to 0.11% over the solar spectral range has been achieved, showing a 50% enhancement in broadband antireflection capability as compared with corresponding uniform moth-eye structures.The largest challenge faced by traditional antireflection proposals is the complex fabrication process. In 2007, biomimetic silicon nanostructures were demonstrated by Huang et al. with improved broadband and quasiomnidirectional antireflection properties [97]. In 2014, Hong et al. used laser direct writing to create microstructures on Si surfaces that reduce light reflection by light trapping [42]. By decoration of the Si nanowires with metallic nanoparticles, surface plasmon resonance can be used to further control the broadband reflections, reducing the reflection to about 0.8% across the bandwidth from 300 to 1200 nm.Although structured surfaces with gradient dielectric constant (e.g., pyramidal rods and moth’s eyes) provide rather good antireflection performance, their thicknesses and mechanical performances are not well balanced. In order to reduce both the thickness and the reflectance, the metallic metasurfaces are recently investigated for this purpose [39–41, 96, 98].In 2008, Thoman et al. demonstrated that nanostructured gold films can serve as broadband impedance-matching coatings for substrates in the terahertz frequency range [39]. They showed in theory and experiment that the internally reflected electric field amplitude of a broadband terahertz pulse in a silicon substrate can be suppressed to below 1% of that without coating, which is at least a factor of 5 better than the best suppression achievable with bulk gold layers (see Figure 14). Subsequently, Zhou et al. examined the potential of stacked multilayer graphene as broadband terahertz (THz) antireflection coating [40]. The reflected pulses from the quartz and silicon substrates were observed to change with the layer number and doping concentration of the graphene coating. Remarkable broadband impedance matching was achieved due to optimized THz conductivity.Figure 14
(a) A schematic of the THz measurement with THz wave normal incident from the left side of Si substrate and square mesh AR coating on the right side of Si substrate. (b) THz TDS transmission signals under normal incidence. The solid curve is for bare Si and the dashed and dotted curves are for AR-coated Si in horizontal polarization and vertical polarization, respectively. (c) FFT of the THz TDS spectra. (d) Schematic of the metasurface antireflection coating on a germanium substrate, consisting of a periodic array of gold cross-resonators on top of a dielectric layer. (e) Schematic of multireflection within the metasurface antireflection structure. (f) The SEM image of a fabricated metasurface antireflection structure. (g) Calculated optical reflectance (R) and transmittance (T) using full-wave numerical simulation. Figures are reproduced from (a)–(c) [41] and (d)–(g) [96].
(a)
(b)
(c)
(d)
(e)
(f)
(g)In a similar work, Teng et al. demonstrated broadband antireflection coatings using deep subwavelength periodic thin metallic lamellar grating [98]. As shown in Figures 14(a)–14(c), the measured reflectance from Cr grating coated sample was reduced over 99% compared with bare Si sample in the whole bandwidth of 0.06–3 THz. Recently, Zhang et al. proposed a metasurface optical antireflection coating [96]. By tuning the cross-shaped metallic patches on a dielectric spacer, the reflection coefficient can be dramatically reduced (Figures 14(d)–14(g)). The bandwidth and incidence angle range were comparable to a quarter-wave antireflection coating.


### 3.4. Perfect Absorbing Metasurfaces

#### 3.4.1. Single-Port Perfect Absorbing Metasurface

Absorption phenomena of electromagnetic wave can be found anywhere in our surrounding world. The colorful leafs and flowers are related to the frequency selective absorption of light. It was also well known that black object, such as carbon, absorbs most of the visible light. In 1860, Kirchhoff proposed the ideal blackbody absorber as “bodies can be imagined which, for infinitely small thicknesses, completely absorb all incident rays, and neither reflect nor transmit any.” Since then, the pursuit of high efficient absorbers never stops.Along with the development of Maxwell equations and invention of radar, the electromagnetic theory of absorbers was brought out after World War II. In the review given by Hans Severin in 1956 [35], the theory of the so-called Salisbury absorber, Jaumann absorber, Dallenbach absorber, pyramidal absorber, and dipole absorber was given in detail. The dipole absorber is just the precursor of the circuit analogy absorber (CAA) [99], which is also one kind of lossy metasurface. Severin also noted that there is a conflict between the thickness and bandwidth of these absorbers. Almost half a century later, Rozanov developed a rigorous theory for the bandwidth-to-thickness ratio [100], illustrating that there is a fundamental limit for this value. Remarkably, this conclusion consists with the prediction of Planck and Masius with respect to the thickness of blackbody [101].In recent years, broadband absorbers with optimal thickness were widely researched [38, 102–111]. Except for broadband absorbers, narrow band absorbers are also of particular importance in frequency selective applications. In 2008, Landy et al. proposed the concept of “Perfect Metamaterial Absorber” with thickness of only λ
/
40, where λ is the working wavelength [36]. They interpreted the principle of this absorber as the simultaneous control of electric and magnetic response such that the impedance is matched to the free space. However, it is now widely known that such impedance match does not ensure that the transmission and reflection can be simultaneously reduced to zero. As stated by Vora et al., it is ambiguous to define the μ
e
f
f and ε
e
f
f in such complex structures, since the metamaterial perfect absorber cannot be strictly considered as homogeneous bulk media [52].In 2008, we extended the meta-absorber into the visible frequencies. By converting the propagating wave into surface wave, perfect absorption of light wave was demonstrated. Antisymmetric surface plasmons coupling formed by subwavelength hole array (SHA) and reflecting layer was proved to dominate the multiorders near-perfect absorption. Although only SHA was investigated in this case, the design idea, realizing perfect absorption based on structured surface combined with thick metal layers, can also be extended to other cases, such as split ring resonator (SRR) combined with metal black plate. The most fascinating potential application of SHA combined with reflecting layer is the introduction of functional material into center dielectric region to realize imaging and detecting. In 2009, we further investigated the loss mechanism of perfect absorber. It was demonstrated that the ohmic loss and the dielectric loss both contributed to the absorption. The energy exchange was recently studied to enhance the efficiency of solar cells [52]. In addition, subwavelength high performance metamaterial absorber was also demonstrated by Hao et al. for optical frequencies [112]. Experimental results show that an absorption peak of 88% is achieved at the wavelength of ~1.58 μm. At almost the same time, Liu et al. demonstrated an infrared perfect absorber and verified its application as plasmonic sensor [113].As shown in Figure15, the reflection and transmission problem can be rewritten as a scattering and reradiation problem of the bounded wave [2]. The propagating wave and bounded wave (M-wave) could exchange with each other with the help of metasurface. In the far fields, we only care about propagating wave. As such, the total electromagnetic fields can be written as(33)
E
total
=
E
in
+
E
sc
=
E
in
+
S
×
E
in
.Here, E
sc is the scattered electric fields, which is determined by the incident electric field E
in and the structure function S. To realize complete absorption, the S function should be designed with no-backward scattering.Figure 15
Exchange between the propagating waves and M-waves. (a) Schematic of the principle. (b) Excitation of M-wave by propagating wave. (c) Conversion of the M-wave to propagating wave. Figures are reproduced from [2].
(a)
(b)
(c)In practical applications, metallic reflecting layers are often used as a ground plane for these absorbers. As illustrated in Figure16, we proposed a circuit model to interpret the electromagnetic interaction in these absorbers [37]. The magnetic response was mathematically treated using a modified equivalence circuit model. The relation between the reflection and impedance can be written as(34)
Y
sretri
=
1
Z
sretri
=
Y
0
1
-
S
11
1
+
S
11
-
Y
1
exp
⁡
-
i
k
d
-
r
m
exp
⁡
i
k
d
exp
⁡
-
i
k
d
+
r
m
exp
⁡
i
k
d
,where Y
0, Y
1
=
ε
1
Y
0, and Y
m
=
ε
m
Y
0 are the intrinsic admittance of vacuum, dielectric spacer, and metal and ε
1 and ε
m are permittivities of dielectric and metal. k
0 and k
=
ε
1
k
0 are the wave vector in the vacuum and dielectric spacer. r
m
=
(
Y
1
-
Y
m
)
/
(
Y
1
+
Y
m
) is the reflectivity of thick metal layer. Equation (34) is the basis of the metasurface-assisted absorption theory (MAT) [2].Figure 16
(a) Schematic of the metasurface-based absorber. (d) Physical model of the absorber, where the metasurface is described by its impedance. (b) Ideal impedance and retrieved impedance for the dispersive metasurface. (c, e) Absorption of the broadband (c) and dual narrowband (e) absorbers at different angles of incidence. (f) Schematic of the plasmonic nanocube based absorber. (g) Typical reflectance of a silver (Ag) nanocube. Figures are reproduced from (a)–(c) [114], (d, e) [37], and (f, g) [115].
(a)
(b)
(c)
(d)
(e)
(f)
(g)Subsequently, Feng et al. showed that the bandwidth can be dramatically increased by tailoring the dispersion of metasurfaces [114]. With a thin layer of structured nichrome, a polarization-independent absorber with absorption larger than 97% was numerically demonstrated over larger than one octave bandwidth. It was shown that the bandwidth enhancement is related to the transformation of Drude model of free electron gas in metal film to Lorentz oscillator model of bound electron in the structured metallic surface. It should be noted that the Lorentz form is just one kind of dispersion that mimics that of ideal absorbing metasurface. Thus, further engineering of the dispersion may lead to even larger bandwidth.In addition, to meet the requirement of bandwidth enhancement, metasurface absorbers are expected to be designed to reduce the fabrication complexity of traditional absorbers. Many works have been devoted to this design. For instance, a simple method was proposed by randomly adsorbing chemically synthesized silver nanocubes onto a nanoscale thick polymer spacer layer on a gold film [115]. The film-coupled nanocubes provide a reflectance spectrum that can be tailored by varying the geometry (the size of the cubes and/or the thickness of the spacer).In general, the maximal absorption bandwidth is limited by the optical thickness as indicated by the thickness-bandwidth ratio. For absorbers working at terahertz and higher frequencies, the physical thickness is very small even for quite large optical thickness. As a result, the thickness is not a big problem for broadband absorption at these frequencies. In contrast, the fabrication technique becomes a challenge since most of the broadband absorbers require multilayer thin films or complicated structures. Recently, we focused on the design of broadband absorber based on doped silicon, which has been considered as a new kind of metamaterials [116]. When the working frequency was larger than the plasmon frequency, doped silicon behaves as a highly lossy dielectric material. Yet a doped silicon slab by itself was not a good absorber due to the impedance mismatch between the silicon slab and free space. The power reflection at the interface was larger than 28% for refractive index n
=
3.3, which was similar with nondoped silicon. In order to reduce the reflection and enhance transmission (the case for nondoped silicon) or absorption (the case for doped silicon), antireflection techniques should be used.In the framework of transmission enhancement, the period of the grating structure should be in deep subwavelength scale to suppress non-zero-order diffractions. However, for high efficient absorber, we showed that the absorption bandwidth can be dramatically increased by utilizing both the zero- and first-order diffractions [117], as illustrated in Figure 17. Compared with previous broadband absorbers, the structure we proposed was mechanically stable and much easier to be fabricated. This idea was further extended by other researchers [104, 118]. The experimental results showed that more than 95% absorption can be obtained from 1 to 2 THz. It was also interesting to investigate whether second-order or higher-order diffraction can be utilized to increase the absorption bandwidth. In order to do this, the diffraction at higher frequencies was calculated for a two-layer grating. The relative absorption bandwidth for A
>
90
% becomes larger than 150%. Further increase of layers may lead to larger bandwidth. Nevertheless, the fabrication process will become more complex and the thickness will become larger.Figure 17
(a) Schematic of the metasurface absorber made out of silicon grating. (b) Calculated diffraction efficiency of a grating. (c) Fabricated sample. (d) Measured absorption coefficients. (e) Fabricated sample of a complex silicon grating. (f) Measured transmission and reflection coefficients with and without pattern. Figures are reproduced from (a, b) [117], (c, d) [118], and (e, f) [104].
(a)
(b)
(c)
(d)
(e)
(f)By stacking metasurfaces in multilayers, the absorption bandwidth could be further increased. As illustrated in Figures18(a) and 18(b), an excellent absorber is designed with a very large bandwidth (3.26–34.65 GHz) [110]. It is shown that the total thickness of the design (14.5 mm) is only a little thicker than the minimum possible thickness dictated by the physical bound. Nevertheless, the multilayered absorber is difficult to be fabricated since the resistance of each metasurface should be accurately controlled. More recently, we fabricated a broadband absorber using magnetic controlled sputtering and optical lithography technique [2]. Since both the substrates and conducting material are transparent in the optical spectra, such absorbers could be utilized in many areas, such as smart windows and cockpits. As can be seen in Figures 18(c) and 18(d), both the optical transmittance and the microwave absorption are large enough for practical applications.Figure 18
(a) The schematic of the ultrawideband absorber with optimal thickness. Top: the equivalent circuit model. Bottom: the actual realization of the absorber. The resistive layers are periodic square patches with periodicity (a), width (w), and sheet resistivity (R
s). (b) The frequency response of the reflection coefficient for the ultrawideband absorber with optimal thickness obtained from both the equivalent circuit model and the full-wave simulation. (c) Optical transmittance for the optical-transparent absorber. Inset shows the photograph. (d) Microwave absorption for both the experiment and the full-wave simulation. Figures are reproduced from (a, b) [110] and (c, d) [2].
(a)
(b)
(c)
(d)


#### 3.4.2. Coherent Perfect Absorber

Recently, coherent perfect absorption of light was proposed and demonstrated in a planar intrinsic silicon slab when illuminated by two beams with equal intensities and proper relative phase [119, 120]. Such a device is termed a “coherent perfect absorber” (CPA) and a “time-reversed laser.” Compared with the perfect absorbers based on metasurfaces or plasmonic structures, the new device provides additional tunability of absorption through the interplay of absorption and interference. The coherent control of absorption is potentially useful in transducers, modulators, or optical switches [121, 122]. However, as a time-reversed process of laser, CPA is characterized by narrow bandwidth and thought to be not applicable in solar-cell and stealth technology.As shown in Figure19, it was demonstrated that the bandwidth of a thin film CPA can be rather large if the thickness is thin enough and the corresponding material has a specific chromatic dispersion resembling that of metal [38]. Two different regimes of metallic thin film CPA were derived based on the general CPA condition, characterized by extremely broad and moderately narrow bandwidth, respectively.Figure 19
(a) Schematic of the coherent perfect absorber. (b) Absorption as a function of the frequency and the thickness of the doped silicon film. (c) Coherent absorption of a 450 nm thick doped silicon film. Red and green solid lines show the absorption forΔ
l equal to 500 and 505.56 μm, respectively. (d) Coherent absorption of 17 nm thick tungsten for symmetrical and antisymmetrical inputs. (e) Schematic of plasmon hybridization and the effective medium description. For the symmetrical (antisymmetrical) resonance, the external E-fields (H-fields) should be parallel. (f) Coherent absorption of antisymmetrical inputs for TE polarization at oblique incidences. The inset of (f) illustrates the configuration of two coherent divergent beams with antisymmetrical phase distribution, where θ is the divergent angle. Figures are reproduced from [38, 123]. (g)–(i) Proposed applications of metasurface CPA in signal processing. Figures are reproduced from [124].
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)For nonmagnetic material, the CPA condition for normal incidence can be obtained:(35)
exp
⁡
i
n
k
d
=
±
n
-
1
n
+
1
.The ± sign is corresponding to the symmetrical or antisymmetrical inputs. In the previous discussion, an infinite number of discrete solutions of (35) have been found for k
d
≫
1. The bandwidth is defined as the frequency width between the maximum absorption and adjacent minimum absorption and is characterized by Δ
f
≈
c
/
(
2
n
d
). In this case, the CPA is rather narrowband and referred to as a time-reversed process of laser.In fact, the bandwidth of CPA can be very large ifd is extremely thin (d
≪
λ, n
k
d
≪
1). In this case, the left side of CPA equation becomes 1
+
i
n
k
d, and the right side can be approximated as ±
(
1
-
2
/
n
). As n
k
d is very small, only plus sign in the right side (symmetric mode) should be chosen and the real and imaginary parts of the refractive index (n
′ and n
′
′) become equal with(36)
n
′
≈
n
′
′
≈
1
k
d
=
c
ω
d
.In this case,n
k
d
≪
1 becomes 2
k
d
≪
1; thus, the working regime can be approximated as k
d
≪
1 and the required refractive index must be much larger than unit (n
≫
1). According to the definition of Yu and Capasso, such kind of thin film can also be thought of as a metasurface [1].Different from the general CPA condition, the CPA condition for ultrathin film is explicit. Obviously, Drude metal could be used as natural material for CPA, with extremely broadband response. We obtained the thickness for CPA at this frequency regime:(37)
d
w
≈
2
c
ω
p
2
τ
,where c is the speed of light in vacuum. This characteristic length is also called the Woltersdorff thickness [12], which quantifies the thickness of a metallic film with maximum absorption for incoherent beam input in the low frequency regime. When d
=
d
w, the maximum absorption is 0.5, while the reflection and transmission are 0.25, respectively. For d
<
d
w, most of the energy is transmitted; for d
>
d
w, most of it is reflected.Since the Woltersdorff thickness is independent of frequency, the absorption is very broadband. Generally, this frequency range covers all the low frequencies up to terahertz. In particular, a 0.3 nm thick tungsten film can absorb almost all the microwave and even terahertz energy under coherent condition, thus breaking the thickness limit proposed by Planck and Rozanov. Compared with the original CPA [120], the bandwidth increased more than 1010 times. In the optical CPA, the thickness of tungsten should be increased to 17 nm, which is still neglectable compared to the operational wavelength. The concept of ultrabroadband CPA was recently experimentally demonstrated in the microwave frequency. As shown in Figure 19(d), the absorption coefficients reach 100% at frequencies ranging from 6 to 18 GHz.Subsequently, a customized CPA was also proposed based on the electric and magnetic resonances in a three layered metal-insulator-metal structure [123]. These kinds of resonances were attributed to the plasmon hybridization effect due to the coupling of individual resonators. Most importantly, it was found that the antisymmetrical absorption associated with magnetic resonance is almost independent of the polarization of light and angle of incidence; thus, the structure is highly suitable for coherent absorption of divergent beams (Figure 19(f)). To interpret the interaction of magnetic and electric fields with the metasurface, effect constitutive parameters are retrieved and general CPA condition for material with both electric and magnetic responses was given:(38)
exp
⁡
i
n
k
d
=
±
1
-
z
1
+
z
,where k is the wave vector in free space and d is the total thickness of the effective slab. The ± signs are corresponding to the symmetrical and antisymmetrical inputs, respectively. This equation provided a general approach to the design of CPA operating at arbitrary frequencies.The coherent control method can also be utilized to realize other functionalities. For example, Zheludev et al. proposed the application of CPA in signal processing [124]. Potential applications include but are not limited to (a) a pulse restoration (clock recovery) device to restore the form of distorted signal pulses according to that of a clock (control) pulse, (b) a coherence filter that improves the coherence of light beams by absorbing incoherent components, and (c) a coherent light-by-light modulator wherein a digital or analogue intensity- or phase-modulated control input governs signal channel output. In addition, they showed that reflection and refraction effects on phase gradient metasurfaces can be coherently controlled by a second wave [125]. In addition, Cao et al. also demonstrated the possibility of coherent subwavelength focus. Broadband operation was made possible by engineering the dispersion of the complex dielectric function, similar to the previous methods [38]. The local enhancement can be significantly improved compared to the standard plane wave illumination of a metallic nanoparticle. Their numerical simulation showed that an optical pulse as short as 6 fs can be focused to an 11 nm region.More recently, coherent perfect rotation (CPR) of electromagnetic polarization states has been proposed by utilizing the odd time reversal symmetry in Faraday rotation [126]. Similar to coherent perfect absorption, the bandwidth of CPR is limited. The main advantage over other polarization transformers is that the polarization states can be dynamically tuned by the phase retardation. Nevertheless, it is pointed out that only Faraday rotation, but not optical activity or anisotropy, is capable of coherent perfect rotation. In our recent work, a dynamic polarization transformer was constructed by taking advantage of the time reversal symmetry of polarization conversion in anisotropic metasurface [76]. It should be noted that no Faraday rotation effect is utilized. The working bandwidth covers the entire microwave and terahertz bands. More interestingly, it is demonstrated that the output polarization states can be easily tuned between linear polarization and arbitrary circular polarization through phase modulation.


### 3.5. Plasmonic Metasurfaces

#### 3.5.1. Superlens and Hyperlens

As discussed in Section2, some particular metasurfaces can support surface waves, such as SPPs. The last several decades have witnessed the rapid development of SPPs and related areas. One of the largest advantages of SPPs is their ability to construct superlens and hyperlens to break the diffraction limit, which prevents the imaging of subwavelength features [34]. As we demonstrated recently, the electromagnetic waves on metasurfaces are characterized by three distinct properties [2]. The most important one is the short wavelength [55], which is actually the basis to break the diffraction limit.In 2000, Pendry firstly proposed the concept of perfect lens [4], in which the amplification of evanescent waves and perfect imaging could be obtained by a negative refraction index slab. The short wavelength characteristic of SPPs on a sliver film was firstly demonstrated in 2003 [127, 128], and surface plasmon resonant interference nanolithography technique (SPRINT) was proposed to achieve resolution of half-pitch 50 nm (~1/9 wavelength) in 2004 [31], as shown in Figures 20(a) and 20(b). Using exposure recording scheme, Fang et al. experimentally demonstrated in 2005 that a 35 nm thick silver superlens was capable of subdiffraction imaging of half-pitch 60 nm objects (~1/6 wavelength) [30]. Figure 20(c) illustrates the experimental scheme of subwavelength imaging through a silver lens, where the objects were located 40 nm away from the silver superlens. Due to the superlens effect, the object of “NANO” characters was imaged on the photoresist and the average line width of images is 89 nm (Figure 20(d)). By utilizing a similar scheme, the superlens effect was also confirmed by other groups [129, 130].Figure 20
Experimental demonstration of near-sighted silver lens. (a) Numerical simulation of intensity distribution of surface plasmons. (b) SEM image of resist pattern for (a). (c) Schematic diagram of the silver superlens experiment. (d) (Top) Focused-ion-beam image of the object with 40 nm line width, (middle) AFM images of topographic characterization in resist layer with a silver superlens, and (bottom) AFM images of topographic characterization in resist layer with the 35 nm thick superlens replaced by PMMA spacer as a control experiment. (e) Schematic of imaging lithography structure with a reflective Ag lens. (f) (Top) SEM image of the mask pattern “OPEN” characters, (bottom) SEM image of resist pattern. SEM image of half-pitch 32 nm dense lines resist pattern with plasmonic cavity lens. AFM image of half-pitch 22 nm resist pattern. Inset shows its two-dimensional (2D) Fourier analysis diagram. Figures are reproduced from (a, b) [31], (c, d) [30], and (e, f) [32].
(a)
(b)
(c)
(d)
(e)
(f)The metasurface-assisted diffraction theory (MDT) can be utilized in plasmonic lithography [2], where the silver lens has practical limits, such as optical loss, surface roughness, and film thickness. To address these issues, some important studies were reported, including active lens and plasmonic reflective slab [32, 131]. Based on the reflective amplification of evanescent wave, Wang et al. experimentally achieved the deep subwavelength imaging lithography for nanocharacters with about 50 nm line width [32], as depicted in Figures 20(e) and 20(f). It was also reported that the plasmonic cavity lens can be utilized to achieve high aspect profile [132]. The profile depth of half-pitch 32 nm resist patterns was enhanced to be about 23 nm, which is much larger than the previously reported results (sub-10 nm). The resolution of SPPs imaging lithography was also extended to be half-pitch of 22 nm, whereas the quality needs to be further increased.The subdiffraction imaging model of a planar plasmonic lens can be written in the form of(39)
E
x
x
,
y
,
z
E
y
x
,
y
,
z
E
z
x
,
y
,
z
=
∫
-
∞
∞
∫
-
∞
∞
A
x
k
x
,
k
y
A
y
k
x
,
k
y
k
x
A
x
+
k
y
A
y
-
k
z
exp
⁡
i
k
x
x
+
i
k
y
y
d
k
x
d
k
y
,
A
x
k
x
,
k
y
A
y
k
x
,
k
y
=
∫
-
∞
∞
∫
-
∞
∞
G
x
x
,
y
t
x
x
,
y
T
x
k
x
,
k
y
G
y
x
,
y
t
y
x
,
y
T
y
k
x
,
k
y
exp
⁡
-
i
k
x
x
-
i
k
y
y
d
x
d
y
,where G
(
x
,
y
), t
(
x
,
y
), and T
(
k
x
,
k
y
) are the illumination function, transmission function of object, and optical transfer function (OTF) of plasmonic lens, respectively. The OTF can be obtained through transfer matrix. If there is reflection plane in the plasmonic lens, the OTF should be determined by using the fields in the photoresist layer, implying that the images can also be modulated by the reflecting layer [32].Although the superlens provided images of nanoobjects well beyond the diffraction limit, the inherent disadvantage of near-sighted mode impedes its widespread application. It is highly desirable to utilize a plasmonic lens system which could resolve subwavelength details of objects in far field. In 2006, Jacob et al. proposed a hyperlens composed of cylindrical metal-dielectric multilayers to magnify subwavelength details of objects so that the subwavelength features are above the diffraction limit at the hyperlens output [133]. Then, conventional microscopy can be utilized to capture the output of hyperlens to achieve far-field super resolution imaging.


#### 3.5.2. Plasmonic Metasurface Lens

Based on Snell’s law, traditional optical lenses must have curved surfaces to focus light. In other words, the phase retardation was accumulated by height variation much larger than the wavelength. In recent years, metasurfaces were widely utilized to achieve planar lenses, based on the metasurface-assisted law of reflection and refraction (MLRR) [2, 134]:(40)
n
1
k
0
sin
⁡
θ
1
+
∇
Φ
=
n
1
k
0
sin
⁡
θ
3
,
n
1
k
0
sin
⁡
θ
1
+
∇
Φ
=
n
2
k
0
sin
⁡
θ
2
,where ∇
Φ is the phase gradient in the metasurface plane, which is determined by the geometric structure and distribution, and may be changed by external stimuli, leading to the adaptive tuning of the law of refraction and reflection. n
1 and n
2 are the refractive index of media at the incident and transmit sides. θ
1, θ
2, and θ
3 are the angles for incident, refracted, and reflected light.In particular, plasmonic lenses have become one widely researched approach, which has now been demonstrated in both one-dimensional and two-dimensional cases [46, 135, 136]. These devices offered an alternative to conventional refraction microlenses. The planar and compact designs are beneficial for obtaining short focal distances on the order of several micrometers.Early in the 21st century, a novel method was proposed to manipulate the phase retardation of light at nanoscale, providing a new approach to develop various nanooptical devices, such as flat lenses, collimators, and splitters. Figure21(a) illustrates the principle of planar lens based on width-tuned plasmonic slits. The slits transport electromagnetic energy in the form of SPPs in nanometric waveguides and provide desired phase retardations with variant phase propagation constant. Under plane wave illumination, the light energy was focused at the focal plane f
=
0.8 μm, as shown in Figure 21(b). According to Fermat’s Principle, such devices could also achieve arbitrary angle of light deflecting such as that shown in Figure 21(c).Figure 21
Planar slit array metal lens. (a) Schematic configuration of light focusing of planar metal nanoslit array lens. (b) Normalized Poynting Vector for light focusing of metallic nanoslits lens. (c) Calculated phase distribution of electric field for the designed deflector. Incident and deflection angles are designed as 30° and −30°, respectively. (d) Far-field angular spectrum for the incident and emitted beams, respectively. (e, f) Schematic of the abnormal refraction in other metasurfaces. Figures are reproduced from (a)–(d) [137], (e) [134], and (f) [138].
(a)
(b)
(c)
(d)
(e)
(f)Although the plasmonic lens is easy to be fabricated, it was only until 2008 that the experimental demonstration of such device was reported [46]. For plane wave illumination, the light was focused at the focal length of 5.3 μm. The excellent agreement between experiment and simulation validated the design principle of this approach. It should be noted that the plasmonic version of abnormal refraction is similar to that in other metasurfaces, as shown in Figures 21(e) and 21(f).More recently, as shown in Figure22, Chen et al. demonstrated that the far-field focusing pattern of planar metal lens could be modulated by slits filled with phase change material (Ge2Sb2Te5, GST) [135]. By varying the crystallization level of GST from 0% to 90%, the Fabry-Pérot resonance supported inside each slit can be spectrally shifted across the working wavelength at 1.55 μm, which results in a transmitted electromagnetic phase modulation as large as 0.56π. Based on this geometrically fixed platform, different phase fronts can be constructed spatially on the lens plane by assigning the designed GST crystallization levels to the corresponding slits, achieving various far-field focusing patterns.Figure 22
(a) Schematic diagram of the planar lens. (b) The cross section showing thex-component of the electric field of the 1st-order mode from a single slit. (c) The evolution of the single-slit transmission spectrum for different crystallization levels. (d) The relative phase and (e) the normalized electric field intensity at 1.55 μm as functions of the crystallization level with a 5% step increment. (f) Focusing pattern measured in x
z-plane by confocal scanning optical microscopy for different status of GST. Figures are reproduced from [135].In 2007, Min et al. investigated a type of metallic nanooptic lens consisting of slits with variant widths, filled with Kerr nonlinear media [139]. As shown in Figure 23(a), each slit is designed to transmit light with specific phase retardation controlled by the intensity of incident light, owing to the nonlinear response. This new lens can actively control the deflection angle and the focus length of output beam. Very recently, Hu et al. proposed an active terahertz (THz) plasmonic lens tuned by an external magnetic field [140]. Different from traditional tunable devices, the proposed active lens is tuned by changing the cyclotron frequency through manipulating magnetoplasmons (MPs). It was shown that THz wave propagating through the designed structure could be focused to a small size spot via the control of MPs. The tuning range of the focal length under the applied magnetic field (up to 1 T) is ~31, about 50% of the original focal length.Figure 23
(a) Schematic view of the three-slit structure under study. (b) and (c) The FDTD simulation of electric field intensityE
2 time-average distribution of beam focusing with a five-slit metallic lens. (d) A semiconductor-insulator-semiconductor structure in a Voigt configuration. The propagation mode is TM polarized, and the magnetic field B is applied along the y-axis. The thickness of the insulator is denoted by w. (e) FDTD-calculated focal length when the external magnetic field is increased from 0 to 1 T. Figures are reproduced from (a)–(c) [139] and (d, e) [140].
(a)
(b)
(c)
(d)
(e)It should be noted that the plasmonic slit lens is polarization selective; that is, only one particularly polarized light beam could be transmitted and modulated in phase, since the SPP is intrinsically polarized. This polarization selectivity has two effects. Firstly, this effect is attractive for some cases where only one polarization type is needed. Secondly, it may become undesired for many other applications. To eliminate this problem, rectangular or circular plasmonic holes were adopted to achieve phase modulation [136, 141]. As illustrated in Figure 24, Ishii et al. experimentally demonstrated a polarization-independent holey-metal lens [136]. They showed that by changing the radii of subwavelength holes in a metallic film, which act as single-mode waveguide elements, they can control the phase of light transmitted through the holes. Finally, it was demonstrated that the focal distance of the lens can be controlled by changing the incident wavelength.Figure 24
(a) Pseudocolor intensity map calculated from the analytical model of the sample. The color scale is normalized to the maximum intensity. The inset shows the beam cross section at the focal point (z
=
10 μm) and the SEM image of the sample. (b) Schematic of a nanowaveguide array that induces wavefront shaping for OAM generation. (c) SEM picture of the nanowaveguide array. Figures are reproduced from [136, 141].
(a)
(b)
(c)More recently, Litchinitser et al. demonstrated that the change of hole radius along the azimuthal direction is able to generate orbital angular momentum (OAM) on the nanoscale. They proposed and experimentally demonstrated that a nanowaveguide array milled in a metal film can be used to control the wavefront of a light beam and that an optical vortex at 532 nm was produced by using such an array (see Figures24(b) and 24(c)).


#### 3.5.3. Plasmonic Metasurfaces for Sensing Applications

Owing to the strong light-matter interaction, metasurfaces can provide a robust and efficient platform for biosensing. In particular, the surface plasmon resonance (SPR) at planar surfaces or localized surface plasmon resonance (LSPR) for nanometer-sized metallic structures is accompanied with dramatic local field enhancement [142]. The implication of the local field enhancement is twofold. Firstly, the spectra of the SPR and LSPR are highly dependent on the environment; thus, a little change of refractive index would result in a considerable spectrum shift. Secondly, the local field enhancement can be exploited to achieve surface-enhanced Raman spectroscopy (SERS) [143]. Both of the two mechanisms can be utilized for clinic detection.As shown in Figures25(a)–25(d), Wu et al. introduced an infrared plasmonic surface based on a Fano-resonant metasurface which exhibits sharp resonances caused by the interference between subradiant and superradiant plasmonic resonances [144]. Owing to the asymmetry, the frequency of the subradiant resonance can be precisely determined and matched to the molecule’s vibrational fingerprints. In these Fano resonances, the near-field coupling of plasmonic modes is crucial to enhance the sensitivity [145, 146]. It was also demonstrated that Young’s interference can be observed in plasmonic structures when two or three nanoparticles with separation on the order of the wavelength are illuminated simultaneously by a plane wave. This effect leads to the formation of intermediate-field hybridized modes with a character distinct of those mediated by near-field and/or far-field radiative effects [147].Figure 25
(a) Schematic representation of subradiant (Q) and superradiant (D) modes. (b) Scanning electron microscopy image of a typical fabricated sample. (c) Schematic representations of proteins’ mono- and bilayers binding to the metal surface. (d) Experimental (solid) and theoretical (dashed) polarized reflectivity spectra. (e) SEM image of a fabricated metasurface consisting of hole array. (f) Resonance shift for the subradiant SPP mode with changing NaCl concentration. Figures are reproduced from (a)–(d) [144] and (e, f) [148].
(a)
(b)
(c)
(d)
(e)
(f)In a similar work [148], by exploiting extraordinary light transmission phenomena through high quality factor subradiant dark modes, Yanik et al. experimentally demonstrated high figures of merits (FOMs as high as 162) for intrinsic detection limits surpassing those of the gold standard prism coupled surface plasmon sensors, as illustrated in Figures 25(e) and 25(f).Over the past several years, the absorption effect of plasmonic metasurface has also been exploited in sensing applications. In 2011, Tittl et al. presented a simple design of plasmonic absorber based on palladium nanowires [149]. Due to hydrogen incorporation, palladium undergoes a phase transition from a metal to a metal hydride which leads to an expansion of the palladium lattice. The fabricated structure showed a reflectance of 0.5% which in combination with a complete suppression of transmission yields an absorbance of A
≈
99.5
%. As shown in Figures 26(a)–26(d), they utilized the absorber structure for hydrogen sensing and were able to reliably detect concentration down to 0.5% H2 in air with response time in the range of seconds.Figure 26
(a) A side view of the sensor. Palladium nanowires are stacked above a gold mirror. The layers are separated by a MgF2 film. (b) A sketch of the experimental setup including the mass flow controllers used to set the desired hydrogen concentrations. (c) Simulated response of the sensor structure to hydrogen exposure. (d) Reflectance of the absorber for different hydrogen concentrations. (e) SEM images of split ring resonators (SRRs) on a graphene layer. (f) Experimental results of the Raman spectra for different conditions. Figures are reproduced from (a)–(d) [149] and (e, f) [150].
(a)
(b)
(c)
(d)
(e)
(f)More recently, it was demonstrated that graphene monolayers transferred on arrays of split ring resonators (SRRs) could exhibit resonances in the visible range. As illustrated in Figures26(e) and 26(f), Raman enhancement factors per area of graphene up to 75 were measured, demonstrating the strong plasmonic coupling between graphene and the metasurface resonances.Recently, an important sensing technique via multifrequency antennas was also demonstrated [151–155]. Such antennas can efficiently detect different vibrational modes of molecular species in a window of several micrometers, where informative fingerprint spectra of many molecules are present.Since there have already been many reviews on this topic [34, 142, 143, 156], we only give a small part of examples here. To completely understand the role of metasurface in sensing applications, we would like to suggest that the readers find more information in these literatures.


### 3.6. Surface Plasmon-Inspired Metasurfaces

In previous discussion, metasurfaces refer to arrays of subwavelength structures on thin films. More generally speaking, any kinds of subwavelength structures on such films can be regarded as metasurfaces, with novel applications in optics and electromagnetics. Early in 1998 [157], it was found that extraordinary light transmission can be observed when it passes through the subwavelength metal pinhole arrays (Figure 27). Also, adding a surface groove structure around the subwavelength aperture can break the traditional diffraction limit and achieve highly directional energy transfer with ultrahigh transmission [158].Figure 27
(a) Optical transmission properties of single rectangular hole in metal films. Inset shows the SEM image. (b) Transmission spectrum of hole arrays. The triangular hole array was milled in a 225 nm thick Au film on a glass substrate with an index matching liquid on the air side (hole diameter 170 nm and period 520 nm). (c) SEM image of the bull’s eye structure. (d) Optical properties of the bull’s eye. Figures are reproduced from [65].
(a)
(b)
(c)
(d)Subsequently, Poujet et al. firstly demonstrated an experimental extraordinary optical transmission up to 90% in the subwavelength annular apertures [159]. In spite of the metal loss, the transmission of incident light has been greatly enlarged by employing the guided mode propagating through the annular aperture array. The subwavelength hole arrays can also act as color filters as the wavelength selectivity is directly related to the period of the holes [65]. An array of dimples is prepared by focused-ion-beam milling an Ag film. Some of the dimples were milled through to the other side so that light can be transmitted. When this structure is illuminated with white light, the transmitted colour is determined by the period of the array. In this case, the periods were chosen to be 550 and 450 nm, respectively, to achieve the red and green colours.Afterwards, several research groups including Martin-Moreno et al. [160] analyzed the underlying physics principle of generation of beaming effect in groove surface and pointed out that transmission enhancement of the groove is attributed to three factors as follows: surface plasmon resonance modes in the grooves, phase match of groove secondary radiation, and waveguide modes in the slot. Considering the SPs in metallic structure at the visible range, Luo and Yan established a physics model, namely, quasiperfect conductor model (QPCM), to optimize the directed radiation characteristics of SPPs [34]. In addition to beaming effect, the multidirectional radiation and abnormal homogeneous radiation phenomenon of subwavelength groove structure were also systematically discussed based on the diffraction theory.More recently, the extraordinary transmission and beaming effect based on cycle groove structures were also expanded to other frequency bands. Pendry et al. demonstrated that even a perfect electric conductor can support surface plasmon [56]. In order to distinguish it from traditional SPs, this surface plasmon supported by groove structures in low frequency is named spoof surface plasmon (SSP). Lockyear et al. [161] demonstrated that microwave energy could be coupled into SSPs through the reflective spectrum experiment of grating structure. Lately, Akarca-Biyikli et al. [162] experimentally validated the abnormal transmission and beaming effect in the 1D groove structure. With the beaming effect and extraordinary transmission, groove structures have wide potential applications in various frequency regions, as shown in the following discussion.


