<figure><img src="image_22.png" /><figcaption>**FIG. 14.** Polarization sensitive metasurface holograms, 2D polarization structures and their combination. (a) Helicity multiplexed holograms. Two central symmetric helicity-dependent holographic images are reconstructed under the illumination of LCP (bee and flower) and RCP light beams (flower and bee). (b)–(d) Schematic diagram of a 3D metasurface hologram. (c) A 3D object (jet) and (d) Experimentally obtained a real holographic image of the jet at an observation plane under the illumination of an RCP light beam. (e)–(g) Schematic for hiding a gray-scale high-resolution image in a laser beam through metasurface based on Malus' law. (f) The hidden image of James Clerk Maxwell is revealed with a linear polarizer (analyzer). (g) Detailed information in the eyebrow area (10 × 10 pixels). The right and left FIGS show the polarization distribution and the corresponding intensity profile. (h)–(j) Mechanism of polarization encryption for encoding a color image. (h) The target image of flower (red) and leaves (green). (i) Detailed information in the selected region (6 × 5 pixels) of the target image (top panel) and the corresponding orientation angles and feature sizes of dielectric nanopillars (bottom panel). (j) Results of metasurfaces for hiding a color image based on color mixing, which is realized with a metasurface consisting of supercells. (k)–(m) A metasurface that can simultaneously realize polarization sensitive and insensitive holograms and 2D polarization profiles for hiding a high-resolution image (a castle), which can increase information channels and information density. Panels (a) reproduced with permission from Wen *et al.*, Nat. Commun. **6**, 1 (2015).<sup>407</sup> Copyright 2015 Springer Nature. (b)–(d) Reproduced with permission Huang *et al.*, Nano Lett. **13**, 3559 (2013). Copyright 2013 Springer Nature.<sup>426</sup> (e)–(g) Reproduced with permission from Yue *et al.*, Light **7**, 17129 (2017).<sup>423</sup> Copyright 2017 Springer Nature. (h)–(j) Reproduced with permission from Zang *et al.*, Adv. Mater. **30**, 1707499 (2018). Copyright 2018 Wiley-VCH.<sup>424</sup> (k)–(m) Reproduced with permission from Intaravanne *et al.*, Adv. Photonics Res. **2**, 2000046 (2021). Copyright 2020 Wiley-VCH.<sup>425</sup></figcaption></figure>

et al. presented a relatively simpler approach to realizing 3D holography using ultrathin metasurface consisting of subwavelength metallic resonators with varying orientation as shown in Fig. 14(b).<sup>392</sup> The phase information of the 3D object was calculated using commercially available CGH algorithm.<sup>422</sup> In the CGH algorithm, the 3D target object [Fig. 14(c)] was considered as a collection of many point sources. The complex amplitude at the hologram interface was numerically calculated through the superposition of the wavefronts of all point sources. Upon the illumination of the CP light beam, the metasurface reconstructed a real 3D holographic image within the Fresnel range of hologram as shown in Figs. 14(b) and 14(d). As explained earlier, the

incorporation of spatially varying polarization along with the phase distribution is essential to fully unlock the potential of metasurfaces for increased information storage. Yue *et al.* proposed such a technique to encrypt a 2D grayscale image (of James Clerk Maxwell) in a structured laser beam with inhomogeneous polarization distribution using metasurface based on Malus' law as shown in Fig. 14(e).<sup>423</sup> The result of the intensity profile of the encrypted grayscale image was revealed with an analyzer (linear polarizer) as shown in Fig. 14(f). To further explain the technique, a selected portion from the eyebrow area (10 × 10 pixels<sup>2</sup>) is enlarged in Fig. 14(g) to show the intensity and its corresponding pixel-level polarization distribution. It is noted that the resultant
beam exhibited a subwavelength resolution. Similarly, metasurfaces
can also be used to encode colorful images in inhomogeneous polariza-
tion profiles based on Malus's law. Zang *et al.* experimentally demon-
strated simultaneous encryption of intensity and color information
into a wavelength-sensitive polarization distribution.⁴²⁴ This technique
was used to embed high-resolution color images with precisely con-
trolled contrast and brightness onto a dielectric metasurface as shown
in Figs. 14(h)–14(j). The target high-resolution color image of a rose
was selected which encompassed green and red pixels with the varia-
tion of spatial brightness as shown in the top panel of Fig. 14(i). The
corresponding wavelength-dependent polarization distributions were
different for both colors and mapped by controlling the orientation
and the feature size of the dielectric nanopillars as shown in the bottom
panel of Fig. 14(i). Vivid red petals and green leaves were revealed with
the right transmission axis of the analyzer under the illumination of
660 and 550 nm wavelengths. The same method was also used to pro-
duce polarization-encrypted colorful images using additive color mix-
ing of the primary colors as shown in Fig. 14(j). In this work, a
supercell contains nanopillars with different feature sizes, which
respond to different wavelengths.⁴²⁴ By integrating such high-
resolution polarization encryption techniques with holography, many
diverse applications can be realized in information security, anticoun-
terfeiting, and high-density data storage. For example, an application
of optical information security was experimentally demonstrated by
integrating an arbitrary polarization distribution for image conceal-
ment and a hybrid CGH as shown in Fig. 14(k).⁴²⁵ The functionality
was achieved by simultaneously concealing a high-resolution image in
the polarization distribution and encoding holographic images
through the superposition of two-phase profiles for orthogonal CP
light beams. As a result, a metasurface was used to reconstruct holo-
graphic images at the observation plane either under the illumination
of linearly polarized light beam without the analyzer or under the illu-
mination of RCP light beam as shown in Fig. 14(m). The desired con-
cealed image was revealed with a predesigned angle combination of
the analyzer and input linear polarizer as shown in Fig. 14(l). In con-
trast, the other transmission axis combination of the analyzer and
input linear polarizer could not generate meaningful information. The
work also investigated the simultaneous incorporation of polarization-
sensitive and insensitive holograms with high-resolution image
encryption in the polarization distribution, which further enhanced
the information capacity and hence can be utilized for high-level anti-
counterfeiting.

C. Toward 3D polarization structures: challenges and future directions

2D high-resolution image encryption based on spatially varying
polarization distributions has been realized with metasurfaces.⁴²³⁻⁴²⁵
However, in addition to the phase, intensity, and color, the encryption
of spatially varying polarization distribution in a 3D space remains a
challenge. To generate the desired wavefront and dynamically manipu-
late the polarization distribution in a 3D space, an independent pixel-
level control of phase and polarization is simultaneously required
along the light's propagation. The biggest challenge to achieve such
functionality is the limited degree of freedom in the current metasur-
face design. Although few studies have shown unprecedented abilities
to break the conventional limits to some extent,⁴¹⁵,⁴²⁷⁻⁴²⁹ they are still
unable to address the complete and dynamic control of light fields in a

3D space. Therefore, a solution is required to address this problem at
the fundamental level where new control variables can be incorporated
into the metasurface design procedure. The required control variables
for an arbitrary 3D polarization structure include wavelength, wave-
front positioning (x, y, z), and dynamic polarization rotation in a 3D
space. Much work has been done to address one control parameter at
a time,⁴⁰⁷,⁴¹²,⁴²⁵,⁴²⁶,⁴³⁰ however, simultaneous control of all parameters
is scarce and challenging. The combinational control of more than one
parameter is also expected to yield unique optical field manipulation.
Recently, Zang *et al.* proposed a metalens with polarization functional-
ity through the superposition of both RCP and LCP components of
the light beam at each focal spot under the illumination of linearly
polarized incident light beam.⁴³¹ The authors started from a simple
lens model by incorporating an additional term for the polarization
rotation φ in the phase profiles of LCP and RCP components. Since a
linearly polarized incident light beam can be divided into LCP and
RCP light components, therefore, a portion of the transmitted wave is
converted to LCP light to focus with an additional phase shift –φ, and
the other portion is converted to RCP light with an additional shift of
φ. The idea was then extended to realize multiple focal points using
the superposition method with independent polarization rotations as
shown in Fig. 15(a). Wang *et al.* presented an off-axis multi-foci metal-
ens model to incorporate polarization rotations in four different focal
points at different locations on the observation plane as shown in
Fig. 15(b).⁴³² Unlike the previous work where only linear polarization
rotations are created, Wang *et al.* introduced RCP, LCP, and linear
polarization rotations for the application of polarimetry to detect the
polarization of arbitrary incident light beams. The ellipticity, handed-
ness, and major axis of the polarization state of the incident light beam
were determined through the measured intensities of the four focal
points.⁴³² Both designs have provided a unique insight into a pixel-
level simultaneous control of wavefront along with the independent
polarization rotations. More specifically, both unique ideas of polariza-
tion rotation at different focal lengths (f1 and f2) along the z-direc-
tion⁴³¹ and the off-axis (xi, yi) multi-foci metalens⁴³² have led to the
generation of 3D polarization structures. An optical focal curve can be
regarded as a continuous structure if the number of focal points along
the curve becomes infinite. Wang *et al.* started from a multi-foci metal-
ens with discretized focal points to a continuous optical curve along an
arbitrary trajectory by increasing the number of focal points.⁴³³ In the
next step, the 2D polarization curve model was transformed to 3D
polarization knot design by introducing the longitudinal parameter (z)
as an additional control variable in the phase terms using the superpo-
sition method. As a result, 3D light fields along with spatially varying
inhomogeneous polarization distributions and intensity patterns were
generated in the form of 3D optical knots as shown in Fig. 15(c).⁴³³
The predesigned polarization distribution was confirmed through the
modulated intensity patterns with an analyzer (linear polarizer). In
addition to the predefined inhomogeneous polarization distribution,
the polarization rotation at each point on the 3D trajectory was
dynamically modulated by changing the polarization state of the inci-
dent light beam. The complete evolution of the 3D structure was also
observed and measured using a CCD camera as shown in Fig. 15(d).
Intaravanne *et al.* introduced a new control variable (wavelength λ) in
the design procedure along with polarization rotation φ and 3D focal
position (u, v, f) to demonstrate wavelength selective 3D polarization
structures as shown in Fig. 15(e).⁴³⁴,⁴³⁵ At a given observation plane,
<figure><img src="image_23.png" /><figcaption>**FIG. 15.** Metalenses for realizing polarization rotation, 3D polarization structure manipulation and a compact spectrometer. (a) A multi-foci metalens with a polarization rotation functionality. (b) Application of multi-foci metalens for the polarization detection in the THz range. (c) Customized 3D polarization structures based on multi-foci metalens. (d) Simulated and experimental intensity distributions of 3D structures at different observation planes under the illumination of an RCP incident light beam. (e) Metasurface for color-selective 3D polarization structures. The left panel and right panel show the light intensity distributions without and with an analyzer, respectively. (f) A compact metasurface spectrometer based on multi-foci metalens. (g) Light intensity distribution under the illumination of different monochromatic incident light beams. (h) Spectrum detected by the metasurface spectrometer under the illumination of the polychromatic incident light beam. Polychromatic light beam contains five different wavelengths. Panels reproduced with permission from: (a) reproduced with permission from Zang *et al.*, Laser Photon. Rev. **13**, 1900182 (2019).<sup>431</sup> Copyright 2019 Wiley-VCH. (b) Reproduced with permission from Chang *et al.*, J. Vac. Sci. Technol., B **21**, 2755 (2003). Copyright 2020 Optica Publishing Group (formerly OSA).<sup>432</sup> (c) and (d) Reproduced with permission from Wang *et al.*, Nano Lett. **21**, 2081 (2021). Copyright 2021 American Chemical Society.<sup>433</sup> (e) Reproduced with permission from Intaravanne *et al.*, Light Sci App **11**, e302 (2022). Copyright 2022 Springer Nature.<sup>434</sup> (f)–(h) Reproduced with permission from Intaravanne *et al.*, Adv. Opt. Mater. **12**, 2203097 (2024). Copyright 2023 Springer Nature.<sup>435</sup></figcaption></figure>

different 3D polarization knots were generated by changing the wavelength of the incident light beam as shown in the left and right panels of Fig. 15(e). The right panel and left panels present the intensity distribution of corresponding 3D polarization structures with and without the analyzer, respectively.

The ability to generate arbitrary wavelength-dependent 3D polarization structures with ultrathin metasurfaces can be of interest to many pragmatic applications such as integration optics for compact spectrometers, and longitudinally variable structures for 2D and 3D optical image steganography. For example, motivated by the intrinsic dispersion property and ability of metalens to generate multiple focal

points at will, the wavelength of the incident light beam can be detected accurately by mapping the wavelength information to the intensity distribution. A compact spectrometer was realized by tailoring the dispersion based on the model of multi-foci metalens as shown in Fig. 15(f).<sup>436</sup> The metasurface-based spectrometer can focus and split the monochromatic [Fig. 15(g)] and polychromatic light beams [Fig. 15(h)] of different wavelengths to desired positions on an observation plane with 1 nm resolution. This unique dispersion control and high nanometer spectral resolution were achieved over a broadband range in the visible domain. The application of the proposed multi-foci metalens-based spectrometer proved that this technology has clear potential for
development in on-chip integrated photonics where wavelength detection, information processing, and spectral analysis are required in a compact platform. Like other emerging technologies, further improvements in the current design are required and new challenges need the attention of the research community. For example, the demonstrated metasurfaces have a low conversion efficiency, which is associated with the symmetric spin-orbit interactions and can be resolved by employing the nanoresonators with asymmetric spin-orbit interactions.<sup>411-413</sup> Furthermore, the polarization manipulation can be extended to incorporate arbitrary polarization states, including linear, elliptical, and circular polarization states. The integration of metasurfaces with materials such as 2D transition metal dichalcogenides,<sup>437</sup> conducting oxides,<sup>138</sup> liquid crystals,<sup>408,409,439</sup> and active materials<sup>209</sup> can add the extra degree of freedom and perform complicated optical tasks that are impossible or extremely challenging only with passive metasurface design.

# IX. META-OPTICS FOR AUGMENTED REALITY APPLICATIONS

Yuhui Gan, Arseny Alexeev, Thomas F. Krauss, and Andrea Di Falco*

*adf10@st-andrews.ac.uk

## A. Introduction

Augmented reality (AR) superimposes computer-generated content onto a transparent medium such that the user can perceive the real world augmented with the artificial content; this contrasts with virtual reality (VR), whereby a computer generates all the content. In AR applications,

the need for a transparent medium precludes the use of conventional displays. This requirement for transparency poses challenges, but it also promotes widespread acceptance of the technology. It benefits specialized applications such as assisted surgical operations or equipment maintenance, as well as end-user applications such as smartphones.

The main elements of an AR system are the image projector, which creates the digital image, and the optical combiner, which blends digital and real images before delivering the combined picture into the user's eyes.<sup>440</sup> Depending on the system architecture, the image projector consists of a light source (laser or LED), a spatial light modulator that modulates the light to create an image, e.g., based on liquid crystals or digital micro-mirrors, and image-forming optics such as lenses and mirrors. The optical combiner has been the subject of intense research over the last few years and is the focus of this paper. Combiners started as bulky and irregularly shaped glass elements,<sup>440</sup> as shown in Fig. 16(a), they then evolved into sophisticated photonic devices, usually involving nanostructures [Figs. 16(b) and 16(d)].

The most common configuration used for optical combiners to date is an optical waveguide that delivers light toward the observer via a Holographic Optical Element (HOE)<sup>441</sup> or a Surface Relief Grating (SRG)<sup>442</sup> [Fig. 16(b)]. Both HOEs and SRGs are manufactured using nanoscale lithographic techniques. Another type of optical combiner uses metalenses [Fig. 16(c)],<sup>443</sup> which are actively being explored for AR applications due to their low weight and their ability to imprint any desired phase distribution onto the incoming wave; therefore, metalenses can replace freeform optical elements due to their advantageous form factor and functionality. We note that several reviews describing AR systems using both waveguide combiners and metalenses are already available,<sup>444</sup> which this perspective article aims to

<figure><img src="image_24.png" /><figcaption>FIG. 16. Four AR architectures: (a) freeform optical combiners; (b) waveguide combiners with metagratings; (c) prism combiners with a metalens; (d) holographic metasurface combiners. (a)–(c) use full-color projectors to generate virtual image; and (d) uses plain laser beams and the virtual image is encoded in the metasurface.</figcaption></figure>
complement. Here, we first introduce the key parameters and figures of merit of an AR near-eye transparent display and then briefly review the state-of-the-art of various meta-optical technologies that are being used in consumer-grade AR glasses. Finally, we discuss the performance tradeoffs of each approach, including the use of transparent holographic displays based on metasurfaces. The holographic approach eliminates the need for an image projector, thus achieving a minimalistic form factor while delivering superior optical performance, as shown in Fig. 16(d).

## B. State of the art

### 1. Parameters

AR display systems must meet a variety of performance metrics, which can sometimes conflict one another. For example, the field of view (FoV) describes the range of angles at which optical rays are delivered to the human eye to form an image on the retina. The FoV is critical, as it defines the perceived size of the virtual object generated by the AR glasses. A typical value for heads-on AR displays is around 60° (diagonally)⁴⁴⁴ while, for reference, the human eye's FoV is approximately 120°;⁴⁴⁰ thus, it is desirable to extend the FoV of AR glasses. However, such an extension poses real challenges for the display brightness and resolution, as the properties of the image are determined by the luminous source. If the FoV increases, the luminous energy must be distributed over a larger range of solid angles, so the luminous energy per solid angle will suffer. Similarly, for a larger FoV, the resolution decreases, as there is only a fixed number of pixels available. A large FoV also has an impact on the eyebox, which describes the geometrical region of eye positions that contribute to image formation without vignetting. AR glasses must have a large eyebox to ensure tolerance to eye movements and to accommodate different users. The size of the eyebox is measured in mm in the x and y directions in the plane coinciding with the plane of the eye hole, where a minimum of 6 mm is required to accommodate inter-pupil distance variations of 95% of the human population. High-performance displays achieve >10 mm in both directions. The product of the FoV and the eyebox is comparable to the etendue of an optical system, as it represents the product of an area and an angle; this product is fixed by the image projector. For a given projector, an increase in the FoV directly results in a decrease in the eyebox size. As discussed further below, this conservation of etendue can be overcome by the method of “pupil replication”—which replicates the image source over the surface of the optical combiner, which is why the waveguide approach is so attractive. Finally, images must be created with good color and brightness uniformity, irrespective of FoV and eyebox, so this requirement cannot be traded off.

### 2. System architectures and technological platforms

**Freeform Optics**—The simplest way to deliver light from a projector to the eye is to reflect the projector signal toward the eye by a suitably shaped, partially reflective mirror, as shown in Fig. 16(a). This approach has the advantage of requiring minimal image pre-processing and results in a relatively simple system architecture while delivering good FoV (90°) and eyebox (>10 mm) as well as producing high-quality images. The main disadvantage of this approach is the need for a bulky, inconvenient headset that imposes an unnatural look

on the user due to the shape and weight of the freeform mirror and its tilt. Additionally, this design is fundamentally restricted by the conservation of etendue, as discussed before.

**Waveguides**—Currently, the most popular implementation of the AR optical combiner function consists of an imaging waveguide with diffractive elements. In a typical arrangement, three linear diffraction gratings are used, (i) to deliver the image rays created by the projector into the first diffracted order below the angle of total internal reflection of the glass-air interface, thus in-coupling image rays into the waveguide; (ii) split the image rays into higher diffraction orders, thereby replicating the image pupil; and (iii) diffract the image rays at multiple points into the user's eye, thus, outcoupling the image rays from the waveguide. The key advantage of this approach is that the waveguide produces copies of the image pupil, thereby surpassing the fundamental trade-off between the FoV and the eyebox imposed by the conservation of etendue, achieving FoV > 60° and eyebox > 10 mm without the need to use bulky free-form optics. The gratings are typically Bragg gratings recorded in holographic media or Surface Relief Gratings—SRGs. The technology of holographic Bragg gratings is very mature but this solution only offers low refractive index contrast. This intrinsically leads to a high selectivity of the diffraction process in terms of angle and wavelength, therefore limiting the FoV of the entire system.⁴⁴⁴ Despite these shortcomings, this approach is well suited for applications that do not require large FoV (for example, displaying notifications or giving instructions for navigation, for automotive

<figure><img src="image_25.png" /><figcaption>**FIG. 17.** (a) Side view of a waveguide combiner consisting of three elements, i.e., to in-couple, spread, and out-couple the image rays. The inset shows an example of a Surface Relief Grating (Reproduced with permission from Levola and Laakkonen, Opt. Express 15, 2067 (2007). Copyright 2007 OSA Publishing).⁴⁴⁵ (b) Top view of a waveguide combiner with two grating elements. The inset shows the cross section of an advanced etched metagrating which constitutes the hybrid element of the waveguide combiner which simultaneously spreads and out-couples the image rays, with a pitch of 300 nm.</figcaption></figure>
applications). SRGs are, in turn, fabricated by nano-structuring wave-
guide surfaces and possess higher refractive index contrast. Therefore,
SRGs support larger FoVs. Such gratings can now be fabricated with
high accuracy and high manufacturing yield because of advances in
nanofabrication, including the use of nanoimprint lithography [see
Fig. 17(a)].<sup>445</sup> This classical three-element grating scheme was pio-
neered by Nokia<sup>440</sup> and then adopted by other companies, including
Microsoft, Magic Leap, Vuzix, and others. A more advanced version of
the waveguide combiner scheme (e.g., that introduced by WaveOptics
uses two-dimensional SRGs to combine the expander and the out-
coupler elements in one hybrid unit). In this configuration, a larger
area of the combiner is available for the outcoupling, resulting in an
increased eyepool of >10 mm in both directions. Realizing these advan-
tages is, however, a challenging task. The grating must not only have
minimal dependence of the diffraction efficiency on the wavelength
and incident angle, but also balance the contributions from the image
rays that are incident from different directions, as specific optical rays
can reach a given extraction point via multiple routes and not just
through a single geometrical path as in the classical configuration, see
Fig. 17(b). In this way, the chromatic and angular aberrations can be
minimized to produce a uniform virtual image. These requirements
can only be met with the introduction of further degrees of freedom,
which has led to the development of 3D metagratings—true nano-
photonics objects sculpted into complex 3D shapes.<sup>446</sup> Each element of
such a 3D metagrating acts as a sub-wavelength antenna. The full
response of the grating is then defined by the convolution of the inter-
ference pattern of the entire grating with the radiation profile of each
grating element.<sup>447</sup> While traditional SRGs are patterned at scales
greater than the wavelength, these advanced metagratings require a
lithography resolution below 50 nm and high-precision alignment.