#### 3.6.1. Surface Plasmon-Inspired Metasurfaces for Microwave Antennas

The directional energy transfer realized in groove structure meets the requirements of high-directivity antennas and a variety of antennas have been proposed in the microwave band. For example, Huang et al. [163] used periodic groove structure in linearly polarized waveguide end slot array antenna. As shown in Figures 28(a) and 28(b), the beam angles in E-plane and H-plane were compressed to be 6 and 13 degrees, respectively. The groove shaped metasurfaces also have great contribution in reducing the level of sidelobes of slot antennas. Huang et al. proposed a method of integrating groove structures with two different periods into slot antenna to obtain low sidelobe radiation (Figures 28(c) and 28(d)). The sidelobe of the antenna with grooves was greatly decreased compared to the slot array without groove structures. Furthermore, after adding the artificial electromagnetic soft-surface structure to one-dimensional subwavelength outer groove, the antenna backward radiation was significantly reduced by 10 dB. However, the antenna gain was only increased by 0.2 dB due to long distance between the edge groove and the central feed.Figure 28
(a) Groove antennas based on slot array. (b) TheE-plane radiation pattern for the antenna in (a). (c) Patch antennas loaded with the groove structure. (d) The E-plane radiation pattern for the antenna in (c). (e) Slot array antenna with low coupling. (f) Coupling efficiency of the antenna in (c). Figures are reproduced from [163].
(a)
(b)
(c)
(d)
(e)
(f)For the characteristics of low cost, light weight, and low profile, microstrip patch antenna has gotten a great prospect on the area of military and civilian applications. However, due to the deterioration of surface wave, the antenna’s radiation efficiency is very low, and this restricts its development. Ying and Kildal [164] improved the radiation performance of the antenna through an artificial electromagnetic soft-surface groove onto a ground.The groove structures can also be loaded between slot elements to achieve low coupling between the slots and thus obtain high aperture efficiency of the slot antenna arrays. The cross-coupling between the two slots was sharply decreased by 30 dB after loading the groove structure, as shown in Figures28(e) and 28(f). Furthermore, after introducing groove structure, the gain of slot antenna array was enhanced by 4 dB, and the sidelobe level on E-plane is low and main lobe on H-plane is compressed.The period of a traditional beaming effect based groove structure is approximate to the wavelength, and the beaming effect usually requires several periods to implement. Thus, they make the size of the whole antenna very large and bring about the low utilization of aperture. Therefore, with no sacrifice of the antenna performance, how to reduce the groove cycle has formed a research direction.Huang et al. have still taken account for the loading of high dielectric constant medium between the grooves to reduce the groove cycle equivalently. Both single slot antenna and two-dimensional slot antenna array loaded dielectric medium with high permittivity were analyzed. The operating frequency of this antenna is 14.5 GHz, and the rectangular waveguide end slots were used as the exciting source. The dielectric constant loaded between the two neighboring grooves was 11.9, and the thickness of the loaded media silicon was 1.1 mm. The introduction of the traditional cycle-groove structure has no effect on antenna’s resonant frequency, while the medium-loading groove structure makes the center resonant point of the antenna shift to the low frequency, and it has a certain impact on antenna input matching. However, the slot antenna can be kept atS
11 < −10 dB by tuning the slot length in the working frequency, meeting the needs of practical engineering. The gain of a traditional cycle-groove slot antenna is 15.11 dB, increasing by about 9 dB compared to the flat-panel slot antenna. However, the antenna gain has further improved by 3 dB after the medium-loading groove structure is used, reaching 18.29 dB. It is notable that the physical diameter of the designed antenna is smaller than the size of a traditional cycle-groove slot antenna, only three-quarters of it, but the gain has improved more significantly instead. From the radiation patterns, we can also find that the E-plane of a traditional cycle-groove antenna shows an obvious beaming effect.This medium-loading method can also increase the performance of two-dimensional slot antenna array. This idea broke through the limit that the traditional array element interval is less than wavelength to widen applications of the periodic groove structure. Afterwards, media with high dielectric constant were loaded between the grooves to reduce the groove cycle equivalently without sacrificing of the antenna performance. This method featured in smaller periods compared to the traditional periodic groove structures, which results in reduced antenna aperture and inspiring more surface wave to improve further antenna gain in the performance of the antenna radiation. Furthermore, it compresses the beam angles of sidesE and H to illustrate prominent directed radiation ability. So it can be considered that the application of this new periodic groove structure was a development direction of high-directionality antenna. It was the first time to use a periodic groove structure as a secondary source and load it between the slot array elements with interval greater than wavelength to avoid sidelobe. This idea broke through the limit that the traditional array element interval is less than wavelength to widen the applications of the periodic groove structure.


#### 3.6.2. Surface Plasmon-Inspired Metasurfaces for Applications in Terahertz and Mid-Infrared Regions

One of the disadvantages of the grooves for directive radiation is that the working bandwidth is limited. Nevertheless, this is not a series problem for some applications. For instance, almost all kinds of lasers are narrowband in spectrum. In this regard, the groove structures can be integrated to lasers in order to improve their performances. By defining a metallic subwavelength slit and groove array on the facet of quantum cascade lasers (QCLs) [165], the divergence angle in the laser polarization direction is only 2.4 degrees as shown in Figure 29. Compared to the original 9.9 μm wavelength laser without a groove array, a reduction in beam spread by a factor of 25 is achieved, without significant reductions in output power. Taking advantage of SSPs, groove array integrated terahertz QCLs were also demonstrated [166]. The beam divergence of the lasers was reduced from ~180 degrees to ~10 degrees, the directivity was improved by over 10 decibels, and the power collection efficiency was increased by a factor of about six compared to the original unpatterned devices. In addition, multibeam QCLs and MID-IR QCLs with integrated plasmonic polarizers were reported through combining the groove structures with QCLs by Capasso’s group [167].Figure 29
(a) Schematic of the small-divergence laser, which comprises a QCL and a metallic slit-grating structure defined on its facet. (b, c) Cross sections of the two device designs. (d) 2D simulation of the intensity distribution of a small-divergence QCL of the second design lasing atλ
=
9.9 μm. (e) Calculated far-field intensity distribution of the device shown in (d); inset: enlarged view of the central lobe. (f) Measured 2D far-field intensity of device B patterned with the slit-grating structure. Figures are reproduced from [165].
(a)
(b)
(c)
(d)
(e)
(f)


#### 3.6.3. Surface Plasmon-Inspired Metasurfaces for Applications in the Visible and Near-Infrared Regime

The intriguing properties of plasmonic waves at metasurfaces can also be utilized to enhance the directivity of classically noncoherent or not-directive radiations. For example, spontaneous emission of fluorescent molecules or quantum dots is radiated along all directions when emitters are diluted in a liquid solution, which severely limits the amount of collected light. Making use of the directional manipulation of the SP-inspired metasurface, Aouani et al. [168] successfully controlled the radiation properties for nanoemitters, as shown in Figure 30. Enhancing the fluorescence intensity and narrowing the emission directivity were simultaneously obtained, and a full control of fluorescence was achieved. However this control is static. In 2011, active control over fluorescent emission was also reported by electrically pumping the similar light-emitting device [169]. This type of device facilitates the realization of a new class of active manipulation for use in new optical sources and a wide range of nanoscale optical spectroscopy applications.Figure 30
Directional radiation of fluorescent molecules. (a) SEM image of the fabricated nanoaperture with five corrugations. (b) Configuration to enhance and control the fluorescence emission of molecules diffusing in the central aperture. (c, d) Radiation patterns (intensity distribution in the back focal plane of the 1.2 NA objective) for a single nanoaperture without (a) and with (b) periodic corrugations. (e) Fluorescence intensity enhancement per single molecule as function of the emission polar angle, relative to the open solution reference case. (f) Angular radiation patterns in the polar angle. Figures are reproduced from [168].
(a)
(b)
(c)
(d)
(e)
(f)In addition to the directional manipulating and transmission enhancing, the applications of groove type SP-inspired metasurface were greatly expanded recently. Orbital angular momentum (OAM) transfer [170] and wavefront shaping [171] were experimentally demonstrated. Chiral plasmonic grooves defined on a metallic film would transform a normal plane wave to the vortex beams with tunable topological charge, as shown in Figures 31(a)–31(c). By surface-wave-holography method, Chen et al. shaped the wavefront of the incident near-infrared light into predesignated complex patterns such as Latin letters, after passing through a 180 nm radius hole that is surrounded by well-designed groove patterns, as depicted in Figures 31(d)–31(g).Figure 31
OAM generation and wavefront shaping by groove type SP-inspired metasurface. (a) Experimental setup of the OAM generation. (b) SEM image of the sample. (c) Intensity distribution imaged through the sample. (d, e) SEM images of the holographic metasurfaces. (f, g) Simulated images of the holographic images. Figures are reproduced from (a)–(c) [170] and (d)–(g) [171].
(a)
(b)
(c)
(d)
(e)
(f)
(g)More recently, we provided a scheme to guide and collimate OAM at the micro- and nanolevels [172]. The coaxial plasmonic waveguide is exploited as a naturally occurring medium for light carrying OAM to transfer. The guided OAM wave is coupled to free space through corrugated grooves surrounding the coaxial waveguide, where coherent scattering of spiral surface plasmon was demonstrated to be responsible for the huge enhancement of beam directivity. Experimental results at λ
=
532 nm validated the near-field transportation of OAM beams, where the topological charge is tunable via the modulation of a liquid crystal spatial light modulator (SLM).


### 3.7. Passive Metasurface Antennas and Generalized Snell’s Law

In many cases, metasurfaces can be considered as passive antennas array. By tuning the geometries and material parameters, the amplitude, phase, and polarization state of the reradiation of these antennas can be fully controlled. In this section, we first review two kinds of phase-type metasurfaces, where only the phase is tuned. Then, the possibility of full control over the phase, polarization, and amplitude is discussed.


#### 3.7.1. Passive Antenna Array Based on Impedance Transition

The impedance boundary conditions of metasurfaces can be utilized to tailor the phase delay within one single layer regardless of its thickness. This means that, theoretically, there exists no thickness limit for this problem. Based on the rigorous form of Huygens’ principle developed by Love and Schelkunoff [173, 174], it has been demonstrated that the transmitted or reflected phase shift can vary between 0 and 2
π to provide complete phase coverage by adjusting the magnitude of the impedance [19, 175, 176].As depicted in Figure32, the concept of Huygens’ metasurface was proposed by Pfeiffer and Grbic in 2013 [176] and realized with two-dimensional arrays of subwavelength structures that provide both electric and magnetic polarization currents to generate the prescribed wavefronts. The applications of the metasurfaces in a beam-refracting surface and a Gaussian-to-Bessel beam transformer were discussed.Figure 32
(a) Principle of the Huygens metasurface. The fields in regions I and II are defined independently of each other, and the surface equivalence principle is employed to find the fictitious electric and magnetic surface currents that satisfy the boundary conditions at the metasurfaces. (b) Simulated time snapshot of the magnetic field (Hz) of ay-polarized plane wave, normally incident upon the designed Huygens’ surface. (c) Dimensions of the unit cells comprising Huygens’ metasurface. (d) SEM images of the optical Huygens’ surfaces. (e) Perspective view of an optically thin, isotropic Huygens’ metasurface that efficiently refracts a normally incident beam at telecommunication wavelengths. (f) Time snapshot of the steady-state, y-polarized electric field when a plane wave is normally incident from the bottom at a wavelength of 1.5 μm. The incident electric field has an amplitude of 1 V/m. Figures are reproduced from [176, 181].
(a)
(b)
(c)
(d)
(e)
(f)As an attempt to increase the energy efficiency and bandwidth, we presented an efficient approach, as depicted in Figure33, to extend the bandwidth of phase modulation by utilizing the broadband characteristic of low-quality factor (Q-factor) metasurface in the reflection mode [177]. The dispersion of the metasurface was engineered to achieve phase modulation within [
0
,
360
°
]. Anomalous nearly perfect reflection with relative bandwidth near 40% was demonstrated in the microwave regime. Similar designs in reflection geometry have also been validated by other authors [178–180].Figure 33
Reflection phases for different values of gap widthg for thickness of (a) d = 2 mm and (b) d = 6 mm. The other geometrical parameters are chosen as l = 4 mm and w = 0.2 mm. (c) y-component and (d) z-component of electric fields for d = 2 mm, g = 2.8 mm, and f = 10 GHz. (e) y-component and (f) z-component of electric fields for d = 6 mm, g = 2.8 mm, and f = 10 GHz. (g) Schematic of the gradient metasurface. (h) Electric field E
y distribution in the scattering region at normal incidence for 8, 8.5, 9, 9.5, 10, and 10.5 GHz. The dashed black arrows indicate the propagation direction evaluated by sin
-
1
⁡
(
k
x
/
k
). Figures are reproduced from [19].
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)


#### 3.7.2. Passive Antenna Array Based on Ultrathin Resonators

In the phase-engineering regime, one interesting but sometimes neglected phenomenon is that a rotation of electric field of circular polarized electromagnetic wave results in a corresponding phase shift. As early as 1955, the rotatory phase shifter was proposed by Sichak and Levine [182]. They showed that the phase of the output voltage of a circularly polarized antenna was proportional to the angle of rotation of the antenna about its longitudinal axis. Two circularly polarized antennas with a proper rotation angle between each other were mounted in a circular waveguide to construct a phase shifter. In 1961, this rotatory phase was utilized in the construction of large radio telescope in the University of Illinois [183]. Subsequently, similar phase shifting results were demonstrated for passive reflectarray antennas [184].In 1984, Berry proposed that an adiabatic polarization can introduce a phase shift [43], which was further experimentally demonstrated in 1988 [185]. Since the phase is associated with circular polarization, it can be termed as one kind of optical spin-orbit interaction. In 1999, polarization gratings were proposed [186]. This idea was further developed by Hasman et al., with various kinds of applications, such as beam splitter, optical vortex generation, and focusing lens [44, 187–189]. In 2006, the famous q-plates were proposed to realize spin-to-orbital angular momentum conversion [190]. These q-plates can also be used as polarization converters [191]. In recent years, nanoantennas were widely adopted to control circularly polarized waves [192–195].In 2011, Yu et al. proposed another phase shifting mechanism with linearly polarized illumination. As shown in Figure34, by varying the angle and length of V-shaped nanoantennas, arbitrary modulation of phase shift and amplitude transmission were demonstrated. The operational principle of such V-shaped antennas relies on the asymmetric transmission enabled by the nanoantennas. Similar to the case of circular polarization, such antennas have low energy efficiency because there always exists one component with the same polarization as the incident beam. Based on this abrupt phase change, they proposed the so-called “generalized Snell’s law.” By properly tuning the geometrical parameters of each antenna, broadband phase change could be achieved, although the phase was not rigorously achromatic [134, 138, 196].Figure 34
(a) SEM image of a representative antenna array fabricated on a silicon wafer. (b) Schematic experimental setup fory-polarized excitation. ((c) and (d)) Measured far-field intensity profiles for the y- and x-polarized excitations, respectively. (e) Schematic view of a representative antenna array. (f) Scanning electron microscope images of the unit cells of four antenna arrays with different periodicities fabricated on a single silicon wafer. ((g) and (h)) The false-color maps indicate the experimentally measured relative intensity profiles for the antenna array. Figures are reproduced from [134, 138].After the pioneering work by Capasso, much work was devoted to the design of phase-discontinuity metasurfaces. Many optical devices were subsequently designed and experimentally demonstrated. For example, Zhang et al. proposed that C-shape metallic elements can also be utilized to tune the amplitude and phase of cross-polarized scattering for linear polarization incidence [196]. In addition to the simple phase-engineering, other applications, such as spiral phase plates and wave plates, were also demonstrated [197, 198].Based on the locality of the phase shift [199], Lin et al. extended the V-shaped antennas in the near-infrared bands. The focus length was also decreased to a large extent to obtain a focus spot close to the diffraction limit. Jiang et al. demonstrated similar effect in the terahertz regime [200]. More recently, Ma et al. used a metasurface to focus vortex beam into a nanodoughnut [201]. As shown in Figures 35(a)–35(d), the proposed metasurface has good performance close to the ideal case. The metasurface tuned the phase distribution of the incident beam based on the concept of discontinuous phase modulation. Consequently, the proposed metasurface has two main functions. Firstly, with a circularly polarized incident beam, the metasurface converts it into a beam carrying OAM. Secondly, the incident field can be focused into a point with a certain focus length. The total energy coefficient of this metasurface exceeds 40%. By properly designing the phase modulation distribution, the copolarized component of the incident field does not participate in the focusing process. Therefore, only optical vortex can be observed in the focused field. The thickness of this planar chiral metasurface is much less than the operational wavelength and thus has potential application in compact integrated optical systems.Figure 35
(a) Schematic of the 2D elliptic antennas array. (b) SEM image of the elliptic antennas. (c) Measured power intensity profile of the focused field in thex
z-plane. (d) The simulated (dashed lines) and measured (solid lines) intensity spectra of the focused field, respectively, along the y-direction. (e) Schematic of the unit cell of rectangular aperture in metallic screen for holography. (f) Amplitude and phase transmission for various rotation angles. (g) SEM image of the sample. (h) Schematic of the measurement setup. Figures are reproduced from [201].
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)The geometric phase in aperture array has direct application in holography. As demonstrated in Figures35(e)–35(h), metasurface with metallic square apertures was constructed in our lab to form a hologram image of a China map based on the concept of discontinuous phase modulation in visible band.Since only part of the transmitted light takes geometric phase, single layered metasurfaces are often characterized by low efficiency. In principle, the efficiency could be increased dramatically with the help of a reflective layer. Taking the circularly polarized geometric phase as an example, the combination of an anisotropic metasurface with a reflective layer would form a reflective wave plate. By rotating the main axis of the embedded antennas, gradient phase could be directly obtained. This technique was utilized in reflectarray to increase the gain of antenna while keeping the reflective surface to be flat [184]. In the optical regime, the reflective nanoantennas array was used as building blocks of high efficient holograms [202]. The metasurface has an ultrathin and uniform thickness of 30 nm and is compatible with scalar diffraction theory, even with subwavelength pixel sizes, thus simplifying the design of holograms.Another important application of the metasurface relies on the fact that phase shifting metasurfaces placed at the optical pupil plane can increase the resolution of telescopes, which means that the far-field diffraction limit can be overcome [203]. As shown in Figure 36, the designed metasurface has several rings, which exert phase shift of 0 and π on the incoming light and change the corresponding spatial frequency [2]. To characterize the performance, we measured the images of two circular and triangular holes with and without the metasurface. After the insertion of the metasurface, the resolution is decreased to 0.625 times of the original value, implying that a 10-meter telescope could have the same resolution as that of a 16-meter one (i.e., a 1.6 times improvement in the resolution power).Figure 36
Far-field superresolution based on metasurface. (a) Schematic of the experimental setup. The inset shows the phase distribution of the metasurface. Gray regions and white regions indicate 0 andπ, respectively. (b) Experimental results for a circular hole at wavelength of λ = 532 nm. (c) Simulation results for a triangular hole. Figures are reproduced from [2].
(a)
(b)
(c)Very recently [204], we proposed and demonstrated the concept of broadband virtual shaping at the visible, infrared, and microwave spectrum by tailoring the spatiotemporal property of spin-orbit interaction in cascaded metasurfaces. When electromagnetic waves impinge on the designed metasurface, they are reflected to predefined directions to avoid being detected by unwanted antennas. Resorting to the dispersion engineering techniques in metasurface-based polarizers, the bandwidth was dramatically enhanced, although the thickness-to-bandwidth ratio may be analogous to that of broadband absorber. The design principle provided a new route for the control of electromagnetic wave for applications ranging from laser beam shaping to 3D holographic display and conformal camouflage [205].As shown in Figures37(a) and 37(b), we measured the specular reflection of an inhomogeneous metasurface. Since the reflected light was designed to depart from its original direction via the metasurface-assisted law reflection, only a small reflection echo was measured. Owing to the flexibility of the metasurface, this approach could be utilized in complex objects. For example, the RCS of a cylinder can be dramatically reduced by covering our metasurfaces on it (Figure 37(c)). The metallic cylinder in our design has a radius of R = 90 mm and height of h = 360 mm. The geometric phase distribution on the metasurface was designed to be Ф
=
k
z
z
+
k
φ
φ, where k
z
=
k
φ
=
104.7 rad/m. As shown in Figure 37(d), the RCS reductions for TE polarization and TM polarization were calculated under normal incidence along the y-direction. We noted that the reduction amount is a bit smaller than the planar case, which possibly stems from the nonoptimized phase profile and the fact that the RCS of a cylinder itself is smaller than its planar counterpart. Nevertheless, the conformal metasurfaces provide a new sight into the virtual shaping of nonplanar objects. In addition, this approach can be exploited to increase or decrease the RCS.Figure 37
(a) Schematic of the measurement setup. (b) Measured results for both TE polarization and TM polarization. The inset shows the photography of the fabricated sample. (c) Schematic of the spin-orbit conversion in the curved metasurface on a metallic cylinder. The insets show the definitions of TE polarization and TM polarization. (d) Calculated broadband RCS reduction for TE polarization and TM polarization at normal incidence alongy-direction. Figures are reproduced from [204].
(a)
(b)
(c)
(d)In general, the metallic metasurfaces suffer from low efficiency due to the intrinsic ohmic loss and the limited scattering cross sections of the antennas, which is not anticipated in many realms. Recently, dielectric metasurfaces based on geometric phase were presented to control the phase [44]. Nevertheless, the discrete phases lead to degradation of the performance. To overcome this issue, we proposed a semicontinuous structure to increase the continuity of phase shift. The metasurfaces consist of high-refractive-index and low-loss silicon annual ring gratings. Ohmic loss is avoided compared to its metallic counterpart. The continuity of annual ring grating ensures the continuity of the transmitted field, thus suppressing high order diffraction effects that may arise from discontinuity.At the end of this section, we would like to comment that metasurface with geometric phase could enable many applications in distinct disciplines. In general, traditional refractive, reflective, and diffractive devices could be replaced by metasurfaces. These elements include the spherical lenses, aspherical lenses, parabolic reflectors, fan-out grating, and laser beam shapers. In the microwave regime, metasurfaces could also be utilized to substitute traditional phased-array antenna. Furthermore, this kind of metasurface is also able to shift the momentum of scanning beam to extend the scanning range of phased array antennas, when it is integrated in radar radomes [206].


#### 3.7.3. Full Control of Phase, Polarization, and Amplitude

In many applications, the phase, polarization state, and amplitude are all important for the manipulation of electromagnetic waves. For example, a low side-lobe phased array antenna needs the full control of phase and amplitude [207], while a planar lens with large longitudinal fields in the focus spots requires that the polarization and phase be simultaneously controlled [208].In order to achieve complete modulation of phase and polarization, Pfeiffer and Grbic proposed a four-layer cascaded metasurface lens that can focus light and control its polarization [209]. By adjusting the dimensions of structure, one can independently adjust the inductance and capacitance in the x- and y-directions so that the phase and polarization can be completely controlled.Kim et al. demonstrated that the local reflection coefficients of gap-plasmon resonators can be independently tailored in both magnitude and phase [181]. Using an array of nanorods closely placed on a metallic layer, it was shown that the magnitude and phase of the surface’s local reflection coefficients can be simultaneously tuned, with a magnitude range of [
0,0.67
] and a phase range of 360°. The power efficiency can reach 45% for an operational wavelength of 800 nm. This method was utilized in the design of a Dolph-Tschebyscheff array, with equal-amplitude sidelobes of prescribed magnitude, as represented in Figures 38(a)–38(d).Figure 38
(a) Magnitude and (b) phase ofS
11 in degrees for different resonator lengths and rotation angles. (c, d) Radiation patterns of (a) Dolph-Tschebyscheff and (b) uniform arrays. Both arrays redirect the normally incident plane wave at 33°. (e) Schematics of the top and bottom nanoapertures forming the super-unit-cell in the plasmonic metasurfaces for the demonstration of anomalous refraction. (f) The transmission phase and amplitude of each nanoaperture pair, calculated under y-polarized incident light at 900 nm. (g) SEM image of the sample (left panel) and measured refraction angle (right panel). Figures are reproduced from [181, 210].
(a)
(b)
(c)
(d)
(e)
(f)
(g)More recently, Li et al. proposed and validated another metasurface that can provide simultaneous manipulation of the phase and polarization of the transmitted light [210]. SPPs were adopted to obtain a π phase shift when the top and bottom nanoapertures are laterally translated by a distance in the y-direction. Hence, the phase difference can cover 0 to 2
π by varying the parameters of nanoaperture for normally incident light polarized in the y-direction. The metasurface enabled anomalous refraction with efficiency of about 21.4% for linearly polarized incident light (Figures 38(c)–38(g)).It also should be noted that the phase over the surface of micro- and nanoantennas can also be measured with the help of scattering near-field techniques [211, 212], which provide a way to further understand the physical processes of these antennas.


### 3.8. Active Metasurfaces

Although passive metasurfaces have been proved to be useful in many applications, the dynamic tuning of performance is always desired in practical applications. Most of the metasurfaces have fixed electromagnetic properties when the structures are designed or fabricated. Nevertheless, there is a type of “reconfigurable” metasurface which is able to tune the electromagnetic response with an outside stimulus [213–217]. The general way to obtain the tunable phase modulation is by loading active devices in its unit cells, such as varactor diodes [218], liquid crystals, and ferroelectric and microelectromechanical switch (MEMS) [219], as can be seen in Figure 39.Figure 39
Examples of active metasurfaces. (a) SEM image (b) transmission spectra for a MEMS-based metasurface. (c) Schematic and (d) transmission spectra for magnetic resonance (left panel) and electric resonance (right panel). Figures are reproduced from [219, 220].
(a)
(b)
(c)
(d)These reconfigurable or tunable metasurfaces efficiently broaden the application range of metamaterial and simplify the optical and communication systems. According to the particular applications, active metasurfaces can be classified into three main subdomains. In the following, we would give a brief review on these novel metasurfaces.


#### 3.8.1. Active Phase Modulation

Aiming at satisfying the requirement of modern communication systems and solving the disadvantages of traditional phased array antenna, metasurfaces with phase-tuned ability have been introduced to construct novel beam scanning antennas. The principle of beam steering for this metasurface is illustrated in Figure40(a). The designed active metasurface is divided into N regions, which can be regarded as a linear array with a period of l
/
N. When a plane wave transmits through these N regions, the phase difference between adjacent regions would be α. As a result, the angle of beaming direction is θ deviated from the normal direction, which is determined by α.Figure 40
(a) Principle of beam steering. (b) Unit cell of the phase reconfigurable metasurface. (c) Phase manipulation results of the active metasurface. (d) Photography of the horn antenna with the active FSS. (e, f) Radiation patterns of the designed horn antenna in (e)E-plane and (f) H-plane for different phase distribution. Figures are reproduced from [221].
(a)
(b)
(c)
(d)
(e)
(f)In Figure40(a), the transmission phase φ
i of region i can be shown as(41)
φ
i
=
-
ζ
i
+
φ
0
+
2
k
π
,where φ
0 is a constant and k is an integer. The phase shift ζ
i and the phase difference α can be expressed as(42)
ζ
i
=
β
i
l
N
sin
⁡
θ
,
α
=
φ
i
-
φ
i
-
1
=
-
β
l
N
sin
⁡
θ
,where β is the wave number. The beam steering angle θ can be then written as(43)
θ
=
arcsin
⁡
-
N
α
β
l
.Clearly, (43) is one particular case of the metasurface-assisted Snell’s law, based on which the beaming direction can be tuned by changing the phase difference α between adjacent elements. In 2012, Jiang et al. [206] introduced an active cascaded metasurface for phase manipulation by tuning varactor-diodes loaded in the unit cell. The tunable metasurface was employed as the radome to tune the E-plane radiation pattern of the antenna array. However, the loss of this active phase modulation metasurface is relatively large due to its eight layered structure.Based on the phase modulation property of the metasurface, we have proposed an active phase modulation metasurface to manipulate the phase of the incident wave and to achieve beam steering of a horn antenna [221], as depicted in Figure 40(d). The unit is composed of a metallic rectangular ring and a patch, with a pair of microwave varactor diodes inserted in between along incident electric field polarization direction. Transmission phase of the emitted wave can be tuned by changing the bias voltage applied to the varactor diodes, and 360° phase difference can be obtained at 5.3 GHz as the capacitance value is tuned from 0.65 pF to 2.6 pF.Through different configurations of the bias voltages, one can obtain the gradient phase distribution of the emitted wave alongE-plane and H-plane. This metasurface loaded antenna can steer the directive beam with an angle of ±30° in both E-plane and H-plane at 5.3 GHz with a bandwidth of 180 MHz. Using an improved approach, the scanning range can also be increased to ±360° in both E-plane and H-plane [2].In previous works, the polarization state and beam direction are not simultaneously controlled. In order to achieve this goal, a novel transmitarray element was proposed, which achieved 1-bit phase shifting at two orthogonal linear polarization modes. The phase tuning and polarization reconfiguration can be independently controlled based on PIN diodes. The unit cell of the dual linearly polarized metasurface consists of two-layer metallic patterns connected by a metalized via-hole. One-layer metallic pattern is a rectangular patch with two PIN diodes loaded in O-slot along electric field polarization direction, which is utilized as a receiver-antenna to achieve 1-bit phase tuning. The other metallic pattern is a dual linearly polarized transmitter-antenna that adopts a square ring patch with two PIN diodes distributed at the cross-polarization directions. The simulation results show that the designed antenna can achieve 1-bit phase tuning and linear polarization reconfiguration at 10.5 GHz with insertion loss of about 1.1 dB. This kind of the metasurface-based antenna has the advantages of low cost and simple implementation, which could be developed for possible applications in some communication and radar systems, especially in the area where high-gain beam steering and the anti-interference capabilities are urgently required.


#### 3.8.2. Active Polarization Modulation

The polarization states can also be dynamically tuned by active metasurfaces. Zhang et al. [215] proposed a reconfigurable chiral metasurface, which switched its handedness when the semiconductor region was illuminated by external light, as shown in Figure 41. This reconfigurable or tunable property efficiently broadens the application range of metasurface and simplifies the optical and communication systems.Figure 41
Geometry and the results of the photoinduced handedness switching metasurface. Figures are reproduced from [164].
(a)
(b)
(c)
(d)
(e)
(f)
(g)In order to achieve polarization conversion with simple metasurface, Ma et al. [92] demonstrated a double-layered active metasurface which changes the structure between chiral and isotropic by tuning the working states of the PIN diodes in its unit cells. When it presented chirality, the handedness could also be tuned. As shown in Figures 42(a) and 42(b), the designed metasurface could convert the incident linearly polarized wave into RCP or LCP one. Furthermore, it could also be switched to be isotropic and keep the polarization state of the incident wave unchanged, by controlling the voltages applied on these diodes.Figure 42
(a) Schematic of the metamolecule of the active metasurface for polarization manipulation, and the transmission spectra are shown in (b). (c) Photography of the fabricated dipole antenna using tunable metasurface with its unit cell in (e), and the measuredS
11 and AR of the designed dipole antenna for different working states are shown in (d) and (f). Figures are reproduced from [92].
(a)
(b)
(c)
(d)
(e)
(f)We have also employed this concept of active polarization manipulation into the design of antennas. As it is well known, the dipole cannot radiate efficiently near a perfect conductor due to its opposite image current; in addition, the single dipole can only produce linearly polarized waves, which cannot satisfy the requirement in many communication fields. To address the above issues, the anisotropic metasurface was proposed as the ground plane for the dipole. This novel reflective metasurface not only reduces the profile of the dipole but also assists it to achieve emission of circularly polarized wave. Through adjusting the PIN diodes loaded on the unit cell of the metasurface, the polarization states of the emitted wave from the dipole, including RHCP, LHCP, and LP waves, can be dynamically tuned.The tunable metasurface can make the dipole antenna work at four states. For states 1 and 2, as seen in Figure42(d), the emitted waves with left- and right-hand circular polarization are produced at 4.6 GHz, and the AR is 1.2 and 0.3 dB, respectively. For states 3 and 4, the dipole antenna radiates the linearly polarized waves with the gains of about 6 dB at 4.6 and 4.25 GHz (see Figure 42(f)), respectively. This kind of the polarization reconfigurable antenna has a strong environmental adaptability, which may find many potential applications in the communication field.Recently, Wang et al. demonstrated a coherent perfect polarization transformer [76]. It was proved that the phase shift between two coherent inputs could be utilized to dynamically tune the polarization states of output waves. Depending on the phase difference, the outputs could be y polarization, LCP, and RCP for x-polarized inputs.


#### 3.8.3. Active Amplitude Modulation

Besides the phase property of the incident electromagnetic wave, the amplitude can also be modulated. As analyzed in the effective impedance theory, the transmitted amplitude and the phase of the incident wave are modulated by the effective impedance of the metasurface. Therefore, the element loading method in metasurface allows the control of the amplitude and hence provides new applications in microwave communication systems, such as controlling the sidelobe and beamwidth of the radiation antennas.Lim et al. [222] had designed a kind of composite right-/left-handed microstrip antenna in which varactors were used to tune the amplitude of each element for achieving dynamic control of the beamwidth. Recently, a partially reflective surface (PRS) was utilized to actively change the beamwidth of the emitted waves by tuning its reflection through the varactors mounted on each element of the PRS [223].Antennas with low side-lobe level (SLL) are urgently required since it can efficiently reduce the electromagnetic interference and improve the ability of signal capture. However, traditional approaches to achieve low SLL are mainly realized by modifying the elements weighting or spacing distribution in antenna array. In comparison, metasurfaces with amplitude tunability were employed to reduce the SLL of antennas since the radiation pattern can be reformed by metasurfaces.Our team proposed an approach to reduce the SLL of antenna array to a desired value by utilizing amplitude modulated metasurface, as shown in Figure43. By manipulating the structure parameters and the PIN diodes loaded in the unit cells, the transmission amplitude of each unit can be distinctly controlled. Then, the metasurface was utilized as the superstrate of the horn antenna array, and the superstrate was divided into several regions with different transmission amplitudes along the electric field polarization direction. With a plane wave illustrated on the superstrate, the transmission amplitudes were designed as Taylor distribution while the transmission phases were equal, which resulted in a tapered amplitude distribution of the output beam. An H-plane sectorial horn array is adopted as a plane wave source to verify the performance of the SLL reduction. The SLL was reduced from −12.4 to −25.9 dB at the desired frequency, while not influencing the gain of the antenna array.Figure 43
(a) Principle of the sidelobe reduction with the metasurface superstrate. (b) The geometry of the amplitude tunable metasurface to reduce the sidelobe of the horn antenna array. (c) Schematic of the unit cell of the metasurface. (d) Comparison of the normalized transmission amplitude distribution of the proposed antenna composite and the ideal Taylor amplitude distribution. (e) Phase distributions at the reference plane. The inset figure shows the electric field distribution atx
z-plane. (f) Radiation pattern in the E-plane of the antenna composite at 10.3 GHz with sidelobe level of −25.9 dB.
(a)
(b)
(c)
(d)
(e)
(f)Wang et al. proposed a kind of metasurface superstrate to control the beamwidth of horn antenna array based on the concept of amplitude modulation [225], as depicted in Figure 44. The unit cell of the metasurface was composed of two-layer periodic structures loaded with varactors. By tuning the capacitance of the varactors, the unit cell can produce two different states which are transparent and absorptive to the incident wave at a certain frequency, respectively. The whole metasurface can be divided into several groups, and each group is composed of some unit cells with the same state. By switching the state of each group, the transparent window of the metasurface can be changed. Consequently, the emitted waves with variable beamwidth can be expected, as validated in Figure 44(c), when this metasurface was placed above the horn antenna array as superstrate.Figure 44
(a) Schematic of the beamwidth controlling using metasurface. (b) Photographs of the fabricated FSS for beamwidth controlling. (c) Response of reflection and transmission coefficients to different capacitance values at the interesting frequency region. (d) Photograph of the low RCS antenna loading partially absorbing metasurface. (e) The RCS results for the PRS antenna with and without PRS. (f) MeasuredE-plane far-field patterns for the beamwidth manipulation antenna at 5.5 GHz. Figures are reproduced from [224].
(a)
(b)
(c)
(d)
(e)
(f)As another method to modulate the amplitude, metasurfaces partially absorbing ability has been introduced and employed in the antenna realm. Compared to the traditional means, such as shaping of target surface and adopting radar absorbing material, such metasurface may efficiently reduce the RCS while not decreasing the radiation performance of the antenna. We proposed a design to reduce the RCS and enhance the gain of a patch antenna by using partially reflecting surface (PRS) that consists of two layers of metallic structure [58], as demonstrated in Figure 44(d). The top absorbing layer is utilized to reduce RCS, while the bottom layer was combined with the ground plane to construct the F-P cavity to achieve high gain. The antenna gain was enhanced by about 6.5 dB at 11.5 GHz, and its RCS is dramatically reduced in a broad frequency range from 6 to 14 GHz. It was fully verified that the designed PRS did not influence the radiation performance of the antenna within the bandwidth of the RCS reduction, but it also obviously improved the antenna gain. This new design provides a good method to solve the conflict between the gain enhancement and the RCS reduction.In the above amplitude modulation metasurface, the normalized amplitude can be controlled in the range of 0-1. However, the amplitude of the incident wave can be gained above unit by utilizing amplifier in the unit cell of the metasurfaces. Recently, we also proposed an amplifying reconfigurable metasurface to achieve simultaneous control of the amplitude and phase of the incident wave. The varactor diodes were adopted to construct the reflection-type phase shifters, which achieved over 400° of phase shift extending the operation bandwidth beyond 10%. Most importantly, the amplifier integrated in the unit cell of the metasurface made the amplitude of the whole element simultaneously gain larger than 7 dB. In addition, the overall thickness of the proposed metasurface element is only0.135
λ in free space, which is more compact compared to the existing metallic elements. This kind of amplifying and phase modulation metasurface could be developed to construct high-gain antenna for beam steering.


#### 3.8.4. Active Absorption Modulation

In order to satisfy the requirement of modern military and civil applications, novel materials with smart absorbing characteristics are needed. In general, active metasurface absorbers have two advantages over traditional absorbers. Firstly, since traditional metamaterials absorbers are limited in the operational bandwidth, active tuning may increase the effective bandwidth in a time-diving way. Secondly, the absorption coefficients can be dynamically tuned to mimic the electromagnetic spectrum of environment, which is not obtained through traditional approaches.The intrinsic circuit property of metasurface absorbers permits an easy way to realize active tuning. As shown in many references, the metasurface can be characterized by its equivalent resistances, inductances, and capacitances [99, 114]. When lumped circuit devices, such as resistors, inductors, capacitors, and various kinds of diodes, are integrated in the metasurface, the electromagnetic response can be greatly improved.Early in 2004, Tennant and Chambers presented an adaptive absorber by controlling the bias voltage of PIN diodes loaded between adjacent metallic bow ties [213]. The absorber was similar with the topology of a Salisbury screen, but in which the conventional resistive layer was replaced by an active metasurface controlled by PIN diodes. The resulting structure had superior absorption characteristics compared to conventional passive absorbers of corresponding thickness. Measured results showed that the reflectivity response of the absorber can be controlled over the frequency band from 9 to 13 GHz. In a similar way, other circuit elements, such as varactors [226, 227], were introduced to change impedance of the metasurfaces.In 2012, an electrical tunable L-band absorbing material for two polarization types was presented by Wang et al. [228]. As shown in Figures 45(a)–45(c), the proposed absorber consisted of a metal resonator and four surrounding metal lines which were connected by pin diodes and exhibited the tunable range of reflectivity reaching −40 dB for both polarization types. Later [227], Zhao et al. demonstrated a tunable absorber with a measured bandwidth of 1.5 GHz (or relative bandwidth of 30%). Since the units are placed along two orthogonal directions, the absorber is insensitive to the polarization of incident waves.Figure 45
(a) Configuration of tunable absorbing material. (b) Measured reflectivity at different bias voltages under incident angle of 15°, and the power loss density at two frequencies is shown in (c). (d) Photograph of the fabricated active absorber; the measured sample has an area of 340 × 340 mm2, consisting of 200 units. Varactor and pin diodes are assembled through hand-soldering techniques. (e) Measured reflectance spectra of the active absorber with different bias voltages applied upon PIN diode. Figures are reproduced from [228, 229].In principle, an active absorber should have the ability of controlling echo characteristics in both aspects of frequency and intensity. However, few active absorbers simultaneously considered the two issues in a single device. As an attempt to accomplish this purpose, Wu et al. demonstrated an electrically active absorber in which the working frequency and absorbing intensity could be separately controlled by the PIN and varactor diodes [229]. The structures and measured results are presented in Figures 45(d) and 45(e). Compared with those metasurfaces proposed before, although at the expense of increased complexity, the interesting characteristic of the absorber designed here is that it contains a special designed active magnetic resonator in which both the resonant frequency and amplitude can be, respectively, tuned and therefore shows separable modulation of absorbing frequency and peak intensity. Both simulation and experimental results revealed that the active absorber simultaneously contains such two working models. Further theoretical analysis based on LC theory also confirmed this dual ability.Along with the increase of working frequency, sealed semiconductor devices become unsuitable due to the limited frequency response. In millimeter wave and terahertz, absorption behaviors can be tuned by modulating the relative position of cells on the top layer [230]. In 2013, Shrekenhamer et al. presented an active absorber in the terahertz regime [231]. By incorporation of liquid crystal into strategic locations within the unit cell, they were able to modify the absorption by 30% at 2.62 THz and also tune the resonant absorption over 4% in bandwidth. Other tunable metasurface absorbers adopted materials, such as vanadium oxide [232] and semiconductors [233].Recently, we constructed self-tuning metasurface absorbers with capability of self-adaptively tracing and absorbing the incident wave with relatively narrow bandwidth. As depicted in Figure46, the operational principle includes two main steps. Firstly, the central frequency of the incident wave was detected by a detection circuit. Secondly, a voltage bias is added to the active metasurface to achieve high efficient absorption of the incident wave. The experimental results show that the echo attenuation within the frequency region of 2.8~3.2 GHz is all larger than 10 dB; for some frequency it even reaches 35 dB.Figure 46
Self-tuning smart absorber. (a) Schematic of the operational principle. (b) Transmission coefficient of the absorber for a narrow incident wave for various capacitances at 2.75 GHz (left panel) and 3.25 GHz (right panel). (c) Experimental setup (left panel) and measured attenuation of the reflection wave when the incident wave is swept from 2.8 to 3.2 GHz (right panel).
(a)
(b)
(c)


### 3.9. Flexible and Stretchable Metasurfaces

One advantage of metasurfaces over traditional 3D materials is its flexibility which is stemming from the ultrathin thickness. Flexible metasurfaces also provide a route to actively tune the performances. In traditional active metasurfaces, the electromagnetic response can be dynamically manipulated by tuning the constitutive parameters of the related optical materials. However, the mechanical properties, such as shape and geometrical size of these metasurfaces, are invariable during the tuning process. Even for MEMS-based metasurface, the macroscopic geometry is not changed in practical operation.In recent years, the concept of flexible and stretchable metasurfaces has accepted particular attention, as inspired by the development of flexible electronic devices. For these metasurfaces, the key properties are determined by the substrate. For most metasurfaces except for some free-standing structures, the substrate not only provides a mechanical support for the metallic or dielectric structures but also offers an additional degree of freedom for the design of metasurface. Up to date, the most commonly used flexible substrates for metasurfaces are polydimethylsiloxane (PDMS), polyimide, metaflex, polyethylene naphthalene (PEN) [234–236], polyethylene terephthalate (PET), polymethylmethacrylate (PMMA), and polystyrene [237].One particular application of flexible metasurface is the conformal devices such as conformal antennas, conformal lenses, and conformal absorbers [238–240]. For nonplanar metasurface absorbers, different areas experience different incident angles. As a result, the large-angle stability is required. Fortunately, it was found that metasurface absorber can have good absorption for large incidence angle by proper design [241]. As a result, conformal absorbers may maintain its absorption. However, earlier designs of metasurface absorbers suffer from the strong polarization dependence [36]. In 2011, we designed and fabricated a polarization-independent wide-angle absorber, following the design principle we established [37]. As shown in Figure 47(a), the absorption does not change dramatically when the metasurface is bent as a cylinder.Figure 47
(a) Experimental results for a flexible metasurface absorber. (b) RCS reduction properties of nonuniform conformal metasurfaces. (c) Absorption of flexible absorbers fabricated on a PDMS substrate. (d) Elasticity of a flexible terahertz wave plate fabricated on polyimide. Figures are reproduced from (b)–(d) [239, 242, 243].
(a)
(b)
(c)
(d)In 2013, a conformal absorber was designed by utilizing nonuniform metasurface [239]. The authors designed three different unit cells, which are optimized at 0°, 30°, and 45° incident angles, respectively. As illustrated in Figure 47(b), the proposed concept was demonstrated by EM simulation and experiments. The RCS reduction with nonuniform unit cells was compared with that of the conventional planar metamaterial absorber with uniform unit cells and superior results were demonstrated.Regarding the wavefront engineering device (Figure48), Aieta et al. designed a conformal metasurface lens to eliminate the off-axis aberration [240]. It was found that aberration-free focusing is possible under axial illumination but off-axis aberrations appear when the excitation is not normal to the interface. An alternative design for an aplanatic metasurface on a curved substrate was proposed to focus light without coma and spherical aberrations.Figure 48
(a) Schematic, PSF, and MTF of a flat metasurface lens. (b) Schematic, PSF, and MTF of a conformal metasurface lens. Figures are reproduced from [240].
(a)
(b)The flexible property of PDMS has direct applications in other optical systems. For example, when a metallic grating was fabricated on PDMS, the period could be changed dynamically by stretching the substrate. As illustrated in Figure49(a), the fabricated metasurface in our experiment looks orange and green, respectively, when stretched properly. Figure 49(b) shows the diffraction angle versus the overall length of the substrate when illuminated by a laser source at λ = 405 nm. The diffraction angle can be dynamically steered between 70 and 46 degrees.Figure 49
(a) Optical images of a flexible metasurface when stretched. (b) Diffraction angle of the metasurface grating for different length of the PDMS substrate. (c) Schematic of a flexible color-filtering metasurface. (d) Measured reflectance spectrum when the substrate is uniformly stretched. (c, d) Figures are reproduced from [244].
(a)
(b)
(c)
(d)In a similar way, Shen et al. proposed a color generation mechanism that produces colors by the Fano resonance effect on thin PMMA metasurface. The metasurface consists of a periodic array of cylinder of nanorods and the resonant frequency was tuned from 400 to 600 nm, as shown in Figures49(c) and 49(d).


### 3.10. Graphene Metasurfaces

Current metasurfaces are often limited to dielectric and metallic structured thin film. In recent years, graphene has attracted special attention owing to its exotic electronic and optical properties. Not surprisingly, graphene has been widely utilized as one kind of metasurfaces or as a key component of functional metasurfaces.Graphene is sp2-hybridized monolayer of carbon atoms densely packed into a honeycomb lattice, which was firstly experimentally isolated from graphite in the lab in 2003 [247]. In 2004, Geim et al. demonstrated that the carrier density in the graphene sheet can be controlled by a gate voltage, paving the way of graphene-based electronic devices. Subsequently, after the magnetic field response of graphene was validated, the studies on graphene’s electrooptics magnetooptics features increased dramatically. Moreover, the approach of growing large-scale pattern graphene film makes the practical applications of such devices possible.Indeed, the unique structural element of graphene gives rise to many excellent electromagnetic properties, permitting various important applications. For example, a single sheet of homogeneous graphene was found to be able to absorb only a little (~2.3%) fraction of incident white light at Dirac point, making it possible to be used as transparent conducing electrodes [248]. Besides, graphene exhibits ultrahigh electron mobility, anomalous quantum Hall effect, ambipolar electric field effect, massless relativistic carriers, over micrometer-scale spin coherence length, highly confined plasmonic propagation, and large nonlinear Kerr effect. Thanks to these properties, graphene, up to now, has been widely used to fabricate field-effect transistors, electrochemical biosensor, solar cells, super capacitors, lithium ion batteries, catalyst carriers, electromagnetic absorber, and so on [247].Surface conductivity is usually adopted to describe the electromagnetic characteristic of 2D graphene. If there is no external magnetostatic bias going through the graphene, the local conductivity is isotropic and can be approximately calculated using the Kubo formula on condition thatK
B
T
≪
μ
c, ħ
ω [249]:(44)
σ
2
D
ω
≈
i
e
2
4
π
ħ
l
n
2
μ
c
-
ω
+
i
2
Γ
ħ
2
μ
c
+
ω
+
i
2
Γ
ħ
+
i
e
2
k
B
T
π
ħ
2
ω
+
i
2
Γ
μ
c
k
B
T
+
2
ln
⁡
e
-
μ
c
/
k
B
T
+
1
,where k
B
T is the thermal energy, μ
c is the chemical potential, Γ is the scattering rate, and e, k
B, and ħ are electron charge, Boltzmann constant, and reduced Plank constant (Dirac constant), respectively. Two inequivalent pairs of cones with apex at the Brillouin zone corners constitute graphene’s band structure; thus, two kinds of electron transition exist: interband and intraband transition. The first term in (44) is due to the contribution of interband transition and the second term arises for intraband transition. From the equation we know that the chemical potential governs the transition frequency of electrons. Further, if the frequency satisfies the condition of ħ
ω
<
2
μ
c, the interband transitions can be neglected and (44) is simplified as Drude formula: (45)
σ
GR
ω
=
2
D
π
i
ω
+
i
2
Γ
,where D is a Drude weight. Owing to the mapping relation between gate voltage and chemical potential, the two equations are fairly enough to describe the conductivity of gate voltage-biased graphene.Moreover, if the graphene sheet is present in a perpendicular magnetostatic bias, owing to the cyclotron motion of charge carriers, a nondiagonal component is introduced, namely, Hall conductivity. In low frequency (<10 THz usually), graphene is represented by full tensor conductivity:(46)
σ
GR
=
σ
x
x
σ
x
y
σ
y
x
σ
y
y
,with(47)
σ
x
x
ω
,
B
=
σ
y
y
ω
,
B
=
2
D
π
·
2
Γ
-
i
ω
ω
c
2
-
ω
+
i
2
Γ
2
,
σ
x
y
ω
,
B
=
-
σ
y
x
ω
,
B
=
-
2
D
π
·
ω
c
ω
c
2
-
ω
+
i
2
Γ
2
,where ω
c
=
e
B
v
f
2
/
μ
c is the cyclotron frequency, B is the amplitude of magnetostatic bias, and v
f is the Fermi velocity of the Dirac fermions in graphene. Thus, the conductivities for the RCP light and the LCP light can be derived as σ
±
=
σ
x
x
±
i
σ
x
y, where sign “+” stands for RCP light and “−” stands for LCP light.More efforts have been devoted to the investigation of graphene in recent years [250]. Some works were focused on enhancing the Faraday rotation angle in the microwave, THz, and infrared region. Meanwhile, graphene as a component of ultrathin electromagnetic absorber has drawn great attention. It is reported that the monolayer graphene is an effective saturable absorber for mode-locking fiber lasers. As illustrated in Figures 50(a) and 50(b), it was demonstrated that complete optical absorption can take place in a single patterned sheet of doped graphene [251]. One interesting phenomenon shows that monolayer graphene shows highly directive comb-like thermal radiation at near-infrared frequency [249]. With the layer number increases, the radiation angle and beamwidth would be changed, as shown in Figures 50(c) and 50(d).Figure 50
(a) Schematic picture showing transverse magnetic light impinging on graphene placed on a periodically structured conducting substrate. The light is converted into surface plasmonic waves and subsequently absorbed in graphene. (b) Dependence of the absorption at resonance on the corrugation height (left panel) for different graphene Fermi energies,E
F, and relative absorption for a nonzero metamaterial relaxation’s rate. (c) Optical conductivity of graphene under electric bias. (d) Thermal emission property of the grapheme layer obtained from Kirchhoff’s law. (e) Schematic of the graphene absorber under both electric bias and magnetic bias. (f) Absorption of the dual-biased absorber. Figures are reproduced from [249, 251, 252].
(a)
(b)
(c)
(d)
(e)
(f)To increase the freedom degree of design, subwavelength structures have been proposed to change of electromagnetic response of graphene. Consequently, the effective conductivity of pattered graphene was investigated. In 2012, effective impedance for a patch patterned graphene sheet was proposed. It can be considered as a combination of two parts: impedance of unpatterned graphene produced by a scaling factor and capacitance caused by the gaps. The accuracy of the proposed impedance is debatable, because the capacitance is originated from the electronic motion which is relative to the magnetic responsible conductivity of graphene. In 2014, we [252] presented an approach for calculating the effective impedance for a hole-patterned graphene sheet based on equivalent surface RLC impedance model. The impedance caused by periodic hole was obviously relative to the magnetostatic bias. Utilizing the model, authors well explained the magnetic circular dichroism of the hole-patterned graphene absorber in a varying bias within 0~7 Tesla.Graphene can also be utilized in plasmonic metasurface to increase the performance of traditional plasmonic devices. It is well known that traditional plasmonic materials do not work well in the infrared band, owing to the significant loss. In 2011, Engheta’s theoretical study showed that one can engineer the patch of surface wave on graphene by varying the chemical potential, making it a new platform of transformation optics [54]. Owing to its complex conductivity, graphene supports surface plasmon modes, accompanied with extremely short effective wavelength. Based on the exotic electronic transfer properties, graphene-based plasmonic waveguide devices and even Luneburg lens were constructed (see Figures 51(a) and 51(b)).Figure 51
(a) Simulation results ofE
y (snapshot in time) for a guided wave at f = 30 THz along the ribbon-like section of graphene. (b) One atom-thick Luneburg lens. (c)–(e) Electric fields for the eigenmodes at a graphene microtube. (f) Schematic of a bent microtube. (g) Simulated electric field distribution on the graphene microtube. (a, b) Figures are reproduced from [54].
(a)
(b)
(c)
(d)
(e)
(f)
(g)Very recently, we demonstrated that spiral surface plasmon could be utilized to transfer orbital angular momentum (OAM) [253]. Graphene-based microtube was demonstrated to be able to accomplish this goal perfectly. When a graphene tube is coated on the dielectric cylinder, the whole structure can also steadily support the steady propagation of light carrying OAM with different topological charges, as shown in Figures 51(c)–51(g). Furthermore, as the effective wavelength of the SPP induced in the graphene is much shorter than that in vacuum, the graphene-based microtube is suitable for the propagation of subwavelength of OAM.


### 3.11. Nonlinear Metasurfaces

Metasurfaces can also be utilized to enhance the nonlinear effect [254]. Different from other broadband applications, the nonlinear process requires strong increase of the local fields, which is only obtainable for resonant metasurface. One of the most important applications of nonlinear metasurface is the harmonic generation, such as second harmonic generation (SHG) and third harmonic generation (THG).One way to enhance SHG is to engineer the metasurface so that they resonate at both the fundamental frequency (FF) and the harmonic frequency (HF) [255–257]. In 2014, Lee et al. proposed and experimentally realized metasurfaces with a record-high nonlinear response based on the coupling of electromagnetic modes in plasmonic metasurfaces with quantum engineered electronic intersubband transitions in semiconductor heterostructures [258]. It was stated that the obtained susceptibility is many orders of magnitude larger than any second-order nonlinear response in optical metasurfaces measured up to then.To obtain stronger nonlinear response, it is critical to understand the intrinsic relation between the linear and nonlinear processes. Fortunately, it was also demonstrated that the nonlinear response can also be predicted by using the information of linear response [259].


## 3.1. Frequency Selective Surfaces

Frequency selective surfaces (FSSs) are planar, periodic arrays of conducting patches on a substrate or a periodic array of apertures in a conducting sheet, which are used to filter electromagnetic waves [14]. The spectral responses of these structures are affected by various physical and electrical parameters, including the shape and type of their constituting elements. These FSSs can be designed to demonstrate low-pass, high-pass, band-pass, or band-stop behavior. Over the years, they have been extensively used in a variety of applications ranging between radar radomes, radar absorbers, and so on [14].Early in 1919, Marconi and Franklin granted a patent that the contribution of a parabolic reflector was mimicked by using half-wavelength metallic wires [14]. Owing to the great potential military applications, FSSs have been the subject of intensive study since the 1960s.The performance of FSS can be interpreted by the impedance and equivalent circuit theory, combined with the boundary condition. For a nonmagnetic freestanding metasurface, the band-pass and band-stop FSSs correspond to parallel and series type LC circuits, respectively. One common feature of the traditional FSSs is that the size of the resonant elements and their spacing are comparable to half a wavelength at the desired frequency of operation [58]. Since the electromagnetic response is a collective effect, the finite surface must include a large number of the constituting elements and be illuminated by a planar phase front to obtain the desired frequency response. At some conditions, such as radomes at lower frequencies, FSSs of relatively small electrical dimensions that are less sensitive to incidence angle and can operate for nonplanar phase fronts are highly desirable. In order to achieve this purpose, Sarabandi and Behdad proposed a new type of FSS. The structure consists of a periodic array of small metallic patches printed on one side of a dielectric substrate and a wire grid structure printed on the other side, both with the same period. The periodicity of the printed patterns is much smaller than the wavelength of the operating wavelength. The validity of this concept was demonstrated by numerical simulations and experiments.One of the recent challenges for FSS is to optimize the frequency spectra with respect to angle of incidence and polarization of the waves impinging on it. In principle, multilayered FSS can improve these performances, but with oversized profiles. By using cavity mode whose resonant frequency is angle-independent, it was recently demonstrated that annular apertures array can show angle and polarization-independent transmission properties [15].Ideal FSSs require that the transmission/reflection at the band edge changes sharply, which cannot be satisfied by most single-layer FSSs. In 2011, we proposed a novel plasmonic FSS with sharp band edges. By making use of plasmon hybridization, the bandwidth of the filter is tunable over a large range from 56.6 to 182.2 THz with magnetic and electric couplings between adjacent unit cells, as shown in Figures4(c)–4(f).Figure 4
(a) Sketch of the large-angle FSS. (b) Evolution of the transmission efficiency as a function of the angle of incidence and incident wavelength. (c, d) Top and side views for the tunable band-stop FSS. (e, f) Evolution of the transmission spectra with different geometric parameters. Figures are reproduced from (a, b) [15] and (c)–(f) [57].
(a)
(b)
(c)
(d)
(e)
(f)More recently, the unique spectral properties of FSS were utilized to mimic many quantum phenomena, such as electromagnetically induced transparency (EIT) [59–61] and Fano resonance [19, 20, 62]. The interactions of different modes in the metasurfaces were tuned independently to achieve the desired spectral distribution of reflection and transmission. In 2007, Fedotov et al. reported a resonance response with a very high quality factor in a planar metasurface with symmetry breaking in the shape of its structural elements [20]. It was shown that this symmetry breaking enabled the excitation of trapped modes, that is, modes that are weakly coupled to free space. The interference of trapped mode and normal mode makes the transmission spectrum be of the famous Fano shape.In order to give a rigorous theory of Fano resonance in metasurface, we studied the electric and magnetic responses of a planar metasurface with perturbed periodicity [19]. Rigorous sheet impedance theory was given to analyze the electric-magnetic and magnetic-magnetic coupling effect. Interestingly, perturbation of the widths of wire pairs makes the adjacent metallic particles couple with each other. Q-factor as large as 100 has been theoretically obtained accompanying huge field enhancement, as described in Figure 5. It was believed that this kind of periodicity perturbation can provide a general approach for Fano resonance with ultrastrong local field enhancement.Figure 5
(a) Transmission coefficients for the symmetric and asymmetric metasurface slabs. Region I shows typical asymmetric line shape of Fano resonance. Region II demonstrates the ultrasharp resonance peak induced by interelement coupling. (b) Normalized magnetic fields (Hz) at the center of these resonators. The inset shows the unit cell and the points where the magnetic fields are extracted. (c) Quality factor of a cylinder array. (d) Scattering parameters of this array. Inset shows the distribution of the electric fields at resonant frequency. Figures are reproduced from (a, b) [19] and (c, d) [63].
(a)
(b)
(c)
(d)Since there are three resonant peaks, the magnetic impedance can be written as a combination of individual magnetic resonances, as described by equivalent LC circuit model:(25)
Z
m
=
∑
n
=
1
3
Z
m
n
=
∑
n
=
1
3
i
ω
L
n
1
-
ω
2
L
n
C
n
.Here,L
1, L
2, L
3, C
1, C
2, and C
3 are the corresponding inductances and capacitances. By fitting (25) with the retrieved magnetic sheet impedance, the LC parameters can be obtained as L
1
=
0.295 nH, L
2
=
0.273 nH, L
3
=
0.27 nH, C
1
=
0.896 pF, C
2
=
0.8 pF, and C
3
=
0.794 pF. The corresponding resonance frequencies are 9.79 GHz, 10.77 GHz, and 10.87 GHz.Similar to the magnetic sheet impedance, the magnetic sheet current is also a summation of all the individual sheet currents:(26)
j
m
=
∑
n
=
1
3
j
m
n
,where (27)
j
m
n
=
2
Z
0
Z
m
n
Z
m
+
2
Z
0
H
,
n
=
1,2
,
3
.Using (25), (26), and (27), the sheet currents for different resonators can be easily calculated. The current of the first resonator dominates at frequencies around 9.79 GHz. On the contrary, the second and third resonators dominate the frequency region around 10.8 GHz. Besides, one can find that the first resonator is out of phase with the other two resonators for 9.79 GHz < f < 10.77 GHz. Also, for 10.77 GHz < f < 10.87 GHz, the third one is out of phase with the others.In fact, theπ phase shift between these resonators is the key of resonant enhancement of sheet current. As an example, at frequency 10.82 GHz, there are Z
m
1
≪
Z
m
2
≈
Z
m
3 and Z
m
1
≪
Z
m. Thus, we have(28)
j
m
1
≪
Z
0
H
i
,
j
m
2
=
i
L
2
L
3
L
2
+
L
3
C
2
+
C
3
L
3
C
3
-
L
2
C
2
H
i
,
j
m
3
=
-
j
m
2
=
i
L
2
L
3
L
2
+
L
3
C
2
+
C
3
L
2
C
2
-
L
3
C
3
H
i
.It is interesting that the second and third sheet currents in (28) are out of phase. As a result, even higher enhancement factor and narrower bandwidth can be achieved by decreasing the difference between ω
2 and ω
3.Up to date, a great deal of previously proposed or demonstrated metasurfaces and nanostructures require the use of metallic inclusions, leading to large ohmic loss, a serious limitation to obtain ultrahigh Q-factor and huge field enhancement when Fano resonance occurs. In 2014, a new type of Fano resonance in silicon rods array was reported, and the maximum Q-factor was achieved at a rather large gap width between adjacent rods [63]. It was also different from the previously reported Fano resonance in photonics crystal slab [64], where the maximum Q-factor corresponds to a vanishing hole diameter.In the optical regime, FSS can be utilized to realize color filtering [17, 65]. Xu et al. demonstrated plasmonic MIM nanoresonator structures to filter white light into individual colors [17]. The key concept of their method is to use the linear dispersion of plasmon to realize the photon-plasmon-photon conversion efficiently at specific resonant wavelengths (Figure 6). Compared with the aforementioned color-filtering methods, the new design significantly improved the absolute transmission, pass bandwidth, and compactness. In addition, the filtered light is naturally polarized, making it attractive for direct integration in liquid crystal displays (LCDs) without a separate polarizer layer.Figure 6
(a) Schematic diagram of the proposed plasmonic nanoresonators. Inset is the scanning electron microscopy (SEM) image of the fabricated device. Scale bar, 1μm. (b) Plasmon dispersions in MIM stack array. The shaded region indicates the visible range. (c) Simulated transmission spectra for the RGB filters. The solid and dash curves correspond to TM and TE illuminations, respectively. (d) Cross section of the time-average magnetic field intensity and electric displacement distribution (red arrow) inside the MIM stack at a wavelength of 650 nm with 360 nm stack period. (e) SEM image of the fabricated 1D plasmonic spectroscope with gradually changing periods from 400 to 200 nm (from left to right). Scale bar, 2 μm. (f) Optical microscopy image of the plasmonic spectroscope illuminated with white light. Figures are reproduced from [17].
(a)
(b)
(c)
(d)
(e)
(f)FSS can be also utilized in selective solar absorbers to suppress infrared reradiation. Owing to the frequency-independent absorption, the equilibrium temperature of an irradiated blackbody in vacuum is only 80°C. In order to realize frequency selective transmission and absorption, multilayered films were utilized. Nevertheless, high-temperature instability limits the highest operating temperatures. In 1974, Horwitz used an array of deep holes in a metal to realize selective solar absorbers with ratios of solar absorbance to thermal emittance of 30 : 1 at temperatures of about 200°C [66]. Recently, we proposed a multilayered pyramidal array made of tungsten to demonstrate the selective solar absorption [67]. The broadband absorber is made up of a periodic array of multilayered truncated pyramids. The absorbance is about 99% from 0.28 μm to 1.5 μm for both TE polarization and TM polarization at room temperature or high temperature (966 K).


## 3.2. Polarization-Manipulating Metasurfaces

Polarization plays an important role in electromagnetic waves since a majority of phenomena are polarization sensitive. Manipulation of polarization has been a hot topic for quite a long time. Traditional birefringent and chiral medium have the ability of polarization modulation. However, these traditional media need large thickness to accumulate enough phase shift between the perpendicular components of the incident electric fields. Thus, the optical systems involving polarization applications have become complex and bulky.With the help of metasurface-assisted law of polarization conversion (MLPC), one can greatly improve the performance and enable high conversion efficiency and ultrathin thickness [2]. In general, metasurfaces for polarization manipulation include transmissive and reflective types and can be classified into anisotropic and chiral ones from the viewpoint of the structure properties.


### 3.2.1. Transmissive Anisotropic Metasurface Polarizer

It is well known that polarization states of light can be changed by naturally occurring anisotropic media as the two axes possess different refractive indexes (n
+ and n
-), leading to a relative phase shift between the two axes. However, as the difference between n
+ and n
- is typically small, the thickness of traditional polarizers is required to be much larger than the operational wavelength. Moreover, the working bandwidth is narrow because the phase shift is frequency dependent.As an alternative, metasurfaces provide new opportunities to achieve polarization manipulation with ultrathin artificial structures, including strip gratings and meander lines [68, 69]. In particular, Wang et al. utilized a single-layer metasurface with asymmetric cross-shaped apertures and demonstrated an ultrathin (0.29
λ) terahertz quarter-wave plate [70].The physical foundation of the polarization control with metasurface is the metasurface-assisted polarization conversion (MLPC), that is, the revised Fresnel equations [2], which can also be written as(29)
r
x
=
Y
1
-
Y
3
-
Y
e
x
Y
1
+
Y
3
+
Y
e
x
,
t
x
=
2
Y
1
Y
1
+
Y
3
+
Y
e
x
,
r
y
=
Y
1
-
Y
3
-
Y
e
y
Y
1
+
Y
3
+
Y
e
y
,
t
y
=
2
Y
1
Y
1
+
Y
3
+
Y
e
y
.Based on (29), we can control the reflection and transmission for both polarization states. One particular simple example of this kind of anisotropic metasurface is shown in Figure 7, where the gaps between the parallel strips can be taken as capacitance and the strips can effectively be equal to inductance. Therefore, the electromagnetic wave with electric perpendicular (E
⊥) or parallel (E
∥) components to the strips would be modulated by the effective capacitance and inductance. Hence, the transmitted phases of E
⊥ and E
∥ would also be, respectively, retarded and advanced. When the differential phase shift equals ±90°, circular polarized wave would emerge.Figure 7
(a) Schematic of the anisotropic polarizer based on meander lines. (b) Decomposition of the incident fields along the two main axes. (c) Equivalent circuits for the two polarized waves. (d) Phase shifts for the two orthogonal polarization types. Figures are reproduced from [68].
(a)
(b)
(c)
(d)In 2010, Euler et al. [71] designed a single-layer circularly polarized convertor using periodic split slot ring structure, and this polarization convertor can realize relative 3 dB axial ratio (AR) bandwidth of 11.75%. In 2011, a λ
/
20 thick metasurface was employed to manipulate EM wave polarization with near 100% efficiency in transmission geometry [72].Recently, Ma et al. reported a single-layer metasurface to convert the incident linearly polarized wave into circularly polarized one in a broadband [45], as shown in Figure 8. This polarizer is composed of metallic periodic structures. Two basic patterns are the metallic annular ring and 135° orientated strip. When a linearly polarized plane wave with E field along the x-axis or y-axis normally irradiates onto the polarizer, it can be converted into the circularly polarized wave. The simulated and measured results show that this polarizer can transform the incident linearly polarized light into circularly polarized one in the frequency range from 13.5 to 15.3 GHz, where the AR is less than 3 dB. The relative bandwidth of this polarizer is 17%, and its thickness is only λ
/
40 (λ is the central working wavelength).Figure 8
Photograph of the (a) fabricated polarizer and (b) high-gain circularly polarized patch antenna. (c, d) Measured and simulated AR for the polarizer and the antenna, respectively. Figures are reproduced from [45].
(a)
(b)
(c)
(d)As depicted in Figures8(b) and 8(d), the circular polarizer was integrated into a conventional linearly polarized patch antenna to realize high gain and circular polarized radiation. The gain of conventional patch antenna is sharply increased from 7 dB to about 11 dB at 13.9 GHz. In addition, near-perfect circularly polarized radiation pattern is realized in the frequency band ranging from 13.55 GHz to 13.9 GHz. This metasurface-based circularly polarized antenna solved the difficulty problem of antenna design, and the radiation character was greatly improved.The above mentioned anisotropic metasurfaces modulate the phase shift in two perpendicular directions, in a way similar to the traditional dielectric polarizers. However, this kind of single-layer metasurface suffers the half power loss; namely, the incident power is 50% reflected by the metasurface, and only half of the incident linearly polarized wave can be converted into the circularly polarized wave. To solve this problem, more layers of metallic structures are needed according to the theory proposed by Markovich et al. [73]. It is proved that the efficiency can reach 100% in the two layered metasurfaces. However, the perfect polarization transformation is limited to a single frequency, and the transformation effect deteriorates drastically away from the central frequency.


### 3.2.2. Reflective Anisotropic Metasurface Polarizer

In order to increase the polarization conversion efficiency and working bandwidth of the metasurfaces, reflective metasurfaces (or metamirrors) have been proposed by various groups [74–79]. In 2007, Hao et al. [75] proposed a circular polarizer based on an ultrathin metasurface reflector. Hao et al. [80] and Pors et al. [74] also obtained similar phenomenon at optical frequencies using orthogonally oriented electrical dipoles. Compared to the transmissive polarization transformers, the metamirrors have much smaller thickness due to the large anisotropy as well as higher energy efficiency since no complicated antireflection technique is applied.Owing to the intrinsic resonance, metamirrors are often realized in narrow frequency band. In order to overcome this problem, we designed a dispersive ultrathin metamirror to extend the bandwidth [81]. In general, the impedance sheet for both the x- and y-directions can be frequency dependent. As a first attempt, we set Z
x as being constant (Z
x
=
∞) and Z
y as being highly dispersive. Since the dielectric spacer is chosen as air (n
=
1), the reflected phase shift can be calculated directly from the well-established transfer matrix method [81]:(30)
Φ
x
=
π
+
2
k
d
,
Φ
y
=
arg
⁡
-
Z
0
/
Z
y
-
2
-
Z
0
/
Z
y
exp
⁡
i
2
k
d
2
+
Z
0
/
Z
y
-
Z
0
/
Z
y
exp
⁡
i
2
k
d
,where k is the wave vector in free space and d is the thickness of dielectric spacer. The optimal impedance for a certain relative phase shift Δ
Ф can be calculated as(31)
Z
y
Z
0
=
-
1
2
A
-
A
B
+
1
-
B
A
+
B
,where A
=
e
x
p
(
i
(
Δ
Ф
+
2
k
d
+
π
)
) and B
=
e
x
p
(
i
2
k
d
). Subsequently, the optimal impedance required for the perfect polarization control can be obtained. The optimal impedance for Δ
Ф
=
π
/
2, that for π, and that for 3
π
/
2 were calculated, which vary slightly with working frequency. In particular, the required impedance for Δ
Ф
=
π
/
2 is mainly capacitive within the whole frequency range. For Δ
Ф
=
π, however, the curve is separated to one capacitive region and the other inductive region at the two sides of the central frequency f
=
0.25
c
/
d, where c is the speed of light. For Δ
Ф
=
3
π
/
2, the requirement of dispersion becomes mainly inductive within the entire frequency range.Using anisotropic metasurface, the optimal impedance can be approximated. Then, metamirror with I-shaped unit cell was constructed, as shown in Figure9. The geometrical parameters were optimized using finite element method (FEM) at near normal incidence. In order to prove the above numerical results experimentally, a sample with 40 × 40 unit cells was fabricated using PCB technology. The measured reflection coefficient was below −15 dB in the frequency range between 5.5 and 16.5 GHz. This large relative bandwidth further confirmed the design of broadband polarization convertor. The reflective metasurface ensures the energy efficiency.Figure 9
(a) Schematic of the anisotropic metamirror inx- and y-directions. (b) Schematic of polarization transformation for a p polarization incident wave. (c) Reflection coefficients for copolarized and cross-polarized components. Inset is the photograph of the fabricated sample, which is comprised of I-shaped resonators. (d) Reflectance of copolarization and cross-polarization for dipole array. Figures are reproduced from (a)–(c) [81] and (d) [77].
(a)
(b)
(c)
(d)Based on the theory of broadband polarization conversion, Guo et al. [82] improved the performance of the broadband polarization convertor. In the design, it was proposed that the operation bandwidth and frequency selectivity of metasurfaces can be increased significantly with fully released dispersion management capability in two dimensions. Multiple resonance mechanism was employed to match the effective impedance of the metamirror with the ideal impedance and significantly broaden the operating bandwidth. Experimental results demonstrated that this metamirror worked well from 3.2 to 16.4 GHz with polarization conversion efficiency higher than 85%. This converter was also superior to the previous devices in the frequency band selectivity because the operation band approximates an ideal rectangle. The rectangular coefficient, defined as the bandwidth ratio between high (>80%) and low (<20%) conversion efficiency, was high up to 0.94.In 2013, Grady et al. experimentally demonstrated a reflective metasurface-based terahertz polarization converter that is capable of rotating a linear polarization state into its orthogonal one [77]. As depicted in Figure 9(d), the device is able to rotate the linear polarization by 90°, with a conversion efficiency exceeding 50% from 0.52 to 1.82 THz, with the highest efficiency of 80% at 1.04 THz. They also created multilayered structures capable of realizing near-perfect anomalous refraction.More recently, Jiang et al. proposed an equivalent theoretical description of metasurface polarizer [78]. As examples to apply this concept, a broadband quarter-wave plate and a half-wave plate were demonstrated. Once again, this approach validated the importance of chromatic dispersion in metasurface polarization control. In a similar work, broadband metasurface polarizers were demonstrated in the visible frequencies with high-efficiency, angle-insensitive polarization transformation over an octave-spanning bandwidth [79]. Nanofabricated reflective half-wave and quarter-wave plates designed using this approach have measured polarization conversion ratios and reflection magnitudes greater than 92% over a broad wavelength range from 640 to 1290 nm and a wide field of view up to ±40°.


### 3.2.3. Chiral Metasurface Polarizer

Beside the anisotropic polarizers, there is another type of material suitable for polarization manipulation, which is called chiral material. Chirality refers to the materials or structures that cannot superpose with their mirror structures by only transferring or rotating the materials or structures. As depicted in Figure10, chirality can be observed in naturally occurring media, including aminophenol, DNA molecule, and crystals.Figure 10
Classical naturally occurring chiral materials including (a) aminophenol, (b) DNA molecule, and (c) crystals. The chiral materials present (d) circular dichroism and (e) optical rotation character when illuminated by electromagnetic waves.
(a)
(b)
(c)
(d)
(e)Due to the lack of mirror symmetry, the cross-coupling between electric field and magnetic field exists in chiral materials, which is the physical original of these special electromagnetic properties. The strength of the coupling can be represented by the chirality parameterκ, and thus the constitutive relation in the chiral materials can be stated as(32)
D
B
=
ε
0
ε
i
k
ε
0
μ
0
i
k
ε
0
μ
0
μ
0
μ
E
H
,where ε
0 and μ
0 are the permittivity and permeability of vacuum, ε and μ are the relative permittivity and permeability, and κ is the strength of the coupling between the electric and magnetic fields. Negative refraction index can be obtained in chiral metamaterials while it is not necessary to realize negative permittivity and negative permeability at the same time. Chiral materials have attracted great attention for their special electromagnetic properties such as circular dichroism and optical activity. Right circularly polarized (RCP) wave and left circularly polarized (LCP) wave would encounter different transmission coefficients at the resonances and exhibit polarization manipulation property, such as circular dichroism (CD) and optical rotation (OR). The refraction indices of the LCP wave (n
-) and RCP wave (n
+) are related to the chiral parameter κ and can be stated as n
±
=
ε
μ
±
κ. Therefore, negative refraction index can be obtained if the chiral parameter κ is large enough. As analyzed above, chiral materials can act as a kind of polarizer for their selection of circularly polarized waves. However, the cross-coupling between the electric and magnetic fields is rather weak in these natural materials, and very thick materials are often needed to produce useful CD and OR properties.The appearance of artificial chiral structures makes it possible to realize giant CD and OR with the thickness of ~λ
/
10 at the operating frequency. Thus, due to their unique properties, chiral metamaterials promise to tailor the polarization state of electromagnetic wave and be functionalized as polarization rotators, circular polarizers, and polarization spectrum filters with ripple-free isolated transmission peaks. Furthermore, chiral metamaterials are more suitable to achieve multiband and multipolarization conversion compared to anisotropic ones.In the extreme case, chiral material can be used to achieve circular polarization selective surface (CPSS), which was thought to be an important polarizer [83]. The ideal CPSS should have thickness much larger than the working wavelength; thus, it cannot be approximated as metasurface. In 2009, Gansel et al. [84] designed a broadband CPSS based on the periodic gold helix structure, which splits the incident circularly polarized waves in an octave bandwidth at mid-infrared frequency. Later, this helix shaped chiral metamaterial was scaled to other frequencies [85, 86].To obtain chiral metasurfaces, the bandwidth needs to be compromised. In recent years, a great number of chiral metasurfaces have been reported in the form of twisted U-shape [87] and L-shape [88], and so forth. Ma et al. proposed chiral metasurfaces based on planar spiral structures to achieve multiband and multipolarization conversion [89].Firstly, a multiband circular polarizer was proposed by using three layered planar spiral metasurface structure in analogy with classic spiral antenna [86]. At three distinct resonant frequencies, as shown in Figures 11(a) and 11(b), the incident linearly polarized wave with electric field parallel to one specific direction was transformed into the left-/right-handed circularly polarized waves.Figure 11
Geometry and the performance of the helix chiral metamaterial. (a) Focused-ion-beam (FIB) cut of a polymer structure partially filled with gold by electroplating. (b) Oblique view of a left-handed helix structure after removal of the polymer by plasma etching. (c) Top-view image revealing the circular cross section of the helices and the homogeneity on a larger scale. (d, e) Normal-incidence measured transmittance spectra for (d) two pitches of left-handed helices and (e) two pitches of right-handed helices. Figures are reproduced from [84].
(a)
(b)
(c)
(d)
(e)Subsequently, a dual-band asymmetric chiral metasurface was constructed by using two pairs of planar spiral structures with a certain twisted angle [89], as shown in Figure 11(c). Two planar spiral structures with different radii in each layer were adopted to achieve more resonant frequencies. The incident linearly polarized wave can be converted into the circularly polarized waves with different rotation directions at four distinct resonances. This multiband chiral metasurface greatly decreased the loss of chiral metamaterials, compared to the results reported before by combining the chiral and anisotropic properties in the unit cells. This design of multiband response by putting together structures with different size into one unit cell can also be extended to other metasurfaces and metamaterials.In order to extend the operational bandwidth, Huang et al. [91] proposed a dual-band wideband polarization rotator which is proposed by using chiral metasurface composed of two pairs of two layered twisted split ring resonators (SRRs) in each unit. This chiral metasurface transformed the incident linearly polarized wave into its cross-polarized one at two distinct frequencies with high efficiency.In some satellite communication systems, different circular polarization types are required, that is, LCP wave for the up-link and RCP wave for the down-link at Ku band. The usual method for the above requirement is to design two antennas with different circular polarization types as transmitter and receiver, respectively. Another solution is integrating dielectric polarizers or orthomode transducers (OMT) into the horn antennas. Though broadband polarization splitting can be realized, these methods may increase the size of the antennas.Owing to the giant polarization conversion efficiency, the chiral metasurfaces are suitable for the construction of high performance circularly polarized antennas with multipolarization and multiband performance. As shown in Figure12(e), a dual-band dual circularly polarized horn antenna was designed [92] based on the planar spiral chiral metamaterial. The chiral metasurface converts the incident linearly polarized wave into the LCP and RCP waves at two resonance frequencies, with insertion loss less than 0.6 dB. The measured 3 dB AR bandwidths of the antenna were, respectively, 0.8% (12.4 GHz–12.5 GHz) and 1.4% (14.2 GHz–14.4 GHz). The radiation patterns of the proposed antenna for the LCP and RCP wave depicted great cross-polarization ratio, which confirmed that the dominant circular polarization was left-handed at the lower frequency and was right-handed at the higher resonance. The gain of the antenna composite was only degraded by 0.6 dB around these two resonant frequencies, in comparison with the horn antenna without the chiral metasurface. The designed antenna has the advantages of low cost and simple structure and thus could be utilized in satellite communication systems.Figure 12
Schematic configuration of the (a) triple-band circular polarizer, (c) four-band chiral metasurface, and (e) dual-band circularly polarized horn antenna based on chiral metasurface. (b, d) Simulated and measured circular transmission for the chiral metasurface of (a) and (c). (f) Radiation patterns in LCP and RCP of the antenna at 14.35 GHz. Figures are reproduced from [86, 89, 90].
(a)
(b)
(c)
(d)
(e)
(f)In order to extend the operational bandwidth, Huang et al. [91] proposed a dual-band wideband polarization rotator by using chiral metasurface composed of two pairs of two layered twisted split ring resonators (SRRs) in each unit, as shown in Figures 13(a) and 13(b). The sizes of the two pairs of SRRs are different. Therefore, this chiral metasurface transformed the incident linearly polarized wave into its cross-polarized one at two distinct frequencies with high efficiency. Pure optical activity was observed at two distinct resonant frequencies. The designed planar polarization rotator had a high transmission in the polarization rotation frequency bands and can be also easily extended for transforming polarization state at the multiple-frequency bands, which may have many potential applications in the microwave domain.Figure 13
(a) Unit cell and (b) photograph of the dual-band wideband polarization rotator. (c) Transmission spectra of (b). (d) The photograph of the twisted Y-shape chiral metasurface and transmission spectra for (e) linear polarization and (f) circular polarization. Figures are reproduced from [91, 93].
(a)
(b)
(c)
(d)
(e)
(f)Lately, Ma et al. proposed a double-layer twisted Y-shape structure to achieve obvious circular dichroism and giant optical rotation at different frequencies [93]. The schematic geometry of the proposed metasurface is depicted in Figure 13(d). The unit cell is composed of two Y-shaped metallic structures at a certain twisted angle printed on two sides of a dielectric lamina. The angle between the neighboring two branches of this Y-shaped structure is designed to be 120°. When a y-polarized wave is incident to this chiral metamaterial, circular dichroism with a great difference of 25 dB between the transmission coefficients for the circularly polarized waves is obtained at 12.28 GHz. Meanwhile, 90° optical rotation is observed at 12.70 GHz, where the incident y-polarized wave is transformed into its cross-polarization with a transmission coefficient of −1.15 dB.