**Metalenses**—Metalenses utilize subwavelength structures to manip-
ulate light at the nanoscale. With their ultra-thin size, sub-wavelength
modulation scale, and ability to imprint any desired phase front onto
the incoming signal, metalenses can be used to make flat versions of tra-
ditional lenses<sup>448</sup> reducing the size, complexity, and cost of the optical
system.<sup>449,450</sup> Remarkably, metalenses can also be engineered to respond
differently to light with specific polarization, wavelength, or angle of
incidence.<sup>451,452</sup> This flexibility makes them very attractive for AR appli-
cations.<sup>453–455</sup> In the example of Fig. 16(c), metalenses are used in the
Maxwellian configuration, whereby the image is focused on the pupil
and the virtual image is always in focus, independent of the accommo-
dation of the eye lens.<sup>456</sup> This approach offers advantages in terms of
FoV. However, the eyepool for the Maxwellian configuration is very
small.<sup>444</sup> While metalenses offer superior control over the wavefront of
the transmitted light, they are characterized by intrinsic tradeoffs.<sup>457</sup> The
main trade-off is the fact that a typical metalens design strongly depends
on the wavelength. The choice of thin film thickness, meta-atom size
and unit cell, as well as the use of Fresnel zones to accommodate multi-
ple 2π phase shifts, are all wavelength-dependent. Moreover, the unit
cell size depends on the numerical aperture (NA) according to the
Nyquist criterion as a <λ/(2 NA), which means that the higher NA
required for AR systems to achieve reasonably large FoV also demands
a smaller unit cell size. This quickly becomes very challenging in terms
of lithographic requirements, especially for operation in the visible. All
these requirements trade-off against each other; for example, the wave-
length dependence can be addressed by controlling the dispersion in
each meta-atom by substructuring the unit cell and using two

meta-atoms instead of one.<sup>458</sup> This is an elegant solution which, how-
ever, restricts the unit cell size for lithographic reasons, so only a low
NA or longer wavelength operation can be achieved. Another example
is the control of aberrations, where in particular, designed phase profiles
have been used to demonstrate a very large FoV,<sup>459</sup> but only for a single
wavelength.

When it comes to AR applications, metalenses face the same chal-
lenge as standard freeform optical elements in terms of balancing a suf-
ficiently large FoV (>60°) with a wide enough eyepool (>10 mm),
while possessing a small form-factor for the convenience of the user.
However, the main limitation is that due to the design and
manufacturing challenges we mention above, modern metalenses are
yet to become suitable for image-forming optical systems. As a result,
many metalenses are designed for security camera operations that do
not require multiple colors and that work best in the near-infrared.

**Holographic Metasurfaces**—In the scheme shown in Fig. 16(d), the microdisplay projector is replaced by a simple laser or an LED. This choice shifts the physical location of the digital information from the image projector to the optical combiner, which is much simpler, but restricts the system to fixed images stored in the hologram.<sup>35,460</sup> While some degree of image multiplexing is possible, the number of independent images that can be stored in the combiner is then rather limited. A solution would be the deployment of dynamically tuned metasurfaces to create AR glasses capable of displaying dynamic images. Such a dynamic holographic display could be achieved using a variety of material platforms and actuation mechanisms, as discussed in Sec. IX C.

C. Future perspectives

**Waveguides and Metalenses**—Metalenses and metagratings used in AR optical combiners exhibit noticeable similarities in terms of controlling a given wavefront and producing a desired optical response. Both approaches utilize engineered patterns of sub-wavelength antennas to create a desired functionality. Likewise, both in metalenses and metagratings, the complexity of the meta-atom design is now surpassing initial simplistic designs by shaping or substructuring the meta-atoms. By exploiting all the degrees of freedom of metaoptics design, it is now possible to improve the brightness and color uniformity of AR systems.

While the design complexity of the meta-atoms and the
manufacturing of metalenses and metagratings have already merged,
these two approaches employ fundamentally different architectures.
Given the advanced technology readiness level reached by the
waveguide-style combiner, it is anticipated that waveguide combiners
will be the choice for the next few generations of commercially avail-
able AR systems. The main advantage that motivates this choice is that
the waveguide architecture addresses the issue of the FoV—eyepool
trade-off, through the pupil replica mechanism. Importantly, from an
engineering point of view, in metagratings, it is also possible to manage
the extraction efficiency and thus maximize the extracted energy along
the propagation path of the image rays. The main challenge for
waveguide-based combiners remains to achieve good color and bright-
ness uniformity. These parameters are still limited by chromatic and
angular aberrations. Regardless of the coupling mechanism, it is
extremely challenging to in-couple and out-couple all the image rays
with the same efficiency, independently of their wavelength and inci-
dent angle. To this end, the shape of the 3D meta-atoms will require
further optimization. Importantly, this development will need to
include consideration of the manufacturing at the scale of the meta-
gratings, e.g., using nano-imprinting technologies and using materials
with a sufficiently high index of refraction. Current efforts in this direc-
tion tend to fabricate gratings with a refractive index greater than 2.5
by imprinting patterns into polymers and using them as an etching
mask.⁴⁶¹ This approach can employ a wide range of conventional opti-
cal materials but possesses the challenge of accurately translating com-
plex metagrating shapes into dielectric materials through a single-step
etch process [see, e.g., Fig. 17(b)]. Alternative approaches include
imprinting into a polymeric matrix with added nanoparticles, which
have been used to create 3D nano-structures with a refractive index
greater than 2⁴⁶²,⁴⁶³ avoiding the etching step.

While waveguide combiners will likely remain the standard approach, they will improve on their limitations by incorporating some of the benefits of metalenses. Next-generation combiners will likely exploit the polarization-dependent response of meta-atoms, implement pupil replica schemes, be achromatic, and offer a high level of sophistication of response. In the process, they will also tackle other key issues like the unwanted scattering of external light, known as the “rainbow effect,” and the outcoupling of the digital image away from the user’s eyes, referred to as “glowing eye.” This will be achieved by designing metagratings that have an asymmetric optical response depending on the direction of the incident light.

While the intrinsic limitations of metalenses make it harder to see them prevailing as combiners in AR glasses, we see potential in their use as AR technology integrated with LiDAR and Time-of-Flight sensors, and as optics for facile recognition applications.⁴⁶⁴ These applications have much less stringent achromatic requirements, as they solely need to operate at a predetermined wavelength and exclusively within the near-infrared (NIR) spectrum. This has the additional benefit of enabling the use of silicon technology, such as nanolithography, which is readily compatible with scaled-up manufacturing processes with high precision in extra small feature size.⁴⁶⁵,⁴⁶⁶

*Freeform combiners with metasurfaces*—Another possible direction in the development of metasurfaces for AR glasses is their use to enhance freeform optical elements.⁴⁶⁷ This type of hybrid freeform meta optics uses both the controlled phase response typical of metamaterials and the geometry of the freeform elements to fix both the image quality and the aberrations. Patterning curved substrates is challenging, but recent results have shown that this is a practically viable solution.⁴⁶⁷ Alternative approaches include the use of conformable meta-surfaces, which have the advantage of decoupling the fabrication constraints from the shape of the substrate to which they are applied.⁴⁶⁸,⁴⁶⁹ This manufacturing approach could also be used to create curved waveguide combiners to mimic curved lenses used in most modern spectacles by first manufacturing diffraction gratings on a transparent flexible film and then transferring this film onto a curved waveguide combiner. This type of combiner would be less bulky than conventional freeform combiners and have a more natural look, however, still be constrained by the conservation of the etendue. It is, therefore, more likely that freeform optics enhanced by metasurfaces will find better use in the image projector, working on a broadband range with a wide field of view.

*Holographic metasurfaces*—Finally, we would like to imagine ulti-
mate AR glasses based on holographic metamaterials. Current solu-
tions only offer static images, at best multiplexed in the same device,
using e.g., polarization, wavelength, the direction of the incoming light,

and their shape.⁴⁷⁰,⁴⁷¹ Future solutions would deploy active tuning mechanisms. The most promising solutions include the incorporation of liquid crystal cells coupled to metasurfaces filters,⁴⁷²,⁴⁷³ metasurfaces based on phase change materials⁴⁷⁴,⁴⁷⁵ and variants of transparent conductive oxide modulators.⁴⁷⁶,⁴⁷⁷ Ideally, the holographic metasurfaces should be tuned electrically, at the level of the single meta-atom, over a sufficiently wide modulation range, and reversibly over a meaningful number of cycles, cycle number still being an issue with phase change materials. Despite the fast and meaningful progress,⁴⁷⁸ at the time of writing this article, it is not clear which, if any, of these approaches will yield the magnitude in change of the optical response required by AR applications, with low dispersion and low loss. If this important issue could be solved, however, such glasses would be lightweight with a form factor barely different from modern spectacles. Their frame would be thin yet contain all the electronics and the light source. The degree of freedom available in the design would also enable the implementation of pupil replica strategies, thus surpassing the etendue constraints. By scanning a laser over various areas of a holographic metasurface and dynamically altering the optical response of specific meta-atoms, it becomes possible to generate wavefronts in any desired shape and direction. This approach could realize the goal of consumer-grade AR glasses that seamlessly integrate digital and real-world visuals.

To conclude, there have been major developments in AR systems over the last few years. Traditional methods have evolved to incorporate more sophisticated strategies to manage the delivery of light to the eye, incorporating nanopatterned optical interfaces. In their evolution, these systems have crossed paths and aligned with the progress made in the various areas of meta-optics, which is indeed one of the most versatile nanophotonic platforms available to optical engineers. Here, we have discussed both the differences and the similarities between the different platforms and practical solutions. While some considerations are unavoidably speculative, and AR systems of the future may look very different from current implementations, meta-optics has already carved a place for itself in this future.

X. METASURFACES FOR QUANTUM STATES GENERATION

Sylvain D. Gennaro, Tomás Santiago-Cruz, Igal Brener,
and Maria V. Chekhova*

*maria.chekhova@mpl.mpg.de

A. Introduction

In the early 20th century, the understanding of light underwent a
significant transformation through the discovery of the photoelectric
effect and the development of quantum theory.⁴⁷⁹ Pioneering physi-
cists of the time postulated the existence of quanta of light called pho-
tons—a term coined by the American physicist Gilbert N. Lewis in
1926 from the Greek word “phōs,” meaning “light.”⁴⁸⁰ However, it was
not until the 1970s that physicists learned to generate single photons
and even more fascinating states—pairs of such photons that behave
as a single quantum object, and exhibit entanglement. Subsequent
advancements enriched the toolbox of quantum optics with other
quantum states of light, such as squeezed states, Schrödinger cat states,
cluster states, and many others, whose description in terms of classical
electromagnetic theory leads to paradoxes. These quantum states of light are now pivotal instruments for quantum photonic technologies, including quantum information processing, communication, metrology, sensing, and imaging.<sup>481</sup>

Over the years, scientists have developed a plethora of single-photon sources<sup>482</sup> using atoms,<sup>483,484</sup> trapped ions,<sup>485</sup> single molecules in solids,<sup>486</sup> epitaxially grown<sup>487</sup> and colloidal<sup>488</sup> quantum dots, carbon nanotubes,<sup>489</sup> color centers in diamond,<sup>490</sup> and defects in two-dimensional materials.<sup>491</sup> The most convenient sources of entangled photons are created using nonlinear optical effects: spontaneous parametric downconversion (SPDC) in second-order nonlinear crystals<sup>492–497</sup> and spontaneous four-wave mixing (SFWM) in fibers.<sup>498,499</sup> SPDC and SFWM can also produce single photons if one photon of a pair is used to herald the presence of the other photon. However, the most significant application of these nonlinear effects is to generate and engineer entanglement between the two photons, whether in polarization or continuous variables, such as time/frequency and position/momentum. With stronger pumping, both SPDC and SFWM produce higher fluxes of photon pairs, forming different kinds of squeezed vacuum states. Being brighter than single- or few-photon states, squeezed vacuum and other squeezed states are especially useful for quantum measurement and sensing.

In recent years, optical metasurfaces have been developed to
manipulate and control the amplitude, phase, and polarization of
light.<sup>1,13,500–502</sup> The latter manipulation combined with enhanced effi-
ciencies due to engineered resonances has been used to promote the
classical process of harmonic generation at the nanoscale.<sup>53,130,135,503–519</sup>
More recently, metasurfaces have evolved into platforms for the genera-
tion and manipulation of quantum light. Thanks to their flexibility in
engineering high-quality optical resonances, metasurfaces can control
and amplify various forms of spontaneous emission—from the emission
of single photons by solid-state emitters<sup>58,100,395,489,520–525</sup> to the genera-
tion of photon pairs through nonlinear optical effects.<sup>137,384,526–529</sup> In
addition to their compact nature, metasurfaces are multifunctional,
capable of combining the generation of quantum light with tasks like
sorting,<sup>530</sup> filtering,<sup>531</sup> polarization transformation,<sup>532,533</sup> sensing,<sup>534</sup> and
engineering photon entanglement.<sup>535,536</sup> Metasurfaces thus present a
promising avenue to generate and control complex quantum states of
light at the nanoscale. In this short perspective, we direct our focus
toward the unique abilities of optical metasurfaces at enhancing the
emission of single photons or photon pairs through the engineering of
optical resonances.

B. Single-photon generation

One of the fundamental building blocks of optical quantum
technologies consists of single-photon sources. A prominent chal-
lenge in this field is thus the search for single-photon sources that
emit indistinguishable photons with well-defined polarization,
high purity, and high emission rates. Many traditional quantum
emitters (QEs) typically face issues such as low quantum yields and
emission rates, a broad emission spectrum, and omnidirectional
emission.<sup>525</sup>

Recently, metasurfaces have facilitated the enhancement of
spontaneous emission rates,<sup>58,100,395,489,520–525</sup> beam steer-
ing,<sup>48,88,537,538</sup> and polarization control of emitters<sup>470,539</sup> using
optical resonances. According to the Fermi golden rule, the emis-
sion rate of a QE increases with the local electromagnetic density

of states in its environment. As demonstrated by Purcell in 1946,
the spontaneous emission rate in an optical cavity is proportional
to the ratio between the quality (Q) factor of the cavity and the
optical mode volume.⁵⁴⁰ Consequently, optical resonances with
high quality factors and/or small optical mode volumes are sought
after for this purpose. From a quantum optical perspective, effects
of spontaneous emission—such as single-photon emission by
atoms or solid-state emitters, and the generation of photon pairs
through SPDC and SFWM—can be elucidated as being stimulated
by the vacuum field. Despite the vacuum field having an average
value of zero, it exhibits non-zero fluctuations around this mean.
The spectral density of these fluctuations is uniform across all
states in the k-space and is equal to one photon per state (per
mode).⁴⁷⁹ A resonance augments the density of states for the reso-
nant mode. Given the uniform population of states due to quantum
vacuum fluctuations, the resonance intensifies the spectral bright-
ness of these fluctuations at its wavelength and for the correspond-
ing orientation of the optical field. This explains the enhancement
of all spontaneous emission effects for resonant modes of optical
metasurfaces.

Similar enhancement of emission can be obtained using plas-
monic nanoantennas and metasurfaces. Plasmonic metasurfaces
harness the power of surface plasmons—collective electron oscil-
lations at interfaces between metals and dielectrics—to amplify
single-photon emission. By tailoring light-matter interactions
within nanoscale mode volumes, these structures improve the
efficiency of QEs. For instance, plasmonic metasurfaces were
shown to enhance the spontaneous emission rate of embedded
InAs quantum dots, as illustrated in Fig. 18(a).<sup>5,23</sup> The quantum
dot entered a superlinear photoluminescence regime, which was
attributed to the excitation of surface plasmon polaritons (SPPs)
and the subsequent room-temperature generation of hot elec-
trons. Plasmonic metasurfaces can also enhance the spontaneous
emission of isolated defects in 2D materials, such as hexagonal
boron nitride (hBN), that are known to emit single photons at
room temperature. For instance, Fig. 18(b) depicts a metasurface
composed of gold nanoparticle arrays that support localized sur-
face plasmon resonances. The strong confinement of the electric
field near the nanoparticle surface intensifies the spontaneous
emission, aligning with the Purcell enhancement in the weak cou-
pling regime.<sup>521</sup>

Plasmonic metasurfaces, while offering remarkable opportunities for enhancing single-photon generation through their ability to concentrate light in small volumes, face limitations in achieving high-Q resonances. These limitations arise due to the inherent Ohmic loss of plasmonic materials. Researchers are thus actively exploring alternative high refractive index dielectric materials to achieve higher Q-factors. All-dielectric metasurfaces offer a promising route to enhance single-photon generation at visible and near infrared wavelengths through the excitation of Mie-type resonances and high-Q bound states in the continuum (BIC). For instance, as depicted in Fig. 18(c), an early experimental demonstration shows an all-dielectric metasurface, made of arrays of high-index nanoresonators supporting magnetic dipole modes, modifying the single-photon emission of oxygen-doped single-walled carbon nanotubes (SWCNTs), by a moderate factor of 0.8 – 4.0. Moreover, single-dopant polarization experiments show an anomalous photoluminescence polarization rotation due to coupling
<figure><img src="image_26.png" /><figcaption>**FIG. 18.** Single-photon generation in metasurfaces. (a) Super-linear photoluminescence dynamics in SPP-quantum-dot coupling systems in a plasmonic metasurface.<sup>523</sup> (b) Deterministic coupling of quantum emitters in 2D materials to plasmonic nanocavity arrays.<sup>521</sup> (c) Solitary oxygen dopant emission from carbon nanotubes modified by dielectric metasurfaces.<sup>489</sup> (d) Mie-resonant GaAs nanocylinders incorporating five layers of InAs quantum dots.<sup>700</sup> (e) and (f) All-dielectric metasurface exhibiting quasi-BICs due to (e) lattice deformation (Si)<sup>58</sup> or (f) resonator deformation (GaAs).<sup>522</sup> On-chip single-photon sources coupled to (g) concentric dielectric rings<sup>539</sup> or (h) anisotropic nanobricks<sup>417</sup> enabling linear polarization and OAM control. (i) Dielectric bifocal metalens enabling the emission of single photons along one of the two different directions depending on their polarization.<sup>542</sup> (a) Reprinted with permission from Iwanaga *et al.*, ACS Photonics **5**, 897 (2018).<sup>523</sup> Copyright 2018 American Chemical Society. (b) Reprinted with permission from Tran *et al.*, Nano Lett. **17**, 2634 (2017).<sup>521</sup> Copyright 2017 American Chemical Society. (c) Reprinted with permission from Ma *et al.*, ACS Nano **11**, 6431 (2017). Copyright 2017 American Chemical Society.<sup>489</sup> (d) Reprinted with permission from Vaskin *et al.*, Opt. Express **29**, 5567 (2021).Copyright The Optical Society.<sup>100</sup> (e) Reprinted with permission from Yuan *et al.*, ACS Nano **11**, 10704 (2017). Copyright 2017 American Chemical Society.<sup>58</sup> (f) Reprinted with permission from Liu *et al.*, ACS Photonics **5**, 1365 (2018). Copyright 2018 American Chemical Society. (g) Reprinted with permission from Kan *et al.*, Adv. Mater. **32**, 1907832 (2020). Copyright 2020 Authors, licensed under a Creative Commons Attribution Noncommercial License4.0 (CC BY-NC).<sup>539</sup> (h) Reprinted with permission from Purcell, Proc. Am. Phys. Soc. **69**, 674 (1946). Copyright 1946 Authors, Creative Commons Attribution Noncommercial License4.0 (CC BY-NC).<sup>540</sup> (i) Reprinted with permission from Bao *et al.*, Sci. Adv. **6**, 8761 (2020). Copyright 2020 Authors, Creative Commons Attribution Noncommercial License4.0 (CC BY-NC).<sup>542</sup></figcaption></figure>

individual SWCNTs to silicon nanoresonators, showcasing the exciting potential of dielectric metasurfaces to control the polarization of QEs.<sup>488</sup>

Using optical modes with higher Q-factors, single-photon genera-
tion can be further enhanced. For instance, consider a metasurface
composed of Mie-resonant GaAs nanocylinders embedding five layers
of InAs quantum dots [Fig. 18(d)<sup>100</sup>]. Although the primary objective
of this study was to modify the photoluminescence polarization and
directionality through the outcoupling of quantum dots emission to
the magnetic quadrupolar modes, the authors also observed a note-
worthy 19-fold enhancement in the emission rate when compared to

an unstructured surface. This improvement in the spontaneous emis-
sion rate aligns with expectations, given the diminished Q factors asso-
ciated with the resonances involved.