## 3.2.1. Transmissive Anisotropic Metasurface Polarizer

It is well known that polarization states of light can be changed by naturally occurring anisotropic media as the two axes possess different refractive indexes (n
+ and n
-), leading to a relative phase shift between the two axes. However, as the difference between n
+ and n
- is typically small, the thickness of traditional polarizers is required to be much larger than the operational wavelength. Moreover, the working bandwidth is narrow because the phase shift is frequency dependent.As an alternative, metasurfaces provide new opportunities to achieve polarization manipulation with ultrathin artificial structures, including strip gratings and meander lines [68, 69]. In particular, Wang et al. utilized a single-layer metasurface with asymmetric cross-shaped apertures and demonstrated an ultrathin (0.29
λ) terahertz quarter-wave plate [70].The physical foundation of the polarization control with metasurface is the metasurface-assisted polarization conversion (MLPC), that is, the revised Fresnel equations [2], which can also be written as(29)
r
x
=
Y
1
-
Y
3
-
Y
e
x
Y
1
+
Y
3
+
Y
e
x
,
t
x
=
2
Y
1
Y
1
+
Y
3
+
Y
e
x
,
r
y
=
Y
1
-
Y
3
-
Y
e
y
Y
1
+
Y
3
+
Y
e
y
,
t
y
=
2
Y
1
Y
1
+
Y
3
+
Y
e
y
.Based on (29), we can control the reflection and transmission for both polarization states. One particular simple example of this kind of anisotropic metasurface is shown in Figure 7, where the gaps between the parallel strips can be taken as capacitance and the strips can effectively be equal to inductance. Therefore, the electromagnetic wave with electric perpendicular (E
⊥) or parallel (E
∥) components to the strips would be modulated by the effective capacitance and inductance. Hence, the transmitted phases of E
⊥ and E
∥ would also be, respectively, retarded and advanced. When the differential phase shift equals ±90°, circular polarized wave would emerge.Figure 7
(a) Schematic of the anisotropic polarizer based on meander lines. (b) Decomposition of the incident fields along the two main axes. (c) Equivalent circuits for the two polarized waves. (d) Phase shifts for the two orthogonal polarization types. Figures are reproduced from [68].
(a)
(b)
(c)
(d)In 2010, Euler et al. [71] designed a single-layer circularly polarized convertor using periodic split slot ring structure, and this polarization convertor can realize relative 3 dB axial ratio (AR) bandwidth of 11.75%. In 2011, a λ
/
20 thick metasurface was employed to manipulate EM wave polarization with near 100% efficiency in transmission geometry [72].Recently, Ma et al. reported a single-layer metasurface to convert the incident linearly polarized wave into circularly polarized one in a broadband [45], as shown in Figure 8. This polarizer is composed of metallic periodic structures. Two basic patterns are the metallic annular ring and 135° orientated strip. When a linearly polarized plane wave with E field along the x-axis or y-axis normally irradiates onto the polarizer, it can be converted into the circularly polarized wave. The simulated and measured results show that this polarizer can transform the incident linearly polarized light into circularly polarized one in the frequency range from 13.5 to 15.3 GHz, where the AR is less than 3 dB. The relative bandwidth of this polarizer is 17%, and its thickness is only λ
/
40 (λ is the central working wavelength).Figure 8
Photograph of the (a) fabricated polarizer and (b) high-gain circularly polarized patch antenna. (c, d) Measured and simulated AR for the polarizer and the antenna, respectively. Figures are reproduced from [45].
(a)
(b)
(c)
(d)As depicted in Figures8(b) and 8(d), the circular polarizer was integrated into a conventional linearly polarized patch antenna to realize high gain and circular polarized radiation. The gain of conventional patch antenna is sharply increased from 7 dB to about 11 dB at 13.9 GHz. In addition, near-perfect circularly polarized radiation pattern is realized in the frequency band ranging from 13.55 GHz to 13.9 GHz. This metasurface-based circularly polarized antenna solved the difficulty problem of antenna design, and the radiation character was greatly improved.The above mentioned anisotropic metasurfaces modulate the phase shift in two perpendicular directions, in a way similar to the traditional dielectric polarizers. However, this kind of single-layer metasurface suffers the half power loss; namely, the incident power is 50% reflected by the metasurface, and only half of the incident linearly polarized wave can be converted into the circularly polarized wave. To solve this problem, more layers of metallic structures are needed according to the theory proposed by Markovich et al. [73]. It is proved that the efficiency can reach 100% in the two layered metasurfaces. However, the perfect polarization transformation is limited to a single frequency, and the transformation effect deteriorates drastically away from the central frequency.


## 3.2.2. Reflective Anisotropic Metasurface Polarizer

In order to increase the polarization conversion efficiency and working bandwidth of the metasurfaces, reflective metasurfaces (or metamirrors) have been proposed by various groups [74–79]. In 2007, Hao et al. [75] proposed a circular polarizer based on an ultrathin metasurface reflector. Hao et al. [80] and Pors et al. [74] also obtained similar phenomenon at optical frequencies using orthogonally oriented electrical dipoles. Compared to the transmissive polarization transformers, the metamirrors have much smaller thickness due to the large anisotropy as well as higher energy efficiency since no complicated antireflection technique is applied.Owing to the intrinsic resonance, metamirrors are often realized in narrow frequency band. In order to overcome this problem, we designed a dispersive ultrathin metamirror to extend the bandwidth [81]. In general, the impedance sheet for both the x- and y-directions can be frequency dependent. As a first attempt, we set Z
x as being constant (Z
x
=
∞) and Z
y as being highly dispersive. Since the dielectric spacer is chosen as air (n
=
1), the reflected phase shift can be calculated directly from the well-established transfer matrix method [81]:(30)
Φ
x
=
π
+
2
k
d
,
Φ
y
=
arg
⁡
-
Z
0
/
Z
y
-
2
-
Z
0
/
Z
y
exp
⁡
i
2
k
d
2
+
Z
0
/
Z
y
-
Z
0
/
Z
y
exp
⁡
i
2
k
d
,where k is the wave vector in free space and d is the thickness of dielectric spacer. The optimal impedance for a certain relative phase shift Δ
Ф can be calculated as(31)
Z
y
Z
0
=
-
1
2
A
-
A
B
+
1
-
B
A
+
B
,where A
=
e
x
p
(
i
(
Δ
Ф
+
2
k
d
+
π
)
) and B
=
e
x
p
(
i
2
k
d
). Subsequently, the optimal impedance required for the perfect polarization control can be obtained. The optimal impedance for Δ
Ф
=
π
/
2, that for π, and that for 3
π
/
2 were calculated, which vary slightly with working frequency. In particular, the required impedance for Δ
Ф
=
π
/
2 is mainly capacitive within the whole frequency range. For Δ
Ф
=
π, however, the curve is separated to one capacitive region and the other inductive region at the two sides of the central frequency f
=
0.25
c
/
d, where c is the speed of light. For Δ
Ф
=
3
π
/
2, the requirement of dispersion becomes mainly inductive within the entire frequency range.Using anisotropic metasurface, the optimal impedance can be approximated. Then, metamirror with I-shaped unit cell was constructed, as shown in Figure9. The geometrical parameters were optimized using finite element method (FEM) at near normal incidence. In order to prove the above numerical results experimentally, a sample with 40 × 40 unit cells was fabricated using PCB technology. The measured reflection coefficient was below −15 dB in the frequency range between 5.5 and 16.5 GHz. This large relative bandwidth further confirmed the design of broadband polarization convertor. The reflective metasurface ensures the energy efficiency.Figure 9
(a) Schematic of the anisotropic metamirror inx- and y-directions. (b) Schematic of polarization transformation for a p polarization incident wave. (c) Reflection coefficients for copolarized and cross-polarized components. Inset is the photograph of the fabricated sample, which is comprised of I-shaped resonators. (d) Reflectance of copolarization and cross-polarization for dipole array. Figures are reproduced from (a)–(c) [81] and (d) [77].
(a)
(b)
(c)
(d)Based on the theory of broadband polarization conversion, Guo et al. [82] improved the performance of the broadband polarization convertor. In the design, it was proposed that the operation bandwidth and frequency selectivity of metasurfaces can be increased significantly with fully released dispersion management capability in two dimensions. Multiple resonance mechanism was employed to match the effective impedance of the metamirror with the ideal impedance and significantly broaden the operating bandwidth. Experimental results demonstrated that this metamirror worked well from 3.2 to 16.4 GHz with polarization conversion efficiency higher than 85%. This converter was also superior to the previous devices in the frequency band selectivity because the operation band approximates an ideal rectangle. The rectangular coefficient, defined as the bandwidth ratio between high (>80%) and low (<20%) conversion efficiency, was high up to 0.94.In 2013, Grady et al. experimentally demonstrated a reflective metasurface-based terahertz polarization converter that is capable of rotating a linear polarization state into its orthogonal one [77]. As depicted in Figure 9(d), the device is able to rotate the linear polarization by 90°, with a conversion efficiency exceeding 50% from 0.52 to 1.82 THz, with the highest efficiency of 80% at 1.04 THz. They also created multilayered structures capable of realizing near-perfect anomalous refraction.More recently, Jiang et al. proposed an equivalent theoretical description of metasurface polarizer [78]. As examples to apply this concept, a broadband quarter-wave plate and a half-wave plate were demonstrated. Once again, this approach validated the importance of chromatic dispersion in metasurface polarization control. In a similar work, broadband metasurface polarizers were demonstrated in the visible frequencies with high-efficiency, angle-insensitive polarization transformation over an octave-spanning bandwidth [79]. Nanofabricated reflective half-wave and quarter-wave plates designed using this approach have measured polarization conversion ratios and reflection magnitudes greater than 92% over a broad wavelength range from 640 to 1290 nm and a wide field of view up to ±40°.


## 3.2.3. Chiral Metasurface Polarizer

Beside the anisotropic polarizers, there is another type of material suitable for polarization manipulation, which is called chiral material. Chirality refers to the materials or structures that cannot superpose with their mirror structures by only transferring or rotating the materials or structures. As depicted in Figure10, chirality can be observed in naturally occurring media, including aminophenol, DNA molecule, and crystals.Figure 10
Classical naturally occurring chiral materials including (a) aminophenol, (b) DNA molecule, and (c) crystals. The chiral materials present (d) circular dichroism and (e) optical rotation character when illuminated by electromagnetic waves.
(a)
(b)
(c)
(d)
(e)Due to the lack of mirror symmetry, the cross-coupling between electric field and magnetic field exists in chiral materials, which is the physical original of these special electromagnetic properties. The strength of the coupling can be represented by the chirality parameterκ, and thus the constitutive relation in the chiral materials can be stated as(32)
D
B
=
ε
0
ε
i
k
ε
0
μ
0
i
k
ε
0
μ
0
μ
0
μ
E
H
,where ε
0 and μ
0 are the permittivity and permeability of vacuum, ε and μ are the relative permittivity and permeability, and κ is the strength of the coupling between the electric and magnetic fields. Negative refraction index can be obtained in chiral metamaterials while it is not necessary to realize negative permittivity and negative permeability at the same time. Chiral materials have attracted great attention for their special electromagnetic properties such as circular dichroism and optical activity. Right circularly polarized (RCP) wave and left circularly polarized (LCP) wave would encounter different transmission coefficients at the resonances and exhibit polarization manipulation property, such as circular dichroism (CD) and optical rotation (OR). The refraction indices of the LCP wave (n
-) and RCP wave (n
+) are related to the chiral parameter κ and can be stated as n
±
=
ε
μ
±
κ. Therefore, negative refraction index can be obtained if the chiral parameter κ is large enough. As analyzed above, chiral materials can act as a kind of polarizer for their selection of circularly polarized waves. However, the cross-coupling between the electric and magnetic fields is rather weak in these natural materials, and very thick materials are often needed to produce useful CD and OR properties.The appearance of artificial chiral structures makes it possible to realize giant CD and OR with the thickness of ~λ
/
10 at the operating frequency. Thus, due to their unique properties, chiral metamaterials promise to tailor the polarization state of electromagnetic wave and be functionalized as polarization rotators, circular polarizers, and polarization spectrum filters with ripple-free isolated transmission peaks. Furthermore, chiral metamaterials are more suitable to achieve multiband and multipolarization conversion compared to anisotropic ones.In the extreme case, chiral material can be used to achieve circular polarization selective surface (CPSS), which was thought to be an important polarizer [83]. The ideal CPSS should have thickness much larger than the working wavelength; thus, it cannot be approximated as metasurface. In 2009, Gansel et al. [84] designed a broadband CPSS based on the periodic gold helix structure, which splits the incident circularly polarized waves in an octave bandwidth at mid-infrared frequency. Later, this helix shaped chiral metamaterial was scaled to other frequencies [85, 86].To obtain chiral metasurfaces, the bandwidth needs to be compromised. In recent years, a great number of chiral metasurfaces have been reported in the form of twisted U-shape [87] and L-shape [88], and so forth. Ma et al. proposed chiral metasurfaces based on planar spiral structures to achieve multiband and multipolarization conversion [89].Firstly, a multiband circular polarizer was proposed by using three layered planar spiral metasurface structure in analogy with classic spiral antenna [86]. At three distinct resonant frequencies, as shown in Figures 11(a) and 11(b), the incident linearly polarized wave with electric field parallel to one specific direction was transformed into the left-/right-handed circularly polarized waves.Figure 11
Geometry and the performance of the helix chiral metamaterial. (a) Focused-ion-beam (FIB) cut of a polymer structure partially filled with gold by electroplating. (b) Oblique view of a left-handed helix structure after removal of the polymer by plasma etching. (c) Top-view image revealing the circular cross section of the helices and the homogeneity on a larger scale. (d, e) Normal-incidence measured transmittance spectra for (d) two pitches of left-handed helices and (e) two pitches of right-handed helices. Figures are reproduced from [84].
(a)
(b)
(c)
(d)
(e)Subsequently, a dual-band asymmetric chiral metasurface was constructed by using two pairs of planar spiral structures with a certain twisted angle [89], as shown in Figure 11(c). Two planar spiral structures with different radii in each layer were adopted to achieve more resonant frequencies. The incident linearly polarized wave can be converted into the circularly polarized waves with different rotation directions at four distinct resonances. This multiband chiral metasurface greatly decreased the loss of chiral metamaterials, compared to the results reported before by combining the chiral and anisotropic properties in the unit cells. This design of multiband response by putting together structures with different size into one unit cell can also be extended to other metasurfaces and metamaterials.In order to extend the operational bandwidth, Huang et al. [91] proposed a dual-band wideband polarization rotator which is proposed by using chiral metasurface composed of two pairs of two layered twisted split ring resonators (SRRs) in each unit. This chiral metasurface transformed the incident linearly polarized wave into its cross-polarized one at two distinct frequencies with high efficiency.In some satellite communication systems, different circular polarization types are required, that is, LCP wave for the up-link and RCP wave for the down-link at Ku band. The usual method for the above requirement is to design two antennas with different circular polarization types as transmitter and receiver, respectively. Another solution is integrating dielectric polarizers or orthomode transducers (OMT) into the horn antennas. Though broadband polarization splitting can be realized, these methods may increase the size of the antennas.Owing to the giant polarization conversion efficiency, the chiral metasurfaces are suitable for the construction of high performance circularly polarized antennas with multipolarization and multiband performance. As shown in Figure12(e), a dual-band dual circularly polarized horn antenna was designed [92] based on the planar spiral chiral metamaterial. The chiral metasurface converts the incident linearly polarized wave into the LCP and RCP waves at two resonance frequencies, with insertion loss less than 0.6 dB. The measured 3 dB AR bandwidths of the antenna were, respectively, 0.8% (12.4 GHz–12.5 GHz) and 1.4% (14.2 GHz–14.4 GHz). The radiation patterns of the proposed antenna for the LCP and RCP wave depicted great cross-polarization ratio, which confirmed that the dominant circular polarization was left-handed at the lower frequency and was right-handed at the higher resonance. The gain of the antenna composite was only degraded by 0.6 dB around these two resonant frequencies, in comparison with the horn antenna without the chiral metasurface. The designed antenna has the advantages of low cost and simple structure and thus could be utilized in satellite communication systems.Figure 12
Schematic configuration of the (a) triple-band circular polarizer, (c) four-band chiral metasurface, and (e) dual-band circularly polarized horn antenna based on chiral metasurface. (b, d) Simulated and measured circular transmission for the chiral metasurface of (a) and (c). (f) Radiation patterns in LCP and RCP of the antenna at 14.35 GHz. Figures are reproduced from [86, 89, 90].
(a)
(b)
(c)
(d)
(e)
(f)In order to extend the operational bandwidth, Huang et al. [91] proposed a dual-band wideband polarization rotator by using chiral metasurface composed of two pairs of two layered twisted split ring resonators (SRRs) in each unit, as shown in Figures 13(a) and 13(b). The sizes of the two pairs of SRRs are different. Therefore, this chiral metasurface transformed the incident linearly polarized wave into its cross-polarized one at two distinct frequencies with high efficiency. Pure optical activity was observed at two distinct resonant frequencies. The designed planar polarization rotator had a high transmission in the polarization rotation frequency bands and can be also easily extended for transforming polarization state at the multiple-frequency bands, which may have many potential applications in the microwave domain.Figure 13
(a) Unit cell and (b) photograph of the dual-band wideband polarization rotator. (c) Transmission spectra of (b). (d) The photograph of the twisted Y-shape chiral metasurface and transmission spectra for (e) linear polarization and (f) circular polarization. Figures are reproduced from [91, 93].
(a)
(b)
(c)
(d)
(e)
(f)Lately, Ma et al. proposed a double-layer twisted Y-shape structure to achieve obvious circular dichroism and giant optical rotation at different frequencies [93]. The schematic geometry of the proposed metasurface is depicted in Figure 13(d). The unit cell is composed of two Y-shaped metallic structures at a certain twisted angle printed on two sides of a dielectric lamina. The angle between the neighboring two branches of this Y-shaped structure is designed to be 120°. When a y-polarized wave is incident to this chiral metamaterial, circular dichroism with a great difference of 25 dB between the transmission coefficients for the circularly polarized waves is obtained at 12.28 GHz. Meanwhile, 90° optical rotation is observed at 12.70 GHz, where the incident y-polarized wave is transformed into its cross-polarization with a transmission coefficient of −1.15 dB.


## 3.3. Antireflection Metasurfaces

In many optical devices and electrooptical equipment, the efficiency of light transmission determines to a large extent the overall performance. For example, it was reported that a normal solar panel absorbs and reflects approximately 25% and 33% of the incident solar radiation, respectively. For lens systems, the reflection would seriously reduce the imaging quality.The first theoretical frame for analyzing antireflection coating (ARC) is Fresnel equation, which was developed in 1823 by Augustin-Jean Fresnel. Before this time, some antireflection phenomena have been already discovered by Lord Rayleigh and Joseph Von Fraunhofer [94].In general, there are two ways to create broadband antireflection surfaces, which are based on either coating multilayer thin films or texturing the substrate surfaces with subwavelength structures. The first method is based on multilayer material with gradient refractive indices, and the latter needs only a single-layer material but gradient morphology. Due to the scarcity of optical materials with refractive indices close to air, multilayer thin films for broadband antireflection surfaces were not realizable until recently [95]. However, the mismatch in thermal properties of different materials hinders multilayer thin film applications.One of the inspirations of ARC design comes from the natural worlds. In the eyes of some moths, broadband antireflection was observed and the physical mechanism is attributed to the effective gradient refractive index distribution. However, it was found that, in moth-eye-like structures, high-reflection frequency bands alternate with low-reflection frequency bands. It is of great interest for us to see if these high-reflection bands can be suppressed and hence obtain a broadband reflection approaching 0.1%. As an effort to achieve this object, it was proposed that a hybrid moth-eye structure could be used to enhance broadband antireflection properties. An ultralow average reflectance down to 0.11% over the solar spectral range has been achieved, showing a 50% enhancement in broadband antireflection capability as compared with corresponding uniform moth-eye structures.The largest challenge faced by traditional antireflection proposals is the complex fabrication process. In 2007, biomimetic silicon nanostructures were demonstrated by Huang et al. with improved broadband and quasiomnidirectional antireflection properties [97]. In 2014, Hong et al. used laser direct writing to create microstructures on Si surfaces that reduce light reflection by light trapping [42]. By decoration of the Si nanowires with metallic nanoparticles, surface plasmon resonance can be used to further control the broadband reflections, reducing the reflection to about 0.8% across the bandwidth from 300 to 1200 nm.Although structured surfaces with gradient dielectric constant (e.g., pyramidal rods and moth’s eyes) provide rather good antireflection performance, their thicknesses and mechanical performances are not well balanced. In order to reduce both the thickness and the reflectance, the metallic metasurfaces are recently investigated for this purpose [39–41, 96, 98].In 2008, Thoman et al. demonstrated that nanostructured gold films can serve as broadband impedance-matching coatings for substrates in the terahertz frequency range [39]. They showed in theory and experiment that the internally reflected electric field amplitude of a broadband terahertz pulse in a silicon substrate can be suppressed to below 1% of that without coating, which is at least a factor of 5 better than the best suppression achievable with bulk gold layers (see Figure 14). Subsequently, Zhou et al. examined the potential of stacked multilayer graphene as broadband terahertz (THz) antireflection coating [40]. The reflected pulses from the quartz and silicon substrates were observed to change with the layer number and doping concentration of the graphene coating. Remarkable broadband impedance matching was achieved due to optimized THz conductivity.Figure 14
(a) A schematic of the THz measurement with THz wave normal incident from the left side of Si substrate and square mesh AR coating on the right side of Si substrate. (b) THz TDS transmission signals under normal incidence. The solid curve is for bare Si and the dashed and dotted curves are for AR-coated Si in horizontal polarization and vertical polarization, respectively. (c) FFT of the THz TDS spectra. (d) Schematic of the metasurface antireflection coating on a germanium substrate, consisting of a periodic array of gold cross-resonators on top of a dielectric layer. (e) Schematic of multireflection within the metasurface antireflection structure. (f) The SEM image of a fabricated metasurface antireflection structure. (g) Calculated optical reflectance (R) and transmittance (T) using full-wave numerical simulation. Figures are reproduced from (a)–(c) [41] and (d)–(g) [96].
(a)
(b)
(c)
(d)
(e)
(f)
(g)In a similar work, Teng et al. demonstrated broadband antireflection coatings using deep subwavelength periodic thin metallic lamellar grating [98]. As shown in Figures 14(a)–14(c), the measured reflectance from Cr grating coated sample was reduced over 99% compared with bare Si sample in the whole bandwidth of 0.06–3 THz. Recently, Zhang et al. proposed a metasurface optical antireflection coating [96]. By tuning the cross-shaped metallic patches on a dielectric spacer, the reflection coefficient can be dramatically reduced (Figures 14(d)–14(g)). The bandwidth and incidence angle range were comparable to a quarter-wave antireflection coating.


## 3.4. Perfect Absorbing Metasurfaces

### 3.4.1. Single-Port Perfect Absorbing Metasurface

Absorption phenomena of electromagnetic wave can be found anywhere in our surrounding world. The colorful leafs and flowers are related to the frequency selective absorption of light. It was also well known that black object, such as carbon, absorbs most of the visible light. In 1860, Kirchhoff proposed the ideal blackbody absorber as “bodies can be imagined which, for infinitely small thicknesses, completely absorb all incident rays, and neither reflect nor transmit any.” Since then, the pursuit of high efficient absorbers never stops.Along with the development of Maxwell equations and invention of radar, the electromagnetic theory of absorbers was brought out after World War II. In the review given by Hans Severin in 1956 [35], the theory of the so-called Salisbury absorber, Jaumann absorber, Dallenbach absorber, pyramidal absorber, and dipole absorber was given in detail. The dipole absorber is just the precursor of the circuit analogy absorber (CAA) [99], which is also one kind of lossy metasurface. Severin also noted that there is a conflict between the thickness and bandwidth of these absorbers. Almost half a century later, Rozanov developed a rigorous theory for the bandwidth-to-thickness ratio [100], illustrating that there is a fundamental limit for this value. Remarkably, this conclusion consists with the prediction of Planck and Masius with respect to the thickness of blackbody [101].In recent years, broadband absorbers with optimal thickness were widely researched [38, 102–111]. Except for broadband absorbers, narrow band absorbers are also of particular importance in frequency selective applications. In 2008, Landy et al. proposed the concept of “Perfect Metamaterial Absorber” with thickness of only λ
/
40, where λ is the working wavelength [36]. They interpreted the principle of this absorber as the simultaneous control of electric and magnetic response such that the impedance is matched to the free space. However, it is now widely known that such impedance match does not ensure that the transmission and reflection can be simultaneously reduced to zero. As stated by Vora et al., it is ambiguous to define the μ
e
f
f and ε
e
f
f in such complex structures, since the metamaterial perfect absorber cannot be strictly considered as homogeneous bulk media [52].In 2008, we extended the meta-absorber into the visible frequencies. By converting the propagating wave into surface wave, perfect absorption of light wave was demonstrated. Antisymmetric surface plasmons coupling formed by subwavelength hole array (SHA) and reflecting layer was proved to dominate the multiorders near-perfect absorption. Although only SHA was investigated in this case, the design idea, realizing perfect absorption based on structured surface combined with thick metal layers, can also be extended to other cases, such as split ring resonator (SRR) combined with metal black plate. The most fascinating potential application of SHA combined with reflecting layer is the introduction of functional material into center dielectric region to realize imaging and detecting. In 2009, we further investigated the loss mechanism of perfect absorber. It was demonstrated that the ohmic loss and the dielectric loss both contributed to the absorption. The energy exchange was recently studied to enhance the efficiency of solar cells [52]. In addition, subwavelength high performance metamaterial absorber was also demonstrated by Hao et al. for optical frequencies [112]. Experimental results show that an absorption peak of 88% is achieved at the wavelength of ~1.58 μm. At almost the same time, Liu et al. demonstrated an infrared perfect absorber and verified its application as plasmonic sensor [113].As shown in Figure15, the reflection and transmission problem can be rewritten as a scattering and reradiation problem of the bounded wave [2]. The propagating wave and bounded wave (M-wave) could exchange with each other with the help of metasurface. In the far fields, we only care about propagating wave. As such, the total electromagnetic fields can be written as(33)
E
total
=
E
in
+
E
sc
=
E
in
+
S
×
E
in
.Here, E
sc is the scattered electric fields, which is determined by the incident electric field E
in and the structure function S. To realize complete absorption, the S function should be designed with no-backward scattering.Figure 15
Exchange between the propagating waves and M-waves. (a) Schematic of the principle. (b) Excitation of M-wave by propagating wave. (c) Conversion of the M-wave to propagating wave. Figures are reproduced from [2].
(a)
(b)
(c)In practical applications, metallic reflecting layers are often used as a ground plane for these absorbers. As illustrated in Figure16, we proposed a circuit model to interpret the electromagnetic interaction in these absorbers [37]. The magnetic response was mathematically treated using a modified equivalence circuit model. The relation between the reflection and impedance can be written as(34)
Y
sretri
=
1
Z
sretri
=
Y
0
1
-
S
11
1
+
S
11
-
Y
1
exp
⁡
-
i
k
d
-
r
m
exp
⁡
i
k
d
exp
⁡
-
i
k
d
+
r
m
exp
⁡
i
k
d
,where Y
0, Y
1
=
ε
1
Y
0, and Y
m
=
ε
m
Y
0 are the intrinsic admittance of vacuum, dielectric spacer, and metal and ε
1 and ε
m are permittivities of dielectric and metal. k
0 and k
=
ε
1
k
0 are the wave vector in the vacuum and dielectric spacer. r
m
=
(
Y
1
-
Y
m
)
/
(
Y
1
+
Y
m
) is the reflectivity of thick metal layer. Equation (34) is the basis of the metasurface-assisted absorption theory (MAT) [2].Figure 16
(a) Schematic of the metasurface-based absorber. (d) Physical model of the absorber, where the metasurface is described by its impedance. (b) Ideal impedance and retrieved impedance for the dispersive metasurface. (c, e) Absorption of the broadband (c) and dual narrowband (e) absorbers at different angles of incidence. (f) Schematic of the plasmonic nanocube based absorber. (g) Typical reflectance of a silver (Ag) nanocube. Figures are reproduced from (a)–(c) [114], (d, e) [37], and (f, g) [115].
(a)
(b)
(c)
(d)
(e)
(f)
(g)Subsequently, Feng et al. showed that the bandwidth can be dramatically increased by tailoring the dispersion of metasurfaces [114]. With a thin layer of structured nichrome, a polarization-independent absorber with absorption larger than 97% was numerically demonstrated over larger than one octave bandwidth. It was shown that the bandwidth enhancement is related to the transformation of Drude model of free electron gas in metal film to Lorentz oscillator model of bound electron in the structured metallic surface. It should be noted that the Lorentz form is just one kind of dispersion that mimics that of ideal absorbing metasurface. Thus, further engineering of the dispersion may lead to even larger bandwidth.In addition, to meet the requirement of bandwidth enhancement, metasurface absorbers are expected to be designed to reduce the fabrication complexity of traditional absorbers. Many works have been devoted to this design. For instance, a simple method was proposed by randomly adsorbing chemically synthesized silver nanocubes onto a nanoscale thick polymer spacer layer on a gold film [115]. The film-coupled nanocubes provide a reflectance spectrum that can be tailored by varying the geometry (the size of the cubes and/or the thickness of the spacer).In general, the maximal absorption bandwidth is limited by the optical thickness as indicated by the thickness-bandwidth ratio. For absorbers working at terahertz and higher frequencies, the physical thickness is very small even for quite large optical thickness. As a result, the thickness is not a big problem for broadband absorption at these frequencies. In contrast, the fabrication technique becomes a challenge since most of the broadband absorbers require multilayer thin films or complicated structures. Recently, we focused on the design of broadband absorber based on doped silicon, which has been considered as a new kind of metamaterials [116]. When the working frequency was larger than the plasmon frequency, doped silicon behaves as a highly lossy dielectric material. Yet a doped silicon slab by itself was not a good absorber due to the impedance mismatch between the silicon slab and free space. The power reflection at the interface was larger than 28% for refractive index n
=
3.3, which was similar with nondoped silicon. In order to reduce the reflection and enhance transmission (the case for nondoped silicon) or absorption (the case for doped silicon), antireflection techniques should be used.In the framework of transmission enhancement, the period of the grating structure should be in deep subwavelength scale to suppress non-zero-order diffractions. However, for high efficient absorber, we showed that the absorption bandwidth can be dramatically increased by utilizing both the zero- and first-order diffractions [117], as illustrated in Figure 17. Compared with previous broadband absorbers, the structure we proposed was mechanically stable and much easier to be fabricated. This idea was further extended by other researchers [104, 118]. The experimental results showed that more than 95% absorption can be obtained from 1 to 2 THz. It was also interesting to investigate whether second-order or higher-order diffraction can be utilized to increase the absorption bandwidth. In order to do this, the diffraction at higher frequencies was calculated for a two-layer grating. The relative absorption bandwidth for A
>
90
% becomes larger than 150%. Further increase of layers may lead to larger bandwidth. Nevertheless, the fabrication process will become more complex and the thickness will become larger.Figure 17
(a) Schematic of the metasurface absorber made out of silicon grating. (b) Calculated diffraction efficiency of a grating. (c) Fabricated sample. (d) Measured absorption coefficients. (e) Fabricated sample of a complex silicon grating. (f) Measured transmission and reflection coefficients with and without pattern. Figures are reproduced from (a, b) [117], (c, d) [118], and (e, f) [104].
(a)
(b)
(c)
(d)
(e)
(f)By stacking metasurfaces in multilayers, the absorption bandwidth could be further increased. As illustrated in Figures18(a) and 18(b), an excellent absorber is designed with a very large bandwidth (3.26–34.65 GHz) [110]. It is shown that the total thickness of the design (14.5 mm) is only a little thicker than the minimum possible thickness dictated by the physical bound. Nevertheless, the multilayered absorber is difficult to be fabricated since the resistance of each metasurface should be accurately controlled. More recently, we fabricated a broadband absorber using magnetic controlled sputtering and optical lithography technique [2]. Since both the substrates and conducting material are transparent in the optical spectra, such absorbers could be utilized in many areas, such as smart windows and cockpits. As can be seen in Figures 18(c) and 18(d), both the optical transmittance and the microwave absorption are large enough for practical applications.Figure 18
(a) The schematic of the ultrawideband absorber with optimal thickness. Top: the equivalent circuit model. Bottom: the actual realization of the absorber. The resistive layers are periodic square patches with periodicity (a), width (w), and sheet resistivity (R
s). (b) The frequency response of the reflection coefficient for the ultrawideband absorber with optimal thickness obtained from both the equivalent circuit model and the full-wave simulation. (c) Optical transmittance for the optical-transparent absorber. Inset shows the photograph. (d) Microwave absorption for both the experiment and the full-wave simulation. Figures are reproduced from (a, b) [110] and (c, d) [2].
(a)
(b)
(c)
(d)


### 3.4.2. Coherent Perfect Absorber

Recently, coherent perfect absorption of light was proposed and demonstrated in a planar intrinsic silicon slab when illuminated by two beams with equal intensities and proper relative phase [119, 120]. Such a device is termed a “coherent perfect absorber” (CPA) and a “time-reversed laser.” Compared with the perfect absorbers based on metasurfaces or plasmonic structures, the new device provides additional tunability of absorption through the interplay of absorption and interference. The coherent control of absorption is potentially useful in transducers, modulators, or optical switches [121, 122]. However, as a time-reversed process of laser, CPA is characterized by narrow bandwidth and thought to be not applicable in solar-cell and stealth technology.As shown in Figure19, it was demonstrated that the bandwidth of a thin film CPA can be rather large if the thickness is thin enough and the corresponding material has a specific chromatic dispersion resembling that of metal [38]. Two different regimes of metallic thin film CPA were derived based on the general CPA condition, characterized by extremely broad and moderately narrow bandwidth, respectively.Figure 19
(a) Schematic of the coherent perfect absorber. (b) Absorption as a function of the frequency and the thickness of the doped silicon film. (c) Coherent absorption of a 450 nm thick doped silicon film. Red and green solid lines show the absorption forΔ
l equal to 500 and 505.56 μm, respectively. (d) Coherent absorption of 17 nm thick tungsten for symmetrical and antisymmetrical inputs. (e) Schematic of plasmon hybridization and the effective medium description. For the symmetrical (antisymmetrical) resonance, the external E-fields (H-fields) should be parallel. (f) Coherent absorption of antisymmetrical inputs for TE polarization at oblique incidences. The inset of (f) illustrates the configuration of two coherent divergent beams with antisymmetrical phase distribution, where θ is the divergent angle. Figures are reproduced from [38, 123]. (g)–(i) Proposed applications of metasurface CPA in signal processing. Figures are reproduced from [124].
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)For nonmagnetic material, the CPA condition for normal incidence can be obtained:(35)
exp
⁡
i
n
k
d
=
±
n
-
1
n
+
1
.The ± sign is corresponding to the symmetrical or antisymmetrical inputs. In the previous discussion, an infinite number of discrete solutions of (35) have been found for k
d
≫
1. The bandwidth is defined as the frequency width between the maximum absorption and adjacent minimum absorption and is characterized by Δ
f
≈
c
/
(
2
n
d
). In this case, the CPA is rather narrowband and referred to as a time-reversed process of laser.In fact, the bandwidth of CPA can be very large ifd is extremely thin (d
≪
λ, n
k
d
≪
1). In this case, the left side of CPA equation becomes 1
+
i
n
k
d, and the right side can be approximated as ±
(
1
-
2
/
n
). As n
k
d is very small, only plus sign in the right side (symmetric mode) should be chosen and the real and imaginary parts of the refractive index (n
′ and n
′
′) become equal with(36)
n
′
≈
n
′
′
≈
1
k
d
=
c
ω
d
.In this case,n
k
d
≪
1 becomes 2
k
d
≪
1; thus, the working regime can be approximated as k
d
≪
1 and the required refractive index must be much larger than unit (n
≫
1). According to the definition of Yu and Capasso, such kind of thin film can also be thought of as a metasurface [1].Different from the general CPA condition, the CPA condition for ultrathin film is explicit. Obviously, Drude metal could be used as natural material for CPA, with extremely broadband response. We obtained the thickness for CPA at this frequency regime:(37)
d
w
≈
2
c
ω
p
2
τ
,where c is the speed of light in vacuum. This characteristic length is also called the Woltersdorff thickness [12], which quantifies the thickness of a metallic film with maximum absorption for incoherent beam input in the low frequency regime. When d
=
d
w, the maximum absorption is 0.5, while the reflection and transmission are 0.25, respectively. For d
<
d
w, most of the energy is transmitted; for d
>
d
w, most of it is reflected.Since the Woltersdorff thickness is independent of frequency, the absorption is very broadband. Generally, this frequency range covers all the low frequencies up to terahertz. In particular, a 0.3 nm thick tungsten film can absorb almost all the microwave and even terahertz energy under coherent condition, thus breaking the thickness limit proposed by Planck and Rozanov. Compared with the original CPA [120], the bandwidth increased more than 1010 times. In the optical CPA, the thickness of tungsten should be increased to 17 nm, which is still neglectable compared to the operational wavelength. The concept of ultrabroadband CPA was recently experimentally demonstrated in the microwave frequency. As shown in Figure 19(d), the absorption coefficients reach 100% at frequencies ranging from 6 to 18 GHz.Subsequently, a customized CPA was also proposed based on the electric and magnetic resonances in a three layered metal-insulator-metal structure [123]. These kinds of resonances were attributed to the plasmon hybridization effect due to the coupling of individual resonators. Most importantly, it was found that the antisymmetrical absorption associated with magnetic resonance is almost independent of the polarization of light and angle of incidence; thus, the structure is highly suitable for coherent absorption of divergent beams (Figure 19(f)). To interpret the interaction of magnetic and electric fields with the metasurface, effect constitutive parameters are retrieved and general CPA condition for material with both electric and magnetic responses was given:(38)
exp
⁡
i
n
k
d
=
±
1
-
z
1
+
z
,where k is the wave vector in free space and d is the total thickness of the effective slab. The ± signs are corresponding to the symmetrical and antisymmetrical inputs, respectively. This equation provided a general approach to the design of CPA operating at arbitrary frequencies.The coherent control method can also be utilized to realize other functionalities. For example, Zheludev et al. proposed the application of CPA in signal processing [124]. Potential applications include but are not limited to (a) a pulse restoration (clock recovery) device to restore the form of distorted signal pulses according to that of a clock (control) pulse, (b) a coherence filter that improves the coherence of light beams by absorbing incoherent components, and (c) a coherent light-by-light modulator wherein a digital or analogue intensity- or phase-modulated control input governs signal channel output. In addition, they showed that reflection and refraction effects on phase gradient metasurfaces can be coherently controlled by a second wave [125]. In addition, Cao et al. also demonstrated the possibility of coherent subwavelength focus. Broadband operation was made possible by engineering the dispersion of the complex dielectric function, similar to the previous methods [38]. The local enhancement can be significantly improved compared to the standard plane wave illumination of a metallic nanoparticle. Their numerical simulation showed that an optical pulse as short as 6 fs can be focused to an 11 nm region.More recently, coherent perfect rotation (CPR) of electromagnetic polarization states has been proposed by utilizing the odd time reversal symmetry in Faraday rotation [126]. Similar to coherent perfect absorption, the bandwidth of CPR is limited. The main advantage over other polarization transformers is that the polarization states can be dynamically tuned by the phase retardation. Nevertheless, it is pointed out that only Faraday rotation, but not optical activity or anisotropy, is capable of coherent perfect rotation. In our recent work, a dynamic polarization transformer was constructed by taking advantage of the time reversal symmetry of polarization conversion in anisotropic metasurface [76]. It should be noted that no Faraday rotation effect is utilized. The working bandwidth covers the entire microwave and terahertz bands. More interestingly, it is demonstrated that the output polarization states can be easily tuned between linear polarization and arbitrary circular polarization through phase modulation.


## 3.4.1. Single-Port Perfect Absorbing Metasurface

Absorption phenomena of electromagnetic wave can be found anywhere in our surrounding world. The colorful leafs and flowers are related to the frequency selective absorption of light. It was also well known that black object, such as carbon, absorbs most of the visible light. In 1860, Kirchhoff proposed the ideal blackbody absorber as “bodies can be imagined which, for infinitely small thicknesses, completely absorb all incident rays, and neither reflect nor transmit any.” Since then, the pursuit of high efficient absorbers never stops.Along with the development of Maxwell equations and invention of radar, the electromagnetic theory of absorbers was brought out after World War II. In the review given by Hans Severin in 1956 [35], the theory of the so-called Salisbury absorber, Jaumann absorber, Dallenbach absorber, pyramidal absorber, and dipole absorber was given in detail. The dipole absorber is just the precursor of the circuit analogy absorber (CAA) [99], which is also one kind of lossy metasurface. Severin also noted that there is a conflict between the thickness and bandwidth of these absorbers. Almost half a century later, Rozanov developed a rigorous theory for the bandwidth-to-thickness ratio [100], illustrating that there is a fundamental limit for this value. Remarkably, this conclusion consists with the prediction of Planck and Masius with respect to the thickness of blackbody [101].In recent years, broadband absorbers with optimal thickness were widely researched [38, 102–111]. Except for broadband absorbers, narrow band absorbers are also of particular importance in frequency selective applications. In 2008, Landy et al. proposed the concept of “Perfect Metamaterial Absorber” with thickness of only λ
/
40, where λ is the working wavelength [36]. They interpreted the principle of this absorber as the simultaneous control of electric and magnetic response such that the impedance is matched to the free space. However, it is now widely known that such impedance match does not ensure that the transmission and reflection can be simultaneously reduced to zero. As stated by Vora et al., it is ambiguous to define the μ
e
f
f and ε
e
f
f in such complex structures, since the metamaterial perfect absorber cannot be strictly considered as homogeneous bulk media [52].In 2008, we extended the meta-absorber into the visible frequencies. By converting the propagating wave into surface wave, perfect absorption of light wave was demonstrated. Antisymmetric surface plasmons coupling formed by subwavelength hole array (SHA) and reflecting layer was proved to dominate the multiorders near-perfect absorption. Although only SHA was investigated in this case, the design idea, realizing perfect absorption based on structured surface combined with thick metal layers, can also be extended to other cases, such as split ring resonator (SRR) combined with metal black plate. The most fascinating potential application of SHA combined with reflecting layer is the introduction of functional material into center dielectric region to realize imaging and detecting. In 2009, we further investigated the loss mechanism of perfect absorber. It was demonstrated that the ohmic loss and the dielectric loss both contributed to the absorption. The energy exchange was recently studied to enhance the efficiency of solar cells [52]. In addition, subwavelength high performance metamaterial absorber was also demonstrated by Hao et al. for optical frequencies [112]. Experimental results show that an absorption peak of 88% is achieved at the wavelength of ~1.58 μm. At almost the same time, Liu et al. demonstrated an infrared perfect absorber and verified its application as plasmonic sensor [113].As shown in Figure15, the reflection and transmission problem can be rewritten as a scattering and reradiation problem of the bounded wave [2]. The propagating wave and bounded wave (M-wave) could exchange with each other with the help of metasurface. In the far fields, we only care about propagating wave. As such, the total electromagnetic fields can be written as(33)
E
total
=
E
in
+
E
sc
=
E
in
+
S
×
E
in
.Here, E
sc is the scattered electric fields, which is determined by the incident electric field E
in and the structure function S. To realize complete absorption, the S function should be designed with no-backward scattering.Figure 15
Exchange between the propagating waves and M-waves. (a) Schematic of the principle. (b) Excitation of M-wave by propagating wave. (c) Conversion of the M-wave to propagating wave. Figures are reproduced from [2].
(a)
(b)
(c)In practical applications, metallic reflecting layers are often used as a ground plane for these absorbers. As illustrated in Figure16, we proposed a circuit model to interpret the electromagnetic interaction in these absorbers [37]. The magnetic response was mathematically treated using a modified equivalence circuit model. The relation between the reflection and impedance can be written as(34)
Y
sretri
=
1
Z
sretri
=
Y
0
1
-
S
11
1
+
S
11
-
Y
1
exp
⁡
-
i
k
d
-
r
m
exp
⁡
i
k
d
exp
⁡
-
i
k
d
+
r
m
exp
⁡
i
k
d
,where Y
0, Y
1
=
ε
1
Y
0, and Y
m
=
ε
m
Y
0 are the intrinsic admittance of vacuum, dielectric spacer, and metal and ε
1 and ε
m are permittivities of dielectric and metal. k
0 and k
=
ε
1
k
0 are the wave vector in the vacuum and dielectric spacer. r
m
=
(
Y
1
-
Y
m
)
/
(
Y
1
+
Y
m
) is the reflectivity of thick metal layer. Equation (34) is the basis of the metasurface-assisted absorption theory (MAT) [2].Figure 16
(a) Schematic of the metasurface-based absorber. (d) Physical model of the absorber, where the metasurface is described by its impedance. (b) Ideal impedance and retrieved impedance for the dispersive metasurface. (c, e) Absorption of the broadband (c) and dual narrowband (e) absorbers at different angles of incidence. (f) Schematic of the plasmonic nanocube based absorber. (g) Typical reflectance of a silver (Ag) nanocube. Figures are reproduced from (a)–(c) [114], (d, e) [37], and (f, g) [115].
(a)
(b)
(c)
(d)
(e)
(f)
(g)Subsequently, Feng et al. showed that the bandwidth can be dramatically increased by tailoring the dispersion of metasurfaces [114]. With a thin layer of structured nichrome, a polarization-independent absorber with absorption larger than 97% was numerically demonstrated over larger than one octave bandwidth. It was shown that the bandwidth enhancement is related to the transformation of Drude model of free electron gas in metal film to Lorentz oscillator model of bound electron in the structured metallic surface. It should be noted that the Lorentz form is just one kind of dispersion that mimics that of ideal absorbing metasurface. Thus, further engineering of the dispersion may lead to even larger bandwidth.In addition, to meet the requirement of bandwidth enhancement, metasurface absorbers are expected to be designed to reduce the fabrication complexity of traditional absorbers. Many works have been devoted to this design. For instance, a simple method was proposed by randomly adsorbing chemically synthesized silver nanocubes onto a nanoscale thick polymer spacer layer on a gold film [115]. The film-coupled nanocubes provide a reflectance spectrum that can be tailored by varying the geometry (the size of the cubes and/or the thickness of the spacer).In general, the maximal absorption bandwidth is limited by the optical thickness as indicated by the thickness-bandwidth ratio. For absorbers working at terahertz and higher frequencies, the physical thickness is very small even for quite large optical thickness. As a result, the thickness is not a big problem for broadband absorption at these frequencies. In contrast, the fabrication technique becomes a challenge since most of the broadband absorbers require multilayer thin films or complicated structures. Recently, we focused on the design of broadband absorber based on doped silicon, which has been considered as a new kind of metamaterials [116]. When the working frequency was larger than the plasmon frequency, doped silicon behaves as a highly lossy dielectric material. Yet a doped silicon slab by itself was not a good absorber due to the impedance mismatch between the silicon slab and free space. The power reflection at the interface was larger than 28% for refractive index n
=
3.3, which was similar with nondoped silicon. In order to reduce the reflection and enhance transmission (the case for nondoped silicon) or absorption (the case for doped silicon), antireflection techniques should be used.In the framework of transmission enhancement, the period of the grating structure should be in deep subwavelength scale to suppress non-zero-order diffractions. However, for high efficient absorber, we showed that the absorption bandwidth can be dramatically increased by utilizing both the zero- and first-order diffractions [117], as illustrated in Figure 17. Compared with previous broadband absorbers, the structure we proposed was mechanically stable and much easier to be fabricated. This idea was further extended by other researchers [104, 118]. The experimental results showed that more than 95% absorption can be obtained from 1 to 2 THz. It was also interesting to investigate whether second-order or higher-order diffraction can be utilized to increase the absorption bandwidth. In order to do this, the diffraction at higher frequencies was calculated for a two-layer grating. The relative absorption bandwidth for A
>
90
% becomes larger than 150%. Further increase of layers may lead to larger bandwidth. Nevertheless, the fabrication process will become more complex and the thickness will become larger.Figure 17
(a) Schematic of the metasurface absorber made out of silicon grating. (b) Calculated diffraction efficiency of a grating. (c) Fabricated sample. (d) Measured absorption coefficients. (e) Fabricated sample of a complex silicon grating. (f) Measured transmission and reflection coefficients with and without pattern. Figures are reproduced from (a, b) [117], (c, d) [118], and (e, f) [104].
(a)
(b)
(c)
(d)
(e)
(f)By stacking metasurfaces in multilayers, the absorption bandwidth could be further increased. As illustrated in Figures18(a) and 18(b), an excellent absorber is designed with a very large bandwidth (3.26–34.65 GHz) [110]. It is shown that the total thickness of the design (14.5 mm) is only a little thicker than the minimum possible thickness dictated by the physical bound. Nevertheless, the multilayered absorber is difficult to be fabricated since the resistance of each metasurface should be accurately controlled. More recently, we fabricated a broadband absorber using magnetic controlled sputtering and optical lithography technique [2]. Since both the substrates and conducting material are transparent in the optical spectra, such absorbers could be utilized in many areas, such as smart windows and cockpits. As can be seen in Figures 18(c) and 18(d), both the optical transmittance and the microwave absorption are large enough for practical applications.Figure 18
(a) The schematic of the ultrawideband absorber with optimal thickness. Top: the equivalent circuit model. Bottom: the actual realization of the absorber. The resistive layers are periodic square patches with periodicity (a), width (w), and sheet resistivity (R
s). (b) The frequency response of the reflection coefficient for the ultrawideband absorber with optimal thickness obtained from both the equivalent circuit model and the full-wave simulation. (c) Optical transmittance for the optical-transparent absorber. Inset shows the photograph. (d) Microwave absorption for both the experiment and the full-wave simulation. Figures are reproduced from (a, b) [110] and (c, d) [2].
(a)
(b)
(c)
(d)


## 3.4.2. Coherent Perfect Absorber

Recently, coherent perfect absorption of light was proposed and demonstrated in a planar intrinsic silicon slab when illuminated by two beams with equal intensities and proper relative phase [119, 120]. Such a device is termed a “coherent perfect absorber” (CPA) and a “time-reversed laser.” Compared with the perfect absorbers based on metasurfaces or plasmonic structures, the new device provides additional tunability of absorption through the interplay of absorption and interference. The coherent control of absorption is potentially useful in transducers, modulators, or optical switches [121, 122]. However, as a time-reversed process of laser, CPA is characterized by narrow bandwidth and thought to be not applicable in solar-cell and stealth technology.As shown in Figure19, it was demonstrated that the bandwidth of a thin film CPA can be rather large if the thickness is thin enough and the corresponding material has a specific chromatic dispersion resembling that of metal [38]. Two different regimes of metallic thin film CPA were derived based on the general CPA condition, characterized by extremely broad and moderately narrow bandwidth, respectively.Figure 19
(a) Schematic of the coherent perfect absorber. (b) Absorption as a function of the frequency and the thickness of the doped silicon film. (c) Coherent absorption of a 450 nm thick doped silicon film. Red and green solid lines show the absorption forΔ
l equal to 500 and 505.56 μm, respectively. (d) Coherent absorption of 17 nm thick tungsten for symmetrical and antisymmetrical inputs. (e) Schematic of plasmon hybridization and the effective medium description. For the symmetrical (antisymmetrical) resonance, the external E-fields (H-fields) should be parallel. (f) Coherent absorption of antisymmetrical inputs for TE polarization at oblique incidences. The inset of (f) illustrates the configuration of two coherent divergent beams with antisymmetrical phase distribution, where θ is the divergent angle. Figures are reproduced from [38, 123]. (g)–(i) Proposed applications of metasurface CPA in signal processing. Figures are reproduced from [124].
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)For nonmagnetic material, the CPA condition for normal incidence can be obtained:(35)
exp
⁡
i
n
k
d
=
±
n
-
1
n
+
1
.The ± sign is corresponding to the symmetrical or antisymmetrical inputs. In the previous discussion, an infinite number of discrete solutions of (35) have been found for k
d
≫
1. The bandwidth is defined as the frequency width between the maximum absorption and adjacent minimum absorption and is characterized by Δ
f
≈
c
/
(
2
n
d
). In this case, the CPA is rather narrowband and referred to as a time-reversed process of laser.In fact, the bandwidth of CPA can be very large ifd is extremely thin (d
≪
λ, n
k
d
≪
1). In this case, the left side of CPA equation becomes 1
+
i
n
k
d, and the right side can be approximated as ±
(
1
-
2
/
n
). As n
k
d is very small, only plus sign in the right side (symmetric mode) should be chosen and the real and imaginary parts of the refractive index (n
′ and n
′
′) become equal with(36)
n
′
≈
n
′
′
≈
1
k
d
=
c
ω
d
.In this case,n
k
d
≪
1 becomes 2
k
d
≪
1; thus, the working regime can be approximated as k
d
≪
1 and the required refractive index must be much larger than unit (n
≫
1). According to the definition of Yu and Capasso, such kind of thin film can also be thought of as a metasurface [1].Different from the general CPA condition, the CPA condition for ultrathin film is explicit. Obviously, Drude metal could be used as natural material for CPA, with extremely broadband response. We obtained the thickness for CPA at this frequency regime:(37)
d
w
≈
2
c
ω
p
2
τ
,where c is the speed of light in vacuum. This characteristic length is also called the Woltersdorff thickness [12], which quantifies the thickness of a metallic film with maximum absorption for incoherent beam input in the low frequency regime. When d
=
d
w, the maximum absorption is 0.5, while the reflection and transmission are 0.25, respectively. For d
<
d
w, most of the energy is transmitted; for d
>
d
w, most of it is reflected.Since the Woltersdorff thickness is independent of frequency, the absorption is very broadband. Generally, this frequency range covers all the low frequencies up to terahertz. In particular, a 0.3 nm thick tungsten film can absorb almost all the microwave and even terahertz energy under coherent condition, thus breaking the thickness limit proposed by Planck and Rozanov. Compared with the original CPA [120], the bandwidth increased more than 1010 times. In the optical CPA, the thickness of tungsten should be increased to 17 nm, which is still neglectable compared to the operational wavelength. The concept of ultrabroadband CPA was recently experimentally demonstrated in the microwave frequency. As shown in Figure 19(d), the absorption coefficients reach 100% at frequencies ranging from 6 to 18 GHz.Subsequently, a customized CPA was also proposed based on the electric and magnetic resonances in a three layered metal-insulator-metal structure [123]. These kinds of resonances were attributed to the plasmon hybridization effect due to the coupling of individual resonators. Most importantly, it was found that the antisymmetrical absorption associated with magnetic resonance is almost independent of the polarization of light and angle of incidence; thus, the structure is highly suitable for coherent absorption of divergent beams (Figure 19(f)). To interpret the interaction of magnetic and electric fields with the metasurface, effect constitutive parameters are retrieved and general CPA condition for material with both electric and magnetic responses was given:(38)
exp
⁡
i
n
k
d
=
±
1
-
z
1
+
z
,where k is the wave vector in free space and d is the total thickness of the effective slab. The ± signs are corresponding to the symmetrical and antisymmetrical inputs, respectively. This equation provided a general approach to the design of CPA operating at arbitrary frequencies.The coherent control method can also be utilized to realize other functionalities. For example, Zheludev et al. proposed the application of CPA in signal processing [124]. Potential applications include but are not limited to (a) a pulse restoration (clock recovery) device to restore the form of distorted signal pulses according to that of a clock (control) pulse, (b) a coherence filter that improves the coherence of light beams by absorbing incoherent components, and (c) a coherent light-by-light modulator wherein a digital or analogue intensity- or phase-modulated control input governs signal channel output. In addition, they showed that reflection and refraction effects on phase gradient metasurfaces can be coherently controlled by a second wave [125]. In addition, Cao et al. also demonstrated the possibility of coherent subwavelength focus. Broadband operation was made possible by engineering the dispersion of the complex dielectric function, similar to the previous methods [38]. The local enhancement can be significantly improved compared to the standard plane wave illumination of a metallic nanoparticle. Their numerical simulation showed that an optical pulse as short as 6 fs can be focused to an 11 nm region.More recently, coherent perfect rotation (CPR) of electromagnetic polarization states has been proposed by utilizing the odd time reversal symmetry in Faraday rotation [126]. Similar to coherent perfect absorption, the bandwidth of CPR is limited. The main advantage over other polarization transformers is that the polarization states can be dynamically tuned by the phase retardation. Nevertheless, it is pointed out that only Faraday rotation, but not optical activity or anisotropy, is capable of coherent perfect rotation. In our recent work, a dynamic polarization transformer was constructed by taking advantage of the time reversal symmetry of polarization conversion in anisotropic metasurface [76]. It should be noted that no Faraday rotation effect is utilized. The working bandwidth covers the entire microwave and terahertz bands. More interestingly, it is demonstrated that the output polarization states can be easily tuned between linear polarization and arbitrary circular polarization through phase modulation.


## 3.5. Plasmonic Metasurfaces

### 3.5.1. Superlens and Hyperlens

As discussed in Section2, some particular metasurfaces can support surface waves, such as SPPs. The last several decades have witnessed the rapid development of SPPs and related areas. One of the largest advantages of SPPs is their ability to construct superlens and hyperlens to break the diffraction limit, which prevents the imaging of subwavelength features [34]. As we demonstrated recently, the electromagnetic waves on metasurfaces are characterized by three distinct properties [2]. The most important one is the short wavelength [55], which is actually the basis to break the diffraction limit.In 2000, Pendry firstly proposed the concept of perfect lens [4], in which the amplification of evanescent waves and perfect imaging could be obtained by a negative refraction index slab. The short wavelength characteristic of SPPs on a sliver film was firstly demonstrated in 2003 [127, 128], and surface plasmon resonant interference nanolithography technique (SPRINT) was proposed to achieve resolution of half-pitch 50 nm (~1/9 wavelength) in 2004 [31], as shown in Figures 20(a) and 20(b). Using exposure recording scheme, Fang et al. experimentally demonstrated in 2005 that a 35 nm thick silver superlens was capable of subdiffraction imaging of half-pitch 60 nm objects (~1/6 wavelength) [30]. Figure 20(c) illustrates the experimental scheme of subwavelength imaging through a silver lens, where the objects were located 40 nm away from the silver superlens. Due to the superlens effect, the object of “NANO” characters was imaged on the photoresist and the average line width of images is 89 nm (Figure 20(d)). By utilizing a similar scheme, the superlens effect was also confirmed by other groups [129, 130].Figure 20
Experimental demonstration of near-sighted silver lens. (a) Numerical simulation of intensity distribution of surface plasmons. (b) SEM image of resist pattern for (a). (c) Schematic diagram of the silver superlens experiment. (d) (Top) Focused-ion-beam image of the object with 40 nm line width, (middle) AFM images of topographic characterization in resist layer with a silver superlens, and (bottom) AFM images of topographic characterization in resist layer with the 35 nm thick superlens replaced by PMMA spacer as a control experiment. (e) Schematic of imaging lithography structure with a reflective Ag lens. (f) (Top) SEM image of the mask pattern “OPEN” characters, (bottom) SEM image of resist pattern. SEM image of half-pitch 32 nm dense lines resist pattern with plasmonic cavity lens. AFM image of half-pitch 22 nm resist pattern. Inset shows its two-dimensional (2D) Fourier analysis diagram. Figures are reproduced from (a, b) [31], (c, d) [30], and (e, f) [32].
(a)
(b)
(c)
(d)
(e)
(f)The metasurface-assisted diffraction theory (MDT) can be utilized in plasmonic lithography [2], where the silver lens has practical limits, such as optical loss, surface roughness, and film thickness. To address these issues, some important studies were reported, including active lens and plasmonic reflective slab [32, 131]. Based on the reflective amplification of evanescent wave, Wang et al. experimentally achieved the deep subwavelength imaging lithography for nanocharacters with about 50 nm line width [32], as depicted in Figures 20(e) and 20(f). It was also reported that the plasmonic cavity lens can be utilized to achieve high aspect profile [132]. The profile depth of half-pitch 32 nm resist patterns was enhanced to be about 23 nm, which is much larger than the previously reported results (sub-10 nm). The resolution of SPPs imaging lithography was also extended to be half-pitch of 22 nm, whereas the quality needs to be further increased.The subdiffraction imaging model of a planar plasmonic lens can be written in the form of(39)
E
x
x
,
y
,
z
E
y
x
,
y
,
z
E
z
x
,
y
,
z
=
∫
-
∞
∞
∫
-
∞
∞
A
x
k
x
,
k
y
A
y
k
x
,
k
y
k
x
A
x
+
k
y
A
y
-
k
z
exp
⁡
i
k
x
x
+
i
k
y
y
d
k
x
d
k
y
,
A
x
k
x
,
k
y
A
y
k
x
,
k
y
=
∫
-
∞
∞
∫
-
∞
∞
G
x
x
,
y
t
x
x
,
y
T
x
k
x
,
k
y
G
y
x
,
y
t
y
x
,
y
T
y
k
x
,
k
y
exp
⁡
-
i
k
x
x
-
i
k
y
y
d
x
d
y
,where G
(
x
,
y
), t
(
x
,
y
), and T
(
k
x
,
k
y
) are the illumination function, transmission function of object, and optical transfer function (OTF) of plasmonic lens, respectively. The OTF can be obtained through transfer matrix. If there is reflection plane in the plasmonic lens, the OTF should be determined by using the fields in the photoresist layer, implying that the images can also be modulated by the reflecting layer [32].Although the superlens provided images of nanoobjects well beyond the diffraction limit, the inherent disadvantage of near-sighted mode impedes its widespread application. It is highly desirable to utilize a plasmonic lens system which could resolve subwavelength details of objects in far field. In 2006, Jacob et al. proposed a hyperlens composed of cylindrical metal-dielectric multilayers to magnify subwavelength details of objects so that the subwavelength features are above the diffraction limit at the hyperlens output [133]. Then, conventional microscopy can be utilized to capture the output of hyperlens to achieve far-field super resolution imaging.


### 3.5.2. Plasmonic Metasurface Lens

Based on Snell’s law, traditional optical lenses must have curved surfaces to focus light. In other words, the phase retardation was accumulated by height variation much larger than the wavelength. In recent years, metasurfaces were widely utilized to achieve planar lenses, based on the metasurface-assisted law of reflection and refraction (MLRR) [2, 134]:(40)
n
1
k
0
sin
⁡
θ
1
+
∇
Φ
=
n
1
k
0
sin
⁡
θ
3
,
n
1
k
0
sin
⁡
θ
1
+
∇
Φ
=
n
2
k
0
sin
⁡
θ
2
,where ∇
Φ is the phase gradient in the metasurface plane, which is determined by the geometric structure and distribution, and may be changed by external stimuli, leading to the adaptive tuning of the law of refraction and reflection. n
1 and n
2 are the refractive index of media at the incident and transmit sides. θ
1, θ
2, and θ
3 are the angles for incident, refracted, and reflected light.In particular, plasmonic lenses have become one widely researched approach, which has now been demonstrated in both one-dimensional and two-dimensional cases [46, 135, 136]. These devices offered an alternative to conventional refraction microlenses. The planar and compact designs are beneficial for obtaining short focal distances on the order of several micrometers.Early in the 21st century, a novel method was proposed to manipulate the phase retardation of light at nanoscale, providing a new approach to develop various nanooptical devices, such as flat lenses, collimators, and splitters. Figure21(a) illustrates the principle of planar lens based on width-tuned plasmonic slits. The slits transport electromagnetic energy in the form of SPPs in nanometric waveguides and provide desired phase retardations with variant phase propagation constant. Under plane wave illumination, the light energy was focused at the focal plane f
=
0.8 μm, as shown in Figure 21(b). According to Fermat’s Principle, such devices could also achieve arbitrary angle of light deflecting such as that shown in Figure 21(c).Figure 21
Planar slit array metal lens. (a) Schematic configuration of light focusing of planar metal nanoslit array lens. (b) Normalized Poynting Vector for light focusing of metallic nanoslits lens. (c) Calculated phase distribution of electric field for the designed deflector. Incident and deflection angles are designed as 30° and −30°, respectively. (d) Far-field angular spectrum for the incident and emitted beams, respectively. (e, f) Schematic of the abnormal refraction in other metasurfaces. Figures are reproduced from (a)–(d) [137], (e) [134], and (f) [138].
(a)
(b)
(c)
(d)
(e)
(f)Although the plasmonic lens is easy to be fabricated, it was only until 2008 that the experimental demonstration of such device was reported [46]. For plane wave illumination, the light was focused at the focal length of 5.3 μm. The excellent agreement between experiment and simulation validated the design principle of this approach. It should be noted that the plasmonic version of abnormal refraction is similar to that in other metasurfaces, as shown in Figures 21(e) and 21(f).More recently, as shown in Figure22, Chen et al. demonstrated that the far-field focusing pattern of planar metal lens could be modulated by slits filled with phase change material (Ge2Sb2Te5, GST) [135]. By varying the crystallization level of GST from 0% to 90%, the Fabry-Pérot resonance supported inside each slit can be spectrally shifted across the working wavelength at 1.55 μm, which results in a transmitted electromagnetic phase modulation as large as 0.56π. Based on this geometrically fixed platform, different phase fronts can be constructed spatially on the lens plane by assigning the designed GST crystallization levels to the corresponding slits, achieving various far-field focusing patterns.Figure 22
(a) Schematic diagram of the planar lens. (b) The cross section showing thex-component of the electric field of the 1st-order mode from a single slit. (c) The evolution of the single-slit transmission spectrum for different crystallization levels. (d) The relative phase and (e) the normalized electric field intensity at 1.55 μm as functions of the crystallization level with a 5% step increment. (f) Focusing pattern measured in x
z-plane by confocal scanning optical microscopy for different status of GST. Figures are reproduced from [135].In 2007, Min et al. investigated a type of metallic nanooptic lens consisting of slits with variant widths, filled with Kerr nonlinear media [139]. As shown in Figure 23(a), each slit is designed to transmit light with specific phase retardation controlled by the intensity of incident light, owing to the nonlinear response. This new lens can actively control the deflection angle and the focus length of output beam. Very recently, Hu et al. proposed an active terahertz (THz) plasmonic lens tuned by an external magnetic field [140]. Different from traditional tunable devices, the proposed active lens is tuned by changing the cyclotron frequency through manipulating magnetoplasmons (MPs). It was shown that THz wave propagating through the designed structure could be focused to a small size spot via the control of MPs. The tuning range of the focal length under the applied magnetic field (up to 1 T) is ~31, about 50% of the original focal length.Figure 23
(a) Schematic view of the three-slit structure under study. (b) and (c) The FDTD simulation of electric field intensityE
2 time-average distribution of beam focusing with a five-slit metallic lens. (d) A semiconductor-insulator-semiconductor structure in a Voigt configuration. The propagation mode is TM polarized, and the magnetic field B is applied along the y-axis. The thickness of the insulator is denoted by w. (e) FDTD-calculated focal length when the external magnetic field is increased from 0 to 1 T. Figures are reproduced from (a)–(c) [139] and (d, e) [140].
(a)
(b)
(c)
(d)
(e)It should be noted that the plasmonic slit lens is polarization selective; that is, only one particularly polarized light beam could be transmitted and modulated in phase, since the SPP is intrinsically polarized. This polarization selectivity has two effects. Firstly, this effect is attractive for some cases where only one polarization type is needed. Secondly, it may become undesired for many other applications. To eliminate this problem, rectangular or circular plasmonic holes were adopted to achieve phase modulation [136, 141]. As illustrated in Figure 24, Ishii et al. experimentally demonstrated a polarization-independent holey-metal lens [136]. They showed that by changing the radii of subwavelength holes in a metallic film, which act as single-mode waveguide elements, they can control the phase of light transmitted through the holes. Finally, it was demonstrated that the focal distance of the lens can be controlled by changing the incident wavelength.Figure 24
(a) Pseudocolor intensity map calculated from the analytical model of the sample. The color scale is normalized to the maximum intensity. The inset shows the beam cross section at the focal point (z
=
10 μm) and the SEM image of the sample. (b) Schematic of a nanowaveguide array that induces wavefront shaping for OAM generation. (c) SEM picture of the nanowaveguide array. Figures are reproduced from [136, 141].
(a)
(b)
(c)More recently, Litchinitser et al. demonstrated that the change of hole radius along the azimuthal direction is able to generate orbital angular momentum (OAM) on the nanoscale. They proposed and experimentally demonstrated that a nanowaveguide array milled in a metal film can be used to control the wavefront of a light beam and that an optical vortex at 532 nm was produced by using such an array (see Figures24(b) and 24(c)).


### 3.5.3. Plasmonic Metasurfaces for Sensing Applications

Owing to the strong light-matter interaction, metasurfaces can provide a robust and efficient platform for biosensing. In particular, the surface plasmon resonance (SPR) at planar surfaces or localized surface plasmon resonance (LSPR) for nanometer-sized metallic structures is accompanied with dramatic local field enhancement [142]. The implication of the local field enhancement is twofold. Firstly, the spectra of the SPR and LSPR are highly dependent on the environment; thus, a little change of refractive index would result in a considerable spectrum shift. Secondly, the local field enhancement can be exploited to achieve surface-enhanced Raman spectroscopy (SERS) [143]. Both of the two mechanisms can be utilized for clinic detection.As shown in Figures25(a)–25(d), Wu et al. introduced an infrared plasmonic surface based on a Fano-resonant metasurface which exhibits sharp resonances caused by the interference between subradiant and superradiant plasmonic resonances [144]. Owing to the asymmetry, the frequency of the subradiant resonance can be precisely determined and matched to the molecule’s vibrational fingerprints. In these Fano resonances, the near-field coupling of plasmonic modes is crucial to enhance the sensitivity [145, 146]. It was also demonstrated that Young’s interference can be observed in plasmonic structures when two or three nanoparticles with separation on the order of the wavelength are illuminated simultaneously by a plane wave. This effect leads to the formation of intermediate-field hybridized modes with a character distinct of those mediated by near-field and/or far-field radiative effects [147].Figure 25
(a) Schematic representation of subradiant (Q) and superradiant (D) modes. (b) Scanning electron microscopy image of a typical fabricated sample. (c) Schematic representations of proteins’ mono- and bilayers binding to the metal surface. (d) Experimental (solid) and theoretical (dashed) polarized reflectivity spectra. (e) SEM image of a fabricated metasurface consisting of hole array. (f) Resonance shift for the subradiant SPP mode with changing NaCl concentration. Figures are reproduced from (a)–(d) [144] and (e, f) [148].
(a)
(b)
(c)
(d)
(e)
(f)In a similar work [148], by exploiting extraordinary light transmission phenomena through high quality factor subradiant dark modes, Yanik et al. experimentally demonstrated high figures of merits (FOMs as high as 162) for intrinsic detection limits surpassing those of the gold standard prism coupled surface plasmon sensors, as illustrated in Figures 25(e) and 25(f).Over the past several years, the absorption effect of plasmonic metasurface has also been exploited in sensing applications. In 2011, Tittl et al. presented a simple design of plasmonic absorber based on palladium nanowires [149]. Due to hydrogen incorporation, palladium undergoes a phase transition from a metal to a metal hydride which leads to an expansion of the palladium lattice. The fabricated structure showed a reflectance of 0.5% which in combination with a complete suppression of transmission yields an absorbance of A
≈
99.5
%. As shown in Figures 26(a)–26(d), they utilized the absorber structure for hydrogen sensing and were able to reliably detect concentration down to 0.5% H2 in air with response time in the range of seconds.Figure 26
(a) A side view of the sensor. Palladium nanowires are stacked above a gold mirror. The layers are separated by a MgF2 film. (b) A sketch of the experimental setup including the mass flow controllers used to set the desired hydrogen concentrations. (c) Simulated response of the sensor structure to hydrogen exposure. (d) Reflectance of the absorber for different hydrogen concentrations. (e) SEM images of split ring resonators (SRRs) on a graphene layer. (f) Experimental results of the Raman spectra for different conditions. Figures are reproduced from (a)–(d) [149] and (e, f) [150].
(a)
(b)
(c)
(d)
(e)
(f)More recently, it was demonstrated that graphene monolayers transferred on arrays of split ring resonators (SRRs) could exhibit resonances in the visible range. As illustrated in Figures26(e) and 26(f), Raman enhancement factors per area of graphene up to 75 were measured, demonstrating the strong plasmonic coupling between graphene and the metasurface resonances.Recently, an important sensing technique via multifrequency antennas was also demonstrated [151–155]. Such antennas can efficiently detect different vibrational modes of molecular species in a window of several micrometers, where informative fingerprint spectra of many molecules are present.Since there have already been many reviews on this topic [34, 142, 143, 156], we only give a small part of examples here. To completely understand the role of metasurface in sensing applications, we would like to suggest that the readers find more information in these literatures.


## 3.5.1. Superlens and Hyperlens

As discussed in Section2, some particular metasurfaces can support surface waves, such as SPPs. The last several decades have witnessed the rapid development of SPPs and related areas. One of the largest advantages of SPPs is their ability to construct superlens and hyperlens to break the diffraction limit, which prevents the imaging of subwavelength features [34]. As we demonstrated recently, the electromagnetic waves on metasurfaces are characterized by three distinct properties [2]. The most important one is the short wavelength [55], which is actually the basis to break the diffraction limit.In 2000, Pendry firstly proposed the concept of perfect lens [4], in which the amplification of evanescent waves and perfect imaging could be obtained by a negative refraction index slab. The short wavelength characteristic of SPPs on a sliver film was firstly demonstrated in 2003 [127, 128], and surface plasmon resonant interference nanolithography technique (SPRINT) was proposed to achieve resolution of half-pitch 50 nm (~1/9 wavelength) in 2004 [31], as shown in Figures 20(a) and 20(b). Using exposure recording scheme, Fang et al. experimentally demonstrated in 2005 that a 35 nm thick silver superlens was capable of subdiffraction imaging of half-pitch 60 nm objects (~1/6 wavelength) [30]. Figure 20(c) illustrates the experimental scheme of subwavelength imaging through a silver lens, where the objects were located 40 nm away from the silver superlens. Due to the superlens effect, the object of “NANO” characters was imaged on the photoresist and the average line width of images is 89 nm (Figure 20(d)). By utilizing a similar scheme, the superlens effect was also confirmed by other groups [129, 130].Figure 20
Experimental demonstration of near-sighted silver lens. (a) Numerical simulation of intensity distribution of surface plasmons. (b) SEM image of resist pattern for (a). (c) Schematic diagram of the silver superlens experiment. (d) (Top) Focused-ion-beam image of the object with 40 nm line width, (middle) AFM images of topographic characterization in resist layer with a silver superlens, and (bottom) AFM images of topographic characterization in resist layer with the 35 nm thick superlens replaced by PMMA spacer as a control experiment. (e) Schematic of imaging lithography structure with a reflective Ag lens. (f) (Top) SEM image of the mask pattern “OPEN” characters, (bottom) SEM image of resist pattern. SEM image of half-pitch 32 nm dense lines resist pattern with plasmonic cavity lens. AFM image of half-pitch 22 nm resist pattern. Inset shows its two-dimensional (2D) Fourier analysis diagram. Figures are reproduced from (a, b) [31], (c, d) [30], and (e, f) [32].
(a)
(b)
(c)
(d)
(e)
(f)The metasurface-assisted diffraction theory (MDT) can be utilized in plasmonic lithography [2], where the silver lens has practical limits, such as optical loss, surface roughness, and film thickness. To address these issues, some important studies were reported, including active lens and plasmonic reflective slab [32, 131]. Based on the reflective amplification of evanescent wave, Wang et al. experimentally achieved the deep subwavelength imaging lithography for nanocharacters with about 50 nm line width [32], as depicted in Figures 20(e) and 20(f). It was also reported that the plasmonic cavity lens can be utilized to achieve high aspect profile [132]. The profile depth of half-pitch 32 nm resist patterns was enhanced to be about 23 nm, which is much larger than the previously reported results (sub-10 nm). The resolution of SPPs imaging lithography was also extended to be half-pitch of 22 nm, whereas the quality needs to be further increased.The subdiffraction imaging model of a planar plasmonic lens can be written in the form of(39)
E
x
x
,
y
,
z
E
y
x
,
y
,
z
E
z
x
,
y
,
z
=
∫
-
∞
∞
∫
-
∞
∞
A
x
k
x
,
k
y
A
y
k
x
,
k
y
k
x
A
x
+
k
y
A
y
-
k
z
exp
⁡
i
k
x
x
+
i
k
y
y
d
k
x
d
k
y
,
A
x
k
x
,
k
y
A
y
k
x
,
k
y
=
∫
-
∞
∞
∫
-
∞
∞
G
x
x
,
y
t
x
x
,
y
T
x
k
x
,
k
y
G
y
x
,
y
t
y
x
,
y
T
y
k
x
,
k
y
exp
⁡
-
i
k
x
x
-
i
k
y
y
d
x
d
y
,where G
(
x
,
y
), t
(
x
,
y
), and T
(
k
x
,
k
y
) are the illumination function, transmission function of object, and optical transfer function (OTF) of plasmonic lens, respectively. The OTF can be obtained through transfer matrix. If there is reflection plane in the plasmonic lens, the OTF should be determined by using the fields in the photoresist layer, implying that the images can also be modulated by the reflecting layer [32].Although the superlens provided images of nanoobjects well beyond the diffraction limit, the inherent disadvantage of near-sighted mode impedes its widespread application. It is highly desirable to utilize a plasmonic lens system which could resolve subwavelength details of objects in far field. In 2006, Jacob et al. proposed a hyperlens composed of cylindrical metal-dielectric multilayers to magnify subwavelength details of objects so that the subwavelength features are above the diffraction limit at the hyperlens output [133]. Then, conventional microscopy can be utilized to capture the output of hyperlens to achieve far-field super resolution imaging.


## 3.5.2. Plasmonic Metasurface Lens

Based on Snell’s law, traditional optical lenses must have curved surfaces to focus light. In other words, the phase retardation was accumulated by height variation much larger than the wavelength. In recent years, metasurfaces were widely utilized to achieve planar lenses, based on the metasurface-assisted law of reflection and refraction (MLRR) [2, 134]:(40)
n
1
k
0
sin
⁡
θ
1
+
∇
Φ
=
n
1
k
0
sin
⁡
θ
3
,
n
1
k
0
sin
⁡
θ
1
+
∇
Φ
=
n
2
k
0
sin
⁡
θ
2
,where ∇
Φ is the phase gradient in the metasurface plane, which is determined by the geometric structure and distribution, and may be changed by external stimuli, leading to the adaptive tuning of the law of refraction and reflection. n
1 and n
2 are the refractive index of media at the incident and transmit sides. θ
1, θ
2, and θ
3 are the angles for incident, refracted, and reflected light.In particular, plasmonic lenses have become one widely researched approach, which has now been demonstrated in both one-dimensional and two-dimensional cases [46, 135, 136]. These devices offered an alternative to conventional refraction microlenses. The planar and compact designs are beneficial for obtaining short focal distances on the order of several micrometers.Early in the 21st century, a novel method was proposed to manipulate the phase retardation of light at nanoscale, providing a new approach to develop various nanooptical devices, such as flat lenses, collimators, and splitters. Figure21(a) illustrates the principle of planar lens based on width-tuned plasmonic slits. The slits transport electromagnetic energy in the form of SPPs in nanometric waveguides and provide desired phase retardations with variant phase propagation constant. Under plane wave illumination, the light energy was focused at the focal plane f
=
0.8 μm, as shown in Figure 21(b). According to Fermat’s Principle, such devices could also achieve arbitrary angle of light deflecting such as that shown in Figure 21(c).Figure 21
Planar slit array metal lens. (a) Schematic configuration of light focusing of planar metal nanoslit array lens. (b) Normalized Poynting Vector for light focusing of metallic nanoslits lens. (c) Calculated phase distribution of electric field for the designed deflector. Incident and deflection angles are designed as 30° and −30°, respectively. (d) Far-field angular spectrum for the incident and emitted beams, respectively. (e, f) Schematic of the abnormal refraction in other metasurfaces. Figures are reproduced from (a)–(d) [137], (e) [134], and (f) [138].
(a)
(b)
(c)
(d)
(e)
(f)Although the plasmonic lens is easy to be fabricated, it was only until 2008 that the experimental demonstration of such device was reported [46]. For plane wave illumination, the light was focused at the focal length of 5.3 μm. The excellent agreement between experiment and simulation validated the design principle of this approach. It should be noted that the plasmonic version of abnormal refraction is similar to that in other metasurfaces, as shown in Figures 21(e) and 21(f).More recently, as shown in Figure22, Chen et al. demonstrated that the far-field focusing pattern of planar metal lens could be modulated by slits filled with phase change material (Ge2Sb2Te5, GST) [135]. By varying the crystallization level of GST from 0% to 90%, the Fabry-Pérot resonance supported inside each slit can be spectrally shifted across the working wavelength at 1.55 μm, which results in a transmitted electromagnetic phase modulation as large as 0.56π. Based on this geometrically fixed platform, different phase fronts can be constructed spatially on the lens plane by assigning the designed GST crystallization levels to the corresponding slits, achieving various far-field focusing patterns.Figure 22
(a) Schematic diagram of the planar lens. (b) The cross section showing thex-component of the electric field of the 1st-order mode from a single slit. (c) The evolution of the single-slit transmission spectrum for different crystallization levels. (d) The relative phase and (e) the normalized electric field intensity at 1.55 μm as functions of the crystallization level with a 5% step increment. (f) Focusing pattern measured in x
z-plane by confocal scanning optical microscopy for different status of GST. Figures are reproduced from [135].In 2007, Min et al. investigated a type of metallic nanooptic lens consisting of slits with variant widths, filled with Kerr nonlinear media [139]. As shown in Figure 23(a), each slit is designed to transmit light with specific phase retardation controlled by the intensity of incident light, owing to the nonlinear response. This new lens can actively control the deflection angle and the focus length of output beam. Very recently, Hu et al. proposed an active terahertz (THz) plasmonic lens tuned by an external magnetic field [140]. Different from traditional tunable devices, the proposed active lens is tuned by changing the cyclotron frequency through manipulating magnetoplasmons (MPs). It was shown that THz wave propagating through the designed structure could be focused to a small size spot via the control of MPs. The tuning range of the focal length under the applied magnetic field (up to 1 T) is ~31, about 50% of the original focal length.Figure 23
(a) Schematic view of the three-slit structure under study. (b) and (c) The FDTD simulation of electric field intensityE
2 time-average distribution of beam focusing with a five-slit metallic lens. (d) A semiconductor-insulator-semiconductor structure in a Voigt configuration. The propagation mode is TM polarized, and the magnetic field B is applied along the y-axis. The thickness of the insulator is denoted by w. (e) FDTD-calculated focal length when the external magnetic field is increased from 0 to 1 T. Figures are reproduced from (a)–(c) [139] and (d, e) [140].
(a)
(b)
(c)
(d)
(e)It should be noted that the plasmonic slit lens is polarization selective; that is, only one particularly polarized light beam could be transmitted and modulated in phase, since the SPP is intrinsically polarized. This polarization selectivity has two effects. Firstly, this effect is attractive for some cases where only one polarization type is needed. Secondly, it may become undesired for many other applications. To eliminate this problem, rectangular or circular plasmonic holes were adopted to achieve phase modulation [136, 141]. As illustrated in Figure 24, Ishii et al. experimentally demonstrated a polarization-independent holey-metal lens [136]. They showed that by changing the radii of subwavelength holes in a metallic film, which act as single-mode waveguide elements, they can control the phase of light transmitted through the holes. Finally, it was demonstrated that the focal distance of the lens can be controlled by changing the incident wavelength.Figure 24
(a) Pseudocolor intensity map calculated from the analytical model of the sample. The color scale is normalized to the maximum intensity. The inset shows the beam cross section at the focal point (z
=
10 μm) and the SEM image of the sample. (b) Schematic of a nanowaveguide array that induces wavefront shaping for OAM generation. (c) SEM picture of the nanowaveguide array. Figures are reproduced from [136, 141].
(a)
(b)
(c)More recently, Litchinitser et al. demonstrated that the change of hole radius along the azimuthal direction is able to generate orbital angular momentum (OAM) on the nanoscale. They proposed and experimentally demonstrated that a nanowaveguide array milled in a metal film can be used to control the wavefront of a light beam and that an optical vortex at 532 nm was produced by using such an array (see Figures24(b) and 24(c)).