All-dielectric metasurfaces can capitalize on high-Q optical reso-
nances such as symmetry-protected quasi-BICs.<sup>506-508</sup> BICs are
discrete-energy modes that do not radiate and possess energy levels
that coincide with a continuous spectrum of radiating modes.<sup>141</sup>
Leveraging their high-Q resonances can lead to increased spontaneous
emission. For instance, as depicted in Fig. 18(e), a 1000-fold enhance-
ment of photoluminescence was observed for four layers of self-
assembled Ge quantum dots (QDs) embedded within a metasurface
composed of a periodic lattice of asymmetric air holes in a silicon-on-insulator (SOI) slab. This metasurface exhibited quasi-BICs with a Q-factor of approximately 1000.⁵⁸

Similarly, a metasurface employing broken-symmetry GaAs resonators, arranged in a square lattice, showcased a several-hundred-fold enhancement in the photoluminescence of monolithically embedded, self-assembled, near-infrared InAs/InGaAs QDs [Fig. 18(f)]. Notably, the symmetry protected quasi-BICs reshaped the emission of the QDs, making it unidirectional along the normal to the metasurface.⁵²²

Optical metasurfaces can go beyond the mere enhancement of spontaneous emission and tailor its polarization and orbital angular momentum properties. Examples are metasurfaces designed in the configuration of a bullseye target through concentric dielectric rings [Fig. 18(g)]⁵³⁹ or anisotropic nanobricks [Fig. 18(h)],⁵⁴¹ allowing the emission of single photons with controllable polarization. Consider a nitrogen-vacancy (NV) center at the center of concentric dielectric nanoridges positioned above a silver film, as shown in Fig. 18(g). This arrangement emits single photons with well-defined circular polarization (chirality >0.8) and remarkable directionality (collection efficiency reaching up to 92%), a result of the tailored phase of the field scattered from the QE and the corresponding excited surface plasmon polaritons.⁵³⁹ Similarly, Fig. 18(h) illustrates how a metasurface composed of dielectric anisotropic nanobricks, enveloping a room-temperature single-photon emitter—germanium vacancy center (GeV-ND) positioned on a silica (SiO₂) spacer-covered silver (Ag) substrate—excites radially diverging SPP waves. In this manner, metasurfaces can confer topological charges to emitted single photons, thus enabling the emission of linearly polarized vortex beams. The authors additionally demonstrated the realization of multiplexing single-photon emission channels with orthogonal linear polarizations carrying distinct topological charges and demonstrate their entanglement.⁵⁴¹ A further application of this concept involves the construction of a dielectric bifocal metalens atop a SiO₂ and gold film, housing a quantum dot within the SiO₂ layer [Fig. 18(i)]. The metalens is designed with its two foci aligned with the positions of the quantum dot and its mirrored image. Consequently, each photon can be emitted along one of the two distinct directions, depending on its polarization.⁵⁴²

To conclude, we have surveyed some of the recent work in using metasurfaces to improve the performance of quantum emitters embedded within them, achieved through optical resonance engineering. In addition, metasurfaces can also tailor the emission direction and polarization. Shifting our focus, we will now turn to showcasing how nonlinear metasurfaces can facilitate the generation of photon pairs via SPDC.

### C. Biphoton generation

Quantum state engineering largely relies on SPDC⁴⁹²,⁴⁹³,⁴⁹⁶,⁴⁹⁷ and SFWM.⁴⁹⁸,⁴⁹⁹ These processes lead to the spontaneous emission of entangled photon pairs, known as biphotons, while adhering to principles of energy and momentum conservation. SPDC and SFWM serve as the foundation for generating a diverse range of quantum states, spanning from heralded single photons and higher-order Fock states to squeezed states and multiphoton non-Gaussian states like Schrödinger cat states or NOON states.

In contrast to bulk crystals, SPDC at the nanoscale relaxes the requirement for longitudinal momentum conservation,⁵⁴³ resulting in a broad range of frequencies and angles for emitted photon pairs. For instance, the broad frequency-angular spectrum of SPDC in ultrathin nonlinear films [Fig. 19(a)]⁵⁴³ leads to a heightened degree of frequency and angular entanglement, along with short correlation times and sub-wavelength correlation distances.¹¹⁶ Moreover, the relaxation of momentum conservation offers the potential for tunable polarization entanglement,⁵⁴⁴ thereby expanding the possibilities for quantum state engineering. However, in optical antennas and metasurfaces, resonances serve to select the wavelengths, directions, and polarizations of enhanced photon emission. Through meticulous selection and design of optical modes and resonances, the generation of entangled photons with improved efficiency can be achieved with control over their emission direction and creation of intricate quantum states.¹¹⁶,¹³⁷,³⁸⁴,⁵²⁷⁻⁵²⁹

Observing SPDC at the nanoscale presents challenges. SPDC is inherently a weak parametric process, and experiments with nanophotonics samples require prolonged data acquisition to detect a signal. To find suitable materials and structures, one can use classical processes such as second harmonic generation (SHG) and sum frequency generation (SFG).⁵²⁷ These processes share the same phase matching condition and effective nonlinearity as SPDC. Alternatively, difference frequency generation (DFG) can be employed within stimulated emission tomography (SET) to investigate the efficiency of SPDC and the entanglement of biphotons.¹¹⁶,⁵⁴³,⁵⁴⁵,⁵⁴⁶

For instance, SFG was used to predict the enhancement of SPDC from a nonlinear plasmonic metagrating made of periodic silver nano-strips atop a thin lithium niobate (LiNbO₃) film and a silver substrate. Through optical excitation, localized surface and gap plasmon resonances were formed around the edges of the nanostrips and within the nanogaps. This amplified the optical field in the nonlinear LiNbO₃ layer.⁵⁴⁷ However, because plasmonic-based systems have high Ohmic losses, they also emit incoherent light, which would reduce the signal-to-noise ratio of the generated biphotons.⁵⁴⁸

Compared to their plasmonic counterparts, metasurfaces crafted from materials with high second-order susceptibility, such as GaAs,⁵⁰⁹,⁵¹⁰,⁵¹⁸,⁵⁴⁹ AlGaAs,⁵⁰³,⁵¹³,⁵⁵⁰ and other materials,⁵¹²,⁵⁵¹,⁵⁵² are attractive alternatives. The initial endeavor to observe SPDC created within nanostructures was centered around a single crystalline AlGaAs nanocylinder, characterized by Mie-like resonances at both the fundamental and down-converted wavelengths [Fig. 19(b)].⁵⁵³ The histogram of the photon arrival time difference revealed a minor peak above the background of accidental coincidences. However, the peak-to-background contrast (referred to as CAR, coincidences-to-accidentals ratio) was insufficient to confirm the emission of SPDC pairs. Given that thermal light can also lead to a peak at zero arrival time difference,⁵⁵⁴ a signature of two-photon emission is the peak exceeding the background (CAR > 1). Another hallmark of biphoton emission is the reciprocal relationship between the CAR and the pump power. The first demonstration of nanoscale SPDC using this approach emerged in the context of a nonlinear film.¹¹⁶ Very recently, SPDC was achieved in a single LiNbO₃ nanoresonator of height 500 nm and diameter 1 µm, which is, perhaps, the most compact 3D source of biphotons to date.⁵⁵⁵

One approach to achieve higher biphoton rates involves using resonances in optical metasurfaces, which enhance the vacuum field and hence the spontaneous emission of photon pairs via SPDC. This
<figure><img src="image_27.png" /><figcaption>**FIG. 19.** Photon pairs generation in optical antennas, metasurfaces, and other nanoscale structures. (a) Relaxed momentum conservation in SPDC for thin crystals (right) compared to thick ones (left).<sup>543</sup> (b) and (c) The excitation of electric and magnetic dipole resonances in (b) an AlGaAs nanoantenna<sup>533</sup> and (c) a lithium niobate metasurface enhances the emission of photon pairs.<sup>526</sup> (d)–(g) Quasi-BIC optical modes drastically enhance the generation of photon pairs, predicted (d) in meta gratings made of nanofins,<sup>528</sup> (e) in AlGaAs metasurfaces made of nanocylinders with two holes in them,<sup>527</sup> measured in (f) a metasurface made of broken symmetry GaAs nanoresonators,<sup>384</sup> and (g) in tilted ellipses nanoresonators.<sup>525</sup> (h) Spatially entangled signal and idler photons from a LiNbO<sub>3</sub> nonlocal metasurface with guided-mode resonances.<sup>137</sup> Other notable approaches of photon pairs generations via SPDC in (i) metalens arrays combined with a BBO crystal<sup>190</sup> and (j) LiNbO<sub>3</sub> microcubes.<sup>557</sup> (a) Reprinted with permission from Okoth et al., Phys. Rev. Lett. 123, 263602 (2019). Copyright 2019 American Physical Society.<sup>543</sup> (b) Reprinted with permission from Marino et al., Optica 6, 1416 (2019). Copyright The Optical Society.<sup>553</sup> (c) Reprinted with permission from Santiago-Cruz et al., Nano Lett. 21(10), 4423–4429. Copyright 2021 American Chemical Society.<sup>528</sup> (d) Reprinted with permission from Mazzanti et al., New J. Phys. 24, 35006 (2022). Copyright 2022 Authors, Creative Commons Attribution Noncommercial License 4.0 (CC BY-NC).<sup>528</sup> (e) Reprinted with permission from Parry et al., Adv. Photonics 3, 550011 (2021). Copyright 2021 Authors, Creative Commons Attribution Noncommercial License 4.0 (CC BY-NC).<sup>527</sup> (f) Reprinted with permission from Santiago-Cruz et al., Science 377, 991 (2022).<sup>384</sup> Copyright 2022 The American Association for the Advancement of Science.<sup>g</sup> Reprinted with permission from Son et al., Nanoscale 15, 2567 (2023). Copyright 2021 Authors, Creative Commons Attribution 3.0 Unported License.<sup>529</sup> (h) Reprinted with permission from Zhang et al., Sci. Adv. 8, 4240 (2022). Copyright 2022 Authors, Creative Commons Attribution Noncommercial License 4.0 (CC BY-NC).<sup>137</sup> (i) Reprinted with permission from Houani et al., Nat. Nanotechnol. 9, 290 (2014).<sup>130</sup> Copyright 2014 The American Association for the Advancement of Science.<sup>j</sup> Reprinted with permission from Hanh Duong et al., Opt. Mater. Express 12, 3696 (2022). Copyright 2022 The Optical Society.<sup>557</sup></figcaption></figure>

was first realized in 2021 using arrays of truncated LiNbO₃ nanopyramids [Fig. 19(c)]. These arrays exhibited Mie-like electric dipole resonances at telecom wavelengths.<sup>526</sup> Given the high reflectivity of the metasurfaces at resonance wavelengths and their low reflectivity elsewhere, an amplified emission of frequency-degenerate biphotons was observed in the backward direction. Notably, the rate of pair generation surpassed that of an unpatterned LiNbO₃ film of equivalent

thickness and crystalline orientation by two orders of magnitude. Remarkably, there was no discernible indication of biphotons emitted in the forward direction.<sup>556</sup> The resonances characterizing the metasurface were adjustable by altering the size and period of the pyramidal nanoresonators, thereby enabling the tuning of the biphoton emission wavelength. However, we note that that only frequency degenerate SPDC exhibited a noticeable rate enhancement.
The enhancement achieved in SPDC due to Mie resonances is generally moderate. For more substantial enhancements in biphoton generation rates for specific directions, optical resonances with higher Q-factors, such as photonic quasi-BIC³⁸⁴,⁵²⁷,⁵²⁸ and guided-mode resonances,¹³⁷ come into play. Symmetry-protected BICs can prevent, via design, the outcoupling of radiation in the direction normal to the metasurface.⁵⁴⁶ However, a symmetry-breaking perturbation of a resonator or the metasurface lattice can convert a symmetry-protected BIC into a quasi-BIC. Quasi-BIC resonances,⁵²⁵ with their elevated Q-factors, can lead to significant enhancements of biphoton generation rates compared to those obtained from traditional Mie metasurfaces. For example, this enhancement was expected in a meta-grating configuration comprising (110)-cut Al₀.₁₈Ga₀.₈₂As nanofins atop a dielectric substrate [Fig. 19(d)],⁵²⁸ and within an array of AlGaAs nanocylinders with pairs of holes [Fig. 19(e)].⁵²⁷ Experimentally, tunable biphoton generation mediated by quasi-BIC has been observed in a metasurface consisting of GaAs nanoresonators arranged in a square lattice [Fig. 19(f)]. The shape of each nanoresonator was designed to disrupt the rotational C2 and C4 symmetries of the lattice.³⁸⁴ This metasurface facilitated not only degenerate, but also non-degenerate SPDC, with the photons of a single pair emitted at different wavelengths. The wavelength separation between the two photons reached almost 200 nm without significant efficiency loss. By coherently exciting this metasurface at various wavelengths, photons at multiple distinct wavelengths can be entangled via pairwise coupling, offering the potential for generating more intricate quantum states. These methods of quantum state engineering, made feasible by the relaxation of momentum conservation and the exploitation of high-Q resonances, thus hold tremendous appeal.

Metasurfaces can also impart distinct directionalities to SPDC. Despite the relaxation in phase matching constraints, even within ultrathin layers, the probability of both photons being emitted backward remains exceedingly low. However, metasurface resonances engineered to exhibit enhanced reflectivity enable such backward pair emission.⁵²⁶ Conversely, resonances configured for enhanced transmissivity result in the forward emission of biphotons.³⁸⁴ By strategically designing a metasurface to possess high reflectivity at the resonance of a quasi-BIC and high transmissivity elsewhere, bidirectional emission of photon pairs was observed⁵²⁹ [Fig. 19(g)]. In this work, the photon at the resonant wavelength was predominantly emitted backwards, while its entangled partner was emitted forwards. The integration of quantum- and nanophotonics thus presents a promising avenue for generating complex photon states encompassing more than two entangled photons. Additionally, as exemplified in Fig. 19(h), guided-mode resonances have facilitated the creation of spatially entangled photon pairs with a degenerate narrowband emission spectrum spanning approximately 3 nm around 1570 nm.¹³⁷ This achievement was realized using a metasurface comprised of a silica metagrating atop a LiNbO₃ film. Notably, the biphoton generation rate was amplified by over 450 times in comparison to an unpatterned film.

Finally, we note other avenues for generating photon pairs at the nanoscale. These alternatives include the incorporation of a metalens—constructed from a 10 × 10 array of GaN nanopillars—onto the surface of a 0.5 mm β-barium borate (BBO) crystal,¹⁹⁰ which enables the generation of pairs in multiple modes as shown in Fig. 19(i). Additional methods encompass the utilization of LiNbO₃

microcubes⁵⁵⁷ [Fig. 19(j)] and GaAs nanowires,⁵⁵⁸ to amplify the biphoton rate while retaining a certain degree of engineering flexibility offered by nanophotonics. In a different vein from SPDC, some groups are investigating SFWM in doubly resonant gold plasmonic nano-antennas and metasurfaces.¹⁵⁸,⁵¹¹,⁵⁴⁶

## D. Future directions

Optical metasurfaces have significantly improved the emission of single and entangled photons, offering unprecedented control over polarization and directionality. For single-photon emission, optical metasurfaces have enabled efficient coupling of QEs to closely located optical resonances, resulting in substantial enhancements in emission rates. Two promising directions have thus emerged in this context.⁵⁸ First, exploring anisotropic quantum metasurfaces has the potential to revolutionize the design of hybrid plasmon-QE coupled metasurfaces. Composed of anisotropic nano-scatterers as elements, these metasurfaces promise greater versatility in controlling photon properties, including polarization. This advancement could facilitate the realization of on-chip single-photon sources with high polarization purity. Second, the development of tunable quantum metasurfaces presents an exciting avenue for actively manipulating emitted photon properties, encompassing emission rate, direction, wavefront, and polarization. Inspired by dynamic optical metasurfaces used for classical light, the incorporation of phase-changing materials into metasurfaces that shape single-photon emission can provide tunability through temperature variation or voltage application, thereby unlocking transformative possibilities for quantum information technologies.

Efficiency remains a critical challenge in the generation of photon pairs using quantum optical metasurfaces (QOMs). State-of-the-art QOMs, due to their extremely thin profile, exhibit very low photon pair-generation rates: tens of Hertz at moderate pump powers.³⁸⁴,⁵²⁹ However, practical quantum optical applications demand pair-generation rates on the order of 100 kHz, a benchmark that is still significantly distant from achieving with current QOMs. Several research directions to enhance the pair-generation rate predominantly rely on elevating the Q-factors of the optical mode at play, improving mode overlap between pump, signal, and idler wavelengths, and involving materials with high second-order susceptibilities, such as (110)-oriented GaAs or van der Waals crystals like niobium oxide dichloride (NbOCl₂).⁵⁵⁹ In this context, polaritonic metasurfaces featuring resonant susceptibilities present a promising avenue as well.⁵¹⁸,⁵⁶⁰,⁵⁶¹ Another challenge is the generation of tunable, polarization-entangled photon pairs, including Bell states, with recent advances in thin films⁵⁴⁴ and optical metasurfaces,⁵⁶² offering promising design approaches.

SPDC is also a source of squeezed states of light. However, the low parametric gain ($G \propto E\chi^{(2)}L$, with E being the electric field amplitude of the pump, and L the length of the nonlinear medium), makes it rather challenging to observe light squeezing in metasurfaces. It might be possible to reach a parametric gain $G \sim 1$, which is needed for squeezing, in optical nonlinear metasurfaces using pulsed pumping. Incidentally, the use of pulsed excitation could help to distinguish between SPDC and photoluminescence, as the latter is orders of magnitude stronger than the former.⁵⁶³

Finally, the generation of quantum states via third-order nonlinear processes, such as SFWM and third order SPDC (TOSPDC)⁵⁶⁴ has yet to be observed in optical metasurfaces. Importantly, the values of
third-order susceptibility $\chi^{(3)}$ differ in various materials by up to four orders of magnitude; therefore, the freedom to choose any material due to relaxed momentum conservation is crucial for third-order effects. The use of strongly nonlinear materials like Si or Ge may facilitate the observation of new nonlinear effects such as TOSPDC.

## ACKNOWLEDGMENTS

I.B. and S.D.G. acknowledge support from the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering. This work was performed, in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science. This article has been authored by an employee of National Technology & Engineering Solutions of Sandia, LLC under Contract No. DE-NA0003525 with the U.S. Department of Energy (DOE). The employee owns all right, title and interest in and to the article and is solely responsible for its contents. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this article or allow others to do so, for United States Government purposes. The DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan https://www.energy.gov/downloads/doi-public-access-plan. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

# XI. METASURFACE LASERS

## Ren-Min Ma

renminma@pku.edu.cn

## A. Introduction

The definition of metasurface lasers can be arguably derived from the conceptual framework of metamaterials. Metasurface lasers exhibit a fundamental similarity to metamaterials by employing artificial functional “atoms” to tailor the properties of the composite matter formed by these constituent atoms. In the realm of metasurface lasers, individual nanolasers serve as the fundamental atoms. The eigenmode of a nanolaser can be deliberately shaped to synthesize the inner laser cavity field and/or emission beam in a highly controlled manner. Furthermore, coordinated ensembles of nanolasers can generate a macroscopic response surpassing the capabilities of conventional lasers. Within the near field, manipulation of the polarization and profile of each nanolaser eigenmode is possible, and additional control over the ensemble can be achieved through coupling, relative phase, symmetry, and topology. This approach has the potential to provide unprecedented control over the macroscopic laser field, offering diverse applications in the far field.

The definition of metasurface lasers proposed in this article aims to capture the essential characteristics of metamaterials and metasurfaces, combined with the features of lasers. We hope this definition offers a stimulating perspective for studying lasers from the standpoint of

metamaterials. We note that some lasers discussed in the article do not strictly meet this definition because their individual units cannot achieve lasing independently. However, the concept of those lasers can indeed be applied to arrays of coupled nanolasers. Therefore, to maintain a broad scope and inspire potential future research, we have included discussions of some metasurface-like, cutting-edge laser studies that do not strictly conform to our definition of metasurface lasers.