## 3.5.3. Plasmonic Metasurfaces for Sensing Applications

Owing to the strong light-matter interaction, metasurfaces can provide a robust and efficient platform for biosensing. In particular, the surface plasmon resonance (SPR) at planar surfaces or localized surface plasmon resonance (LSPR) for nanometer-sized metallic structures is accompanied with dramatic local field enhancement [142]. The implication of the local field enhancement is twofold. Firstly, the spectra of the SPR and LSPR are highly dependent on the environment; thus, a little change of refractive index would result in a considerable spectrum shift. Secondly, the local field enhancement can be exploited to achieve surface-enhanced Raman spectroscopy (SERS) [143]. Both of the two mechanisms can be utilized for clinic detection.As shown in Figures25(a)–25(d), Wu et al. introduced an infrared plasmonic surface based on a Fano-resonant metasurface which exhibits sharp resonances caused by the interference between subradiant and superradiant plasmonic resonances [144]. Owing to the asymmetry, the frequency of the subradiant resonance can be precisely determined and matched to the molecule’s vibrational fingerprints. In these Fano resonances, the near-field coupling of plasmonic modes is crucial to enhance the sensitivity [145, 146]. It was also demonstrated that Young’s interference can be observed in plasmonic structures when two or three nanoparticles with separation on the order of the wavelength are illuminated simultaneously by a plane wave. This effect leads to the formation of intermediate-field hybridized modes with a character distinct of those mediated by near-field and/or far-field radiative effects [147].Figure 25
(a) Schematic representation of subradiant (Q) and superradiant (D) modes. (b) Scanning electron microscopy image of a typical fabricated sample. (c) Schematic representations of proteins’ mono- and bilayers binding to the metal surface. (d) Experimental (solid) and theoretical (dashed) polarized reflectivity spectra. (e) SEM image of a fabricated metasurface consisting of hole array. (f) Resonance shift for the subradiant SPP mode with changing NaCl concentration. Figures are reproduced from (a)–(d) [144] and (e, f) [148].
(a)
(b)
(c)
(d)
(e)
(f)In a similar work [148], by exploiting extraordinary light transmission phenomena through high quality factor subradiant dark modes, Yanik et al. experimentally demonstrated high figures of merits (FOMs as high as 162) for intrinsic detection limits surpassing those of the gold standard prism coupled surface plasmon sensors, as illustrated in Figures 25(e) and 25(f).Over the past several years, the absorption effect of plasmonic metasurface has also been exploited in sensing applications. In 2011, Tittl et al. presented a simple design of plasmonic absorber based on palladium nanowires [149]. Due to hydrogen incorporation, palladium undergoes a phase transition from a metal to a metal hydride which leads to an expansion of the palladium lattice. The fabricated structure showed a reflectance of 0.5% which in combination with a complete suppression of transmission yields an absorbance of A
≈
99.5
%. As shown in Figures 26(a)–26(d), they utilized the absorber structure for hydrogen sensing and were able to reliably detect concentration down to 0.5% H2 in air with response time in the range of seconds.Figure 26
(a) A side view of the sensor. Palladium nanowires are stacked above a gold mirror. The layers are separated by a MgF2 film. (b) A sketch of the experimental setup including the mass flow controllers used to set the desired hydrogen concentrations. (c) Simulated response of the sensor structure to hydrogen exposure. (d) Reflectance of the absorber for different hydrogen concentrations. (e) SEM images of split ring resonators (SRRs) on a graphene layer. (f) Experimental results of the Raman spectra for different conditions. Figures are reproduced from (a)–(d) [149] and (e, f) [150].
(a)
(b)
(c)
(d)
(e)
(f)More recently, it was demonstrated that graphene monolayers transferred on arrays of split ring resonators (SRRs) could exhibit resonances in the visible range. As illustrated in Figures26(e) and 26(f), Raman enhancement factors per area of graphene up to 75 were measured, demonstrating the strong plasmonic coupling between graphene and the metasurface resonances.Recently, an important sensing technique via multifrequency antennas was also demonstrated [151–155]. Such antennas can efficiently detect different vibrational modes of molecular species in a window of several micrometers, where informative fingerprint spectra of many molecules are present.Since there have already been many reviews on this topic [34, 142, 143, 156], we only give a small part of examples here. To completely understand the role of metasurface in sensing applications, we would like to suggest that the readers find more information in these literatures.


## 3.6. Surface Plasmon-Inspired Metasurfaces

In previous discussion, metasurfaces refer to arrays of subwavelength structures on thin films. More generally speaking, any kinds of subwavelength structures on such films can be regarded as metasurfaces, with novel applications in optics and electromagnetics. Early in 1998 [157], it was found that extraordinary light transmission can be observed when it passes through the subwavelength metal pinhole arrays (Figure 27). Also, adding a surface groove structure around the subwavelength aperture can break the traditional diffraction limit and achieve highly directional energy transfer with ultrahigh transmission [158].Figure 27
(a) Optical transmission properties of single rectangular hole in metal films. Inset shows the SEM image. (b) Transmission spectrum of hole arrays. The triangular hole array was milled in a 225 nm thick Au film on a glass substrate with an index matching liquid on the air side (hole diameter 170 nm and period 520 nm). (c) SEM image of the bull’s eye structure. (d) Optical properties of the bull’s eye. Figures are reproduced from [65].
(a)
(b)
(c)
(d)Subsequently, Poujet et al. firstly demonstrated an experimental extraordinary optical transmission up to 90% in the subwavelength annular apertures [159]. In spite of the metal loss, the transmission of incident light has been greatly enlarged by employing the guided mode propagating through the annular aperture array. The subwavelength hole arrays can also act as color filters as the wavelength selectivity is directly related to the period of the holes [65]. An array of dimples is prepared by focused-ion-beam milling an Ag film. Some of the dimples were milled through to the other side so that light can be transmitted. When this structure is illuminated with white light, the transmitted colour is determined by the period of the array. In this case, the periods were chosen to be 550 and 450 nm, respectively, to achieve the red and green colours.Afterwards, several research groups including Martin-Moreno et al. [160] analyzed the underlying physics principle of generation of beaming effect in groove surface and pointed out that transmission enhancement of the groove is attributed to three factors as follows: surface plasmon resonance modes in the grooves, phase match of groove secondary radiation, and waveguide modes in the slot. Considering the SPs in metallic structure at the visible range, Luo and Yan established a physics model, namely, quasiperfect conductor model (QPCM), to optimize the directed radiation characteristics of SPPs [34]. In addition to beaming effect, the multidirectional radiation and abnormal homogeneous radiation phenomenon of subwavelength groove structure were also systematically discussed based on the diffraction theory.More recently, the extraordinary transmission and beaming effect based on cycle groove structures were also expanded to other frequency bands. Pendry et al. demonstrated that even a perfect electric conductor can support surface plasmon [56]. In order to distinguish it from traditional SPs, this surface plasmon supported by groove structures in low frequency is named spoof surface plasmon (SSP). Lockyear et al. [161] demonstrated that microwave energy could be coupled into SSPs through the reflective spectrum experiment of grating structure. Lately, Akarca-Biyikli et al. [162] experimentally validated the abnormal transmission and beaming effect in the 1D groove structure. With the beaming effect and extraordinary transmission, groove structures have wide potential applications in various frequency regions, as shown in the following discussion.


### 3.6.1. Surface Plasmon-Inspired Metasurfaces for Microwave Antennas

The directional energy transfer realized in groove structure meets the requirements of high-directivity antennas and a variety of antennas have been proposed in the microwave band. For example, Huang et al. [163] used periodic groove structure in linearly polarized waveguide end slot array antenna. As shown in Figures 28(a) and 28(b), the beam angles in E-plane and H-plane were compressed to be 6 and 13 degrees, respectively. The groove shaped metasurfaces also have great contribution in reducing the level of sidelobes of slot antennas. Huang et al. proposed a method of integrating groove structures with two different periods into slot antenna to obtain low sidelobe radiation (Figures 28(c) and 28(d)). The sidelobe of the antenna with grooves was greatly decreased compared to the slot array without groove structures. Furthermore, after adding the artificial electromagnetic soft-surface structure to one-dimensional subwavelength outer groove, the antenna backward radiation was significantly reduced by 10 dB. However, the antenna gain was only increased by 0.2 dB due to long distance between the edge groove and the central feed.Figure 28
(a) Groove antennas based on slot array. (b) TheE-plane radiation pattern for the antenna in (a). (c) Patch antennas loaded with the groove structure. (d) The E-plane radiation pattern for the antenna in (c). (e) Slot array antenna with low coupling. (f) Coupling efficiency of the antenna in (c). Figures are reproduced from [163].
(a)
(b)
(c)
(d)
(e)
(f)For the characteristics of low cost, light weight, and low profile, microstrip patch antenna has gotten a great prospect on the area of military and civilian applications. However, due to the deterioration of surface wave, the antenna’s radiation efficiency is very low, and this restricts its development. Ying and Kildal [164] improved the radiation performance of the antenna through an artificial electromagnetic soft-surface groove onto a ground.The groove structures can also be loaded between slot elements to achieve low coupling between the slots and thus obtain high aperture efficiency of the slot antenna arrays. The cross-coupling between the two slots was sharply decreased by 30 dB after loading the groove structure, as shown in Figures28(e) and 28(f). Furthermore, after introducing groove structure, the gain of slot antenna array was enhanced by 4 dB, and the sidelobe level on E-plane is low and main lobe on H-plane is compressed.The period of a traditional beaming effect based groove structure is approximate to the wavelength, and the beaming effect usually requires several periods to implement. Thus, they make the size of the whole antenna very large and bring about the low utilization of aperture. Therefore, with no sacrifice of the antenna performance, how to reduce the groove cycle has formed a research direction.Huang et al. have still taken account for the loading of high dielectric constant medium between the grooves to reduce the groove cycle equivalently. Both single slot antenna and two-dimensional slot antenna array loaded dielectric medium with high permittivity were analyzed. The operating frequency of this antenna is 14.5 GHz, and the rectangular waveguide end slots were used as the exciting source. The dielectric constant loaded between the two neighboring grooves was 11.9, and the thickness of the loaded media silicon was 1.1 mm. The introduction of the traditional cycle-groove structure has no effect on antenna’s resonant frequency, while the medium-loading groove structure makes the center resonant point of the antenna shift to the low frequency, and it has a certain impact on antenna input matching. However, the slot antenna can be kept atS
11 < −10 dB by tuning the slot length in the working frequency, meeting the needs of practical engineering. The gain of a traditional cycle-groove slot antenna is 15.11 dB, increasing by about 9 dB compared to the flat-panel slot antenna. However, the antenna gain has further improved by 3 dB after the medium-loading groove structure is used, reaching 18.29 dB. It is notable that the physical diameter of the designed antenna is smaller than the size of a traditional cycle-groove slot antenna, only three-quarters of it, but the gain has improved more significantly instead. From the radiation patterns, we can also find that the E-plane of a traditional cycle-groove antenna shows an obvious beaming effect.This medium-loading method can also increase the performance of two-dimensional slot antenna array. This idea broke through the limit that the traditional array element interval is less than wavelength to widen applications of the periodic groove structure. Afterwards, media with high dielectric constant were loaded between the grooves to reduce the groove cycle equivalently without sacrificing of the antenna performance. This method featured in smaller periods compared to the traditional periodic groove structures, which results in reduced antenna aperture and inspiring more surface wave to improve further antenna gain in the performance of the antenna radiation. Furthermore, it compresses the beam angles of sidesE and H to illustrate prominent directed radiation ability. So it can be considered that the application of this new periodic groove structure was a development direction of high-directionality antenna. It was the first time to use a periodic groove structure as a secondary source and load it between the slot array elements with interval greater than wavelength to avoid sidelobe. This idea broke through the limit that the traditional array element interval is less than wavelength to widen the applications of the periodic groove structure.


### 3.6.2. Surface Plasmon-Inspired Metasurfaces for Applications in Terahertz and Mid-Infrared Regions

One of the disadvantages of the grooves for directive radiation is that the working bandwidth is limited. Nevertheless, this is not a series problem for some applications. For instance, almost all kinds of lasers are narrowband in spectrum. In this regard, the groove structures can be integrated to lasers in order to improve their performances. By defining a metallic subwavelength slit and groove array on the facet of quantum cascade lasers (QCLs) [165], the divergence angle in the laser polarization direction is only 2.4 degrees as shown in Figure 29. Compared to the original 9.9 μm wavelength laser without a groove array, a reduction in beam spread by a factor of 25 is achieved, without significant reductions in output power. Taking advantage of SSPs, groove array integrated terahertz QCLs were also demonstrated [166]. The beam divergence of the lasers was reduced from ~180 degrees to ~10 degrees, the directivity was improved by over 10 decibels, and the power collection efficiency was increased by a factor of about six compared to the original unpatterned devices. In addition, multibeam QCLs and MID-IR QCLs with integrated plasmonic polarizers were reported through combining the groove structures with QCLs by Capasso’s group [167].Figure 29
(a) Schematic of the small-divergence laser, which comprises a QCL and a metallic slit-grating structure defined on its facet. (b, c) Cross sections of the two device designs. (d) 2D simulation of the intensity distribution of a small-divergence QCL of the second design lasing atλ
=
9.9 μm. (e) Calculated far-field intensity distribution of the device shown in (d); inset: enlarged view of the central lobe. (f) Measured 2D far-field intensity of device B patterned with the slit-grating structure. Figures are reproduced from [165].
(a)
(b)
(c)
(d)
(e)
(f)


### 3.6.3. Surface Plasmon-Inspired Metasurfaces for Applications in the Visible and Near-Infrared Regime

The intriguing properties of plasmonic waves at metasurfaces can also be utilized to enhance the directivity of classically noncoherent or not-directive radiations. For example, spontaneous emission of fluorescent molecules or quantum dots is radiated along all directions when emitters are diluted in a liquid solution, which severely limits the amount of collected light. Making use of the directional manipulation of the SP-inspired metasurface, Aouani et al. [168] successfully controlled the radiation properties for nanoemitters, as shown in Figure 30. Enhancing the fluorescence intensity and narrowing the emission directivity were simultaneously obtained, and a full control of fluorescence was achieved. However this control is static. In 2011, active control over fluorescent emission was also reported by electrically pumping the similar light-emitting device [169]. This type of device facilitates the realization of a new class of active manipulation for use in new optical sources and a wide range of nanoscale optical spectroscopy applications.Figure 30
Directional radiation of fluorescent molecules. (a) SEM image of the fabricated nanoaperture with five corrugations. (b) Configuration to enhance and control the fluorescence emission of molecules diffusing in the central aperture. (c, d) Radiation patterns (intensity distribution in the back focal plane of the 1.2 NA objective) for a single nanoaperture without (a) and with (b) periodic corrugations. (e) Fluorescence intensity enhancement per single molecule as function of the emission polar angle, relative to the open solution reference case. (f) Angular radiation patterns in the polar angle. Figures are reproduced from [168].
(a)
(b)
(c)
(d)
(e)
(f)In addition to the directional manipulating and transmission enhancing, the applications of groove type SP-inspired metasurface were greatly expanded recently. Orbital angular momentum (OAM) transfer [170] and wavefront shaping [171] were experimentally demonstrated. Chiral plasmonic grooves defined on a metallic film would transform a normal plane wave to the vortex beams with tunable topological charge, as shown in Figures 31(a)–31(c). By surface-wave-holography method, Chen et al. shaped the wavefront of the incident near-infrared light into predesignated complex patterns such as Latin letters, after passing through a 180 nm radius hole that is surrounded by well-designed groove patterns, as depicted in Figures 31(d)–31(g).Figure 31
OAM generation and wavefront shaping by groove type SP-inspired metasurface. (a) Experimental setup of the OAM generation. (b) SEM image of the sample. (c) Intensity distribution imaged through the sample. (d, e) SEM images of the holographic metasurfaces. (f, g) Simulated images of the holographic images. Figures are reproduced from (a)–(c) [170] and (d)–(g) [171].
(a)
(b)
(c)
(d)
(e)
(f)
(g)More recently, we provided a scheme to guide and collimate OAM at the micro- and nanolevels [172]. The coaxial plasmonic waveguide is exploited as a naturally occurring medium for light carrying OAM to transfer. The guided OAM wave is coupled to free space through corrugated grooves surrounding the coaxial waveguide, where coherent scattering of spiral surface plasmon was demonstrated to be responsible for the huge enhancement of beam directivity. Experimental results at λ
=
532 nm validated the near-field transportation of OAM beams, where the topological charge is tunable via the modulation of a liquid crystal spatial light modulator (SLM).


## 3.6.1. Surface Plasmon-Inspired Metasurfaces for Microwave Antennas

The directional energy transfer realized in groove structure meets the requirements of high-directivity antennas and a variety of antennas have been proposed in the microwave band. For example, Huang et al. [163] used periodic groove structure in linearly polarized waveguide end slot array antenna. As shown in Figures 28(a) and 28(b), the beam angles in E-plane and H-plane were compressed to be 6 and 13 degrees, respectively. The groove shaped metasurfaces also have great contribution in reducing the level of sidelobes of slot antennas. Huang et al. proposed a method of integrating groove structures with two different periods into slot antenna to obtain low sidelobe radiation (Figures 28(c) and 28(d)). The sidelobe of the antenna with grooves was greatly decreased compared to the slot array without groove structures. Furthermore, after adding the artificial electromagnetic soft-surface structure to one-dimensional subwavelength outer groove, the antenna backward radiation was significantly reduced by 10 dB. However, the antenna gain was only increased by 0.2 dB due to long distance between the edge groove and the central feed.Figure 28
(a) Groove antennas based on slot array. (b) TheE-plane radiation pattern for the antenna in (a). (c) Patch antennas loaded with the groove structure. (d) The E-plane radiation pattern for the antenna in (c). (e) Slot array antenna with low coupling. (f) Coupling efficiency of the antenna in (c). Figures are reproduced from [163].
(a)
(b)
(c)
(d)
(e)
(f)For the characteristics of low cost, light weight, and low profile, microstrip patch antenna has gotten a great prospect on the area of military and civilian applications. However, due to the deterioration of surface wave, the antenna’s radiation efficiency is very low, and this restricts its development. Ying and Kildal [164] improved the radiation performance of the antenna through an artificial electromagnetic soft-surface groove onto a ground.The groove structures can also be loaded between slot elements to achieve low coupling between the slots and thus obtain high aperture efficiency of the slot antenna arrays. The cross-coupling between the two slots was sharply decreased by 30 dB after loading the groove structure, as shown in Figures28(e) and 28(f). Furthermore, after introducing groove structure, the gain of slot antenna array was enhanced by 4 dB, and the sidelobe level on E-plane is low and main lobe on H-plane is compressed.The period of a traditional beaming effect based groove structure is approximate to the wavelength, and the beaming effect usually requires several periods to implement. Thus, they make the size of the whole antenna very large and bring about the low utilization of aperture. Therefore, with no sacrifice of the antenna performance, how to reduce the groove cycle has formed a research direction.Huang et al. have still taken account for the loading of high dielectric constant medium between the grooves to reduce the groove cycle equivalently. Both single slot antenna and two-dimensional slot antenna array loaded dielectric medium with high permittivity were analyzed. The operating frequency of this antenna is 14.5 GHz, and the rectangular waveguide end slots were used as the exciting source. The dielectric constant loaded between the two neighboring grooves was 11.9, and the thickness of the loaded media silicon was 1.1 mm. The introduction of the traditional cycle-groove structure has no effect on antenna’s resonant frequency, while the medium-loading groove structure makes the center resonant point of the antenna shift to the low frequency, and it has a certain impact on antenna input matching. However, the slot antenna can be kept atS
11 < −10 dB by tuning the slot length in the working frequency, meeting the needs of practical engineering. The gain of a traditional cycle-groove slot antenna is 15.11 dB, increasing by about 9 dB compared to the flat-panel slot antenna. However, the antenna gain has further improved by 3 dB after the medium-loading groove structure is used, reaching 18.29 dB. It is notable that the physical diameter of the designed antenna is smaller than the size of a traditional cycle-groove slot antenna, only three-quarters of it, but the gain has improved more significantly instead. From the radiation patterns, we can also find that the E-plane of a traditional cycle-groove antenna shows an obvious beaming effect.This medium-loading method can also increase the performance of two-dimensional slot antenna array. This idea broke through the limit that the traditional array element interval is less than wavelength to widen applications of the periodic groove structure. Afterwards, media with high dielectric constant were loaded between the grooves to reduce the groove cycle equivalently without sacrificing of the antenna performance. This method featured in smaller periods compared to the traditional periodic groove structures, which results in reduced antenna aperture and inspiring more surface wave to improve further antenna gain in the performance of the antenna radiation. Furthermore, it compresses the beam angles of sidesE and H to illustrate prominent directed radiation ability. So it can be considered that the application of this new periodic groove structure was a development direction of high-directionality antenna. It was the first time to use a periodic groove structure as a secondary source and load it between the slot array elements with interval greater than wavelength to avoid sidelobe. This idea broke through the limit that the traditional array element interval is less than wavelength to widen the applications of the periodic groove structure.


## 3.6.2. Surface Plasmon-Inspired Metasurfaces for Applications in Terahertz and Mid-Infrared Regions

One of the disadvantages of the grooves for directive radiation is that the working bandwidth is limited. Nevertheless, this is not a series problem for some applications. For instance, almost all kinds of lasers are narrowband in spectrum. In this regard, the groove structures can be integrated to lasers in order to improve their performances. By defining a metallic subwavelength slit and groove array on the facet of quantum cascade lasers (QCLs) [165], the divergence angle in the laser polarization direction is only 2.4 degrees as shown in Figure 29. Compared to the original 9.9 μm wavelength laser without a groove array, a reduction in beam spread by a factor of 25 is achieved, without significant reductions in output power. Taking advantage of SSPs, groove array integrated terahertz QCLs were also demonstrated [166]. The beam divergence of the lasers was reduced from ~180 degrees to ~10 degrees, the directivity was improved by over 10 decibels, and the power collection efficiency was increased by a factor of about six compared to the original unpatterned devices. In addition, multibeam QCLs and MID-IR QCLs with integrated plasmonic polarizers were reported through combining the groove structures with QCLs by Capasso’s group [167].Figure 29
(a) Schematic of the small-divergence laser, which comprises a QCL and a metallic slit-grating structure defined on its facet. (b, c) Cross sections of the two device designs. (d) 2D simulation of the intensity distribution of a small-divergence QCL of the second design lasing atλ
=
9.9 μm. (e) Calculated far-field intensity distribution of the device shown in (d); inset: enlarged view of the central lobe. (f) Measured 2D far-field intensity of device B patterned with the slit-grating structure. Figures are reproduced from [165].
(a)
(b)
(c)
(d)
(e)
(f)


## 3.6.3. Surface Plasmon-Inspired Metasurfaces for Applications in the Visible and Near-Infrared Regime

The intriguing properties of plasmonic waves at metasurfaces can also be utilized to enhance the directivity of classically noncoherent or not-directive radiations. For example, spontaneous emission of fluorescent molecules or quantum dots is radiated along all directions when emitters are diluted in a liquid solution, which severely limits the amount of collected light. Making use of the directional manipulation of the SP-inspired metasurface, Aouani et al. [168] successfully controlled the radiation properties for nanoemitters, as shown in Figure 30. Enhancing the fluorescence intensity and narrowing the emission directivity were simultaneously obtained, and a full control of fluorescence was achieved. However this control is static. In 2011, active control over fluorescent emission was also reported by electrically pumping the similar light-emitting device [169]. This type of device facilitates the realization of a new class of active manipulation for use in new optical sources and a wide range of nanoscale optical spectroscopy applications.Figure 30
Directional radiation of fluorescent molecules. (a) SEM image of the fabricated nanoaperture with five corrugations. (b) Configuration to enhance and control the fluorescence emission of molecules diffusing in the central aperture. (c, d) Radiation patterns (intensity distribution in the back focal plane of the 1.2 NA objective) for a single nanoaperture without (a) and with (b) periodic corrugations. (e) Fluorescence intensity enhancement per single molecule as function of the emission polar angle, relative to the open solution reference case. (f) Angular radiation patterns in the polar angle. Figures are reproduced from [168].
(a)
(b)
(c)
(d)
(e)
(f)In addition to the directional manipulating and transmission enhancing, the applications of groove type SP-inspired metasurface were greatly expanded recently. Orbital angular momentum (OAM) transfer [170] and wavefront shaping [171] were experimentally demonstrated. Chiral plasmonic grooves defined on a metallic film would transform a normal plane wave to the vortex beams with tunable topological charge, as shown in Figures 31(a)–31(c). By surface-wave-holography method, Chen et al. shaped the wavefront of the incident near-infrared light into predesignated complex patterns such as Latin letters, after passing through a 180 nm radius hole that is surrounded by well-designed groove patterns, as depicted in Figures 31(d)–31(g).Figure 31
OAM generation and wavefront shaping by groove type SP-inspired metasurface. (a) Experimental setup of the OAM generation. (b) SEM image of the sample. (c) Intensity distribution imaged through the sample. (d, e) SEM images of the holographic metasurfaces. (f, g) Simulated images of the holographic images. Figures are reproduced from (a)–(c) [170] and (d)–(g) [171].
(a)
(b)
(c)
(d)
(e)
(f)
(g)More recently, we provided a scheme to guide and collimate OAM at the micro- and nanolevels [172]. The coaxial plasmonic waveguide is exploited as a naturally occurring medium for light carrying OAM to transfer. The guided OAM wave is coupled to free space through corrugated grooves surrounding the coaxial waveguide, where coherent scattering of spiral surface plasmon was demonstrated to be responsible for the huge enhancement of beam directivity. Experimental results at λ
=
532 nm validated the near-field transportation of OAM beams, where the topological charge is tunable via the modulation of a liquid crystal spatial light modulator (SLM).


## 3.7. Passive Metasurface Antennas and Generalized Snell’s Law

In many cases, metasurfaces can be considered as passive antennas array. By tuning the geometries and material parameters, the amplitude, phase, and polarization state of the reradiation of these antennas can be fully controlled. In this section, we first review two kinds of phase-type metasurfaces, where only the phase is tuned. Then, the possibility of full control over the phase, polarization, and amplitude is discussed.


### 3.7.1. Passive Antenna Array Based on Impedance Transition

The impedance boundary conditions of metasurfaces can be utilized to tailor the phase delay within one single layer regardless of its thickness. This means that, theoretically, there exists no thickness limit for this problem. Based on the rigorous form of Huygens’ principle developed by Love and Schelkunoff [173, 174], it has been demonstrated that the transmitted or reflected phase shift can vary between 0 and 2
π to provide complete phase coverage by adjusting the magnitude of the impedance [19, 175, 176].As depicted in Figure32, the concept of Huygens’ metasurface was proposed by Pfeiffer and Grbic in 2013 [176] and realized with two-dimensional arrays of subwavelength structures that provide both electric and magnetic polarization currents to generate the prescribed wavefronts. The applications of the metasurfaces in a beam-refracting surface and a Gaussian-to-Bessel beam transformer were discussed.Figure 32
(a) Principle of the Huygens metasurface. The fields in regions I and II are defined independently of each other, and the surface equivalence principle is employed to find the fictitious electric and magnetic surface currents that satisfy the boundary conditions at the metasurfaces. (b) Simulated time snapshot of the magnetic field (Hz) of ay-polarized plane wave, normally incident upon the designed Huygens’ surface. (c) Dimensions of the unit cells comprising Huygens’ metasurface. (d) SEM images of the optical Huygens’ surfaces. (e) Perspective view of an optically thin, isotropic Huygens’ metasurface that efficiently refracts a normally incident beam at telecommunication wavelengths. (f) Time snapshot of the steady-state, y-polarized electric field when a plane wave is normally incident from the bottom at a wavelength of 1.5 μm. The incident electric field has an amplitude of 1 V/m. Figures are reproduced from [176, 181].
(a)
(b)
(c)
(d)
(e)
(f)As an attempt to increase the energy efficiency and bandwidth, we presented an efficient approach, as depicted in Figure33, to extend the bandwidth of phase modulation by utilizing the broadband characteristic of low-quality factor (Q-factor) metasurface in the reflection mode [177]. The dispersion of the metasurface was engineered to achieve phase modulation within [
0
,
360
°
]. Anomalous nearly perfect reflection with relative bandwidth near 40% was demonstrated in the microwave regime. Similar designs in reflection geometry have also been validated by other authors [178–180].Figure 33
Reflection phases for different values of gap widthg for thickness of (a) d = 2 mm and (b) d = 6 mm. The other geometrical parameters are chosen as l = 4 mm and w = 0.2 mm. (c) y-component and (d) z-component of electric fields for d = 2 mm, g = 2.8 mm, and f = 10 GHz. (e) y-component and (f) z-component of electric fields for d = 6 mm, g = 2.8 mm, and f = 10 GHz. (g) Schematic of the gradient metasurface. (h) Electric field E
y distribution in the scattering region at normal incidence for 8, 8.5, 9, 9.5, 10, and 10.5 GHz. The dashed black arrows indicate the propagation direction evaluated by sin
-
1
⁡
(
k
x
/
k
). Figures are reproduced from [19].
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)


### 3.7.2. Passive Antenna Array Based on Ultrathin Resonators

In the phase-engineering regime, one interesting but sometimes neglected phenomenon is that a rotation of electric field of circular polarized electromagnetic wave results in a corresponding phase shift. As early as 1955, the rotatory phase shifter was proposed by Sichak and Levine [182]. They showed that the phase of the output voltage of a circularly polarized antenna was proportional to the angle of rotation of the antenna about its longitudinal axis. Two circularly polarized antennas with a proper rotation angle between each other were mounted in a circular waveguide to construct a phase shifter. In 1961, this rotatory phase was utilized in the construction of large radio telescope in the University of Illinois [183]. Subsequently, similar phase shifting results were demonstrated for passive reflectarray antennas [184].In 1984, Berry proposed that an adiabatic polarization can introduce a phase shift [43], which was further experimentally demonstrated in 1988 [185]. Since the phase is associated with circular polarization, it can be termed as one kind of optical spin-orbit interaction. In 1999, polarization gratings were proposed [186]. This idea was further developed by Hasman et al., with various kinds of applications, such as beam splitter, optical vortex generation, and focusing lens [44, 187–189]. In 2006, the famous q-plates were proposed to realize spin-to-orbital angular momentum conversion [190]. These q-plates can also be used as polarization converters [191]. In recent years, nanoantennas were widely adopted to control circularly polarized waves [192–195].In 2011, Yu et al. proposed another phase shifting mechanism with linearly polarized illumination. As shown in Figure34, by varying the angle and length of V-shaped nanoantennas, arbitrary modulation of phase shift and amplitude transmission were demonstrated. The operational principle of such V-shaped antennas relies on the asymmetric transmission enabled by the nanoantennas. Similar to the case of circular polarization, such antennas have low energy efficiency because there always exists one component with the same polarization as the incident beam. Based on this abrupt phase change, they proposed the so-called “generalized Snell’s law.” By properly tuning the geometrical parameters of each antenna, broadband phase change could be achieved, although the phase was not rigorously achromatic [134, 138, 196].Figure 34
(a) SEM image of a representative antenna array fabricated on a silicon wafer. (b) Schematic experimental setup fory-polarized excitation. ((c) and (d)) Measured far-field intensity profiles for the y- and x-polarized excitations, respectively. (e) Schematic view of a representative antenna array. (f) Scanning electron microscope images of the unit cells of four antenna arrays with different periodicities fabricated on a single silicon wafer. ((g) and (h)) The false-color maps indicate the experimentally measured relative intensity profiles for the antenna array. Figures are reproduced from [134, 138].After the pioneering work by Capasso, much work was devoted to the design of phase-discontinuity metasurfaces. Many optical devices were subsequently designed and experimentally demonstrated. For example, Zhang et al. proposed that C-shape metallic elements can also be utilized to tune the amplitude and phase of cross-polarized scattering for linear polarization incidence [196]. In addition to the simple phase-engineering, other applications, such as spiral phase plates and wave plates, were also demonstrated [197, 198].Based on the locality of the phase shift [199], Lin et al. extended the V-shaped antennas in the near-infrared bands. The focus length was also decreased to a large extent to obtain a focus spot close to the diffraction limit. Jiang et al. demonstrated similar effect in the terahertz regime [200]. More recently, Ma et al. used a metasurface to focus vortex beam into a nanodoughnut [201]. As shown in Figures 35(a)–35(d), the proposed metasurface has good performance close to the ideal case. The metasurface tuned the phase distribution of the incident beam based on the concept of discontinuous phase modulation. Consequently, the proposed metasurface has two main functions. Firstly, with a circularly polarized incident beam, the metasurface converts it into a beam carrying OAM. Secondly, the incident field can be focused into a point with a certain focus length. The total energy coefficient of this metasurface exceeds 40%. By properly designing the phase modulation distribution, the copolarized component of the incident field does not participate in the focusing process. Therefore, only optical vortex can be observed in the focused field. The thickness of this planar chiral metasurface is much less than the operational wavelength and thus has potential application in compact integrated optical systems.Figure 35
(a) Schematic of the 2D elliptic antennas array. (b) SEM image of the elliptic antennas. (c) Measured power intensity profile of the focused field in thex
z-plane. (d) The simulated (dashed lines) and measured (solid lines) intensity spectra of the focused field, respectively, along the y-direction. (e) Schematic of the unit cell of rectangular aperture in metallic screen for holography. (f) Amplitude and phase transmission for various rotation angles. (g) SEM image of the sample. (h) Schematic of the measurement setup. Figures are reproduced from [201].
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)The geometric phase in aperture array has direct application in holography. As demonstrated in Figures35(e)–35(h), metasurface with metallic square apertures was constructed in our lab to form a hologram image of a China map based on the concept of discontinuous phase modulation in visible band.Since only part of the transmitted light takes geometric phase, single layered metasurfaces are often characterized by low efficiency. In principle, the efficiency could be increased dramatically with the help of a reflective layer. Taking the circularly polarized geometric phase as an example, the combination of an anisotropic metasurface with a reflective layer would form a reflective wave plate. By rotating the main axis of the embedded antennas, gradient phase could be directly obtained. This technique was utilized in reflectarray to increase the gain of antenna while keeping the reflective surface to be flat [184]. In the optical regime, the reflective nanoantennas array was used as building blocks of high efficient holograms [202]. The metasurface has an ultrathin and uniform thickness of 30 nm and is compatible with scalar diffraction theory, even with subwavelength pixel sizes, thus simplifying the design of holograms.Another important application of the metasurface relies on the fact that phase shifting metasurfaces placed at the optical pupil plane can increase the resolution of telescopes, which means that the far-field diffraction limit can be overcome [203]. As shown in Figure 36, the designed metasurface has several rings, which exert phase shift of 0 and π on the incoming light and change the corresponding spatial frequency [2]. To characterize the performance, we measured the images of two circular and triangular holes with and without the metasurface. After the insertion of the metasurface, the resolution is decreased to 0.625 times of the original value, implying that a 10-meter telescope could have the same resolution as that of a 16-meter one (i.e., a 1.6 times improvement in the resolution power).Figure 36
Far-field superresolution based on metasurface. (a) Schematic of the experimental setup. The inset shows the phase distribution of the metasurface. Gray regions and white regions indicate 0 andπ, respectively. (b) Experimental results for a circular hole at wavelength of λ = 532 nm. (c) Simulation results for a triangular hole. Figures are reproduced from [2].
(a)
(b)
(c)Very recently [204], we proposed and demonstrated the concept of broadband virtual shaping at the visible, infrared, and microwave spectrum by tailoring the spatiotemporal property of spin-orbit interaction in cascaded metasurfaces. When electromagnetic waves impinge on the designed metasurface, they are reflected to predefined directions to avoid being detected by unwanted antennas. Resorting to the dispersion engineering techniques in metasurface-based polarizers, the bandwidth was dramatically enhanced, although the thickness-to-bandwidth ratio may be analogous to that of broadband absorber. The design principle provided a new route for the control of electromagnetic wave for applications ranging from laser beam shaping to 3D holographic display and conformal camouflage [205].As shown in Figures37(a) and 37(b), we measured the specular reflection of an inhomogeneous metasurface. Since the reflected light was designed to depart from its original direction via the metasurface-assisted law reflection, only a small reflection echo was measured. Owing to the flexibility of the metasurface, this approach could be utilized in complex objects. For example, the RCS of a cylinder can be dramatically reduced by covering our metasurfaces on it (Figure 37(c)). The metallic cylinder in our design has a radius of R = 90 mm and height of h = 360 mm. The geometric phase distribution on the metasurface was designed to be Ф
=
k
z
z
+
k
φ
φ, where k
z
=
k
φ
=
104.7 rad/m. As shown in Figure 37(d), the RCS reductions for TE polarization and TM polarization were calculated under normal incidence along the y-direction. We noted that the reduction amount is a bit smaller than the planar case, which possibly stems from the nonoptimized phase profile and the fact that the RCS of a cylinder itself is smaller than its planar counterpart. Nevertheless, the conformal metasurfaces provide a new sight into the virtual shaping of nonplanar objects. In addition, this approach can be exploited to increase or decrease the RCS.Figure 37
(a) Schematic of the measurement setup. (b) Measured results for both TE polarization and TM polarization. The inset shows the photography of the fabricated sample. (c) Schematic of the spin-orbit conversion in the curved metasurface on a metallic cylinder. The insets show the definitions of TE polarization and TM polarization. (d) Calculated broadband RCS reduction for TE polarization and TM polarization at normal incidence alongy-direction. Figures are reproduced from [204].
(a)
(b)
(c)
(d)In general, the metallic metasurfaces suffer from low efficiency due to the intrinsic ohmic loss and the limited scattering cross sections of the antennas, which is not anticipated in many realms. Recently, dielectric metasurfaces based on geometric phase were presented to control the phase [44]. Nevertheless, the discrete phases lead to degradation of the performance. To overcome this issue, we proposed a semicontinuous structure to increase the continuity of phase shift. The metasurfaces consist of high-refractive-index and low-loss silicon annual ring gratings. Ohmic loss is avoided compared to its metallic counterpart. The continuity of annual ring grating ensures the continuity of the transmitted field, thus suppressing high order diffraction effects that may arise from discontinuity.At the end of this section, we would like to comment that metasurface with geometric phase could enable many applications in distinct disciplines. In general, traditional refractive, reflective, and diffractive devices could be replaced by metasurfaces. These elements include the spherical lenses, aspherical lenses, parabolic reflectors, fan-out grating, and laser beam shapers. In the microwave regime, metasurfaces could also be utilized to substitute traditional phased-array antenna. Furthermore, this kind of metasurface is also able to shift the momentum of scanning beam to extend the scanning range of phased array antennas, when it is integrated in radar radomes [206].