Nanolaser research gained traction around 1990 when it was discovered that the threshold and modulation rate of lasers are influenced by their size.<sup>563-568</sup> First, miniaturized lasers with a smaller gain material volume and a larger spontaneous radiation coupling factor exhibit lower thresholds. Simultaneously, miniaturized lasers can achieve faster rates of spontaneous and stimulated emission, resulting in faster modulation rates. Since then, achieving miniaturized lasers with smaller mode volumes, lower threshold power consumption, and faster modulation rates has been a focal point of research in the relevant field. Innovations such as the microdisk laser, photonic crystal defect-state lasers, and nanowire lasers have significantly reduced the characteristic dimensions of lasers to the order of a vacuum wavelength.<sup>569-571</sup> In 2009, the experimental realization of plasmonic nanolasers achieved characteristic scales one-tenth of a vacuum wavelength, approaching the characteristic scales of electronic devices.<sup>572-575</sup>

In recent years, novel methods of controlling optical fields have continually been introduced into the micro and nanolaser domain, creating the development of metasurface lasers. These encompass plasmonic lattice lasers,<sup>576-579</sup> topological lasers,<sup>91,113,580-616</sup> bound-state in the continuum (BIC) lasers,<sup>617-619,624,625</sup> non-Hermitian parity-time symmetric lasers,<sup>624-637</sup> supersymmetry lasers,<sup>638-640</sup> and moiré lasers,<sup>641-644</sup> injecting renewed vitality into the advancement of micro and nanolasers. In this article, we first briefly discuss the significance of metasurface lasers in the context of laser development, specifically addressing why these mode control methods are introduced from a laser perspective. Following that, we delve into the mode engineering of individual nanolasers. Finally, we explore the characteristics of metasurface lasers formed by the coupling of multiple nanolasers.

## B. Key performance parameters

The key performance parameters of a laser include threshold power density, lasing linewidth, external quantum efficiency, modulation speed, power consumption, emission directionality, emission power, and side mode suppression ratio, among others. These parameters are intricately linked, often imposing constraints on one another. For example, the pursuit of reduced size to achieve lower threshold power and enhanced modulation speed may inadvertently lead to a broadening of the lasing linewidth, increased divergence angles, and diminished output power. However, the silver lining lies in the fact that various applications necessitate the fine-tuning of specific parameters, making the optimization process application-dependent. Consequently, the performance of lasers is contingent upon the unique requirements of a given application context.

To illustrate, industries employing lasers for precise material processing, such as cutting, welding, and marking, demand higher power. In contrast, applications like data communication or consumer electronics necessitate lower output power to achieve energy efficiency.

Beyond these traditional laser characteristics, the incorporation of novel optical field control introduces a transformative dimension to metasurface lasers, endowing them with features not inherent in
conventional counterparts. This includes the attainment of higher radi-
ation field dimensions, superior single-mode characteristics, relative
phase control, and reconfigurability.

C. Eigenmode engineering in a single microscale laser cavity

In the domain of microscale lasers centered on individual cavities, the impetus for eigenmode engineering manifests through three primary objectives.⁶⁴⁵ First, the focus is on advancing laser performance by reducing lasing thresholds and accelerating modulation speeds. Second, there is a concerted effort to generate a strong local field. Finally, the goal is to control field properties of a nanolaser in near and far field.

**1. Enhance laser performance**

The lasing threshold power can be categorized into two compo-
nents. The first involves achieving population inversion of the gain
material, essentially rendering the gain medium transparent. The sec-
ond requires compensation for cavity loss, ensuring the condition of
having one real photon in the cavity mode is met. The quest for
smaller lasers has been a persistent research goal, striving for a more
compact size and reduced power consumption. Whispering-gallery-
mode microlasers, photonic crystal defect nanolasers, nanowire lasers,
plasmonic nanolasers, bound states in the continuum nanolasers,
magic angle nanolasers have been invented to miniaturize lasers and
consequently lower their threshold power. In both dielectric and plas-
monic cavities, cavity loss increases as the volume decreases.⁶⁴⁶,⁶⁴⁷
Therefore, the exploration of materials with higher optical gain and
the meticulous design of nanocavities with lower cavity loss are pivotal
for the advancement of nanolasers.⁶⁴⁸ In the case of a small laser cavity
with a large free spectral range, the meticulous design of the lasing res-
onance wavelength becomes crucial in lowering the total cavity loss.
This is due to the wavelength dependence of gain material loss, empha-
sizing the importance of aligning the resonance wavelength of the cav-
ity for optimal performance. Additionally, it is important to carefully
balance the radiation rate and the cavity loss rate to ensure that micro-
scale lasers have a high external quantum efficiency.⁶⁰⁷,⁶⁴⁹

**2. Enhancing local field**

The interaction between light and matter is generally a weak pro-
cess owing to the disparity in wavelength between photons and elec-
trons. Over the decades, artificial microstructures have been employed
to enlarge and manipulate the density of states of photons, thereby
enhancing light-matter interaction.<sup>645,650–662</sup> In this context, the ratio of
quality factor to mode volume (Q/V) emerges as a crucial figure of
merit, signifying the strength of light field confinement on both spatial
and spectral scales. Various localization mechanisms, including total
internal reflection,<sup>655,663–670</sup> photonic bandgap,<sup>671–680</sup> plasmonic reso-
nance,<sup>681–686</sup> and bound states in the continuum (BICs),<sup>151,177,624,687,688</sup>
have been developed over the years to craft optical cavities with
high Q/V. However, in photonics, a persistent trade-off exists between
confining a light field in space and in frequency due to the limitations of
the applicable finite potential well. Recent innovations of twisted lattice
nanocavities can overcome this trade-off by enabling a mode volume
approaching to diffraction limit, accompanied by an exceptional quality

factor exceeding 2.9 × 10¹¹ (Ref. 689). A cavity with an extremely large
Q/V enables exploration of light-matter interaction in extreme condi-
tions, facilitating tests of fundamental physics. Moreover, it can be used
in nanolasing, ultrasensing, nonlinear optics, optomechanics, and
quantum-optical devices.

**3. Controlling radiation field**

The advantage of nanoscale lasers lies in the minimal number of modes permitted within the cavity, facilitating the targeted design of eigenmodes for controlling the near-field and far-field properties.⁶⁴⁵ Each laser mode represents a specific eigenmode of the cavity. The estimated number of eigenmodes (N) allowed in a cavity is given by the expression N = ρV<sub>PHY</sub>Δν<sub>E</sub>, where ρ denotes the density of states of the cavity, V<sub>PHY</sub> is the physical size of the cavity, and Δν<sub>E</sub> is the gain spectrum bandwidth. As typically Δν<sub>E</sub> spans a few tens of terahertz for conventional organic dyes and semiconductor materials, only a few eigenmodes generally coincide spectrally with the gain spectrum when the laser cavity size is subwavelength scale in all three dimensions. This characteristic enables precise engineering of the eigenmode in a nanolaser in a controllable manner, leading to novel inner laser cavity fields and/or emission beam synthesis. Various eigenmode engineering mechanisms have been proposed to control the optical field distributions inside and outside nanoscale laser cavities, including parity-time symmetry, exceptional point, supersymmetry, topological nanocavity, among others. Optical fields exhibit rich dimensions,⁶⁹⁰ providing a vast development space for eigenmode engineering.

**D. Eigenmode engineering in arrayed lasers**

We can classify arrayed lasers into two categories: those originat-
ing from photonic crystals and those stemming from individual nano-
lasers. While there is no fundamental difference between the two, the
approaches and methods employed to construct arrayed lasers differ.
Both strive for characteristics such as large-area single-mode lasing,
higher laser field dimensions, and reconfigurability (Fig. 20), empha-
sizing similar performance goals despite the varied methodologies.

**1. Large area single mode**

Semiconductor lasers, valued for their compactness, efficiency, and controllability, play vital roles in information technology. However, achieving semiconductor lasers with single-mode operation over a large area presents a significant challenge. The attainment of single-mode operation in a spacious region is essential for semiconductor lasers to exhibit high output power and superior beam quality, crucial attributes for various applications such as laser processing, remote sensing, and long-range free-space communications.

Achieving a semiconductor laser with a large-area single mode using photonic crystals involves two primary physical aspects. First, to enable surface emitting, it is necessary to utilize the lattice momentum formed by the photonic crystal to scatter a portion of the guided modes within the photonic crystal into the light cone, preferably at the Gamma point. Second, to achieve a large-area single mode, it is essential to enhance the contrast between the lasing thresholds of the fundamental mode and higher-order modes.

**Photonic-crystal surface-emitting lasers:** Photonic-crystal surface-emitting lasers (PCSELs) currently stand as the most mature
<figure><img src="image_28.png" /><figcaption>**FIG. 20.** Metasurface lasers. (a) and (b) Photograph (a) and schematic of the cross-sectional structure (b) of a 3-mm-diameter photonic-crystal surface-emitting laser (PCSEL).<sup>110</sup> (c) and (d) Schematic (c) and SEM image (d) of a surface emitting topological bulk laser based on band-inversion induced reflection.<sup>590</sup> (e) and (f) Schematic (e) and SEM image (f) of a topological vortex laser based on spin-momentum-locked edge mode.<sup>591</sup> (g) Schematic of a supersymmetric microlaser array.<sup>640</sup> (h) SEM image of a hyperdimensional spin-orbit microlaser.<sup>591</sup> (i) and (j) SEM images (i) and schematic of reconfigurable moiré nanolaser array.<sup>542</sup> Reproduced with permission from Yoshida *et al.*, *Nature* **618**, 727 (2023). Copyright 2023 Springer Nature. Reproduced with permission from Shao *et al.*, *Nat. Nanotechnol.* **15**, 67 (2020). Copyright 2020 Springer Nature. Reproduced with permission from Yang *et al.*, *Phys. Rev. Lett.* **125**, 13903 (2020). Copyright 2020 American Physical Society. Reproduced with permission from Qiao *et al.*, *Science* **372**, 403 (2021). Copyright 2021 AAAS. Reproduced with permission from Luan *et al.*, *Nature* **624**, 282 (2023). Copyright 2023 Springer Nature. Reproduced with permission from Zhang *et al.*, *Nature* **612**, 246 (2022). Copyright 2022 Springer Nature and Copyright Remains with the respective publishers.</figcaption></figure>

system for realizing semiconductor lasers with single-mode operation. PCSELs achieve single-mode oscillation across expansive areas through careful tailoring of the photonic crystal's unit cell design. Recent research outcomes showcase the capability of PCSELs to achieve 50 W continuous-wave operation in a single mode, even in areas with diameters exceeding 3 mm.<sup>110</sup> Notably, these lasers boast a very narrow beam divergence angle of 0.05° and an impressive brightness of 1 GW cm<sup>-2</sup> sr<sup>-1</sup>.

**Plasmonic surface lattice nanolasers:** Plasmonic surface lattice nanolasers leverage collective coupling among metal nanoparticles in a lattice to establish the resonance mode for lasing.<sup>76</sup> This coupling involves the localized surface plasmon mode and lattice-defined diffraction mode, resulting in sharp Fano lines with reduced radiative loss. The integration of dye molecules within a polymer matrix or organic solvent with plasmonic nanoparticles in a surface lattice enables lasing, with the wavelength tunable by modifying the refractive index, nanoparticle size, interparticle spacing, or lattice geometry. Plasmonic surface lattice nanolasers can achieve a small divergence angle (<0.5°) and provide a robust platform for mode control.<sup>578,692</sup> Modifying the shape or symmetry of plasmonic NP lattices allows for precise control over lasing emission properties. Low-symmetry lattices exhibit polarization-dependent lasing, while multiscale plasmonic superlattices support multiple plasmon resonances for controlled multimodal nanolasing. The spatial organization of photoactive materials

around plasmon nanocavities leads to nanoscale exciton-plasmon coupling and mixed photon modes.

**Topological surface-emitting lasers:** In recent years, significant progress has been achieved in the field of topological lasers, with the integration of a novel degree of freedom linked to band topology in photonic crystals. This integration holds the promise of providing topological protection characteristics and introducing innovative optical feedback mechanisms for laser cavity design. Such advancements prove particularly beneficial for driving the development of surface emitting semiconductor lasers with large-area single-mode. Effective mechanisms in this context include topological bulk modes, topological insulator edge modes, topological vortex defect modes, and open-Dirac modes. Surface-emitting topological bulk lasers have been realized through band-inversion-induced reflection, emitting vertically with divergence angles less than 6%, despite their microscale cavity size.<sup>590</sup>

The topological bulk laser achieves high-performance single-mode lasing due to the exclusive operation of band-inversion-induced reflection around the Γ point, where the band inversion occurs. This topology-induced mode selection not only restricts the number of cavity modes with efficient confinement but also enhances the quality factor of the mode closer to the band edge. Furthermore, an array of vertical-cavity surface-emitting lasers (VCSELs) has been strategically arranged to form photonic crystals featuring topological insulator edge modes for collective array lasing.<sup>599</sup> Additionally, the utilization of the
topological vortex defect mode has led to the creation of a surface-emitting topological laser with a device diameter of 500 µm and a sub-1° divergence angle.⁶⁰⁶ In open-Dirac cavities, surface-emitting lasing has been achieved, demonstrating that single-mode lasing can be maintained as the cavity size is scaled up.⁶⁰⁴

**Supersymmetry lasers:** Recently, leveraging concepts from supersymmetric quantum mechanics has led to the development of scalable laser arrays with the distinctive features of single-mode operation. In a supersymmetric laser array, the linear spectrum of the superpartner is meticulously constructed to mirror that of the primary array, with the exception of the fundamental supermode. The operating principle of the supersymmetric laser array is derived from the deliberate coupling of the main array with its dissipative superpartner, strategically reducing supermode competition by limiting the available lasing modes. The mode matching between the supersymmetric partners guarantees the suppression of all except for the fundamental supermodes. This fundamental supermode, confined solely in the main array without a superpartner, exhibits the lowest threshold and is conducive to lasing under suitably applied pumping. The initial realization of a supersymmetric laser array was based on a one dimensional waveguide structure.⁶³⁸,⁶³⁹ Subsequently, two-dimensional supersymmetry lasers were developed, exemplified by a two dimensional five-by-five supersymmetric microlaser array.⁶⁴⁰

**Moiré lasers array:** The utilization of a moiré nanolaser array can result in extensive single-mode operation over a large area.⁶⁴² The synchronization of emission within the moiré nanolaser array is contingent upon the flatness of the band structure in momentum space. The use of a moiré superlattice with a predetermined twisted angle ensures the necessary periodicity for the formation of a flatband, thereby facilitating the scalability of the moiré nanolaser array. However, practical limitations may arise due to nonuniformities induced during the fabrication process. Enhancing the uniformity of the fabricated devices, the fabrication of the moiré nanolaser array onto a SiO₂ substrate eliminates any deformations that may occur when suspending the membrane. Through this process, more than 160 nanolasers have been synchronized to achieve single-mode lasing with a divergence angle of only about 3°.⁶⁴²

## 2. High dimensional radiation

The optical field is a transverse wave field with two polarization degrees of freedom, which can also be transformed into two spin degrees of freedom. In addition to polarization, spatial modes provide a promising avenue for creating high-dimensional Hilbert spaces. In 1992, the orbital angular momentum degree of freedom of optical fields was discovered.⁶⁹³ Optical vortex beams, carrying orbital angular momentum, are distinguished by a helical phase front and a phase singularity at the beam center. The number of phase front twists around the axis of propagation within one wavelength determines the beam's topological charge. Vortex beams with different topological charges are orthogonal, implying the potential for high-dimensional multiplexing. This property has been leveraged in applications such as optical communication and quantum information processing. Various methods, including the use of spiral phase plates, metasurfaces, synthesized holograms, plasmonic nanostructures, and photonic crystals,⁶⁹⁴ exist to convert a normal laser beam into a vortex beam. A compact vortex emitter can be constructed by engineering the eigenmode of a micro-scale laser. Chiral eigenmodes of a whispering gallery mode resonator

serve as a natural source, sharing the azimuthal phase factor of a vortex beam propagating in free space and controlling the topological charge of the emitted vortex beam.⁶⁹⁵

However, constructing a robust chiral whispering gallery mode that circulates only in one direction has been a long-standing challenge. Typically, at a resonant frequency, two degenerate chiral modes travel in opposite directions, leading to potential coupling caused by backscattering, bending, or defects. This coupling transforms circling waves into standing waves, resulting in zero orbital angular momentum in the emission. To overcome this challenge and directly generate a vortex beam, the symmetry of whispering gallery mode lasers needs to be broken.

In recent years, the introduction of new physics such as exceptional points,⁶³¹,⁶³²,⁶⁹⁶–⁶⁹⁸ unidirectional topological edge states,⁵⁹¹,⁵⁹⁷ and spin–orbit coupling⁶⁹¹ has enriched the capability of laser cavity eigenmode engineering. This enables the direct use of chiral whispering gallery modes in a microscale laser to directly generate radiation fields carrying high-dimensional information.

## 3. Reconfigurable phased array nanolasers

One of the ultimate objectives in nanolaser research is to develop reconfigurable coherent nanolaser arrays. This advancement will broaden the applications of nanolasers, encompassing areas such as coherent computing and communication, laser displays, and LiDAR (light detection and ranging). Recently, reconfigurable moiré nanolaser arrays with phase synchronization has been realized.⁶⁴² This device is based on moiré-angle nanolasers, whose modes are highly localized within a single moiré unit cell.⁶⁴¹

The optical moiré superlattice structure is formed by processing two sets of twisted photonic crystal lattices in the same layer of a semiconductor membrane. Non-local Bloch modes in the structure are coupled through moiré reciprocal vectors, resulting in spatially localized eigenmodes in real space. In the band structure, these localized eigenmodes correspond to Moiré flat bands. The wavefunction localized in a single moiré unit is employed to construct single-cavity moiré nanolasers.

When moiré-angle nanolasers are arranged in an array, the localized wave functions of individual moiré-angle nanolasers form Moiré flat bands. These bands ensure the degeneracy of frequencies, enabling coherent emission of nanolaser arrays in arbitrary shapes. Building upon this principle, synchronized nanolaser arrays have been realized, demonstrating high spatial and spectral coherence across various distinct patterns, including P, K, and U shapes, as well as the Chinese characters “中” and “国” (“China” in Chinese). Furthermore, the introduction of spatially varying relative phases has enabled the realization of phased-array nanolasers, facilitating the manipulation of emission directions.

## E. Future directions

Navigating the current landscape of metasurface lasers and their evolving mode engineering capabilities reveals a field in continuous evolution, characterized by emerging concepts and innovative approaches. Looking ahead, several promising directions stand out, guiding the trajectory of future research in this dynamic domain.

In the realm of single cavity microscale lasers, the most crucial future research direction remains miniaturization. Much like the
miniaturization of transistors for electronic chips, miniaturizing lasers is pivotal for optoelectronic technology. Efforts should be directed toward constructing lasers with smaller volumes, lower power consumption, and faster speeds. This dual focus aims to explore the limits of coherent light sources in various dimensions while promoting their applications in integrated photonics, super-resolution imaging, high-resolution displays, and beyond. Simultaneously, constructing stronger local fields is a crucial research direction, particularly for investigating light-material interactions and developing coherent light sources with atomic-scale characteristics in extremely localized optical fields. Finally, further development and exploration of single nanolaser mode control are advantageous for the advancement of nanolaser arrays.

For photonic crystals or nanolaser arrays, achieving large-area single-mode outputs to realize kilowatt-level or even higher output powers in semiconductor lasers remains a crucial research direction, poised to extend the current application scope of semiconductor lasers. Integrating new physics concepts into the toolbox for laser cavity eigenmode engineering is another promising avenue. By leveraging recent advancements in physics, researchers can enhance the capabilities of metasurface lasers, potentially unlocking new possibilities for high-dimensional information processing and communication.

The realization of the reconfigurable moiré nanolaser arrays highlights the potential to construct phased array nanolasers with significantly enhanced information capacity and functionality. Through phase synchronization, nanolaser arrays can achieve large-area, high-power single-mode lasing. Precise adjustment of relative phases enables accurate control of the emission direction of the laser array. Complete control of the intensity and phase of individual nanolasers within an array will enable the customization of the outgoing wavefront of metasurface lasers, resulting in outputs such as holograms, focused beams, or other desired emission patterns. Simultaneously, the coherence between nanolasers can be utilized for coherent computing and communication. In the realm of fundamental physics research, the extreme localization of the optical field in a twisted lattice nanocavity provides an excellent platform for studying cavity quantum electrodynamics, nonlinear optics, quantum optics, and other related phenomena.

## F. Summary

In summary, the field of metasurface lasers has witnessed significant progress and diversification in recent years, marked by the integration of innovative methods to control optical fields in micro and nanolasers. Metasurface lasers, stemming from the conceptual framework of metamaterials, utilize individual nanolasers as artificial functional atoms to tailor the properties of the composite matter they form. This approach enables unprecedented control over the macroscopic laser field. The future of metasurface lasers presents exciting prospects for groundbreaking discoveries and advancements that can further push the boundaries of laser technology, opening up new possibilities for applications in communication, computing, sensing, and beyond.

## ACKNOWLEDGMENTS

This work was supported by the National Natural Science Foundation of China (Grant Nos. 12225402, 91950115, 11774014, and 62321004) and the New Cornerstone Science Foundation through the XPLORER PRIZE.

# XII. SOLUTION-DERIVED NANOFABRICATION FOR NONLINEAR METASTRUCTURES

Helena C. Weigand, Ülle-Linda Talts, Irene Occhiodori, Viola V. Vogler-Neuling, and Rachel Grange*

*grange@phys.ethz.ch

## A. Introduction

Miniaturization of optical components without compromising functionality or scalability is a main challenge for deploying compact photonic solutions in current and future technologies, such as telecommunication with fast data transmission, imaging with small mobile cameras, or light sources with quantum features. Nonlinear materials used in telecommunication, lasers, and quantum applications are typically bulk metal-oxide single crystals.⁶⁹⁹ Those high-quality bulk crystals are neither integratable, due to limited compatibility with top-down nanofabrication methods compared to typical semiconductors, nor scalable, due to the low generated signals, especially in frequency conversion at small scale. Current material platforms rely on a top-down fabrication approach with standard semiconductors (Si, InP, GaAs), which is limited to the available wafers, crystalline orientation, and transparency range. To access more sophisticated features such as parametric or electro-optic effects, metal-oxides thin films, i.e., lithium niobate on insulator have been commercially available for a few years.⁷⁰⁰ However, they come at high wafer cost and huge constraints to master the smart-cut technique and etching process flow of a thin layer of metal-oxides to obtain the best photonic integrated chip performances.⁷⁰¹

The quest for a material or fabrication method to harvest their functional response at the nanoscale that will favor energy requirements and simplify their production is still widely open. Recent advances based on photonic assemblies of randomly oriented nanocrystals instead of bulk crystals have shown excellent tailored optical properties in the linear regime.⁷⁰³ More rarely, also frequency doubling and electro-optic responses have been demonstrated, mainly in isolated nanoparticles,⁵¹⁶ individual microstructures,⁵²² and rare-earth doped nanoparticles for the quantum regime⁷⁰⁴—all not very well suited for integration in large surface areas with fully controlled design.

These limitations are key motivations for exploring bottom-up polycrystalline nonlinear assemblies of metal-oxides for miniaturized photonic components, which, in fabrication complexity, energy consumption, footprint, and functionalities, can compete with the performance of bulk crystals or top-down thin films. Overcoming the intuitive, yet disproven, perception that nonlinear optical effects are limited or even completely eradicated in random assemblies of nanocrystals gives rise to puzzling questions and new functionalities that we aim to address. Hence, bottom-up assembly of nonlinear materials may potentially become the most agile technique for classical and quantum devices.

## B. Nanoimprint and solution derived principles and advantages

Nonlinear optical metal-oxides such as lithium niobate (LiNbO₃ or LNO) or barium titanate (BaTiO₃ or BTO) are chemically inert due to
<figure><img src="image_29.png" /><figcaption>**FIG. 21.** Process flow of the direct soft nanoimprint lithography (SNIL). (a) The only step with top-down approach is to produce the master mold by EBL. (b) Stamps (daughter molds) are used to transfer the pattern from the Si master mold to the PDMS daughter mold. (c) Preparation of the nonlinear material sol-gel liquid film for (d) imprinting and annealing to obtain the metasurface.</figcaption></figure>

their oxide character, which prohibits chemical wet etching techniques for nanostructuring these materials.⁷⁰⁵ They possess strong nonlinear susceptibility ($d_{33,max,LNO} = -34$ pmV⁻¹, $d_{15,max,BTO} = 17$ pmV⁻¹) and electro-optic tensor components ($r_{33,max,LNO} = 31.8$ pmV⁻¹, $r_{42,max,BTO} = 730$ pmV⁻¹) at around 1060 nm.

Nevertheless, nonlinear metasurfaces have been top-down fabricated using, e.g., gallium-based focused-ion beam milling, to realize nano-gratings for second-harmonic generation and electro-optically active metasurfaces.⁷⁰⁶⁻⁷⁰⁸ Alternatively, electron-beam lithography (EBL) and physical dry etching were employed for pillar-based metasurfaces from LNO thin films.⁷⁰⁹ Finally, nonlinear thin films can serve as a substrate on which nanostructured metasurfaces from e.g., plasmonic materials have been fabricated.⁷¹⁰,⁷¹¹ BTO top-down second-harmonic metasurfaces have been achieved by pulsed-laser deposition (PLD) of polycrystalline BTO thin films, EBL, and physical etching.⁵⁵¹ These top-down processes are limited in footprint, typically in the range of a few hundreds of $\mu$m², in aspect-ratio and sidewall angles. However, they allow the processing of monocrystalline materials.

An alternative and upscalable process is soft-nanoimprint lithography (SNIL) combined with solution-derived metal-oxides. Direct SNIL, also known as substrate conformal imprint lithography, is a bottom-up fabrication method that utilizes a polydimethylsiloxane (PDMS) elastomer intermediate mold to replicate nanostructures from a silicon master mold (Fig. 21). Applying this highly scalable and cost-efficient technique to form nanostructures directly from solution-derived metal oxides has shown to drastically reduce the embossing temperatures and pressure while being

compatible with various substrates. Furthermore, the elastomer molds are permeable to trapped air and solvent vapors, enabling higher conformity to the design and lower remaining organic residues.⁷¹²,⁷¹³ The latter is essential for ensuring dense and uniformly filled metal-oxide unit cells. This etchless method entails dispersing or synthesizing the material of interest in a liquid and malleable solvent. Nanoparticle solutions may be used, but this can result in limited conformity to the design and increased porosity, which reduces the quality of the effective material and causes unwanted scattering effects. However, specific metal-oxide sol-gels optimized for imprint lithography can overcome these limitations and provide a flexible material platform based on chemical synthesis protocols. Third-order nonlinear optical effects can be investigated in metasurfaces fabricated using binary sol-gel recipes, which have been relatively well-established for silica and titanium dioxide.⁷¹² Second-order nonlinear optical effects arise from the non-centrosymmetric crystalline properties of ternary metal oxides. This means the sol-gel precursors for nonlinear metal-oxide photonic devices must be tailored to incorporate two metal elements in a defined stoichiometry. This makes the synthesis more complex and sensitive to small environmental or composition variations. Nevertheless, sol-gel derived non-centrosymmetric crystalline films and assemblies have been shown to exhibit nonlinear optical properties for example in potassium titanyl phosphate,⁷¹⁴ barium titanate,⁷¹⁵,⁷¹⁶ or lithium niobate.⁷¹⁷,⁷¹⁸

Solution deposition for crystalline materials requires the removal of organic solvents and stabilizers by pyrolysis steps and final annealing at high temperatures to enable the formation of dense crystallites from the cross-linked xerogel matrix. Material characterization techniques, such as x-ray and Raman spectroscopy, can be used to verify the final composition after imprinting and annealing. The chemistry-based approach enables adjusting the chemical composition to account for the evaporation of volatile precursors. Considerable research has been dedicated to enhancing ternary metal-oxide sol-gel formulas for creating thin film transistors or capacitors,⁷¹⁹ and bridging this interdisciplinary research field with developing materials for nonlinear optics has significant potential, particularly when combined with SNIL nanofabrication. The advantages of the SNIL process over the top-down fabrication of quadratic nonlinear metasurfaces are the large surface areas up to full wafer scale [Fig. 22(a)] shows imprints over approximately 5 mm], high-aspect-ratio more than 10 [Fig. 22(b)], the potential to increase the dimensionality of the system to three-dimensions, the ability to avoid material redeposition-caused artefacts such as slanted sidewalls [Fig. 22(b)], access to more diverse geometries and more economical processing.⁷²⁰ Metal-oxides such as BTO and LNO also have a high refractive index in the visible to IR spectrum and are transparent over the whole visible range down to the UV [Fig. 22(c)], resulting in sufficient refractive index contrast for resonant structures even with sol-gel processing. Applying SNIL for metasurfaces, second-harmonic enhancing nanohole arrays,⁷¹⁶ second-harmonic generating nano-gratings,⁷²¹ and imprinted metalenses with a broadband focus⁷²² have been demonstrated so far.

### C. The challenges of solution-based processing of metasurfaces

While the advantages of sol-gel-based fabrication can be primarily found in the flexibility due to the initial liquid solution, there are
<figure><img src="image_30.png" /><figcaption>**FIG. 22.** SNIL metasurfaces and their properties (a) metasurface array with color responses over the whole visible spectrum (b) Overview of different achievable metaatom geometries with maximum aspect ratios included in brackets: (i) pillars (4), (ii) fins (16), (iii) triangles, (iv) nanoholes, (c) refractive index comparison for barium titanate for bulk, sol-gel derived and a nanoparticle film. (d) Polarization-dependence of second-harmonic generation for a thin film (gray) and off resonance (pink) nanohole array (NhA) showing an isotropic response. The nonlinear behavior becomes however polarization dependent at the structures optical resonance (green). (e) Two-photon microscopy image of the second-harmonic response of an imprinted metalens with a large surface area (diameter 100 µm).</figcaption></figure>

challenges regarding the material composition. Solution-based techniques do not give monocrystalline material structures as opposed to ion-slicing thin films used for, e.g., LNO thin films. The crystallization process starts from numerous nuclei in the solution, yielding a polycrystalline yet very dense material structure.⁷²³ While polycrystallinity, especially with random domain orientation, can be exploited for its advantageous properties,⁷²⁴ it could also, if needed, be mitigated by aligning the domains with an external (e.g., electric) field.⁷²⁵ However, the overall effectiveness of nonlinear processes, be it SHG or electro-optic modulation, will be decreased compared to a monocrystalline material.⁷²⁶ It is attributed not only to the polycrystallinity of the sol-gel-based material, which might not result in fully pure crystals but also to the formation of voids during the annealing process [see Fig. 22(b), e.g., in the triangle]. In the context of signal modulation via an applied electric field, these voids decrease modulation efficiency, as any voltage drop will occur over the air inclusions instead of the sol-gel material. In addition to that, scattering of light currently limits, e.g., sol-gel-based waveguides, but slightly rough surface profiles do not pose a problem for imprinted metasurfaces as can be seen in some of the SEM images of Fig. 22(b). Furthermore, the crystallization results in a decrease of the total nanostructure volume due to the restructuring of the material into a crystal lattice and the evaporation of organic materials present in the solution. This implies, on the one hand, the formation of cracks in large structures (such as thin films or waveguides), while on the other hand, it restricts the parameter

space available for metasurface designs, as volume shrinkage needs to be taken into account from the initial master mold design and can be as large as 80%.⁷¹² Annealing conditions need careful engineering, as the temperature, ramping rate, atmosphere, and pressure can be used to optimize the density, domain size, and crystalline phase of the nonlinear material. For example, the electro-optic properties of BTO sol-gel were enhanced by a factor of 3 under oxygen annealing.⁷¹⁵ Keeping in mind the restrictions of high annealing temperatures (up to 800°C), chemical compatibility, or transparency requirements, the choice of substrate can additionally enhance the formation of pure crystalline phases (e.g., by choosing lattice-matching MgO for BTO sol-gel⁷²⁷). Finally, the presence of solvents or organic stabilizers in the sol-gels induces void formation and poses a technical challenge for SNIL, as the imprint with the PDMS mold needs to happen while the spin-coated sol-gel is still in a liquid phase. This adds significant time constraints to the process, limiting complicated multilayer imprints with precise alignment.⁷²⁸ However, considerable progress has been made to develop specialized SNIL tools for imprinting volatile sol-gel solutions.⁷¹³

## D. Roadmap towards high-performing solution-based metasurfaces

Overcoming the mentioned challenges will be key to the success of this material platform for future metasurface-based devices. There
are several handles for optimization. One key parameter will be the quality of the crystalline domains in terms of increased size and preferred crystalline structure. This will improve the nonlinear properties of the material and minimize void formation for reduced scattering and smooth surfaces. Handles for these improvements range from controlling the nucleation by chemical composition engineering to optimizing the annealing conditions and substrates. In addition, one could use hybrid systems of sol-gel and nanoparticles, which could serve as crystallization nuclei and prevent the nanostructure shrinkage. The nanoparticles could be derived from the same sol-gel in a separate process to ensure identical chemical composition.⁷²⁹ However, applications might directly use the sol-gel shrinkage, for instance, to increase the aspect ratio of the structures. The same holds for the roughness of the surface of SNIL devices, as it also increases the surface area, which is a property commonly sought for and exploited in sensing or electrochemical applications. The randomly distributed domain orientation is also a factor that one can try to mitigate (poling after or during the annealing) or exploit, e.g., with respect to quasi-random phase matching.⁵⁵² In addition, it offers the freedom to engineer the nonlinear susceptibility components based solely on the geometrically chosen symmetries thereby imprinting an artificial tensor structure on an otherwise unpolarized SHG-emitting material. For example, an imprinted nanohole array was shown to exhibit SHG orientation at the resonance compared to off-resonant behavior [Fig. 22(d)].⁷¹⁶ Specifically considering the efforts of the metasurface community to overcome unfavorable tensor parameter orientations by beam steering,⁷³⁰ this would be an exciting approach to follow up on, as crystal-symmetry considerations would not restrict the freedom in design due to the effectively isotropic $\chi^{(2)}$ of the polycrystalline material. Particular attention should be given here to the field of Pancharatnam-Berry phase-based nonlinear structures [e.g., metalenses emitting SHG as shown in Fig. 22(e)], as they are commonly thought to follow specific symmetry-selection rules.⁵³ To what extent these can be influenced by unoriented but intrinsically emitting $\chi^{(2)}$-materials remains unclear. To ease the imprint process, engineering the chemical composition of sol-gels with selected precursors or solvents that have lower vapor pressure would allow more time for precise alignment to enable large-scale stacking of imprints. Further technological advancements can be made in the imprint process itself. Different daughter mold materials with, e.g., hybrid PDMS stacks (hPDMS/sPDMS) or polyvinyl alcohol (PVA) can be used to achieve high-aspect ratio structures.⁷²²,⁷³¹ Employing degassing processes, curing in a vacuum or under high pressures, or inverse application of sol-gel on the PDMS could reduce residual layers and improve uniformity. Alternative imprint techniques like hard imprints from the master, microcontact printing, capillary force-based or microfluidic-based imprinting, or eventually roll-to-roll imprinting will pave the way for higher quality or larger-scale nonlinear photonic devices, similar to developments in the field of photovoltaics.⁷¹³,⁷³²,⁷³³ An asset not discussed so far is also the possibility of extending this imprint technique to non-flat substrates like curved lens surfaces or fiber facets. Already the possibility of these applications demonstrates the resilience of this fabrication technology toward defects like dust particles.

## E. Future directions

### 1. Exploration of other materials and processes

Soft-nanoimprint lithography relies on capillary forces, and the infiltration works best if the solution is still liquid. Still, the density of the final material will be less than in bulk crystals. Aging the sol-gels could be a solution to densify the materials and avoid shrinking, leading to higher linear and nonlinear properties. However, the aged sol-gels cannot be structured with SNIL. Therefore, one should start investigating other templating methods: (i) hard nanoimprint lithography might be an option as the imprinting relies on the applied external forces and not on the capillary forces; (ii) block copolymer self-assembled templates in which the sol-gels could be infiltrated, already been demonstrated with titanium-dioxide sol-gels;⁷³⁴,⁷³⁵ and (iii) controlled dewetting of optical glass thin films could be adapted for nonlinear optical materials.⁷³⁶

Interdisciplinary collaboration between the fields of material sciences, chemistry, and nanosciences will play a crucial role in the future not only to help the optimization of the soft-nanoimprint process and the nonlinear properties of the sol-gel derived metaloxides but also in the development of new materials with very high nonlinear optical properties.⁷³⁷ Existing sol-gel recipes for other nonlinear materials, e.g., KTP, could be further developed.⁷¹⁴ By using more sophisticated alignment tools for soft nanoimprint lithography, one could stack several metasurfaces on top of each other to compensate hereby the lower electro-optic and nonlinear material intrinsic coefficients.

### 2. Nonlinear applications with high scalability, transparency ranges, robustness, and dimensionality

One clear advantage of solution-processed nanofabrication of nonlinear metasurfaces compared to standard top-down protocols is the upscalability. Soft-nanoimprint lithography has been demonstrated on the wafer scale and roll-to-roll fabrication.⁷³⁸ From an economic viewpoint, the bare material cost of quadratic nonlinear thin films is at least two orders of magnitude higher than that of the solution-derived materials. The only expensive part for the latter is determined by what substrate wafer is required for the intended device.

Recently, metalenses have been realized on the length scales of 10 cm in diameter with which the moon and nebulae could be imaged.⁷³⁹,⁷⁴⁰ Nonlinear metalenses based on frequency conversion could allow access to other wavelength ranges, e.g., up to the mid-infrared and down to the ultraviolet wavelength ranges, thanks to their high transparency window. Metasurface sensors from these materials could be used in harsh environments. They would be easy to clean, increasing their reusability and decreasing waste by exploiting the intrinsic inertness of metal oxides. Furthermore, the inherent material robustness also results in a high optical damage threshold, making these photonic devices more sustainable and long-lasting. The second-harmonic generation mechanism, combined with photonic crystal design, could add to the linear responses in advanced security features. In addition to flat devices, three-dimensional metasurfaces could be applied, e.g., if stacked to realize electrically tunable metalenses for fast switching that might be an alternative to membrane-type liquid lenses, which suffer from gravitational lag.⁷⁴¹
### 3. Unexplored properties and more fundamental aspects

We focused on the classical nonlinear and electro-optic properties of LNO and BTO, though both materials belong to the class of ferroelectrics, which also exhibit other compelling effects such as piezoelectricity and pyroelectricity. Therefore, the potential of further exploring the functionalities of this type of compound is enormous, mostly unexplored at the nanoscale and in the polycrystalline form of those materials.

Finally, spontaneous parametric downconversion, used in the early sources of entangled photons for quantum cryptography from periodically poled LNO,⁷⁴² remains to be demonstrated in polycrystalline sol-gel. In doing so, the miniaturization of quantum sources may benefit from a new type of fabrication process that can further help the integration of current bulky quantum systems.

### ACKNOWLEDGMENTS

The authors acknowledge ScopeM and D-MATL X-Ray Service Platform at ETH Zurich for providing instrumentation for characterization, nanofabrication support from the operation team of the Binning and Rohrer Nanotechnology Center (BRNC) and the operation team of FIRST-Center for Micro and Nanoscience at ETHZ. This work was supported by the Swiss National Science Foundation SNSF (Consolidator Grant Nos. 2022 213713 and 179099), the European Union's Horizon 2020 research and innovation program from the European Research Council under the Grant Agreement No. 714837 (Chi2-nanooxides). H.C.W. acknowledges financial support from the Physics Department at ETH Zurich.

## XIII. SEMICONDUCTOR METASURFACES: MATERIALS AND NANOFABRICATION APPROACHES

Mohsen Rahmani and Lei Xu

*mohsen.rahmani@ntu.ac.uk

### A. Introduction

Metasurfaces consist of artificial atoms, also referred to as subunits, with dimensions and separations much smaller than the light wavelength. The light passing through the metasurfaces interacts with the material's effective parameters, such as permeability ($\mu$) and permittivity ($\epsilon$). In other words, in addition to the lattice constant, i.e., separation, the refractive indices ($n^2 = \mu\epsilon$) of the atoms and their surrounding environment also play an essential role in stimulating and controlling the light interactions with metasurfaces. Meanwhile, to obtain strong light confinement in these atoms and enhance the optical effects produced by the metasurfaces, fabricating metasurfaces on low-refractive-index insulators, such as glass and sapphire, has become an important factor in designing the geometry of metasurfaces.⁷⁴³

In the past decades, advanced nanofabrication techniques have enabled complicated assemblies of nanoscale structures that can be employed for engineering the metasurfaces. Metals were among the first exploited materials for producing nanoscale particles and metasurfaces,⁵ mainly employing the oscillation of free electrons on the surface, so-called surface plasmons.⁷⁴⁴⁻⁷⁴⁶ Fabrication of metallic

nanostructures is relatively straightforward by using electron beam lithography (EBL). As a result, many high-quality metallic nanostructures have been proposed, fabricated, and studied. Despite numerous advantages allowing for near-field enhancement, metallic nanostructures suffer from Ohmic losses at optical frequencies, leading to light absorption. Hence, metallic nanostructures can be irreversibly damaged under illumination by high-power lasers, which is not preferable in many applications, particularly nonlinear metasurfaces.⁵³,⁷⁴⁷,⁷⁴⁸ Subsequently, a quest has taken place to employ other materials with more intrinsic and extrinsic properties to offer more versatile degree of freedom to produce metasurfaces with exotic properties.⁵¹⁰ As a result, materials' intrinsic and extrinsic properties have been employed as a versatile degree of freedom to produce metasurfaces with exotic properties. Several scenarios, such as solution-drive nanofabrication or nanofabrication on flexible metasurfaces are discussed in this roadmap. This section focuses on recently demonstrated approaches for fabricating semiconductor metasurfaces on insulators—a task that has been deemed challenging for decades.⁵¹⁰

### B. Semiconductor metasurfaces and fabrication challenges

Semiconductor metasurfaces, driven by their high refractive index and wide bandgap, have attracted significant attention in the photonics community recently. In addition to their loss-free nature, which distinguishes them from metals, semiconductor metasurfaces benefit from exotic electronic properties and controllable crystalline structures that provide vast and new opportunities to engineer light-matter interaction.⁷⁴⁹ Therefore, semiconductors have been deemed as major building blocks for the development of advanced optical devices such as meta-lenses, holograms, displays, sensors, and more.¹⁵ As a result, precise control of the geometry of sub-unit nanoparticles via top-down nanofabrication approaches has gained remarkable importance. However, unlike metallic nanostructures, regular lithographic and liftoff processes cannot be exploited for fabricating semiconductor metasurfaces, as discussed below.