### 3.7.3. Full Control of Phase, Polarization, and Amplitude

In many applications, the phase, polarization state, and amplitude are all important for the manipulation of electromagnetic waves. For example, a low side-lobe phased array antenna needs the full control of phase and amplitude [207], while a planar lens with large longitudinal fields in the focus spots requires that the polarization and phase be simultaneously controlled [208].In order to achieve complete modulation of phase and polarization, Pfeiffer and Grbic proposed a four-layer cascaded metasurface lens that can focus light and control its polarization [209]. By adjusting the dimensions of structure, one can independently adjust the inductance and capacitance in the x- and y-directions so that the phase and polarization can be completely controlled.Kim et al. demonstrated that the local reflection coefficients of gap-plasmon resonators can be independently tailored in both magnitude and phase [181]. Using an array of nanorods closely placed on a metallic layer, it was shown that the magnitude and phase of the surface’s local reflection coefficients can be simultaneously tuned, with a magnitude range of [
0,0.67
] and a phase range of 360°. The power efficiency can reach 45% for an operational wavelength of 800 nm. This method was utilized in the design of a Dolph-Tschebyscheff array, with equal-amplitude sidelobes of prescribed magnitude, as represented in Figures 38(a)–38(d).Figure 38
(a) Magnitude and (b) phase ofS
11 in degrees for different resonator lengths and rotation angles. (c, d) Radiation patterns of (a) Dolph-Tschebyscheff and (b) uniform arrays. Both arrays redirect the normally incident plane wave at 33°. (e) Schematics of the top and bottom nanoapertures forming the super-unit-cell in the plasmonic metasurfaces for the demonstration of anomalous refraction. (f) The transmission phase and amplitude of each nanoaperture pair, calculated under y-polarized incident light at 900 nm. (g) SEM image of the sample (left panel) and measured refraction angle (right panel). Figures are reproduced from [181, 210].
(a)
(b)
(c)
(d)
(e)
(f)
(g)More recently, Li et al. proposed and validated another metasurface that can provide simultaneous manipulation of the phase and polarization of the transmitted light [210]. SPPs were adopted to obtain a π phase shift when the top and bottom nanoapertures are laterally translated by a distance in the y-direction. Hence, the phase difference can cover 0 to 2
π by varying the parameters of nanoaperture for normally incident light polarized in the y-direction. The metasurface enabled anomalous refraction with efficiency of about 21.4% for linearly polarized incident light (Figures 38(c)–38(g)).It also should be noted that the phase over the surface of micro- and nanoantennas can also be measured with the help of scattering near-field techniques [211, 212], which provide a way to further understand the physical processes of these antennas.


## 3.7.1. Passive Antenna Array Based on Impedance Transition

The impedance boundary conditions of metasurfaces can be utilized to tailor the phase delay within one single layer regardless of its thickness. This means that, theoretically, there exists no thickness limit for this problem. Based on the rigorous form of Huygens’ principle developed by Love and Schelkunoff [173, 174], it has been demonstrated that the transmitted or reflected phase shift can vary between 0 and 2
π to provide complete phase coverage by adjusting the magnitude of the impedance [19, 175, 176].As depicted in Figure32, the concept of Huygens’ metasurface was proposed by Pfeiffer and Grbic in 2013 [176] and realized with two-dimensional arrays of subwavelength structures that provide both electric and magnetic polarization currents to generate the prescribed wavefronts. The applications of the metasurfaces in a beam-refracting surface and a Gaussian-to-Bessel beam transformer were discussed.Figure 32
(a) Principle of the Huygens metasurface. The fields in regions I and II are defined independently of each other, and the surface equivalence principle is employed to find the fictitious electric and magnetic surface currents that satisfy the boundary conditions at the metasurfaces. (b) Simulated time snapshot of the magnetic field (Hz) of ay-polarized plane wave, normally incident upon the designed Huygens’ surface. (c) Dimensions of the unit cells comprising Huygens’ metasurface. (d) SEM images of the optical Huygens’ surfaces. (e) Perspective view of an optically thin, isotropic Huygens’ metasurface that efficiently refracts a normally incident beam at telecommunication wavelengths. (f) Time snapshot of the steady-state, y-polarized electric field when a plane wave is normally incident from the bottom at a wavelength of 1.5 μm. The incident electric field has an amplitude of 1 V/m. Figures are reproduced from [176, 181].
(a)
(b)
(c)
(d)
(e)
(f)As an attempt to increase the energy efficiency and bandwidth, we presented an efficient approach, as depicted in Figure33, to extend the bandwidth of phase modulation by utilizing the broadband characteristic of low-quality factor (Q-factor) metasurface in the reflection mode [177]. The dispersion of the metasurface was engineered to achieve phase modulation within [
0
,
360
°
]. Anomalous nearly perfect reflection with relative bandwidth near 40% was demonstrated in the microwave regime. Similar designs in reflection geometry have also been validated by other authors [178–180].Figure 33
Reflection phases for different values of gap widthg for thickness of (a) d = 2 mm and (b) d = 6 mm. The other geometrical parameters are chosen as l = 4 mm and w = 0.2 mm. (c) y-component and (d) z-component of electric fields for d = 2 mm, g = 2.8 mm, and f = 10 GHz. (e) y-component and (f) z-component of electric fields for d = 6 mm, g = 2.8 mm, and f = 10 GHz. (g) Schematic of the gradient metasurface. (h) Electric field E
y distribution in the scattering region at normal incidence for 8, 8.5, 9, 9.5, 10, and 10.5 GHz. The dashed black arrows indicate the propagation direction evaluated by sin
-
1
⁡
(
k
x
/
k
). Figures are reproduced from [19].
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)


## 3.7.2. Passive Antenna Array Based on Ultrathin Resonators

In the phase-engineering regime, one interesting but sometimes neglected phenomenon is that a rotation of electric field of circular polarized electromagnetic wave results in a corresponding phase shift. As early as 1955, the rotatory phase shifter was proposed by Sichak and Levine [182]. They showed that the phase of the output voltage of a circularly polarized antenna was proportional to the angle of rotation of the antenna about its longitudinal axis. Two circularly polarized antennas with a proper rotation angle between each other were mounted in a circular waveguide to construct a phase shifter. In 1961, this rotatory phase was utilized in the construction of large radio telescope in the University of Illinois [183]. Subsequently, similar phase shifting results were demonstrated for passive reflectarray antennas [184].In 1984, Berry proposed that an adiabatic polarization can introduce a phase shift [43], which was further experimentally demonstrated in 1988 [185]. Since the phase is associated with circular polarization, it can be termed as one kind of optical spin-orbit interaction. In 1999, polarization gratings were proposed [186]. This idea was further developed by Hasman et al., with various kinds of applications, such as beam splitter, optical vortex generation, and focusing lens [44, 187–189]. In 2006, the famous q-plates were proposed to realize spin-to-orbital angular momentum conversion [190]. These q-plates can also be used as polarization converters [191]. In recent years, nanoantennas were widely adopted to control circularly polarized waves [192–195].In 2011, Yu et al. proposed another phase shifting mechanism with linearly polarized illumination. As shown in Figure34, by varying the angle and length of V-shaped nanoantennas, arbitrary modulation of phase shift and amplitude transmission were demonstrated. The operational principle of such V-shaped antennas relies on the asymmetric transmission enabled by the nanoantennas. Similar to the case of circular polarization, such antennas have low energy efficiency because there always exists one component with the same polarization as the incident beam. Based on this abrupt phase change, they proposed the so-called “generalized Snell’s law.” By properly tuning the geometrical parameters of each antenna, broadband phase change could be achieved, although the phase was not rigorously achromatic [134, 138, 196].Figure 34
(a) SEM image of a representative antenna array fabricated on a silicon wafer. (b) Schematic experimental setup fory-polarized excitation. ((c) and (d)) Measured far-field intensity profiles for the y- and x-polarized excitations, respectively. (e) Schematic view of a representative antenna array. (f) Scanning electron microscope images of the unit cells of four antenna arrays with different periodicities fabricated on a single silicon wafer. ((g) and (h)) The false-color maps indicate the experimentally measured relative intensity profiles for the antenna array. Figures are reproduced from [134, 138].After the pioneering work by Capasso, much work was devoted to the design of phase-discontinuity metasurfaces. Many optical devices were subsequently designed and experimentally demonstrated. For example, Zhang et al. proposed that C-shape metallic elements can also be utilized to tune the amplitude and phase of cross-polarized scattering for linear polarization incidence [196]. In addition to the simple phase-engineering, other applications, such as spiral phase plates and wave plates, were also demonstrated [197, 198].Based on the locality of the phase shift [199], Lin et al. extended the V-shaped antennas in the near-infrared bands. The focus length was also decreased to a large extent to obtain a focus spot close to the diffraction limit. Jiang et al. demonstrated similar effect in the terahertz regime [200]. More recently, Ma et al. used a metasurface to focus vortex beam into a nanodoughnut [201]. As shown in Figures 35(a)–35(d), the proposed metasurface has good performance close to the ideal case. The metasurface tuned the phase distribution of the incident beam based on the concept of discontinuous phase modulation. Consequently, the proposed metasurface has two main functions. Firstly, with a circularly polarized incident beam, the metasurface converts it into a beam carrying OAM. Secondly, the incident field can be focused into a point with a certain focus length. The total energy coefficient of this metasurface exceeds 40%. By properly designing the phase modulation distribution, the copolarized component of the incident field does not participate in the focusing process. Therefore, only optical vortex can be observed in the focused field. The thickness of this planar chiral metasurface is much less than the operational wavelength and thus has potential application in compact integrated optical systems.Figure 35
(a) Schematic of the 2D elliptic antennas array. (b) SEM image of the elliptic antennas. (c) Measured power intensity profile of the focused field in thex
z-plane. (d) The simulated (dashed lines) and measured (solid lines) intensity spectra of the focused field, respectively, along the y-direction. (e) Schematic of the unit cell of rectangular aperture in metallic screen for holography. (f) Amplitude and phase transmission for various rotation angles. (g) SEM image of the sample. (h) Schematic of the measurement setup. Figures are reproduced from [201].
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)The geometric phase in aperture array has direct application in holography. As demonstrated in Figures35(e)–35(h), metasurface with metallic square apertures was constructed in our lab to form a hologram image of a China map based on the concept of discontinuous phase modulation in visible band.Since only part of the transmitted light takes geometric phase, single layered metasurfaces are often characterized by low efficiency. In principle, the efficiency could be increased dramatically with the help of a reflective layer. Taking the circularly polarized geometric phase as an example, the combination of an anisotropic metasurface with a reflective layer would form a reflective wave plate. By rotating the main axis of the embedded antennas, gradient phase could be directly obtained. This technique was utilized in reflectarray to increase the gain of antenna while keeping the reflective surface to be flat [184]. In the optical regime, the reflective nanoantennas array was used as building blocks of high efficient holograms [202]. The metasurface has an ultrathin and uniform thickness of 30 nm and is compatible with scalar diffraction theory, even with subwavelength pixel sizes, thus simplifying the design of holograms.Another important application of the metasurface relies on the fact that phase shifting metasurfaces placed at the optical pupil plane can increase the resolution of telescopes, which means that the far-field diffraction limit can be overcome [203]. As shown in Figure 36, the designed metasurface has several rings, which exert phase shift of 0 and π on the incoming light and change the corresponding spatial frequency [2]. To characterize the performance, we measured the images of two circular and triangular holes with and without the metasurface. After the insertion of the metasurface, the resolution is decreased to 0.625 times of the original value, implying that a 10-meter telescope could have the same resolution as that of a 16-meter one (i.e., a 1.6 times improvement in the resolution power).Figure 36
Far-field superresolution based on metasurface. (a) Schematic of the experimental setup. The inset shows the phase distribution of the metasurface. Gray regions and white regions indicate 0 andπ, respectively. (b) Experimental results for a circular hole at wavelength of λ = 532 nm. (c) Simulation results for a triangular hole. Figures are reproduced from [2].
(a)
(b)
(c)Very recently [204], we proposed and demonstrated the concept of broadband virtual shaping at the visible, infrared, and microwave spectrum by tailoring the spatiotemporal property of spin-orbit interaction in cascaded metasurfaces. When electromagnetic waves impinge on the designed metasurface, they are reflected to predefined directions to avoid being detected by unwanted antennas. Resorting to the dispersion engineering techniques in metasurface-based polarizers, the bandwidth was dramatically enhanced, although the thickness-to-bandwidth ratio may be analogous to that of broadband absorber. The design principle provided a new route for the control of electromagnetic wave for applications ranging from laser beam shaping to 3D holographic display and conformal camouflage [205].As shown in Figures37(a) and 37(b), we measured the specular reflection of an inhomogeneous metasurface. Since the reflected light was designed to depart from its original direction via the metasurface-assisted law reflection, only a small reflection echo was measured. Owing to the flexibility of the metasurface, this approach could be utilized in complex objects. For example, the RCS of a cylinder can be dramatically reduced by covering our metasurfaces on it (Figure 37(c)). The metallic cylinder in our design has a radius of R = 90 mm and height of h = 360 mm. The geometric phase distribution on the metasurface was designed to be Ф
=
k
z
z
+
k
φ
φ, where k
z
=
k
φ
=
104.7 rad/m. As shown in Figure 37(d), the RCS reductions for TE polarization and TM polarization were calculated under normal incidence along the y-direction. We noted that the reduction amount is a bit smaller than the planar case, which possibly stems from the nonoptimized phase profile and the fact that the RCS of a cylinder itself is smaller than its planar counterpart. Nevertheless, the conformal metasurfaces provide a new sight into the virtual shaping of nonplanar objects. In addition, this approach can be exploited to increase or decrease the RCS.Figure 37
(a) Schematic of the measurement setup. (b) Measured results for both TE polarization and TM polarization. The inset shows the photography of the fabricated sample. (c) Schematic of the spin-orbit conversion in the curved metasurface on a metallic cylinder. The insets show the definitions of TE polarization and TM polarization. (d) Calculated broadband RCS reduction for TE polarization and TM polarization at normal incidence alongy-direction. Figures are reproduced from [204].
(a)
(b)
(c)
(d)In general, the metallic metasurfaces suffer from low efficiency due to the intrinsic ohmic loss and the limited scattering cross sections of the antennas, which is not anticipated in many realms. Recently, dielectric metasurfaces based on geometric phase were presented to control the phase [44]. Nevertheless, the discrete phases lead to degradation of the performance. To overcome this issue, we proposed a semicontinuous structure to increase the continuity of phase shift. The metasurfaces consist of high-refractive-index and low-loss silicon annual ring gratings. Ohmic loss is avoided compared to its metallic counterpart. The continuity of annual ring grating ensures the continuity of the transmitted field, thus suppressing high order diffraction effects that may arise from discontinuity.At the end of this section, we would like to comment that metasurface with geometric phase could enable many applications in distinct disciplines. In general, traditional refractive, reflective, and diffractive devices could be replaced by metasurfaces. These elements include the spherical lenses, aspherical lenses, parabolic reflectors, fan-out grating, and laser beam shapers. In the microwave regime, metasurfaces could also be utilized to substitute traditional phased-array antenna. Furthermore, this kind of metasurface is also able to shift the momentum of scanning beam to extend the scanning range of phased array antennas, when it is integrated in radar radomes [206].


## 3.7.3. Full Control of Phase, Polarization, and Amplitude

In many applications, the phase, polarization state, and amplitude are all important for the manipulation of electromagnetic waves. For example, a low side-lobe phased array antenna needs the full control of phase and amplitude [207], while a planar lens with large longitudinal fields in the focus spots requires that the polarization and phase be simultaneously controlled [208].In order to achieve complete modulation of phase and polarization, Pfeiffer and Grbic proposed a four-layer cascaded metasurface lens that can focus light and control its polarization [209]. By adjusting the dimensions of structure, one can independently adjust the inductance and capacitance in the x- and y-directions so that the phase and polarization can be completely controlled.Kim et al. demonstrated that the local reflection coefficients of gap-plasmon resonators can be independently tailored in both magnitude and phase [181]. Using an array of nanorods closely placed on a metallic layer, it was shown that the magnitude and phase of the surface’s local reflection coefficients can be simultaneously tuned, with a magnitude range of [
0,0.67
] and a phase range of 360°. The power efficiency can reach 45% for an operational wavelength of 800 nm. This method was utilized in the design of a Dolph-Tschebyscheff array, with equal-amplitude sidelobes of prescribed magnitude, as represented in Figures 38(a)–38(d).Figure 38
(a) Magnitude and (b) phase ofS
11 in degrees for different resonator lengths and rotation angles. (c, d) Radiation patterns of (a) Dolph-Tschebyscheff and (b) uniform arrays. Both arrays redirect the normally incident plane wave at 33°. (e) Schematics of the top and bottom nanoapertures forming the super-unit-cell in the plasmonic metasurfaces for the demonstration of anomalous refraction. (f) The transmission phase and amplitude of each nanoaperture pair, calculated under y-polarized incident light at 900 nm. (g) SEM image of the sample (left panel) and measured refraction angle (right panel). Figures are reproduced from [181, 210].
(a)
(b)
(c)
(d)
(e)
(f)
(g)More recently, Li et al. proposed and validated another metasurface that can provide simultaneous manipulation of the phase and polarization of the transmitted light [210]. SPPs were adopted to obtain a π phase shift when the top and bottom nanoapertures are laterally translated by a distance in the y-direction. Hence, the phase difference can cover 0 to 2
π by varying the parameters of nanoaperture for normally incident light polarized in the y-direction. The metasurface enabled anomalous refraction with efficiency of about 21.4% for linearly polarized incident light (Figures 38(c)–38(g)).It also should be noted that the phase over the surface of micro- and nanoantennas can also be measured with the help of scattering near-field techniques [211, 212], which provide a way to further understand the physical processes of these antennas.


## 3.8. Active Metasurfaces

Although passive metasurfaces have been proved to be useful in many applications, the dynamic tuning of performance is always desired in practical applications. Most of the metasurfaces have fixed electromagnetic properties when the structures are designed or fabricated. Nevertheless, there is a type of “reconfigurable” metasurface which is able to tune the electromagnetic response with an outside stimulus [213–217]. The general way to obtain the tunable phase modulation is by loading active devices in its unit cells, such as varactor diodes [218], liquid crystals, and ferroelectric and microelectromechanical switch (MEMS) [219], as can be seen in Figure 39.Figure 39
Examples of active metasurfaces. (a) SEM image (b) transmission spectra for a MEMS-based metasurface. (c) Schematic and (d) transmission spectra for magnetic resonance (left panel) and electric resonance (right panel). Figures are reproduced from [219, 220].
(a)
(b)
(c)
(d)These reconfigurable or tunable metasurfaces efficiently broaden the application range of metamaterial and simplify the optical and communication systems. According to the particular applications, active metasurfaces can be classified into three main subdomains. In the following, we would give a brief review on these novel metasurfaces.


### 3.8.1. Active Phase Modulation

Aiming at satisfying the requirement of modern communication systems and solving the disadvantages of traditional phased array antenna, metasurfaces with phase-tuned ability have been introduced to construct novel beam scanning antennas. The principle of beam steering for this metasurface is illustrated in Figure40(a). The designed active metasurface is divided into N regions, which can be regarded as a linear array with a period of l
/
N. When a plane wave transmits through these N regions, the phase difference between adjacent regions would be α. As a result, the angle of beaming direction is θ deviated from the normal direction, which is determined by α.Figure 40
(a) Principle of beam steering. (b) Unit cell of the phase reconfigurable metasurface. (c) Phase manipulation results of the active metasurface. (d) Photography of the horn antenna with the active FSS. (e, f) Radiation patterns of the designed horn antenna in (e)E-plane and (f) H-plane for different phase distribution. Figures are reproduced from [221].
(a)
(b)
(c)
(d)
(e)
(f)In Figure40(a), the transmission phase φ
i of region i can be shown as(41)
φ
i
=
-
ζ
i
+
φ
0
+
2
k
π
,where φ
0 is a constant and k is an integer. The phase shift ζ
i and the phase difference α can be expressed as(42)
ζ
i
=
β
i
l
N
sin
⁡
θ
,
α
=
φ
i
-
φ
i
-
1
=
-
β
l
N
sin
⁡
θ
,where β is the wave number. The beam steering angle θ can be then written as(43)
θ
=
arcsin
⁡
-
N
α
β
l
.Clearly, (43) is one particular case of the metasurface-assisted Snell’s law, based on which the beaming direction can be tuned by changing the phase difference α between adjacent elements. In 2012, Jiang et al. [206] introduced an active cascaded metasurface for phase manipulation by tuning varactor-diodes loaded in the unit cell. The tunable metasurface was employed as the radome to tune the E-plane radiation pattern of the antenna array. However, the loss of this active phase modulation metasurface is relatively large due to its eight layered structure.Based on the phase modulation property of the metasurface, we have proposed an active phase modulation metasurface to manipulate the phase of the incident wave and to achieve beam steering of a horn antenna [221], as depicted in Figure 40(d). The unit is composed of a metallic rectangular ring and a patch, with a pair of microwave varactor diodes inserted in between along incident electric field polarization direction. Transmission phase of the emitted wave can be tuned by changing the bias voltage applied to the varactor diodes, and 360° phase difference can be obtained at 5.3 GHz as the capacitance value is tuned from 0.65 pF to 2.6 pF.Through different configurations of the bias voltages, one can obtain the gradient phase distribution of the emitted wave alongE-plane and H-plane. This metasurface loaded antenna can steer the directive beam with an angle of ±30° in both E-plane and H-plane at 5.3 GHz with a bandwidth of 180 MHz. Using an improved approach, the scanning range can also be increased to ±360° in both E-plane and H-plane [2].In previous works, the polarization state and beam direction are not simultaneously controlled. In order to achieve this goal, a novel transmitarray element was proposed, which achieved 1-bit phase shifting at two orthogonal linear polarization modes. The phase tuning and polarization reconfiguration can be independently controlled based on PIN diodes. The unit cell of the dual linearly polarized metasurface consists of two-layer metallic patterns connected by a metalized via-hole. One-layer metallic pattern is a rectangular patch with two PIN diodes loaded in O-slot along electric field polarization direction, which is utilized as a receiver-antenna to achieve 1-bit phase tuning. The other metallic pattern is a dual linearly polarized transmitter-antenna that adopts a square ring patch with two PIN diodes distributed at the cross-polarization directions. The simulation results show that the designed antenna can achieve 1-bit phase tuning and linear polarization reconfiguration at 10.5 GHz with insertion loss of about 1.1 dB. This kind of the metasurface-based antenna has the advantages of low cost and simple implementation, which could be developed for possible applications in some communication and radar systems, especially in the area where high-gain beam steering and the anti-interference capabilities are urgently required.


### 3.8.2. Active Polarization Modulation

The polarization states can also be dynamically tuned by active metasurfaces. Zhang et al. [215] proposed a reconfigurable chiral metasurface, which switched its handedness when the semiconductor region was illuminated by external light, as shown in Figure 41. This reconfigurable or tunable property efficiently broadens the application range of metasurface and simplifies the optical and communication systems.Figure 41
Geometry and the results of the photoinduced handedness switching metasurface. Figures are reproduced from [164].
(a)
(b)
(c)
(d)
(e)
(f)
(g)In order to achieve polarization conversion with simple metasurface, Ma et al. [92] demonstrated a double-layered active metasurface which changes the structure between chiral and isotropic by tuning the working states of the PIN diodes in its unit cells. When it presented chirality, the handedness could also be tuned. As shown in Figures 42(a) and 42(b), the designed metasurface could convert the incident linearly polarized wave into RCP or LCP one. Furthermore, it could also be switched to be isotropic and keep the polarization state of the incident wave unchanged, by controlling the voltages applied on these diodes.Figure 42
(a) Schematic of the metamolecule of the active metasurface for polarization manipulation, and the transmission spectra are shown in (b). (c) Photography of the fabricated dipole antenna using tunable metasurface with its unit cell in (e), and the measuredS
11 and AR of the designed dipole antenna for different working states are shown in (d) and (f). Figures are reproduced from [92].
(a)
(b)
(c)
(d)
(e)
(f)We have also employed this concept of active polarization manipulation into the design of antennas. As it is well known, the dipole cannot radiate efficiently near a perfect conductor due to its opposite image current; in addition, the single dipole can only produce linearly polarized waves, which cannot satisfy the requirement in many communication fields. To address the above issues, the anisotropic metasurface was proposed as the ground plane for the dipole. This novel reflective metasurface not only reduces the profile of the dipole but also assists it to achieve emission of circularly polarized wave. Through adjusting the PIN diodes loaded on the unit cell of the metasurface, the polarization states of the emitted wave from the dipole, including RHCP, LHCP, and LP waves, can be dynamically tuned.The tunable metasurface can make the dipole antenna work at four states. For states 1 and 2, as seen in Figure42(d), the emitted waves with left- and right-hand circular polarization are produced at 4.6 GHz, and the AR is 1.2 and 0.3 dB, respectively. For states 3 and 4, the dipole antenna radiates the linearly polarized waves with the gains of about 6 dB at 4.6 and 4.25 GHz (see Figure 42(f)), respectively. This kind of the polarization reconfigurable antenna has a strong environmental adaptability, which may find many potential applications in the communication field.Recently, Wang et al. demonstrated a coherent perfect polarization transformer [76]. It was proved that the phase shift between two coherent inputs could be utilized to dynamically tune the polarization states of output waves. Depending on the phase difference, the outputs could be y polarization, LCP, and RCP for x-polarized inputs.


### 3.8.3. Active Amplitude Modulation

Besides the phase property of the incident electromagnetic wave, the amplitude can also be modulated. As analyzed in the effective impedance theory, the transmitted amplitude and the phase of the incident wave are modulated by the effective impedance of the metasurface. Therefore, the element loading method in metasurface allows the control of the amplitude and hence provides new applications in microwave communication systems, such as controlling the sidelobe and beamwidth of the radiation antennas.Lim et al. [222] had designed a kind of composite right-/left-handed microstrip antenna in which varactors were used to tune the amplitude of each element for achieving dynamic control of the beamwidth. Recently, a partially reflective surface (PRS) was utilized to actively change the beamwidth of the emitted waves by tuning its reflection through the varactors mounted on each element of the PRS [223].Antennas with low side-lobe level (SLL) are urgently required since it can efficiently reduce the electromagnetic interference and improve the ability of signal capture. However, traditional approaches to achieve low SLL are mainly realized by modifying the elements weighting or spacing distribution in antenna array. In comparison, metasurfaces with amplitude tunability were employed to reduce the SLL of antennas since the radiation pattern can be reformed by metasurfaces.Our team proposed an approach to reduce the SLL of antenna array to a desired value by utilizing amplitude modulated metasurface, as shown in Figure43. By manipulating the structure parameters and the PIN diodes loaded in the unit cells, the transmission amplitude of each unit can be distinctly controlled. Then, the metasurface was utilized as the superstrate of the horn antenna array, and the superstrate was divided into several regions with different transmission amplitudes along the electric field polarization direction. With a plane wave illustrated on the superstrate, the transmission amplitudes were designed as Taylor distribution while the transmission phases were equal, which resulted in a tapered amplitude distribution of the output beam. An H-plane sectorial horn array is adopted as a plane wave source to verify the performance of the SLL reduction. The SLL was reduced from −12.4 to −25.9 dB at the desired frequency, while not influencing the gain of the antenna array.Figure 43
(a) Principle of the sidelobe reduction with the metasurface superstrate. (b) The geometry of the amplitude tunable metasurface to reduce the sidelobe of the horn antenna array. (c) Schematic of the unit cell of the metasurface. (d) Comparison of the normalized transmission amplitude distribution of the proposed antenna composite and the ideal Taylor amplitude distribution. (e) Phase distributions at the reference plane. The inset figure shows the electric field distribution atx
z-plane. (f) Radiation pattern in the E-plane of the antenna composite at 10.3 GHz with sidelobe level of −25.9 dB.
(a)
(b)
(c)
(d)
(e)
(f)Wang et al. proposed a kind of metasurface superstrate to control the beamwidth of horn antenna array based on the concept of amplitude modulation [225], as depicted in Figure 44. The unit cell of the metasurface was composed of two-layer periodic structures loaded with varactors. By tuning the capacitance of the varactors, the unit cell can produce two different states which are transparent and absorptive to the incident wave at a certain frequency, respectively. The whole metasurface can be divided into several groups, and each group is composed of some unit cells with the same state. By switching the state of each group, the transparent window of the metasurface can be changed. Consequently, the emitted waves with variable beamwidth can be expected, as validated in Figure 44(c), when this metasurface was placed above the horn antenna array as superstrate.Figure 44
(a) Schematic of the beamwidth controlling using metasurface. (b) Photographs of the fabricated FSS for beamwidth controlling. (c) Response of reflection and transmission coefficients to different capacitance values at the interesting frequency region. (d) Photograph of the low RCS antenna loading partially absorbing metasurface. (e) The RCS results for the PRS antenna with and without PRS. (f) MeasuredE-plane far-field patterns for the beamwidth manipulation antenna at 5.5 GHz. Figures are reproduced from [224].
(a)
(b)
(c)
(d)
(e)
(f)As another method to modulate the amplitude, metasurfaces partially absorbing ability has been introduced and employed in the antenna realm. Compared to the traditional means, such as shaping of target surface and adopting radar absorbing material, such metasurface may efficiently reduce the RCS while not decreasing the radiation performance of the antenna. We proposed a design to reduce the RCS and enhance the gain of a patch antenna by using partially reflecting surface (PRS) that consists of two layers of metallic structure [58], as demonstrated in Figure 44(d). The top absorbing layer is utilized to reduce RCS, while the bottom layer was combined with the ground plane to construct the F-P cavity to achieve high gain. The antenna gain was enhanced by about 6.5 dB at 11.5 GHz, and its RCS is dramatically reduced in a broad frequency range from 6 to 14 GHz. It was fully verified that the designed PRS did not influence the radiation performance of the antenna within the bandwidth of the RCS reduction, but it also obviously improved the antenna gain. This new design provides a good method to solve the conflict between the gain enhancement and the RCS reduction.In the above amplitude modulation metasurface, the normalized amplitude can be controlled in the range of 0-1. However, the amplitude of the incident wave can be gained above unit by utilizing amplifier in the unit cell of the metasurfaces. Recently, we also proposed an amplifying reconfigurable metasurface to achieve simultaneous control of the amplitude and phase of the incident wave. The varactor diodes were adopted to construct the reflection-type phase shifters, which achieved over 400° of phase shift extending the operation bandwidth beyond 10%. Most importantly, the amplifier integrated in the unit cell of the metasurface made the amplitude of the whole element simultaneously gain larger than 7 dB. In addition, the overall thickness of the proposed metasurface element is only0.135
λ in free space, which is more compact compared to the existing metallic elements. This kind of amplifying and phase modulation metasurface could be developed to construct high-gain antenna for beam steering.


### 3.8.4. Active Absorption Modulation

In order to satisfy the requirement of modern military and civil applications, novel materials with smart absorbing characteristics are needed. In general, active metasurface absorbers have two advantages over traditional absorbers. Firstly, since traditional metamaterials absorbers are limited in the operational bandwidth, active tuning may increase the effective bandwidth in a time-diving way. Secondly, the absorption coefficients can be dynamically tuned to mimic the electromagnetic spectrum of environment, which is not obtained through traditional approaches.The intrinsic circuit property of metasurface absorbers permits an easy way to realize active tuning. As shown in many references, the metasurface can be characterized by its equivalent resistances, inductances, and capacitances [99, 114]. When lumped circuit devices, such as resistors, inductors, capacitors, and various kinds of diodes, are integrated in the metasurface, the electromagnetic response can be greatly improved.Early in 2004, Tennant and Chambers presented an adaptive absorber by controlling the bias voltage of PIN diodes loaded between adjacent metallic bow ties [213]. The absorber was similar with the topology of a Salisbury screen, but in which the conventional resistive layer was replaced by an active metasurface controlled by PIN diodes. The resulting structure had superior absorption characteristics compared to conventional passive absorbers of corresponding thickness. Measured results showed that the reflectivity response of the absorber can be controlled over the frequency band from 9 to 13 GHz. In a similar way, other circuit elements, such as varactors [226, 227], were introduced to change impedance of the metasurfaces.In 2012, an electrical tunable L-band absorbing material for two polarization types was presented by Wang et al. [228]. As shown in Figures 45(a)–45(c), the proposed absorber consisted of a metal resonator and four surrounding metal lines which were connected by pin diodes and exhibited the tunable range of reflectivity reaching −40 dB for both polarization types. Later [227], Zhao et al. demonstrated a tunable absorber with a measured bandwidth of 1.5 GHz (or relative bandwidth of 30%). Since the units are placed along two orthogonal directions, the absorber is insensitive to the polarization of incident waves.Figure 45
(a) Configuration of tunable absorbing material. (b) Measured reflectivity at different bias voltages under incident angle of 15°, and the power loss density at two frequencies is shown in (c). (d) Photograph of the fabricated active absorber; the measured sample has an area of 340 × 340 mm2, consisting of 200 units. Varactor and pin diodes are assembled through hand-soldering techniques. (e) Measured reflectance spectra of the active absorber with different bias voltages applied upon PIN diode. Figures are reproduced from [228, 229].In principle, an active absorber should have the ability of controlling echo characteristics in both aspects of frequency and intensity. However, few active absorbers simultaneously considered the two issues in a single device. As an attempt to accomplish this purpose, Wu et al. demonstrated an electrically active absorber in which the working frequency and absorbing intensity could be separately controlled by the PIN and varactor diodes [229]. The structures and measured results are presented in Figures 45(d) and 45(e). Compared with those metasurfaces proposed before, although at the expense of increased complexity, the interesting characteristic of the absorber designed here is that it contains a special designed active magnetic resonator in which both the resonant frequency and amplitude can be, respectively, tuned and therefore shows separable modulation of absorbing frequency and peak intensity. Both simulation and experimental results revealed that the active absorber simultaneously contains such two working models. Further theoretical analysis based on LC theory also confirmed this dual ability.Along with the increase of working frequency, sealed semiconductor devices become unsuitable due to the limited frequency response. In millimeter wave and terahertz, absorption behaviors can be tuned by modulating the relative position of cells on the top layer [230]. In 2013, Shrekenhamer et al. presented an active absorber in the terahertz regime [231]. By incorporation of liquid crystal into strategic locations within the unit cell, they were able to modify the absorption by 30% at 2.62 THz and also tune the resonant absorption over 4% in bandwidth. Other tunable metasurface absorbers adopted materials, such as vanadium oxide [232] and semiconductors [233].Recently, we constructed self-tuning metasurface absorbers with capability of self-adaptively tracing and absorbing the incident wave with relatively narrow bandwidth. As depicted in Figure46, the operational principle includes two main steps. Firstly, the central frequency of the incident wave was detected by a detection circuit. Secondly, a voltage bias is added to the active metasurface to achieve high efficient absorption of the incident wave. The experimental results show that the echo attenuation within the frequency region of 2.8~3.2 GHz is all larger than 10 dB; for some frequency it even reaches 35 dB.Figure 46
Self-tuning smart absorber. (a) Schematic of the operational principle. (b) Transmission coefficient of the absorber for a narrow incident wave for various capacitances at 2.75 GHz (left panel) and 3.25 GHz (right panel). (c) Experimental setup (left panel) and measured attenuation of the reflection wave when the incident wave is swept from 2.8 to 3.2 GHz (right panel).
(a)
(b)
(c)


## 3.8.1. Active Phase Modulation

Aiming at satisfying the requirement of modern communication systems and solving the disadvantages of traditional phased array antenna, metasurfaces with phase-tuned ability have been introduced to construct novel beam scanning antennas. The principle of beam steering for this metasurface is illustrated in Figure40(a). The designed active metasurface is divided into N regions, which can be regarded as a linear array with a period of l
/
N. When a plane wave transmits through these N regions, the phase difference between adjacent regions would be α. As a result, the angle of beaming direction is θ deviated from the normal direction, which is determined by α.Figure 40
(a) Principle of beam steering. (b) Unit cell of the phase reconfigurable metasurface. (c) Phase manipulation results of the active metasurface. (d) Photography of the horn antenna with the active FSS. (e, f) Radiation patterns of the designed horn antenna in (e)E-plane and (f) H-plane for different phase distribution. Figures are reproduced from [221].
(a)
(b)
(c)
(d)
(e)
(f)In Figure40(a), the transmission phase φ
i of region i can be shown as(41)
φ
i
=
-
ζ
i
+
φ
0
+
2
k
π
,where φ
0 is a constant and k is an integer. The phase shift ζ
i and the phase difference α can be expressed as(42)
ζ
i
=
β
i
l
N
sin
⁡
θ
,
α
=
φ
i
-
φ
i
-
1
=
-
β
l
N
sin
⁡
θ
,where β is the wave number. The beam steering angle θ can be then written as(43)
θ
=
arcsin
⁡
-
N
α
β
l
.Clearly, (43) is one particular case of the metasurface-assisted Snell’s law, based on which the beaming direction can be tuned by changing the phase difference α between adjacent elements. In 2012, Jiang et al. [206] introduced an active cascaded metasurface for phase manipulation by tuning varactor-diodes loaded in the unit cell. The tunable metasurface was employed as the radome to tune the E-plane radiation pattern of the antenna array. However, the loss of this active phase modulation metasurface is relatively large due to its eight layered structure.Based on the phase modulation property of the metasurface, we have proposed an active phase modulation metasurface to manipulate the phase of the incident wave and to achieve beam steering of a horn antenna [221], as depicted in Figure 40(d). The unit is composed of a metallic rectangular ring and a patch, with a pair of microwave varactor diodes inserted in between along incident electric field polarization direction. Transmission phase of the emitted wave can be tuned by changing the bias voltage applied to the varactor diodes, and 360° phase difference can be obtained at 5.3 GHz as the capacitance value is tuned from 0.65 pF to 2.6 pF.Through different configurations of the bias voltages, one can obtain the gradient phase distribution of the emitted wave alongE-plane and H-plane. This metasurface loaded antenna can steer the directive beam with an angle of ±30° in both E-plane and H-plane at 5.3 GHz with a bandwidth of 180 MHz. Using an improved approach, the scanning range can also be increased to ±360° in both E-plane and H-plane [2].In previous works, the polarization state and beam direction are not simultaneously controlled. In order to achieve this goal, a novel transmitarray element was proposed, which achieved 1-bit phase shifting at two orthogonal linear polarization modes. The phase tuning and polarization reconfiguration can be independently controlled based on PIN diodes. The unit cell of the dual linearly polarized metasurface consists of two-layer metallic patterns connected by a metalized via-hole. One-layer metallic pattern is a rectangular patch with two PIN diodes loaded in O-slot along electric field polarization direction, which is utilized as a receiver-antenna to achieve 1-bit phase tuning. The other metallic pattern is a dual linearly polarized transmitter-antenna that adopts a square ring patch with two PIN diodes distributed at the cross-polarization directions. The simulation results show that the designed antenna can achieve 1-bit phase tuning and linear polarization reconfiguration at 10.5 GHz with insertion loss of about 1.1 dB. This kind of the metasurface-based antenna has the advantages of low cost and simple implementation, which could be developed for possible applications in some communication and radar systems, especially in the area where high-gain beam steering and the anti-interference capabilities are urgently required.


## 3.8.2. Active Polarization Modulation

The polarization states can also be dynamically tuned by active metasurfaces. Zhang et al. [215] proposed a reconfigurable chiral metasurface, which switched its handedness when the semiconductor region was illuminated by external light, as shown in Figure 41. This reconfigurable or tunable property efficiently broadens the application range of metasurface and simplifies the optical and communication systems.Figure 41
Geometry and the results of the photoinduced handedness switching metasurface. Figures are reproduced from [164].
(a)
(b)
(c)
(d)
(e)
(f)
(g)In order to achieve polarization conversion with simple metasurface, Ma et al. [92] demonstrated a double-layered active metasurface which changes the structure between chiral and isotropic by tuning the working states of the PIN diodes in its unit cells. When it presented chirality, the handedness could also be tuned. As shown in Figures 42(a) and 42(b), the designed metasurface could convert the incident linearly polarized wave into RCP or LCP one. Furthermore, it could also be switched to be isotropic and keep the polarization state of the incident wave unchanged, by controlling the voltages applied on these diodes.Figure 42
(a) Schematic of the metamolecule of the active metasurface for polarization manipulation, and the transmission spectra are shown in (b). (c) Photography of the fabricated dipole antenna using tunable metasurface with its unit cell in (e), and the measuredS
11 and AR of the designed dipole antenna for different working states are shown in (d) and (f). Figures are reproduced from [92].
(a)
(b)
(c)
(d)
(e)
(f)We have also employed this concept of active polarization manipulation into the design of antennas. As it is well known, the dipole cannot radiate efficiently near a perfect conductor due to its opposite image current; in addition, the single dipole can only produce linearly polarized waves, which cannot satisfy the requirement in many communication fields. To address the above issues, the anisotropic metasurface was proposed as the ground plane for the dipole. This novel reflective metasurface not only reduces the profile of the dipole but also assists it to achieve emission of circularly polarized wave. Through adjusting the PIN diodes loaded on the unit cell of the metasurface, the polarization states of the emitted wave from the dipole, including RHCP, LHCP, and LP waves, can be dynamically tuned.The tunable metasurface can make the dipole antenna work at four states. For states 1 and 2, as seen in Figure42(d), the emitted waves with left- and right-hand circular polarization are produced at 4.6 GHz, and the AR is 1.2 and 0.3 dB, respectively. For states 3 and 4, the dipole antenna radiates the linearly polarized waves with the gains of about 6 dB at 4.6 and 4.25 GHz (see Figure 42(f)), respectively. This kind of the polarization reconfigurable antenna has a strong environmental adaptability, which may find many potential applications in the communication field.Recently, Wang et al. demonstrated a coherent perfect polarization transformer [76]. It was proved that the phase shift between two coherent inputs could be utilized to dynamically tune the polarization states of output waves. Depending on the phase difference, the outputs could be y polarization, LCP, and RCP for x-polarized inputs.