The major categories of semiconductor metasurfaces include: (a) Group IV semiconductors, such as silicon or germanium, which are widely explored using the complementary metal-oxide-semiconductor (CMOS) processes, (b) III-V compound semiconductors, like GaN, GaAs, or AlGaAs, renowned for their high intrinsic nonlinearity, or (c) recently emerging materials, such as perovskites, with strong light absorption, high charge-carrier mobilities and long lifetimes.⁷⁵⁰ The common challenge for fabricating metasurfaces out of these semiconductors is the high-temperature requirements for the growth of a thin film. Therefore, the regular liftoff process (i.e., patterning, film deposition, and liftoff) cannot be exploited, as photo/electro resist is vulnerable against high temperatures. In addition, each category comes with its own set of fabrication challenges, including but not limited to lattice mismatch between film and substrate (particularly insulators), controlling the crystalline orientation, or resistance against dry or wet etching, etc.,⁵¹⁰ high-light a need for innovative approaches for fabricating semiconductor metasurfaces. This section reviews the community's effort to balance these fabrication challenges with the inherent properties of different semiconductor materials to advance both the fabrication techniques and the applications of these versatile materials in metasurface design.
### C. Group IV semiconductor metasurfaces

Group IV semiconductor nanostructures and metasurfaces, especially those made of silicon and germanium, have come to the forefront as viable alternatives to traditional metallic nanostructures, largely motivated by their ability to mitigate the Ohmic losses prevalent at optical frequencies in metal materials.<sup>146,751-754</sup> High-refractive index materials offer a promising platform for different nanophotonics applications in the visible and infrared regions, such as flat optics, sensing, computing, imaging, etc.<sup>15</sup> They support both electric and magnetic resonant optical modes, facilitating enhanced linear and nonlinear optical effects.<sup>755</sup> Notably, the ability to finely tune these materials through sophisticated fabrication methods allows for the precise manipulation of their optical properties, making them even more promising for the aforementioned applications.<sup>15</sup>

Given that germanium can be deposited with standard evaporation techniques, Germanium nanostructures can be fabricated through the standard top-down techniques, involving EBL for patterning hard masks, transferring the masks to the germanium film via inductively coupled plasma (ICP)/reactive ion etching (RIE), and mask removal via dry or wet etching.<sup>146</sup> On the other hand, silicon films cannot be deposited through evaporation or sputtering. Therefore, the fabrication of silicon nanostructures often leverages silicon-on-insulator (SoI) technology, which was initially developed for electronic applications. However, SoI wafers, benefiting from a crystalline silicon film, have been recently employed in photonics, as well. SoI enables planar waveguides that strongly confine light, thanks to the high refractive index contrast between the silicon core and a SiO₂ substrate.<sup>756</sup>

More recently, the use of amorphous silicon (a-Si), which can be grown directly on any substrate by plasma-enhanced chemical vapor deposition (PECVD), has opened up new possibilities in fabrication.<sup>757</sup> a-Si films can then be converted to any complicated metasurfaces via EBL patterning followed by ICP/RIE etching.<sup>758</sup> PECVD allows for the growth of thin films of hydrogenated amorphous silicon under lower temperatures compared to crystalline silicon, making it suitable for a broader range of substrates, including fully transparent ones, e.g., SiO₂ or quartz. This method involves the decomposition of silane gas in a plasma environment, where the ions and radicals facilitate the deposition of silicon on the substrate. The ability to control the deposition parameters, such as gas flow rates, power, and temperature, allows for tuning the properties of the amorphous silicon layer, such as its optical bandgap and conductivity. This control is crucial for tailoring the materials to specific applications, such as absorbers, holograms, metalenses, and other optical components. Amorphous silicon's flexibility in deposition and adaptability to different substrates have significantly broadened its applicability in the nanophotonics field, making it an invaluable material in the fabrication of advanced semiconductor metasurfaces.<sup>758</sup>

### D. Group III-V semiconductor metasurfaces

As explained in Sec. IV (Nonlinear Optical Metasurfaces) above, nonlinear metasurfaces have great potential to revolutionize modern photonic devices, including optical signal processing, control over the frequency spectrum of laser light, ultrafast switching and generation of ultrashort pulses.<sup>759</sup> However, weak nonlinear optical responses of metasurfaces have guided the community's attention to materials, which naturally possess large nonlinearities. III-V semiconductor

nanoantennas and metasurfaces, comprised of materials such as Gallium Arsenide (GaAs), Gallium Phosphide (GaP), Indium Phosphide (InP), benefit from the non-centrosymmetric crystal structure, large second-order susceptibilities,<sup>503</sup> and fast carrier recombination times.<sup>760</sup> The strong second-order bulk susceptibility of III-V materials would, therefore, intrinsically increase the nonlinear conversion efficiency as compared to silicon or germanium. Furthermore, like IV semiconductors, III-V semiconductors also exhibit high refractive indices that allow the use of strong Mie resonances to amplify the nonlinear signals. Moreover, III-V semiconductors are pivotal in various advanced technological areas in optoelectronic applications due to their direct bandgap and high electron mobility. Therefore, the unique electronic and optical properties of III-V semiconductors enable superior performance for various applications ranging from high-efficiency solar cells, light-emitting diodes, and photodetectors to quantum computing and photonic integrated circuits.

Unfortunately, the full fruition of III-V metasurfaces in photonics has been bottle-necked because of the absence of good-quality dielectric-semiconductor interfaces. The main challenge is that III-V semiconductors, which are generally grown epitaxially, must be grown on a substrate with a minimal lattice mismatch to avoid defects.<sup>761</sup> Over the years, various techniques for fabricating III-V semiconductor nanostructures and metasurfaces on insulators have been developed. Recently, a solution was achieved by Cambiasso *et al.*, who introduced a novel approach to circumvent the challenges associated with growing III-V films on mismatched substrates. Instead of using conventional film growth, they directly fabricated GaP nanoantennas on a GaP wafer. This technique involves using EBL to create highly precise and intricate patterns on the GaP wafers. Following the EBL process, these patterns are transferred into the wafer using ICP etching. Eventually, GaP nanopillars with a height of 200 nm were created and optimized for visible light applications, demonstrating enhanced SHG characteristics as described in Ref. 762.

Pioneering a novel approach in III-V semiconductor fabrication, Person *et al.* focused on creating GaAs nanoantennas on glass substrates.<sup>763</sup> Initially, they grew a thin film of GaAs on a GaAs substrate using molecular beam epitaxy (MBE). This was followed by an epitaxial liftoff process, where the GaAs film was separated from its substrate and then transferred onto a fused silica substrate via a water-bounding procedure. Subsequently, by using RIE, the thickness of the film was reduced to the desired value, and then the nanoantennas were patterned onto the film through EBL, followed by another RIE process. This technique marks a significant step in fabricating GaAs nanostructures on transparent substrates.<sup>763</sup> Although it was the first of its kind, the relatively low quality of resonators and the rough side walls restricted its performance for nanophotonics applications, such as the obtained field confinement for nonlinear enhancement. In the pursuit of efficient nonlinear optical materials, Gili *et al.* introduced an AlGaAs-based monolithic platform. Their process starts with growing a layered structure on a non-intentionally doped GaAs wafer through MBE. This structure includes a layer of AlGaAs on the top an aluminum-rich layer for later oxidation. Following the growth, the sample then undergoes patterning using the EBL, and the resultant patterns are etched into the substrate using nonselective ICP-RIE. Subsequently, the aluminum-rich layer was oxidized to create a uniform AlOx substrate. Such a substrate with a low refractive index plays a crucial role in enabling effective optical confinement within the
<figure><img src="image_31.png" /><figcaption>**FIG. 23.** (a-i) SEM image of an array of monolithic AlGaAs-on-AlOx nanoantennas. (a-ii) Schematic of a single monolithic AlGaAs-on-AlOx nanoantenna. Adapted from Ref. 504. (b-i) Steps illustration for fabricating GaAs metasurfaces, proposed by Adapted from Ref. 764. (b-ii) A side view and (b-iii) top view SEM images of the fabricated GaAs metasurfaces. The inset gives the reflectivity spectrum of the GaAs metasurface. Liu *et al.*, Nano Lett. 16, 5426 (2016). Copyright 2016 American Chemical Society. [(c-i)-(c-v)] Fabrication procedure for the AlGaAs nanoresonators in a transparent media Rocio *et al.* Adapted from Camacho-Morales *et al.*, Nano Lett. 16, 7191 (2016). Copyright 2016 American Chemical Society. 197 (d-i) Fabrication process flow for slicing the nanowires. (d-i) SEM image of one nanowire sliced by FIB into standing disks (highlighted in blue). (d-ii) SEM image of the resulting single standing disk (blue) on an ITO substrate. Scale bars are 300 nm. [(d-i)-(d-iii)] Adapted with permission from Timofeeva *et al.*, Nano Lett. 18, 3695 (2018). Copyright 2018 American Chemical Society. 512</figcaption></figure>

AlGaAs nanocylinders to facilitate strong nanoscale light-matter interactions, as shown in Fig. 23(a).504

Shortly afterward, Liu *et al.* demonstrated a similar approach for creating nonlinear metasurfaces composed of a square lattice of GaAs nanodisk resonators.764 These resonators were placed on a low refractive index AlGa oxide spacer layer, formed by selectively oxidizing high-Al content AlGaAs layers. It began with the growth of alternating layers of AlGaAs and GaAs on a GaAs substrate via MBE. A negative hydrogen silsesquioxane (HSQ) mask was then applied for patterning. The shapes of the SiO₂ nanodisks were transferred onto the GaAs and AlGaAs layers using ICP etching. Finally, via the selective wet oxidation process, the AlGaAs layer has converted into a low refractive index (AlxGa1-x) layer. In parallel with these studies, Camacho *et al.* implemented a recipe for III-V in insulator fabrication, enabling the production of metasurfaces on fully transparent substrates like glass or sapphire. Their approach includes metal-organic chemical vapor deposition (MOCVD) growth of AlGaAs or GaAs on a thin sacrificial AlAs layer, pre-grown on a semi-insulating GaAs substrate. The process was followed by EBL patterning and RIE etching to imprint the designs onto the top and AlAs layer. Subsequently, the AlAs layer was removed by wet etching, and loosely bound nanostructures are embedded in a benzocyclobutene (BCB) polymer layer that can be transferred to a glass substrate. As a result, high-quality AlGaAs nanoresonators were obtained on a fully transparent matrix [see Fig. 23(c)].197 Furthermore, several alternative approaches were reported for fabricating III-V metasurfaces on insulators. Timofeeva *et al.* proposed free-

standing III-V disks, by slicing nanowires with focused ion beam (FIB) milling to create disk-based configurations on any substrate, as shown in Fig. 23(d).512 Another promising technique is to grow GaP on GaAs substrate with an AlGaInP buffer layer, then bond it to a sapphire substrate after depositing SiO₂ layer on top of both surfaces. By removing the AlGaInP/GaAs layer with wet etching, one can obtain GaP film on an insulator that can be used to produce high-quality nonlinear metasurfaces.152,765 Depositing GaN on sapphire by MOCVD is another exciting technique enabling many applications of both linear and nonlinear metasurfaces in the visible range, particularly meta-lenses.737 Overall, all these advances in fabricating III-V metasurfaces on a wide range of substrates open many doors to make them compatible with CMOS technologies in the near future.

### E. Multi-layered semiconductor metasurfaces

Stacking several metasurfaces on each other, to benefit from several functionalities simultaneously, is an important step forward for realizing multi-functional end-user devices. This concept was first studied in plasmonic bilayered chiral structure,766 and stacked metamaterials, so-called Stereometamaterials.767 The concept of multi-layered semiconductor metasurfaces is a recently developing field, with the vision of integrating multi-functions, such as linear, nonlinear, passive, and active metasurfaces, into a single, compact device.768,769 This approach promises significant advancements in optical technology, enabling more sophisticated and versatile functionalities.770
<figure><img src="image_32.png" /><figcaption>**FIG. 24.** (a-i) A schematic of a three-layered silicon metasurface triplet lens. (a-ii)–(a-iv) Illustration of the fabrication of layered silicon metalens doublet. Adapted with permission from Zhou *et al.*, Nano Lett. **18**, 7529 (2018). Copyright 2018 American Chemical Society. **771** (b) Schematic illustration of a chiral bilayer dielectric metasurface. Adapted with permission from Tanaka *et al.*, ACS Nano **14**, 15926 (2020). **773** Copyright 2020 American Chemical Society. (c) Sketch illustrating the evolution from the design of independent 2D metasurfaces to a multi-layer stack exploiting a single-shot thin film self-rolling mechanism. Side-view (bottom left) and top-view (bottom right) SEM images of self-rolled microtubes after the sacrificial layer removal, revealing the two nanohole array stacks in the microtube walls. Adapted with permission from Bermudez-Urena and Steiner, ACS Photonics **6**, 2198 (2019). Copyright 2019 American Chemical Society. **774** (d) SEM image of the fabricated three-layer AlGaAs metasurface. Adapted from Ref. **775**. (e-i)–(e-v) Illustration of the steps for fabricating stacked AlGaAs/GaAs alternating multi-layer resonators. (e-ii) A top view image of the final pillar structures, scale bar 1 µm. (e-iii)–(e-v) Tilted views of the finalized one, two and three AlGaAs nanodisk stacks. The scale bars are 100 nm in (e-ii)–(e-v). (e-i)–(e-v) Adapted from Ref. **778**.</figcaption></figure>

Recently, Zhou *et al.* demonstrated tightly spaced multi-layer metasurfaces for multiwavelength focusing.⁷⁷¹ They fabricated two a-Si meta-lens embedded in PDMS, separately. The two layers were bounded by heating and curing the PDMS. As a result, they demonstrated a multiwavelength metalens doublet (NA = 0.42) with focusing efficiencies of 38% and 52% at wavelengths of 1180 and 1680 nm, respectively [see Fig. 24(a)]. Later, the same group extended this fabrication technique to realize bilayer metasurfaces for multiwavelength holograms, multiwavelength waveplates, and polarization-insensitive 3D holograms.⁷⁷² A similar technique, shown in Fig. 24(b), but using a spin-on-glass layer instead, has been proposed for the creation of

bilayer semiconductor chiral metasurfaces.⁷⁷³ Figure 24(c) demonstrates another approach proposed by Bermudez-Urena and Steiner. It involves a thin film self-rolling technique to fabricate multi-layered semiconductor metasurfaces.⁷⁷⁴ During the fabrication process, the semiconductor materials primarily used include Ge and SiO₂, along with gold, for certain steps. When the sacrificial underlayer (Ge) is selectively removed, these strained layers naturally roll up, either upwards or downwards, creating a microtubular structure with multi-layered surface walls, depending on the number of turns completed. This method reduces the number of steps required for creating multi-layer metasurface devices.
In 2021, Marino et al. employed a novel fabrication technique for a three-layer metasurface in the AlGaAs-on-insulator platform designed to enhance the optical performance in applications like ultrafast optical switching and high harmonic generations.⁷⁷⁵ As depicted in Fig. 24(d), the metasurface features three AlGaAs layers separated by a low-index AlOx spacer, all resting on an AlOx optical substrate. The fabrication process involves MOCVD growth of the epitaxial structure on a GaAs wafer, PECVD deposition of a SiO₂ hard mask, EBL, Electron-Beam Physical Vapor Deposition (EBPVD) nickel deposition, liftoff, ICP-RIE etching, and selective oxidation of AlGaAs layers, resulting in a deeply etched, high-efficiency metasurface. The lower refractive index contrast between the resonator and the spacer layers (AlOx) reduces the energy confinement within the resonators. To maximize the index contrast and field confinement, later in 2022, Vennberg et al. proposed another approach to fabricate vertically stacked AlGaAs/GaAs nanodisk resonators with a fast and scalable patterning method using charged sphere colloidal lithography, where they have under-etched the spacer layer (GaAs), as illustrated in Fig. 24(e).⁷⁷⁶

## F. Metasurfaces made of hybrid and emerging materials

Despite the recent progress in semiconductor metasurfaces, there is still a quest to explore new materials for various applications to address the major issues hampering the full-scale development of metasurface technology, such as high loss, cost-ineffective fabrication, and challenging integration.³,⁷⁷⁷⁻⁷⁷⁹ Some research works have demonstrated that combining the advantages of the metal and semiconductor approaches can address such issues. Various types of hybrid nanoantennas, consisting of metallic resonators embedded in semiconductor media or vice versa, have been proposed and realized in recent years, such as hybrid metal-oxide nanostructures¹⁹¹ or nanopatterned plasmonic films filled with GaAs,⁷⁸⁰ metal/dielectric core-shell nanoparticles,⁷⁸¹ plasmonic ring filled by concentric lithium niobate,⁷⁸² silicon,¹⁴⁸ or AlGaAs.⁷⁸³ The fabrication technique for hybrid nanostructuring is generally a combination of the techniques discussed above, consisting of multiple EBL steps, requiring precise alignment of every subsequent mask to the previous steps.

2D materials, ranging from WS₂, MoS₂, MoSe₂ to WSe₂ with semiconducting band gaps on the order of 1–2.5 eV, to hexagonal boron nitride (h-BN) with a wideband gap of 6 eV, are recently proposed materials for semiconductor metasurfaces, particularly in nonlinear regime,⁷⁸⁴,⁷⁸⁵ Chemical vapor deposition (CVD) technique is the most employed method that has enabled the synthesis of large area and uniform thickness 2D layer of metal and insulating surfaces for the large-scale device fabrication including electronic and flexible optoelectronic devices.⁷⁸⁶ II–VI compound semiconductors, such as ZnS or CdHgTe, with a large range of electronic energy bandgaps, have also been considered for optoelectronic metasurfaces,⁷⁸⁷ and Cd–Te helices have been proposed for chiral nonlinearity.⁷⁸⁸ More recently, perovskite materials with a large ability of tunability have been proposed for reconfigurable semiconductor metasurfaces.⁹¹,⁷⁸⁹⁻⁷⁹⁴ The optical properties of perovskite metasurfaces can be tuned by changing the composition of the perovskite material or the thickness of the perovskite film. All these emerging materials are already subjects of heavy studies in the community of semiconductor metasurfaces.

## G. Conclusions and future perspectives

Today, semiconductor nanoscale devices are routinely used in the electronics industry. The possibility to engineer their bandgap and electrical conductivity has made them an ideal platform for making transistors and integrated circuits.⁷⁹⁵ Alongside this, the optoelectronic properties of semiconductor nanomaterials, mainly based on quantum mechanical effects of light on electronic materials, have also been employed to find, detect and control the light via photo-diodes, solar cells, plasma displays, nano-lasers, etc.⁷⁹⁶ However, engineering and exploiting purely optical properties of semiconductor nanostructures, including metasurfaces on insulators, is a relatively new field of research that has recently flourished via developing novel fabricating techniques.⁵¹⁰ As briefly summarized in this section, despite challenges for growing semiconductor films, including high-temperature deposition and lattice mismatch, which forbid regular liftoff nanolithography, many innovative techniques have been recently proposed for fabricating high-quality semiconductor metasurfaces. It is worth noting that this concept differs from fabricating quantum dots via the synthesis of sub-30-nm semiconductor nanoparticles. Quantum dots employ semiconductors' optoelectronic properties, which is beyond the scope of this section.

Given the recent development in the fabrication techniques of semiconductor metasurfaces, there is a promising perspective on the capability to fabricate more complex and hybrid metasurfaces. As a result, significant interest has grown in integrating metasurfaces in photonics chips and tunable metasurfaces, two areas requiring well-controlled and precise nanoscale devices. Recently, the incorporation of metasurface principles into integrated photonics has grown rapidly. This capability opens opportunities to control the off-chip emission of customized free-space wavefronts and on-chip manipulation of light.⁷⁹⁷ Similarly, a great interest has appeared in tunable metasurfaces where external tools, such as mechanical force, heat, applied voltage, etc., can be used to control the light emission, propagation direction, polarization, phase, or wavelength.⁷⁹⁸⁻⁸⁰¹ These developments are not only enhancing the performance and efficiency of existing applications for semiconductor metasurfaces but also paving the way for future applications of nanostructures ranging from advanced imaging and signal processing to sensing and energy harvesting, unlocking more potential in nanotechnology and photonics fields.

## ACKNOWLEDGMENTS

M.R. and L.X. acknowledge support from the UK Research and Innovation Future Leaders Fellowship (No. MR/T040513/1). M.R. appreciates the support of the Royal Society and the Wolfson Foundation.

## XIV. CONFORMAL AND FLEXIBLE METASURFACES: A BRIEF PERSPECTIVE

S. M. Kamali, E. Arbabi, and Andrei Faraon

faraon@caltech.edu

## A. Introduction and brief history

Metasurfaces designed for, and fabricated on, flexible substrates enable very interesting concepts and have potential for applications in conformal optics where a thin metasurface can vastly alter the optical
function of an optical element with a given shape,⁴⁶⁷,⁴⁶⁸,⁸⁰²,⁸⁰³ or a stretchable metasurface can act as a compact tuning element in an optical system.⁸⁰⁴⁻⁸⁰⁶ Nevertheless, despite the attention and advances made over the past decade, this technology has not been adopted beyond academic and research efforts. In this Perspective, we give a short account of the history of conformal and flexible metasurfaces, briefly discuss their design, fabrication, and potential applications, and share our view of their opportunities and the challenges that must be overcome before those opportunities can be realized.

The applications of gratings fabricated on curved surfaces goes back more than a century where concave gratings have extensively been used in spectroscopes to reduce the optical aberrations and improve spectral resolution.⁸⁰⁷⁻⁸¹⁰ Since then, diffractive structures patterned on non-planar surfaces have also been used to mitigate the chromatic aberrations of lenses⁸¹¹,⁸¹² or enhance the power of optical system without compromising size and weight.⁸¹³ Independently, conformal RF and microwave phased array antennas⁸¹⁴,⁸¹⁵ and metasurfaces⁸¹⁶⁻⁸¹⁸ have been developed over the past many decades to fit certain functionalities in structures dictated by other factors such as aerodynamics, stealth, or physical constraints of the host structure.

Over the past decade, the increased availability and reduced cost of advanced nano-fabrication and computational resources have allowed for the design and fabrication of conformal metasurfaces at optical length scales, see Figs. 25(a) and 25(b).⁸²¹⁻⁸²³ As intrinsically quasi-2D structures (i.e., having a third dimension much smaller than the first two), metasurfaces are suited for conforming to non-planar structures and can be directly fabricated on the target surface.⁸⁰² Direct fabrication, however, is only possible if the target surface has small curvature (i.e., a very large radius of curvature) and very small height variation overall (in the tens of micrometers, maximum).⁸⁰² Otherwise, pattern generation

machines with special capabilities are needed to define the metasurface pattern, and the utility of regular planar techniques that are widely developed and used for electronics will be very limited in fabrication of conformal metasurfaces. The requirement of special equipment and methods for their fabrication severely limits the types and shapes of structures that could be directly made as well as the shape and material of the target non-planar surfaces, and would thus hinder the development and scaling of conformal metasurfaces. To circumvent these issues, the idea of transferring metasurfaces to flexible substrates, that could later conform to a non-planar surface, was developed.⁴⁶⁸ Using this method, flexible metasurfaces can be fabricated separately and later fitted to the target structure, altering its optical function to one that does not match its form, or adding totally new functionalities.⁴⁶⁷ For instance, a specially designed metasurface can be used to make a diverging cylindrical lens work like a converging spherical one,⁴⁶⁸ or metasurfaces can be added to regular eyepieces and turn them into visors for near eye displays.⁴⁶⁷

Since many flexible substrate materials are also stretchable, transferring of metasurfaces to these substrates enables other lines of applications utilizing this property.⁸⁰⁶,⁸²²,⁸²³ For instance, a main property of optical gratings is their period, which would change proportional to the local strain if a metasurface on a flexible material is stretched. This would in turn change the grating momentum and thus can be used to tune the diffraction angle at a certain wavelength of light, or change the color appearance at a given angle.⁸²⁴ The focal length of diffractive and metasurface lenses can also be tuned through radial stretching [albeit with introduction of additional geometric aberrations, see Fig. 25(c)].⁸²² The deformations of the substrate, such as stretching, can significantly alter the optical function of flexible metasurfaces, providing an opportunity to tune their functionality. Various tunable and

<figure><img src="image_33.png" /><figcaption>**FIG. 25.** Conformal and flexible metasurface concepts. (a) A metasurface conforming to an optical element modifies the optical function of the element in a desired way.⁴⁶⁸ (b) Concept of a flexible metasurface conformed to an eyeglass's eyepiece to redirect display light from the micro-display to the eye. Similar to holographic optical elements, metasurfaces can implement a grating and wavefront control functions simultaneously in a single layer, allowing for the thin metasurface to both correct for the eyepiece shape and redirect light.⁴⁶⁷ (c) Schematic illustration of a flexible tunable metasurface. Upon stretching, the focal length of the metasurface changes proportional to strain squared.⁸²² (d) Schematic of a stretchable filter, where the transmission and reflection spectra can be modified upon stretching the metasurface.⁸²³ All images are reprinted (adapted) with permission from the respective Journal and copyright remains with the original publisher.</figcaption></figure>
stretchable metasurface lenses and gratings have been demonstrated using different metasurface platforms (see Fig. 25),$^{806,824}$ in addition to tunable filters and color tuning in metasurfaces.$^{825–827}$

It is worth noting here that fabrication of diffractive optical elements (e.g., surface relief optics like blazed gratings, Fresnel lenses, diffusers, etc.) using non-rigid materials such as polymers and resins is relatively mature and multiple companies (Luminit, Viavi, etc.) have already commercialized these technologies for many years now. While these technologies, and devices fabricated using them, are in many aspects similar to metasurfaces fabricated on or transferred to

flexible substrates, we would like to distinguish and separate them for the purposes of this paper by the effective volume thickness (i.e., wavelength and subwavelength scale thickness for metasurfaces vs multiple to several wavelengths for these more conventional devices), and the critical dimensions of the structures involved (i.e., subwavelength for metasurfaces and single to multiple wavelength scales for the conventional ones). Each of these technologies have their own benefits and drawbacks and the specific choice of which one to use depends on many technical and non-technical factors involved. Nevertheless, in the rest of this chapter we will focus on metasurfaces

<figure><img src="image_34.png" /><figcaption>**FIG. 26.** Fabrication methods for flexible metasurfaces. (a) For non-planar surfaces with small bumps (i.e., a few tens of micrometers of height variation and slopes smaller than a few degrees) the pattern can be directly generated on the non-planar surface using electron-beam lithography, and then transferred to the active metasurface layer using etch or liftoff processes.$^{802}$ (b) Metasurface can be patterned directly on the non-planar surface using nano-imprint lithography. The patterned layer can then be used as an etch mask or liftoff agent to transfer the pattern to the metasurface layer material.$^{821}$ (c) A pre-patterned layer can be used like a stencil shadow mask to transfer a pattern to a flexible substrate using a directional deposition method.$^{831}$ (d) The metasurface pattern can be generated using master and soft molds and a nano-imprint lithography process.$^{832}$ (e) The metasurface structure can be fabricated on a conventional rigid substrate, and then transferred to a flexible substrate using spin and cure and a sacrificial layer.$^{468}$ (f) Spin-coat and peel-off method can be used to transfer plasmonic metasurfaces fabricated on conventional rigid substrates to a flexible layer.$^{803}$ All images are reprinted (adapted) with permission from the respective Journal and copyright remains with the original publisher.</figcaption></figure>
<figure><img src="image_35.png" /><figcaption>**FIG. 27.** Potential applications for flexible metasurfaces. (a) Image of a flexible metasurface conformed to a concave cylindrical lens, and the measured focal spot intensity of the combined optical system.<sup>468</sup> (b) A free-form metasurface optical element with wavefront shaping and grating deflection ability combined, fabricated on a non-planar substrate.<sup>467</sup> Metasurfaces designed and fabricated with the same mindset could be integrated on eyepieces of headmounted displays. (c) Simulated performance of a metasurface spectral filter proposed as a mitigating solution for deuteranomaly. Original image (left), simulated image without correction (middle), and simulated image after correction (right) are shown.<sup>803</sup> (d) A stretchable metasurface with tunable reflection spectrum showing full spectral tuning from blue to red for both linear polarizations of light.<sup>804</sup> (e) Focal length tuning using a stretchable tunable metasurface singlet. The change in focal length is proportional to strain squared.<sup>822</sup> (f) A tunable grating with enhanced first order diffraction efficiency used to achieve color tuning. As the grating period changes when stretched, the appearing color varies with it.<sup>826</sup> All images are reprinted (adapted) with permission from the respective Journal and copyright remains with the original publisher.</figcaption></figure>

to fabricate and transfer most types of metasurfaces. The transfer step to the flexible substrate can be done through simple transfer printing in cases where adhesion to the flexible substrate can be higher than the rigid one, or using a sacrificial layer that can be dissolved away from underneath the metasurface and release the metasurface inside the flexible substrate.<sup>822</sup> The main disadvantage with this method is the complication and number of process steps involved that could increase the process cost and lower the total yield.

### 3. Applications

In a coarse division, we can categorize the applications of conformal metasurfaces to modify/improve performance of a non-planar object, or add a totally new functionality to an optical element. One example of the first category was wavefront shaping plasmonic reflective metasurfaces used to compensate for phase distortions caused by height variations on a reflective surface [Fig. 25(a)].<sup>802</sup> While called cloaking, the phase compensation only works over a narrow band and the direct fabrication method utilized limits the application to small surfaces with bumps in the few micrometers, also requiring very precise alignment between the non-planar surface and the metasurface.

Dielectric conformal metasurfaces have been used to alter the optical function of conventional refractive optical elements [Fig. 27(a)].<sup>822</sup> The phase profile of the metasurfaces were chosen to change the function of diverging and converging cylindrical lenses to converging spherical ones. In practice, this method can be useful when there is need for optical windows through transparent surfaces whose shapes are dictated by factors other than optics. Similar to other metasurfaces and diffractive optics wavefront shaping elements, chromatic aberrations limit the bandwidth of the light that can be used. Another main challenge with this line of application is that it requires high accuracy alignment between the metasurface and the target surface, which doesn't necessarily have suitable alignment marks, or might require deformations in the flexible substrate that cause non-uniform strain throughout.

As mentioned in the first section, adding gratings and diffractive optical elements to non-planar surfaces has had a long line of applications, for instance in spectroscopes that use it to reduce aberrations and improve resolution.<sup>808</sup> More recently, the use of metasurfaces as the combining element on near eye display systems has been proposed where the metasurface would be integrated onto the visor or eyepiece element in lieu of a holographic optical element and work either as a pure grating or a grating with wavefront
shaping [Fig. 27(b)].⁴⁶⁷ This is an interesting line of applications, yet cost, scalability, and worse see-through compared with volume holographic elements are challenges (among others) that should be overcome for it to become promising.

Apart from wavefront shaping, metasurfaces have shown other functionalities like spectral filtering.⁵⁰⁰ Similarly, conformal metasurfaces integrated on contact lenses have been used as spectral filters to improve color separation for colorblind users [Figs. 27(c) and 27(d)].⁸⁰³ When the substrate is stretchable, the transmission/reflection spectra can be tuned with stretching as well, and therefore flexible metasurfaces can be used as tunable color filters.

Stretching has also been used to tune grating pitch and deflection angle to steer beams⁸²² or generate variable color structures [Figs. 27(d) and 27(f)]⁸²⁶ or tune lenses and make lenses with tunable optical power [Fig 27(e)].⁸²² In both cases, the tunable range is significantly larger than what is possible with other methods like liquid crystal integration or electro-optic modulation, but the tuning speed is very limited, the tuning mechanism is relatively large, and the long term reliability and number of cycles are very limited compared to those alternative methods. Due to these limitations, it might be more appropriate to call these devices *reconfigurable* rather than *tunable*.

### C. Challenges, opportunities, and future perspectives

Flexible and conformal metasurfaces have some similarities with flexible electronics (mostly in fabrication processes and materials), and therefore the vast body of knowledge developed around flexible electronics can be (and has been) utilized here. Nevertheless, there are both fundamental and technical differences between flexible metasurfaces and flexible electronics (or even integrated photonics). First, functionality and form are tightly correlated in optics, and as such the shape of the structure and the conforming metasurface should remain controlled and known during operation, unlike flexible electronics where the capability to operate under various deformations is usually a key characteristics. One exception where flexible metasurfaces might be fine with deformations is the case of arrays of small elements (e.g., a micro-lens array). In such cases, it is possible that the metasurface remains functional under deformation as long as the deformation in each element remains small. One potential application could be for a micro-lens array integrated with a flexible OLED panel.⁴⁰³,⁸³⁴,⁸³⁵

On the technical side, the target substrate of a conformal metasurface should be well-known and well characterized, and the conforming metasurface should be aligned with it to the regular optomechanical alignment accuracy of the system. In addition, if the conformal metasurface goes through a planar deformation or local stretching during the alignment and fitting steps (e.g., due to a finite Gaussian curvature of the target surface), these deformations need to be well-controlled and understood, and their impacts need to be considered in the design and fabrication steps.

Tunable flexible metasurfaces can be very light and compact by themselves (e.g., they can be as thin as a few tens of micrometers). However, the mechanical system required to stretch the metasurface can be relatively large and heavy as the stretch generally should be very uniform and well-controlled. This necessitates close attention to the design and implementation of the mechanical tunable system for the benefits of low weight and volume to be realized. Reliability and cycle count are other important factors that need improvement, requiring the exploration and use of better flexible substrates.

Finally, conformal and tunable metasurfaces have a chromatic dispersion similar to other diffractive optical elements that could severely limit their useful operation bandwidth, unless the dispersion is useful for the application (like in spectrometers), or could be compensated for (e.g., in diffractive-refractive combinations, or augmented reality waveguides).

A major opportunity for flexible substrates is in roll-to-roll fabrication of metasurfaces. Whether the flexibility and conforming ability of the metasurface is critical for an application or not, nano-imprint or cast-and-cure methods of fabricating metasurfaces can provide significant cost reduction over other methods that rely on lithography and etch.

With the growing interest in wearable and head mounted displays in recent years (and potentially over the coming decade), metasurfaces in general, and flexible metasurfaces in particular, face a great opportunity. With stringent requirements on weight, volume, and power consumption, while demanding high performance optics for various parts of the system like cameras, eye tracking, and the display system all in a fashionable form factor, conformal metasurfaces pose many appealing properties that could make them suitable for sensor optics, holographic elements on visors, or diffractive optics on waveguides.

In addition to wearable displays, various types of compact consumer electronics (e.g., smart watches, wireless headphones, etc.),

<figure><img src="image_36.png" /><figcaption>**FIG. 28.** Scattering of light traveling in the x direction at a (a) spatial and (b) temporal interface can be illustrated with dispersion diagrams, where the full and dashed lines denote the dispersion cones for the two media. (c) An illustration of a device that combines advanced structuring of both spatial and temporal inhomogeneities to provide dynamic control over the momentum and frequency of scattered light, adapted from Ref. 48. Copyright remains with the original publisher.</figcaption></figure>
smart appliances, medical imaging systems, and many other smart and electronic systems are becoming ubiquitous with an ever increasing push for integrating more sensors and machine vision cameras. If the challenges facing flexible metasurfaces are overcome or circumvented for the relevant applications, these areas could become significant growth opportunities for flexible metasurfaces, in particular if low-cost and scalable fabrication pipelines are developed.

Optical metasurfaces, in general, and flexible metasurfaces, in particular, have gone through a major cycle of attention and research growth in the past decade. We believe over the coming years there are many opportunities for them to enable consumer level applications, but they have to overcome the multiple barriers and challenges outlined above.

# XV. TIME MODULATED METASURFACES

A. C. Harwood, S. Vezzoli, and R. Sapienza

a.harwood22@imperial.ac.uk

## A. Introduction

Traditional, bulk optical components are ubiquitous in modern day life, providing a means to transform light into an essential technological tool through the use of engineered spatial inhomogeneities. This framework for light manipulation is underpinned by Noether's theorem, which dictates that light scattered at a spatial interface between two media must conserve energy, and thus frequency, as the system is invariant in time [Fig. 28(a)]. Conversely, a system exhibiting homogeneous and instantaneous changes in its optical properties scatters light in time through non-conservative processes. This temporal scattering modifies the frequency of light while maintaining the conservation of its momentum [Fig. 21(b)]. These novel processes of light scattering are known as time reflection and refraction, the temporal counterparts to the familiar, spatial reflection and refraction derived from Fermat's principle. The parallels between scattering in space and time can be readily visualized by using a phase diagram Figs. 21(a) and 21(b). As a consequence, the arrangement of temporal inhomogeneities in time-varying media serves as a mechanism through which a device may effectively manipulate the spectral content of light.⁸³⁶,⁸³⁷

Initial studies into time-varying phenomena were undertaken in the field of plasma physics,⁸³⁸ as well as systems of mechanical waves⁸³⁹ and low frequency electromagnetic waves.⁸⁴⁰,⁸⁴¹ These systems facilitated high-efficiency time-varying experiments, as the desired high-contrast modulations could be easily manipulated at frequencies equal to that of the propagating waves using convenient electronic or mechanical driving mechanisms. On the other hand, systems that demonstrate high-contrast, sub-period modulations in the optical regime rely upon Kerr-like processes, which are exclusively mediated by powerful femtosecond lasers. Consequently, the exploration of time-varying photonics has been dependent upon the development of ultrafast laser science and compatible material platforms for nonlinear optics. Since its conception this decade, time-varying photonics has been studied across a broad range of systems, such as 2D materials,⁸⁴² ultracold atoms,⁸⁴³ and quantum wells.⁸⁴⁴ However, the discussion herein will concentrate on systems that have demonstrated the most profound capabilities and potential—time-varying optical metasurfaces.

Time-varying optical metasurfaces emerge through temporal modulations of the optical properties of a sub-wavelength medium, forming an interface characterized by time-varying reflectivity and transmissivity. The scattering of light from the temporal inhomogeneities of such an interface inherently deviates from the temporally switched medium illustrated in Fig. 1(b), where propagation may lead to complications from effects such as self-broadening.⁸³⁶ The control obtained with a temporally modulated interface mimics the approach employed by spatial metasurfaces, which leverage sub-wavelength structuring of high-contrast inhomogeneities to efficiently manipulate the momentum of scattered light. Likewise, high efficiency time-varying metasurfaces require a mechanism which acts on sub-period timescales and provides a large modulation contrast between the time-varying structure and its unmodulated surroundings.⁸⁴⁵ Furthermore, the framework of temporally structured interfaces lends itself to the development of space-time structured devices that combine the matured science of spatial metasurfaces with complex temporal modulations. This envisioned device, a space-time metasurface [XXI(c)], would utilize engineered spatial and temporal inhomogeneities to provide simultaneous and dynamic control of the momentum and spectral content of scattered light from a nanoscale component. This versatile device holds promise for a wide range of applications, spanning from temporal aiming and antireflection coatings to the exploration of photonic time crystals and the development of magnet-free nonreciprocal devices.⁵⁰,⁸⁴⁶

To explore the extensive and varied research avenues concerning time-varying optical metasurfaces, the current state-of-the-art for temporally engineered metasurfaces will first be reviewed in Sec. XV B. This section will discuss the prevalent experimental systems that have illustrated the great potential, alongside challenges that must be resolved to be able to realize more complex temporal structures. In extension to this paradigm, Secs. XV C and XV D will proceed to investigate the use of structuring in space and time simultaneously to provide enhanced time-varying interactions and 4D control over scattered light, via spatially static and varying modulations. To conclude, the current state of the field will be summarized, alongside the prevailing obstacles that will determine the future of time-varying optical metasurfaces.