## 3.8.3. Active Amplitude Modulation

Besides the phase property of the incident electromagnetic wave, the amplitude can also be modulated. As analyzed in the effective impedance theory, the transmitted amplitude and the phase of the incident wave are modulated by the effective impedance of the metasurface. Therefore, the element loading method in metasurface allows the control of the amplitude and hence provides new applications in microwave communication systems, such as controlling the sidelobe and beamwidth of the radiation antennas.Lim et al. [222] had designed a kind of composite right-/left-handed microstrip antenna in which varactors were used to tune the amplitude of each element for achieving dynamic control of the beamwidth. Recently, a partially reflective surface (PRS) was utilized to actively change the beamwidth of the emitted waves by tuning its reflection through the varactors mounted on each element of the PRS [223].Antennas with low side-lobe level (SLL) are urgently required since it can efficiently reduce the electromagnetic interference and improve the ability of signal capture. However, traditional approaches to achieve low SLL are mainly realized by modifying the elements weighting or spacing distribution in antenna array. In comparison, metasurfaces with amplitude tunability were employed to reduce the SLL of antennas since the radiation pattern can be reformed by metasurfaces.Our team proposed an approach to reduce the SLL of antenna array to a desired value by utilizing amplitude modulated metasurface, as shown in Figure43. By manipulating the structure parameters and the PIN diodes loaded in the unit cells, the transmission amplitude of each unit can be distinctly controlled. Then, the metasurface was utilized as the superstrate of the horn antenna array, and the superstrate was divided into several regions with different transmission amplitudes along the electric field polarization direction. With a plane wave illustrated on the superstrate, the transmission amplitudes were designed as Taylor distribution while the transmission phases were equal, which resulted in a tapered amplitude distribution of the output beam. An H-plane sectorial horn array is adopted as a plane wave source to verify the performance of the SLL reduction. The SLL was reduced from −12.4 to −25.9 dB at the desired frequency, while not influencing the gain of the antenna array.Figure 43
(a) Principle of the sidelobe reduction with the metasurface superstrate. (b) The geometry of the amplitude tunable metasurface to reduce the sidelobe of the horn antenna array. (c) Schematic of the unit cell of the metasurface. (d) Comparison of the normalized transmission amplitude distribution of the proposed antenna composite and the ideal Taylor amplitude distribution. (e) Phase distributions at the reference plane. The inset figure shows the electric field distribution atx
z-plane. (f) Radiation pattern in the E-plane of the antenna composite at 10.3 GHz with sidelobe level of −25.9 dB.
(a)
(b)
(c)
(d)
(e)
(f)Wang et al. proposed a kind of metasurface superstrate to control the beamwidth of horn antenna array based on the concept of amplitude modulation [225], as depicted in Figure 44. The unit cell of the metasurface was composed of two-layer periodic structures loaded with varactors. By tuning the capacitance of the varactors, the unit cell can produce two different states which are transparent and absorptive to the incident wave at a certain frequency, respectively. The whole metasurface can be divided into several groups, and each group is composed of some unit cells with the same state. By switching the state of each group, the transparent window of the metasurface can be changed. Consequently, the emitted waves with variable beamwidth can be expected, as validated in Figure 44(c), when this metasurface was placed above the horn antenna array as superstrate.Figure 44
(a) Schematic of the beamwidth controlling using metasurface. (b) Photographs of the fabricated FSS for beamwidth controlling. (c) Response of reflection and transmission coefficients to different capacitance values at the interesting frequency region. (d) Photograph of the low RCS antenna loading partially absorbing metasurface. (e) The RCS results for the PRS antenna with and without PRS. (f) MeasuredE-plane far-field patterns for the beamwidth manipulation antenna at 5.5 GHz. Figures are reproduced from [224].
(a)
(b)
(c)
(d)
(e)
(f)As another method to modulate the amplitude, metasurfaces partially absorbing ability has been introduced and employed in the antenna realm. Compared to the traditional means, such as shaping of target surface and adopting radar absorbing material, such metasurface may efficiently reduce the RCS while not decreasing the radiation performance of the antenna. We proposed a design to reduce the RCS and enhance the gain of a patch antenna by using partially reflecting surface (PRS) that consists of two layers of metallic structure [58], as demonstrated in Figure 44(d). The top absorbing layer is utilized to reduce RCS, while the bottom layer was combined with the ground plane to construct the F-P cavity to achieve high gain. The antenna gain was enhanced by about 6.5 dB at 11.5 GHz, and its RCS is dramatically reduced in a broad frequency range from 6 to 14 GHz. It was fully verified that the designed PRS did not influence the radiation performance of the antenna within the bandwidth of the RCS reduction, but it also obviously improved the antenna gain. This new design provides a good method to solve the conflict between the gain enhancement and the RCS reduction.In the above amplitude modulation metasurface, the normalized amplitude can be controlled in the range of 0-1. However, the amplitude of the incident wave can be gained above unit by utilizing amplifier in the unit cell of the metasurfaces. Recently, we also proposed an amplifying reconfigurable metasurface to achieve simultaneous control of the amplitude and phase of the incident wave. The varactor diodes were adopted to construct the reflection-type phase shifters, which achieved over 400° of phase shift extending the operation bandwidth beyond 10%. Most importantly, the amplifier integrated in the unit cell of the metasurface made the amplitude of the whole element simultaneously gain larger than 7 dB. In addition, the overall thickness of the proposed metasurface element is only0.135
λ in free space, which is more compact compared to the existing metallic elements. This kind of amplifying and phase modulation metasurface could be developed to construct high-gain antenna for beam steering.


## 3.8.4. Active Absorption Modulation

In order to satisfy the requirement of modern military and civil applications, novel materials with smart absorbing characteristics are needed. In general, active metasurface absorbers have two advantages over traditional absorbers. Firstly, since traditional metamaterials absorbers are limited in the operational bandwidth, active tuning may increase the effective bandwidth in a time-diving way. Secondly, the absorption coefficients can be dynamically tuned to mimic the electromagnetic spectrum of environment, which is not obtained through traditional approaches.The intrinsic circuit property of metasurface absorbers permits an easy way to realize active tuning. As shown in many references, the metasurface can be characterized by its equivalent resistances, inductances, and capacitances [99, 114]. When lumped circuit devices, such as resistors, inductors, capacitors, and various kinds of diodes, are integrated in the metasurface, the electromagnetic response can be greatly improved.Early in 2004, Tennant and Chambers presented an adaptive absorber by controlling the bias voltage of PIN diodes loaded between adjacent metallic bow ties [213]. The absorber was similar with the topology of a Salisbury screen, but in which the conventional resistive layer was replaced by an active metasurface controlled by PIN diodes. The resulting structure had superior absorption characteristics compared to conventional passive absorbers of corresponding thickness. Measured results showed that the reflectivity response of the absorber can be controlled over the frequency band from 9 to 13 GHz. In a similar way, other circuit elements, such as varactors [226, 227], were introduced to change impedance of the metasurfaces.In 2012, an electrical tunable L-band absorbing material for two polarization types was presented by Wang et al. [228]. As shown in Figures 45(a)–45(c), the proposed absorber consisted of a metal resonator and four surrounding metal lines which were connected by pin diodes and exhibited the tunable range of reflectivity reaching −40 dB for both polarization types. Later [227], Zhao et al. demonstrated a tunable absorber with a measured bandwidth of 1.5 GHz (or relative bandwidth of 30%). Since the units are placed along two orthogonal directions, the absorber is insensitive to the polarization of incident waves.Figure 45
(a) Configuration of tunable absorbing material. (b) Measured reflectivity at different bias voltages under incident angle of 15°, and the power loss density at two frequencies is shown in (c). (d) Photograph of the fabricated active absorber; the measured sample has an area of 340 × 340 mm2, consisting of 200 units. Varactor and pin diodes are assembled through hand-soldering techniques. (e) Measured reflectance spectra of the active absorber with different bias voltages applied upon PIN diode. Figures are reproduced from [228, 229].In principle, an active absorber should have the ability of controlling echo characteristics in both aspects of frequency and intensity. However, few active absorbers simultaneously considered the two issues in a single device. As an attempt to accomplish this purpose, Wu et al. demonstrated an electrically active absorber in which the working frequency and absorbing intensity could be separately controlled by the PIN and varactor diodes [229]. The structures and measured results are presented in Figures 45(d) and 45(e). Compared with those metasurfaces proposed before, although at the expense of increased complexity, the interesting characteristic of the absorber designed here is that it contains a special designed active magnetic resonator in which both the resonant frequency and amplitude can be, respectively, tuned and therefore shows separable modulation of absorbing frequency and peak intensity. Both simulation and experimental results revealed that the active absorber simultaneously contains such two working models. Further theoretical analysis based on LC theory also confirmed this dual ability.Along with the increase of working frequency, sealed semiconductor devices become unsuitable due to the limited frequency response. In millimeter wave and terahertz, absorption behaviors can be tuned by modulating the relative position of cells on the top layer [230]. In 2013, Shrekenhamer et al. presented an active absorber in the terahertz regime [231]. By incorporation of liquid crystal into strategic locations within the unit cell, they were able to modify the absorption by 30% at 2.62 THz and also tune the resonant absorption over 4% in bandwidth. Other tunable metasurface absorbers adopted materials, such as vanadium oxide [232] and semiconductors [233].Recently, we constructed self-tuning metasurface absorbers with capability of self-adaptively tracing and absorbing the incident wave with relatively narrow bandwidth. As depicted in Figure46, the operational principle includes two main steps. Firstly, the central frequency of the incident wave was detected by a detection circuit. Secondly, a voltage bias is added to the active metasurface to achieve high efficient absorption of the incident wave. The experimental results show that the echo attenuation within the frequency region of 2.8~3.2 GHz is all larger than 10 dB; for some frequency it even reaches 35 dB.Figure 46
Self-tuning smart absorber. (a) Schematic of the operational principle. (b) Transmission coefficient of the absorber for a narrow incident wave for various capacitances at 2.75 GHz (left panel) and 3.25 GHz (right panel). (c) Experimental setup (left panel) and measured attenuation of the reflection wave when the incident wave is swept from 2.8 to 3.2 GHz (right panel).
(a)
(b)
(c)


## 3.9. Flexible and Stretchable Metasurfaces

One advantage of metasurfaces over traditional 3D materials is its flexibility which is stemming from the ultrathin thickness. Flexible metasurfaces also provide a route to actively tune the performances. In traditional active metasurfaces, the electromagnetic response can be dynamically manipulated by tuning the constitutive parameters of the related optical materials. However, the mechanical properties, such as shape and geometrical size of these metasurfaces, are invariable during the tuning process. Even for MEMS-based metasurface, the macroscopic geometry is not changed in practical operation.In recent years, the concept of flexible and stretchable metasurfaces has accepted particular attention, as inspired by the development of flexible electronic devices. For these metasurfaces, the key properties are determined by the substrate. For most metasurfaces except for some free-standing structures, the substrate not only provides a mechanical support for the metallic or dielectric structures but also offers an additional degree of freedom for the design of metasurface. Up to date, the most commonly used flexible substrates for metasurfaces are polydimethylsiloxane (PDMS), polyimide, metaflex, polyethylene naphthalene (PEN) [234–236], polyethylene terephthalate (PET), polymethylmethacrylate (PMMA), and polystyrene [237].One particular application of flexible metasurface is the conformal devices such as conformal antennas, conformal lenses, and conformal absorbers [238–240]. For nonplanar metasurface absorbers, different areas experience different incident angles. As a result, the large-angle stability is required. Fortunately, it was found that metasurface absorber can have good absorption for large incidence angle by proper design [241]. As a result, conformal absorbers may maintain its absorption. However, earlier designs of metasurface absorbers suffer from the strong polarization dependence [36]. In 2011, we designed and fabricated a polarization-independent wide-angle absorber, following the design principle we established [37]. As shown in Figure 47(a), the absorption does not change dramatically when the metasurface is bent as a cylinder.Figure 47
(a) Experimental results for a flexible metasurface absorber. (b) RCS reduction properties of nonuniform conformal metasurfaces. (c) Absorption of flexible absorbers fabricated on a PDMS substrate. (d) Elasticity of a flexible terahertz wave plate fabricated on polyimide. Figures are reproduced from (b)–(d) [239, 242, 243].
(a)
(b)
(c)
(d)In 2013, a conformal absorber was designed by utilizing nonuniform metasurface [239]. The authors designed three different unit cells, which are optimized at 0°, 30°, and 45° incident angles, respectively. As illustrated in Figure 47(b), the proposed concept was demonstrated by EM simulation and experiments. The RCS reduction with nonuniform unit cells was compared with that of the conventional planar metamaterial absorber with uniform unit cells and superior results were demonstrated.Regarding the wavefront engineering device (Figure48), Aieta et al. designed a conformal metasurface lens to eliminate the off-axis aberration [240]. It was found that aberration-free focusing is possible under axial illumination but off-axis aberrations appear when the excitation is not normal to the interface. An alternative design for an aplanatic metasurface on a curved substrate was proposed to focus light without coma and spherical aberrations.Figure 48
(a) Schematic, PSF, and MTF of a flat metasurface lens. (b) Schematic, PSF, and MTF of a conformal metasurface lens. Figures are reproduced from [240].
(a)
(b)The flexible property of PDMS has direct applications in other optical systems. For example, when a metallic grating was fabricated on PDMS, the period could be changed dynamically by stretching the substrate. As illustrated in Figure49(a), the fabricated metasurface in our experiment looks orange and green, respectively, when stretched properly. Figure 49(b) shows the diffraction angle versus the overall length of the substrate when illuminated by a laser source at λ = 405 nm. The diffraction angle can be dynamically steered between 70 and 46 degrees.Figure 49
(a) Optical images of a flexible metasurface when stretched. (b) Diffraction angle of the metasurface grating for different length of the PDMS substrate. (c) Schematic of a flexible color-filtering metasurface. (d) Measured reflectance spectrum when the substrate is uniformly stretched. (c, d) Figures are reproduced from [244].
(a)
(b)
(c)
(d)In a similar way, Shen et al. proposed a color generation mechanism that produces colors by the Fano resonance effect on thin PMMA metasurface. The metasurface consists of a periodic array of cylinder of nanorods and the resonant frequency was tuned from 400 to 600 nm, as shown in Figures49(c) and 49(d).


## 3.10. Graphene Metasurfaces

Current metasurfaces are often limited to dielectric and metallic structured thin film. In recent years, graphene has attracted special attention owing to its exotic electronic and optical properties. Not surprisingly, graphene has been widely utilized as one kind of metasurfaces or as a key component of functional metasurfaces.Graphene is sp2-hybridized monolayer of carbon atoms densely packed into a honeycomb lattice, which was firstly experimentally isolated from graphite in the lab in 2003 [247]. In 2004, Geim et al. demonstrated that the carrier density in the graphene sheet can be controlled by a gate voltage, paving the way of graphene-based electronic devices. Subsequently, after the magnetic field response of graphene was validated, the studies on graphene’s electrooptics magnetooptics features increased dramatically. Moreover, the approach of growing large-scale pattern graphene film makes the practical applications of such devices possible.Indeed, the unique structural element of graphene gives rise to many excellent electromagnetic properties, permitting various important applications. For example, a single sheet of homogeneous graphene was found to be able to absorb only a little (~2.3%) fraction of incident white light at Dirac point, making it possible to be used as transparent conducing electrodes [248]. Besides, graphene exhibits ultrahigh electron mobility, anomalous quantum Hall effect, ambipolar electric field effect, massless relativistic carriers, over micrometer-scale spin coherence length, highly confined plasmonic propagation, and large nonlinear Kerr effect. Thanks to these properties, graphene, up to now, has been widely used to fabricate field-effect transistors, electrochemical biosensor, solar cells, super capacitors, lithium ion batteries, catalyst carriers, electromagnetic absorber, and so on [247].Surface conductivity is usually adopted to describe the electromagnetic characteristic of 2D graphene. If there is no external magnetostatic bias going through the graphene, the local conductivity is isotropic and can be approximately calculated using the Kubo formula on condition thatK
B
T
≪
μ
c, ħ
ω [249]:(44)
σ
2
D
ω
≈
i
e
2
4
π
ħ
l
n
2
μ
c
-
ω
+
i
2
Γ
ħ
2
μ
c
+
ω
+
i
2
Γ
ħ
+
i
e
2
k
B
T
π
ħ
2
ω
+
i
2
Γ
μ
c
k
B
T
+
2
ln
⁡
e
-
μ
c
/
k
B
T
+
1
,where k
B
T is the thermal energy, μ
c is the chemical potential, Γ is the scattering rate, and e, k
B, and ħ are electron charge, Boltzmann constant, and reduced Plank constant (Dirac constant), respectively. Two inequivalent pairs of cones with apex at the Brillouin zone corners constitute graphene’s band structure; thus, two kinds of electron transition exist: interband and intraband transition. The first term in (44) is due to the contribution of interband transition and the second term arises for intraband transition. From the equation we know that the chemical potential governs the transition frequency of electrons. Further, if the frequency satisfies the condition of ħ
ω
<
2
μ
c, the interband transitions can be neglected and (44) is simplified as Drude formula: (45)
σ
GR
ω
=
2
D
π
i
ω
+
i
2
Γ
,where D is a Drude weight. Owing to the mapping relation between gate voltage and chemical potential, the two equations are fairly enough to describe the conductivity of gate voltage-biased graphene.Moreover, if the graphene sheet is present in a perpendicular magnetostatic bias, owing to the cyclotron motion of charge carriers, a nondiagonal component is introduced, namely, Hall conductivity. In low frequency (<10 THz usually), graphene is represented by full tensor conductivity:(46)
σ
GR
=
σ
x
x
σ
x
y
σ
y
x
σ
y
y
,with(47)
σ
x
x
ω
,
B
=
σ
y
y
ω
,
B
=
2
D
π
·
2
Γ
-
i
ω
ω
c
2
-
ω
+
i
2
Γ
2
,
σ
x
y
ω
,
B
=
-
σ
y
x
ω
,
B
=
-
2
D
π
·
ω
c
ω
c
2
-
ω
+
i
2
Γ
2
,where ω
c
=
e
B
v
f
2
/
μ
c is the cyclotron frequency, B is the amplitude of magnetostatic bias, and v
f is the Fermi velocity of the Dirac fermions in graphene. Thus, the conductivities for the RCP light and the LCP light can be derived as σ
±
=
σ
x
x
±
i
σ
x
y, where sign “+” stands for RCP light and “−” stands for LCP light.More efforts have been devoted to the investigation of graphene in recent years [250]. Some works were focused on enhancing the Faraday rotation angle in the microwave, THz, and infrared region. Meanwhile, graphene as a component of ultrathin electromagnetic absorber has drawn great attention. It is reported that the monolayer graphene is an effective saturable absorber for mode-locking fiber lasers. As illustrated in Figures 50(a) and 50(b), it was demonstrated that complete optical absorption can take place in a single patterned sheet of doped graphene [251]. One interesting phenomenon shows that monolayer graphene shows highly directive comb-like thermal radiation at near-infrared frequency [249]. With the layer number increases, the radiation angle and beamwidth would be changed, as shown in Figures 50(c) and 50(d).Figure 50
(a) Schematic picture showing transverse magnetic light impinging on graphene placed on a periodically structured conducting substrate. The light is converted into surface plasmonic waves and subsequently absorbed in graphene. (b) Dependence of the absorption at resonance on the corrugation height (left panel) for different graphene Fermi energies,E
F, and relative absorption for a nonzero metamaterial relaxation’s rate. (c) Optical conductivity of graphene under electric bias. (d) Thermal emission property of the grapheme layer obtained from Kirchhoff’s law. (e) Schematic of the graphene absorber under both electric bias and magnetic bias. (f) Absorption of the dual-biased absorber. Figures are reproduced from [249, 251, 252].
(a)
(b)
(c)
(d)
(e)
(f)To increase the freedom degree of design, subwavelength structures have been proposed to change of electromagnetic response of graphene. Consequently, the effective conductivity of pattered graphene was investigated. In 2012, effective impedance for a patch patterned graphene sheet was proposed. It can be considered as a combination of two parts: impedance of unpatterned graphene produced by a scaling factor and capacitance caused by the gaps. The accuracy of the proposed impedance is debatable, because the capacitance is originated from the electronic motion which is relative to the magnetic responsible conductivity of graphene. In 2014, we [252] presented an approach for calculating the effective impedance for a hole-patterned graphene sheet based on equivalent surface RLC impedance model. The impedance caused by periodic hole was obviously relative to the magnetostatic bias. Utilizing the model, authors well explained the magnetic circular dichroism of the hole-patterned graphene absorber in a varying bias within 0~7 Tesla.Graphene can also be utilized in plasmonic metasurface to increase the performance of traditional plasmonic devices. It is well known that traditional plasmonic materials do not work well in the infrared band, owing to the significant loss. In 2011, Engheta’s theoretical study showed that one can engineer the patch of surface wave on graphene by varying the chemical potential, making it a new platform of transformation optics [54]. Owing to its complex conductivity, graphene supports surface plasmon modes, accompanied with extremely short effective wavelength. Based on the exotic electronic transfer properties, graphene-based plasmonic waveguide devices and even Luneburg lens were constructed (see Figures 51(a) and 51(b)).Figure 51
(a) Simulation results ofE
y (snapshot in time) for a guided wave at f = 30 THz along the ribbon-like section of graphene. (b) One atom-thick Luneburg lens. (c)–(e) Electric fields for the eigenmodes at a graphene microtube. (f) Schematic of a bent microtube. (g) Simulated electric field distribution on the graphene microtube. (a, b) Figures are reproduced from [54].
(a)
(b)
(c)
(d)
(e)
(f)
(g)Very recently, we demonstrated that spiral surface plasmon could be utilized to transfer orbital angular momentum (OAM) [253]. Graphene-based microtube was demonstrated to be able to accomplish this goal perfectly. When a graphene tube is coated on the dielectric cylinder, the whole structure can also steadily support the steady propagation of light carrying OAM with different topological charges, as shown in Figures 51(c)–51(g). Furthermore, as the effective wavelength of the SPP induced in the graphene is much shorter than that in vacuum, the graphene-based microtube is suitable for the propagation of subwavelength of OAM.


## 3.11. Nonlinear Metasurfaces

Metasurfaces can also be utilized to enhance the nonlinear effect [254]. Different from other broadband applications, the nonlinear process requires strong increase of the local fields, which is only obtainable for resonant metasurface. One of the most important applications of nonlinear metasurface is the harmonic generation, such as second harmonic generation (SHG) and third harmonic generation (THG).One way to enhance SHG is to engineer the metasurface so that they resonate at both the fundamental frequency (FF) and the harmonic frequency (HF) [255–257]. In 2014, Lee et al. proposed and experimentally realized metasurfaces with a record-high nonlinear response based on the coupling of electromagnetic modes in plasmonic metasurfaces with quantum engineered electronic intersubband transitions in semiconductor heterostructures [258]. It was stated that the obtained susceptibility is many orders of magnitude larger than any second-order nonlinear response in optical metasurfaces measured up to then.To obtain stronger nonlinear response, it is critical to understand the intrinsic relation between the linear and nonlinear processes. Fortunately, it was also demonstrated that the nonlinear response can also be predicted by using the information of linear response [259].


## 4. Fabrication Techniques of Metasurface

Up to date, there are many fabrication techniques available for the physical realization of metasurface. In microwave frequencies, since the line width of metasurface is larger than ten microns, traditional optical or mechanical approaches could be used, such as printed circuit board (PCB) technologies based on mechanical milling, chemical etching, and laser ablation. In terahertz to mid-infrared region, the typical feature size of the metasurface structure is around 1~100μm. Traditional optical lithography and laser direct writing are commonly used for the structure fabrication in this frequency region.However, when the working frequency range goes into the near-infrared and visible spectra, the fine features of metasurfaces generally could not be realized by traditional mechanical or optical methods. Instead, electron beam or iron beams are required to accomplish the fabrication goal. Electron beam lithography (EBL) and focused ion beam milling (FIB) are frequently adopted to make the related structures working in this wavelength range, as shown in Figure52. Nevertheless, the fabrication processes of both of these techniques are based on the moving of the beam or stage, which makes them of slow speed and high cost, thus limiting their practical applications in metasurfaces fabrication in a certain extent.Figure 52
Typical fabricated metasurfaces at optical frequencies via EBL and FIB. Figures are reproduced from (a) [134], (b) [172], and (c) and (d) [2].
(a)
(b)
(c)
(d)Recently, some novel techniques are proposed in the fabrications of specific design of metasurfaces. Interference lithography is a very useful strategy in the fabrication of regular periodic patterns, such as grating and dot array. Periodic structures with feature size of hundred nanometers are easily realized by using UV laser. In order to further shrink the fabrication size of interference lithography, surface plasmon interference technique was developed. Subdiffraction limit patterns were obtained by employing the interference effect of SPPs [31, 260, 261]. The surface plasmon interference technique is considered to be the most promising plasmonic lithography technique for fabricating large-area simple periodic structures. However, it is difficult to generate complex and nonperiodic structures due to the limited propagating space for evanescent waves. More recently, reflective plasmonic slab or SPP cavity was proposed to improve the aspect profile and contrast of imaging pattern [32, 132], with experimentally reported 22 nm line width. As shown in Figures 53(a) and 53(b), it was shown that surface plasmon could be utilized to achieve line width of 50 nm. Very recently, hyperbolic metasurfaces composed of SiO2/Al films are explored to squeeze out bulk plasmon polaritons (BPPs) to produce large-area and uniform deep subwavelength interference patterns. As examples, two and four bulk plasmon polaritons (BPPs) interference lithography with a half pitch of 45 nm (~λ
/
8) were demonstrated in experiments. Much deeper resolution up to 22.5 nm (~λ
/
16) and variety of BPPs interference patterns are feasible.Figure 53
Interference lithography by surface plasmon polariton. (a) SEM image of the fabricated sample. (b) Simulated electric field distribution. (c) Schematic of the improved lithography technique. (d) Two-dimensional interference patterns. Figures are reproduced from [31, 260].
(a)
(b)
(c)
(d)With the purpose of achieving high efficient, large-area fabrication of the nanoscale metasurfaces with arbitrary shape, we propose to utilize surface plasmon imaging lithography to transfer the patterns on mask. As shown in Figures54(a) and 54(b), a Babinet-inverted plasmonic gradient metalens was fabricated. The metalens consists of anisotropic nanohole arrays with parabolic phase distributions. The size of approximate elliptic nanohole is 75 nm × 140 nm. We characterized the focusing property of metalens at visible light with wavelengths of 633 nm and 532 nm. The results of simulations show good agreement with the measured results. The results of experiment demonstrate that surface plasmonic lithography not only offers the ability of transfer pattern with nanoscale resolution but also could be applied in the fabrication of planar metasurface devices.Figure 54
Novel fabrication techniques for optical metasurfaces. (a) Schematic of the surface plasmon lithography and simulated intensity distributions for a metasurface lens. (b) SEM images of the mask (left) and fabricated sample (right). (c) Schematic of the multiangled NSL. (d) SEM images of fabricated samples. (c, d) Figures are reproduced from [262].
(a)
(b)
(c)
(d)Nanosphere lithography (NSL) is another promising technology in fabrication of metasurface with nanoscale feature size. The NSL was primely developed in the 1995, which was also referred to colloidal lithography. When NSL was just invented, only simple periodic nanoparticles could be produced. In recent years, the power of NSL was improved greatly. As shown in Figures54(c) and 54(d), Nemiroski et al. showed that the parameter space of shadow-derived shapes could enable a substantial expansion of the power of NSL [262]. They used custom-designed software to engineer compositions of shadows that guide multiangled deposition of one or multiple materials through a plasma-etched monolayer colloidal crystal (MCC). Meanwhile, Zhao et al. demonstrated multiple repetitions of hole-mask colloidal nanolithography to create single-layer metasurfaces with complex, multishape plasmonic nanostructures that exhibit desired optical functionalities [263]. This fabrication method is particularly suited for the creation of large-area, single-layer C3-rotationally symmetric, 3D chiral metasurfaces. It should be noted that a similar glancing angle deposition technique with shadowing effect is able to produce 3D film structures with fine control on a scale less than 10 nm [264].In addition to the fabrication technologies aforementioned, some other methods are introduced in some special situations. The capacity of nanoimprinting, multiple photons polymerization, microsphere lithography, and so forth [265] are also demonstrated in making the structures of metasurfaces. To overview, one should choose the proper fabrication method based on the corresponding requirement of specific structures which are designed.


## 5. Discussion

### 5.1. Unified Bandwidth Limit of Broadband Metasurfaces

As shown in the above discussion, the metasurfaces have many different applications depending on their constitutive materials and geometry. Nevertheless, all these devices can be classified as broadband, wideband, and narrowband according to their frequency responses. In this section, we would give a unified theory for the bandwidth limit of these metasurfaces, especially regarding the absorbers and polarizers. For the simplification of the discussion, we would like to consider only the narrowband and broadband cases.The typical case of narrowband application is the Fano resonance. One of the most important aspects of Fano resonance is the sharp resonance peak accompanied with strong local field enhancement, which is the basis of many applications, such as biological sensing and nonlinear photonics [21]. Unfortunately, ultrahigh Q-factor is difficult to be realized for two-dimensional metasurfaces due to the lack of large volume confinement of electromagnetic fields and strong coupling to free space [20]. Recently, we showed that there is fundamentally no limit for the bandwidth when no absorption loss is considered and the metasurface is infinite in the horizontal plane [19]. However, a further study is needed to show the limit for the finite metasurface.For broadband and multiband applications, the dispersion of metasurfaces can be exploited. As illustrated in Figure55, it is shown that the dispersion of metasurface can enable superresolution imaging beyond the diffraction limit, high performance color filter, broadband absorbers, and polarizers.Figure 55
(a) Dispersion of an ultrathin metallic film with ultrasmall effective wavelength. (b) Dispersion of a metasurface consisting of metal-insulator-metal (MIM) structure, which acts as a high efficient color filter. (c) Lorentz dispersion for broadband metasurface absorber. (d) Lorentz-type dispersion for broadband polarization control. Figures are reproduced from (a) [55], (b) [17], (c) [114], and (d) [81].
(a)
(b)
(c)
(d)Most importantly, the results on coherent perfect absorber and coherent perfect rotation have shown that there is also no bandwidth limit for these applications [38, 76]. However, for noncoherent absorbers and polarizers, the classic limits are still applicable [100, 266], if we do not consider the case of non-Foster and active devices [267]. It is important to note that the bandwidth limits for the absorbers and polarizers have the same origin, and both of them can be deduced from the concept of artificial magnetic conductor (AMC). For AMC, there is a fundamental limit on the bandwidth [266](48)
h
≥
λ
max
⁡
-
λ
min
⁡
π
2
ln
⁡
2
Δ
ϕ
,where Δ
ϕ is the reflective phase shift, which should be 0 for perfect magnetic conductor and π for perfect electric conductor.For perfect absorber comprised of a resistive sheet on a lossless AMC, the relation between the absorption and phase shift can be written as(49)
r
=
exp
⁡
i
Δ
ϕ
-
1
exp
⁡
i
Δ
ϕ
+
3
.The 10 dB and 20 dB copolarized reflection coincides withΔ
ϕ
=
1.176 and 0.4. The thickness limit can be written as 0.054
Δ
λ and 0.163
Δ
λ. From Rozanov’s theory, this limit should be written as(50)
h
≥
λ
m
a
x
-
λ
m
i
n
Γ
172
,where Γ is the reflectance in dB. For 10 dB and 20 dB reflectance, the thickness limits are 0.058
Δ
λ and 0.116
Δ
λ, agreeing well with the above results. As shown in Table 1, the thickness ratios of all the current available absorbers except the thin film CPA are smaller than the ideal case.Table 1
Overview of the bandwidth limit for metasurface-based absorbers.
Journal and time
Thickness
Δ
λ (20 dB)
Ratio (limit: 0.163)
IEEE Trans. Antennas Propagat.  2011 [110]
14.5 mm
83.4 mm
0.174
Opt. Express, 2011 [245]
4.5 mm
25.7 mm
0.175
Opt. Lett., 2012 [114]
1.5μm
8.72μm
0.172
Opt. Express, 2012 [38]
0.3 nm
∞
0
Appl. Phys. Lett., 2012 [102]
5 mm
13.86 mm
0.36
ACS Nano, 2014 [105]
0.86μm
3.57μm
0.24
Phys. Rev. Lett., 2013 [246]
40 mm
80.2 mm
0.498For perfect reflective half-wave plate, the copolarized reflection can be written as(51)
r
=
1
-
exp
⁡
i
Δ
ϕ
2
.The 10 dB and 20 dB copolarized reflection coincides withΔ
ϕ
=
0.6435 and 0.2. The thickness limit can be written as 0.115
Δ
λ and 0.233
Δ
λ. In this regard, our recent results have given an approach to overcome this limitation [81, 82].In addition, we would like to comment that the thickness-bandwidth limitation of perfect absorbers can also be extended to the broadband antireflection coatings. Considering light passing from a medium with high refractive indexε to air, the energy can be nearly perfectly absorbed if a resistive layer with frequency-independent resistance R is added at the boundary [39]. As a result, the maximum thickness for the antireflection coating is that of the perfect absorbers.


### 5.2. Future Trends of Metasurfaces

In summary, the area of metasurfaces has become a cutting-edge and promising researching direction in recent years, although long histories can be found in almost any of their branches. In general, there is an obvious trend to extend the researching frequency regime from microwave to optical regime or the new emerging terahertz region. One may wonder that the extension of frequency range is straightforward and thus not so physically meaningful. However, we must note that the materials properties would change dramatically at different frequencies. The fabrication techniques and measurement equipment will also vary. At optical frequencies, even quantum phenomena would play an important role [21].As illustrated in Figure56, in the next few years, the researches in metasurfaces will be focused on the aspects including but not limited to [2] the following.Figure 56
Outlook of the future trends of metasurface and metadevices. Figures are reproduced from [2].Functional Metasurfaces with Better Performances. For example, current flat lenses suffered from the strong chromatic dispersion. Although these devices are thin, lightweight, and capable of working at a wide range of frequencies, the focus lengths would vary as the change of operational wavelength. Recently, some works have been devoted to solving this problem, but the performance is still far from perfect [268]. Another drawback of these metasurfaces is that efficiencies are typically very low, especially for the devices based on geometric phase [134, 193]. As a result, much work should be paid to enhance the efficiency [204].Fabrication Technologies for Large-Area Metasurfaces. One of the huge challenges for the successful application of metasurfaces is how to fabricate these metasurfaces fast and low-costly. With these fabrication techniques [269], a bright future of metasurfaces and metasurface-based devices can be envisioned.


## 5.1. Unified Bandwidth Limit of Broadband Metasurfaces

As shown in the above discussion, the metasurfaces have many different applications depending on their constitutive materials and geometry. Nevertheless, all these devices can be classified as broadband, wideband, and narrowband according to their frequency responses. In this section, we would give a unified theory for the bandwidth limit of these metasurfaces, especially regarding the absorbers and polarizers. For the simplification of the discussion, we would like to consider only the narrowband and broadband cases.The typical case of narrowband application is the Fano resonance. One of the most important aspects of Fano resonance is the sharp resonance peak accompanied with strong local field enhancement, which is the basis of many applications, such as biological sensing and nonlinear photonics [21]. Unfortunately, ultrahigh Q-factor is difficult to be realized for two-dimensional metasurfaces due to the lack of large volume confinement of electromagnetic fields and strong coupling to free space [20]. Recently, we showed that there is fundamentally no limit for the bandwidth when no absorption loss is considered and the metasurface is infinite in the horizontal plane [19]. However, a further study is needed to show the limit for the finite metasurface.For broadband and multiband applications, the dispersion of metasurfaces can be exploited. As illustrated in Figure55, it is shown that the dispersion of metasurface can enable superresolution imaging beyond the diffraction limit, high performance color filter, broadband absorbers, and polarizers.Figure 55
(a) Dispersion of an ultrathin metallic film with ultrasmall effective wavelength. (b) Dispersion of a metasurface consisting of metal-insulator-metal (MIM) structure, which acts as a high efficient color filter. (c) Lorentz dispersion for broadband metasurface absorber. (d) Lorentz-type dispersion for broadband polarization control. Figures are reproduced from (a) [55], (b) [17], (c) [114], and (d) [81].
(a)
(b)
(c)
(d)Most importantly, the results on coherent perfect absorber and coherent perfect rotation have shown that there is also no bandwidth limit for these applications [38, 76]. However, for noncoherent absorbers and polarizers, the classic limits are still applicable [100, 266], if we do not consider the case of non-Foster and active devices [267]. It is important to note that the bandwidth limits for the absorbers and polarizers have the same origin, and both of them can be deduced from the concept of artificial magnetic conductor (AMC). For AMC, there is a fundamental limit on the bandwidth [266](48)
h
≥
λ
max
⁡
-
λ
min
⁡
π
2
ln
⁡
2
Δ
ϕ
,where Δ
ϕ is the reflective phase shift, which should be 0 for perfect magnetic conductor and π for perfect electric conductor.For perfect absorber comprised of a resistive sheet on a lossless AMC, the relation between the absorption and phase shift can be written as(49)
r
=
exp
⁡
i
Δ
ϕ
-
1
exp
⁡
i
Δ
ϕ
+
3
.The 10 dB and 20 dB copolarized reflection coincides withΔ
ϕ
=
1.176 and 0.4. The thickness limit can be written as 0.054
Δ
λ and 0.163
Δ
λ. From Rozanov’s theory, this limit should be written as(50)
h
≥
λ
m
a
x
-
λ
m
i
n
Γ
172
,where Γ is the reflectance in dB. For 10 dB and 20 dB reflectance, the thickness limits are 0.058
Δ
λ and 0.116
Δ
λ, agreeing well with the above results. As shown in Table 1, the thickness ratios of all the current available absorbers except the thin film CPA are smaller than the ideal case.Table 1
Overview of the bandwidth limit for metasurface-based absorbers.
Journal and time
Thickness
Δ
λ (20 dB)
Ratio (limit: 0.163)
IEEE Trans. Antennas Propagat.  2011 [110]
14.5 mm
83.4 mm
0.174
Opt. Express, 2011 [245]
4.5 mm
25.7 mm
0.175
Opt. Lett., 2012 [114]
1.5μm
8.72μm
0.172
Opt. Express, 2012 [38]
0.3 nm
∞
0
Appl. Phys. Lett., 2012 [102]
5 mm
13.86 mm
0.36
ACS Nano, 2014 [105]
0.86μm
3.57μm
0.24
Phys. Rev. Lett., 2013 [246]
40 mm
80.2 mm
0.498For perfect reflective half-wave plate, the copolarized reflection can be written as(51)
r
=
1
-
exp
⁡
i
Δ
ϕ
2
.The 10 dB and 20 dB copolarized reflection coincides withΔ
ϕ
=
0.6435 and 0.2. The thickness limit can be written as 0.115
Δ
λ and 0.233
Δ
λ. In this regard, our recent results have given an approach to overcome this limitation [81, 82].In addition, we would like to comment that the thickness-bandwidth limitation of perfect absorbers can also be extended to the broadband antireflection coatings. Considering light passing from a medium with high refractive indexε to air, the energy can be nearly perfectly absorbed if a resistive layer with frequency-independent resistance R is added at the boundary [39]. As a result, the maximum thickness for the antireflection coating is that of the perfect absorbers.


## 5.2. Future Trends of Metasurfaces

In summary, the area of metasurfaces has become a cutting-edge and promising researching direction in recent years, although long histories can be found in almost any of their branches. In general, there is an obvious trend to extend the researching frequency regime from microwave to optical regime or the new emerging terahertz region. One may wonder that the extension of frequency range is straightforward and thus not so physically meaningful. However, we must note that the materials properties would change dramatically at different frequencies. The fabrication techniques and measurement equipment will also vary. At optical frequencies, even quantum phenomena would play an important role [21].As illustrated in Figure56, in the next few years, the researches in metasurfaces will be focused on the aspects including but not limited to [2] the following.Figure 56
Outlook of the future trends of metasurface and metadevices. Figures are reproduced from [2].Functional Metasurfaces with Better Performances. For example, current flat lenses suffered from the strong chromatic dispersion. Although these devices are thin, lightweight, and capable of working at a wide range of frequencies, the focus lengths would vary as the change of operational wavelength. Recently, some works have been devoted to solving this problem, but the performance is still far from perfect [268]. Another drawback of these metasurfaces is that efficiencies are typically very low, especially for the devices based on geometric phase [134, 193]. As a result, much work should be paid to enhance the efficiency [204].Fabrication Technologies for Large-Area Metasurfaces. One of the huge challenges for the successful application of metasurfaces is how to fabricate these metasurfaces fast and low-costly. With these fabrication techniques [269], a bright future of metasurfaces and metasurface-based devices can be envisioned.



---

*Source: 204127-2015-10-04.xml*