## B. Time-varying metasurfaces

To identify a suitable material for a time-varying optical metasurface, one must first examine electronic state transitions that may give rise to large changes in permittivity and occur over sub-picosecond timescales. A familiar example of such a mechanism is the virtual-state transition of electrons induced by nonlinear polarizations, giving rise to oscillating regions of permittivity. Although this modulation process meets the ideal requirement of being ultrafast, the change in permittivity induced by such processes is conventionally minimal. Alternatively, one may consider the modulation of a material's refractive index via real-state transitions of electrons, for example the excitation, and subsequent relaxation of electrons via photoexcitation. These real state transitions are typically linked to substantial changes in permittivity; however, they predominantly unfold over time periods exceeding picoseconds.⁸⁴⁷ Consequently, traditional nonlinear materials do not provide an efficient platform for time-varying photonics. However, this paradigm is notably disrupted by transparent conductive oxides, a variety of epsilon-near-zero materials. Although constricted to the
region about their near-infrared epsilon-near-zero wavelengths, indium tin oxide and aluminum zinc oxide in particular, have been used to demonstrate vastly enhanced, non-perturbative nonlinearities,⁸⁴⁸ as well as interband and intraband transitions of electrons in sub-picosecond timescales.¹⁸⁴,¹⁸⁵,⁸⁴⁹ It is this latter characteristic, arising from their non-parabolic band structure, which distinguishes them from most semiconductors and dielectrics, where real-state transitions occur over nanosecond periods.⁸⁵⁰

In wake of their discovery, sub-wavelength films of transparent conductive oxides have facilitated the fundamental explorations of time-varying photonics. By pumping these films with high intensity, ultrafast pulses of light, it is possible to inhibit ultrafast changes in permittivity via both the real and virtual electronic transitions. Through the utilization of the fast, virtual transitions, these systems have been used to demonstrate negative refraction⁸⁵¹ and time reflection,⁸⁵² as predicted a decade earlier.⁸⁵³ Congruently, the ultrafast, real-state transitions have enabled investigations into temporal interfaces, characterized by unity changes in refractive index with ultrafast rise and decay dynamics, see Fig. 21(a).⁸⁵⁴ Temporal scattering from these temporal interfaces has been studied extensively via pump-probe experiments, demonstrating a novel method of frequency control via the ultrafast dynamics of the transition's rise and decay time, leading to red and blue shifted light respectively.⁸⁵⁵ Moreover, these phenomena not only provide innovative approaches for nanophotonic frequency control but also serve as diagnostic tools for inferring the temporal dynamics of the material's ultrafast response.⁸⁵⁵ However, the spectral control obtained from these simple responses is limited. Thus, the natural evolution of time-modulated metasurfaces involves exploring more complex temporal inhomogeneities. In the case of the aforementioned system, this would materialize as designing the pump pulse's temporal profile. Through the pursuit of this avenue, it would be possible to investigate the eigenpulses of a time-varying system—temporal modulations related to the Fresnel coefficients for the dispersive, time-varying interface in question, which leaves scattered light spectrally unchanged.⁸⁵⁶ Conversely, through careful design of the temporal profile of the modulation, one would also be able to design the spectral profile of the scattered light, offering applications across the fields of optical switching and computing.⁸⁵⁷ Moreover, promising theoretical investigations into systems that exhibit isotropic-to-anisotropic switching have motivated the concurrent pursuit of compatible media capable of hosting unique temporal phenomena.⁸⁵⁸⁻⁸⁶⁰

Another direction of research regarding increased complexity of temporal structuring, is the generation of periodic modulations. A first step toward this goal has been the investigation of double slit time diffraction a study which utilized two temporally adjacent modulation responses to obtain the characteristic diffraction response in the spectra of scattered light [Fig. 29(b)].⁸⁶¹ A challenging extension to this framework of patterning numerous responses in time is the generation of a photonic time crystal. By mimicking the configuration of photonic space crystals in the time domain, periodic temporal modulations, generated with a frequency comparable or greater than the probe frequency, create bandgaps in momentum. The relative width of these bandgaps is dependent on the contrast of the temporal interfaces induced. Light propagating within these momentum bandgaps does so with an energy that exponentially grows in time, comprising a non-resonant amplification system.¹¹⁴,⁸⁶² Additionally, periodic temporal modulations have been proposed as mechanisms for realizing surface-wave excitation in

the absence of any surface structure,⁸⁶³ advanced absorption systems that surpass their static counterparts⁸⁵⁰ and the temporal analogue to Bragg gratings.⁸⁶⁴ In the case of transparent conductive oxides, the realization of such temporal structures is resisted by the problem of heat accumulation and dissipation due to high intensity optical pumping. Thus, the discussion as to whether or not transparent conductive oxides may offer a platform to explore photonic time crystals is an open one that hinges on the limits of the materials and the demand for power densities on the order of TWs/cm².⁸⁴⁵ As a result, the realization of a periodic modulation may demand a sacrifice in magnitude of the momentum bandgap, or duration of the periodic temporal modulation. More clarity regarding the future of photonic time crystals generated with transparent conductive oxides will come from comprehensively theoretical model of these materials, including electronic and lattice temperature and their effect on the optical properties.⁸⁶⁵ As a result, the realization of a periodic modulation may demand a sacrifice in magnitude of the momentum bandgap, or duration of the periodic temporal modulation, possibly led by use of the ultrafast virtual transitions.⁸⁶⁶ Moreover, the observation of momentum bandgap characteristics, induced by $\chi^{(3)}$ nonlinear phenomena may also be marred by the presence of undesirable nonlinear processes, a concern that has begun discourse into the use of $\chi^{(2)}$ processes⁸⁴⁵ and investigations into new media.

### C. Time-modulation in spatial metasurfaces

As detailed throughout topics Secs. III and X in this roadmap, metasurfaces are great resonance-hosting systems capable of increasing the efficiency of nonlinear interactions, via increased field localization, offering control over the directionality and propagation of emitted light. The increased localization of electric field and thus energy has allowed for time-varying systems that enhance effects engineered by spatial structures. For example, in semiconductor-based metasurfaces, temporal boundaries have been studied as tools for the enhancement and control of nonlinear spectral effects induced by resonance-hosting structures.⁸⁶⁷⁻⁸⁷² Notably, the utilization of gold nanoantennas has been central to numerous studies that observed reduced intensity requirements for significant frequency shifts based on temporal refraction by localizing energy in a transparent conductive oxide structure.⁸⁵¹,⁸⁷⁶ In these spatially structured devices, resonances are leveraged to provide increased modulation amplitude at the expense of an increased interaction time. Hence, while these structures significantly enhance nonlinear efficiencies, temporal phenomena are constrained due to increased modulation timescales and the diminished optical damage threshold.⁸⁷⁵ Yet despite the presence of these deleterious characteristics, this paradigm offers a route to realizing low-power technological applications of these phenomena. In addition, the 1D temporal modulation of a resonant structure that hosts an effective lattice of states, constructed via the structure's supported modes, provides a method for accessing synthetic frequency dimensions. By using a time-varying modulation with a configurable amplitude, modulation frequency or phase, one can utilize the temporal domain as a method to navigate the system's synthetic dimensions.⁸⁷⁶ The realization of these synthetic dimensions promises to uncover a wealth of higher-dimensional topological effects, as well as a potential route toward N dimensional control, alongside the benefits of conventional time-varying.⁸³⁶,⁸⁷⁶
Alongside the amplification of nonlinear processes, static struc-
tures offer systems from which the momentum of scattered light may
be configured. This framework, embodied by the pioneering metasur-
face work of the early 2000s,⁸⁷⁷,⁸⁷⁸ in conjunction with temporal mod-
ulations, enables frequency and momentum control over scattered
light. By temporally modulating a gold gradient metasurface upon a
transparent conductive oxide substrate, pioneering work by Karimi
et al.⁸⁷⁹ demonstrated simultaneous, dynamic control over the spectral
content of light that has been diffracted [Fig. 21(c)]. Moreover, the
process of frequency translation via temporal refraction leads to beam
steering, via the conservation of the forward momentum, and thus
dynamic control over the angle of the generated diffraction orders. It
can be envisioned that this framework offers a logical extension to the
impressive metalens work of the past decade,⁸⁸⁰ providing an all-
optical method of fine-tuning the focal distance through beam steering
or offering simultaneous spectral control. At present, these systems for
4D optical control offer potential applications across the field of
dynamic metasurface designed for sensing and beam steering, how-
ever, they also present a stepping stone toward unlocking the potential
of simultaneous frequency and momentum control.⁸⁴⁶

D. Space-time metasurfaces

In the previous section, spatially static, yet temporally varying,
optical metasurfaces were initially discussed as the most mature method
of structuring a device in space and time. Herein, space-time metasurfa-
ces are differentiated by their use of a modulation mechanism that is
configured in both space and time in order to exhibit control over the
momentum and frequency of scattered light. In the context of

photocarrier excitation in transparent conductive oxides, the modula-
tion can be controlled in space and time by manipulating the intensity
and shape of the pump beam in both domains. This premise relies
heavily on the profound advancements made throughout digital micro-
mirror devices and spatial light modulators and has been effectively
applied to the fields of ultrafast beam steering,⁸⁸ electron optics,⁸⁸¹
reconfigurable metasurfaces,⁸⁸² and the generation of reconfigurable
integrated photonic circuits.⁸⁸³ Following in this vein, pursuit of such a
modulation strategy would reveal all-optical, reconfigurable metasurfa-
ces capable of also harnessing temporal frequency generation.⁵⁰,⁸⁸⁴ In
2023, Fan et al. demonstrated ultrafast wavefront control via the all-
optical structuring of a thin film’s refractive index in both space and
time [Fig. 21(d)].⁸⁸⁵ This work used the induced space-time modulation
to provide a spatially dependent response of temporal refraction, result-
ing in the focusing of probe light due to the subsequent beam steering.
In extension to this work, one can easily envisage simultaneous control
over spatial diffraction from configurable diffraction-limited transient
structures alongside this time-varying control. This paradigm of simul-
taneous structuring in space and time for ultrafast control of light lends
itself straight-forwardly to 4D optics but also the advancement of opti-
cal holography,⁸⁸⁶ analogue optical computation,⁴⁶ and neural net-
works.⁸⁸⁷ However, the generation of space-time modulations using
photocarrier excitation in transparent conductive oxides will encounter
the constraint of the material’s high intensity requirements for high
contrast modulations (≈ 100 GW/cm² for 100 fs pulses¹⁸⁴) limiting
their complexity and size. This represents an avenue that may greatly
benefit from the use of efficiency-increasing gold nanoantennas in
order to not only reduce power requirements but also as a method of
localizing modulations to non-diffraction-limited regions. Thus, in

<figure><img src="image_37.png" /><figcaption>FIG. 29. (a) A spectrogram of negative and positive frequency translation via sub-cycle pumping of ITO.⁸⁵⁴ (b) Full experimental and theoretical interferograms for diffracted light from a temporal double slit as a function of slit separation and frequency.⁸⁵¹ (c) Spectrogram showing the ultrafast beam steering of light diffracted by a temporally modulated static gradient metasurface.⁸⁷⁹ (d) Schematic displaying wavefront manipulation from a material structured in space and time.⁸⁸⁵ (e) A schematic illustrating the theoretical demonstration of amplification and compression of light incident upon a luminal grating.⁸⁸⁸ (f) An illustration of non-reciprocal beam steering generated by a space-time modulated metasurface based upon the illumination of a static, dielectric metasurface.⁸⁸⁹ Figures adapted from Refs. 854, 861, 879, 885, 888, and 889 and copyright remains with the respective publishers.</figcaption></figure>
closing, achieving simultaneous spatial and temporal structuring of inhomogeneities is a significant milestone for space-time metasurfaces, but unlocking their full potential requires the development of new and improved time-varying systems.

The exploration of traveling modulations of permittivity within dielectric media signifies this report's concluding frontier in the investigation of optical time-varying metasurfaces, presenting experimental challenges beyond the previously discussed space-time metasurfaces. Systems which host traveling regions of modulated permittivity are generally referred to spatiotemporal metasurfaces. These traveling regions can be defined by a permittivity (and corresponding permeability) that is described by $\delta\epsilon(x, t) = \delta\epsilon(gx - \Omega t)$, where g and $\Omega$ are the spatial and temporal reciprocal lattice vectors. Spatiotemporal modulations have promised to result in a broad variety of phenomena and are thus defined by the modulation's speed of travel $v_m = \Omega/g$. By consequence of this traveling modulation, physically realized through the conjunction of a modulation and the material response, probing light will observe synthetic motion of the modulation. This phenomenon has been explored as a method to exert control over the spectrum of scattered light via an artificial Doppler shift,⁸⁹⁰ capable of compensating for the Doppler shift of moving objects.⁸⁹¹ Furthermore, slab structures that host a traveling wave modulation offer unique applications throughout beam splitting⁹² and recombination.⁹³ Moreover, there has been broad research into the phenomena demonstrated by such spatiotemporal synthetic motion, including Fresnel drag,⁸⁹⁴ Čerenkov radiation,⁸⁹⁵ and Hawking Radiation.⁸⁹⁶ Discussions into the demonstration of these phenomena have remarked the viability in low frequency regimes, as well as potentially the terahertz regime in graphene, however, their demonstration in the optical regime is closely linked to the discussion of hosting period modulations in time alone (Sec. XV B).

In parallel, linear or rotational traveling modulations have been investigated throughout numerous wave domains as novel systems for leveraging non-reciprocal responses. Notably, the inherently non-reciprocity of luminal synthetic motion represents a platform capable of the amplification and compression of incident light [Fig. 21(e)].⁸⁸⁸ Moreover, such mechanisms have been heralded as a method for efficiently breaking the constraints of a system's reciprocal symmetry and thus offering a route toward compact, non-reciprocal devices without need for magnetic bias, see Fig. 21.⁸⁸⁹,⁸⁹⁷ Consequently, a core motivation of research in this direction of spatiotemporal modulations is the pursuit of phenomena that do not rely upon high modulation frequencies that are difficult to realize in physical systems.⁸⁹⁸ Moreover, could spatiotemporal modulations substitute for modulations in time alone, resulting in more feasible realizations of the temporal woods analogy or Bragg grating? Unlike periodic temporal modulations, the material limitations imposed upon the exploration of spatiotemporal modulations have not been theoretically characterized—leaving the door open to a rich experimental future.

## E. Conclusion

Research into time-varying systems has reshaped the way we perceive and control the propagation of waves. The last decade has brought time-varying physics to the optical regime with seminal studies being performed upon the framework of photocarrier excitation in transparent conductive oxides. As discussed herein, the multitude of pathways to enhance the complexity of current straightforward

temporal and spatial modulations unveils a plethora of exciting research avenues in the field. Modulations in time alone provide a theoretical research destination of prophesied photonic time crystals, while complex space-time modulations unlock the potential of 4D optical components and synthetic motion. However, most advanced discussions and explorations have predominantly existed within the realm of theoretical and computational physics. In order for a majority of these phenomena to be fully realized, the restrictions of the current systems must be overcome. It is possible that many applications may be realized, in a less efficient form, via a compromise with regard to the desired modulation strength or frequency. However, in order to observe many advanced temporal or spatiotemporal phenomena, new systems or mechanisms will be required. These considerations have begun to occupy an increasing presence in modern discussions of time-varying optical experiments, applying pressure on this direction of research. Nevertheless, the future of the field still promises to offer great potential to light-based technologies and studies of novel physics.

# XVI. DISORDERED OPTICAL METASURFACES: PHYSICS, THEORY AND DESIGN

Philippe Lalanne,\* Alexandre Dmitriev, Carsten Rockstuhl, Alexander Sprafke, and Kevin Vynck

\*philippe.lalanne@institutoptique.fr

The use of coherent wave phenomena to enhance device performance is a cornerstone of modern optics. In juxtaposition to (locally) periodic metasurfaces, their disordered counterparts exhibit an interplay of destructive and constructive interferences occurring at the same spatial and spectral frequencies. This attribute provides disorder with many degrees of freedom. Recognizing and comprehending their utility across diverse applications is invaluable. Hereafter, we provide a concise overview of the cutting-edge developments and offer insights into the forthcoming research in this dynamic field.

## A. Introduction

Disorder has often been viewed as a constraining element in nanophotonics, which might explain the limited coverage of the subject of disordered metasurfaces in the existing literature.⁵²⁴,⁸⁹⁹ Nevertheless, there exist plenty of reasons to delve into this area. Let us highlight just a few. The presence of disorder is ubiquitous across manifold complex structures. Leveraging disordered metasurfaces, as opposed to their meticulously ordered counterparts, holds promise in realizing extensive, cost-effective devices. It also paves the way to a wealth of specialized applications, such as anti-reflection coatings,⁹⁰⁰ augmented absorption,⁹⁰¹ surface-enhanced Raman scattering,⁹⁰² alongside contemporary applications to be discussed below.

This article aims to survey the current state of research and offer a forward-looking perspective on the topic. We highlight a few promising future applications and anticipate forthcoming advancements in design and fabrication.

## B. State-of-the-art

The general problem of light scattering by disordered metasurfaces made of resonant nano-objects (a.k.a. meta-atoms) is very complicated due to multiscale effects, namely the multipolar
<figure><img src="image_38.png" /><figcaption>FIG. 30. Illustration of the average (coherent) and fluctuating (incoherent) components of the scattered field [Eq. (4)] with fully vectorial simulations for a finite-size disordered metasurface composed of identical Si nanocylinders in air. The incident (background) field $E_b$ is a plane wave ($\lambda = 440$ nm) polarized along the y-direction. It is incident from the top with an angle of 30° with respect to the surface normal. The rods are parallel to the y-axis and are placed using a random sequential addition algorithm with a non-overlapping condition. The 2D simulations are made for assemblies of 15 infinitely-long nanocylinders (140 nm diameter, $n_{si|440nm} = 4.793 + 0.109i$), resulting in a side length of $7.0 \mu m$ ($\approx 16 \lambda$) at a surface coverage of 30%. The y-component of the scattered field (component parallel to the cylinder y-axis), $E_s$, is normalized to the amplitude of the background field $|E_b|$.</figcaption></figure>

resonances of the individual particles, their interaction with the substrate, and their mutual interaction.⁹⁰³,⁹⁰⁴ In this section, we start by outlining some fundamental concepts on coherent vs incoherent scattering. We then familiarize the reader with computational tools and approximate models that predict the scattering properties of disordered metasurfaces, and finally examine recent advances in fabrication techniques.

## 1. Diffuse (incoherent) vs. specular (coherent) light

Within the context of wave scattering by rough surfaces—a long-standing topic with many applications⁹⁰⁵⁻⁹⁰⁷—, the distinction between diffuse (incoherent) light and specular (coherent) light emerges as a pivotal consideration. These two components have different physical origins, as we will see below, and have significant implications for optical effects—for instance, their relative weight play a decisive role in determining the glossiness or mattness of a surface.

This distinction can be understood from the statistical properties of the scattered light. In this framework, one considers separately the average and fluctuating values of physical parameters, with the averages computed among a large statistical ensemble of independent realizations. The quantities of main interest in the present case are electromagnetic field characteristics, including the field itself, its intensity or root mean square, along with auxiliary quantities such as the Poynting vector and the energy density that a wave carries.

Formally, the electric field $E_s$ scattered by a disordered system can be expressed as the sum of its ensemble average (the specular light), calculated among many disorder realizations, and a fluctuating term (the diffuse light) that varies from configuration to configuration,

$$E_s = \langle E_s \rangle + \delta E_s, \quad (4)$$

with $\langle \delta E_s \rangle = 0$.

Figure 30 illustrates this decomposition using fully vectorial simulations conducted on a finite metasurface composed of parallel infinitely long silicon nanocylinders in air. The metasurface is illuminated at a 30° angle of incidence by a plane wave polarized parallel to the cylinder y-axis. In the rightmost panel, the fluctuating field $\delta E_s$ showcases a complex pattern known as speckle,⁹⁰⁸ which arises from the intricate interplay of near-field interactions among many monochromatic waves scattered by multiple scatterers. In contrast, the central panel presents the average field $\langle E_s \rangle$ that readily takes the form of a directional reflected light beam indicated by black arrows. This average field

describes the diffracted light from a homogenized metasurface characterized by effective parameters that vary non-uniformly in both the x and z directions due to boundary effects.

Given $\langle \delta E_s \rangle = 0$, we can readily demonstrate that the averaged intensity $\langle |E_s|^2 \rangle$ of the light scattered by the metasurface can be decomposed into two components,

$$\langle |E_s|^2 \rangle = |\langle E_s \rangle|^2 + \langle |\delta E_s|^2 \rangle, \quad (5)$$

in which we identify the squared norm of the average field, which corresponds to the specular intensity (first term), and the average of the squared norm of the fluctuating field, i.e., the diffuse intensity or the averaged speckle intensity (second term).

The properties of statistically translationally invariant (i.e., infinite) disordered metasurfaces are fully determined by the Bidirectional Scattering Distribution Function (BSDF), a radiometric quantity introduced in the 1960s, which describes how surfaces scatter light for all possible plane wave illuminations. Formally, the BSDF relates an incoming irradiance $E_i$ (in W m⁻²) to a scattered radiance $L_s$ (in W m⁻² sr⁻¹),

$$\text{BSDF}(\hat{\mathbf{k}}_s, \hat{\mathbf{e}}_s, \hat{\mathbf{k}}_i, \hat{\mathbf{e}}_i, \omega) = \frac{dL_s(\hat{\mathbf{k}}_s, \hat{\mathbf{e}}_s, \omega)}{dE_i(\hat{\mathbf{k}}_i, \hat{\mathbf{e}}_i, \omega)}, \quad (6)$$

where $\omega$ is the frequency, $\hat{\mathbf{k}}_i$ and $\hat{\mathbf{k}}_s$ are the (unit) wavevectors of the incident and scattered plane waves, and $\hat{\mathbf{e}}_i$ and $\hat{\mathbf{e}}_s$ are the polarization (unit) vectors of those waves. Following the previous considerations, the BSDF can then be conveniently decomposed into two terms, $\text{BSDF}_{\text{spec}} + \text{BSDF}_{\text{diff}}$ the specular and diffuse components.

## 2. Full-wave analysis

Predicting the BSDF of statistically translationally invariant metasurfaces featuring resonant particles on layered substrates stands as an outstanding challenge.⁹⁰⁹,⁹¹⁰ Two complementary strategies are employed. The first approach involves solving Maxwell equations with utmost precision, while the second approach (Sec. XVI B 3) relies on approximate models.

In the former approach, the strategy is twofold: first, solving Maxwell equations for larger and larger metasurfaces, and second, inferring the BSDF of infinitely large metasurfaces by extrapolation. In contrast to traditional general-purpose solvers such as the finite-difference time-domain method, disordered metasurfaces benefit significantly from specialized numerical techniques. The latter harness