# Using a Semiconductor-to-Metal Transition to Control Optical Transmission through Subwavelength Hole Arrays

Authors: E. U. Donev; J. Y. Suh; R. Lopez; L. C. Feldman; R. F. Haglund Jr.
Journal: Advances in OptoElectronics
 (2008-01-24)

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## Abstract

We describe a simple configuration in which the extraordinary optical transmission effect through subwavelength hole arrays in noble-metal films can be switched by the semiconductor-to-metal transition in an underlying thin film of vanadium dioxide. In these experiments, the transition is brought about by thermal heating of the bilayer film. The surprising reverse hysteretic behavior of the transmission through the subwavelength holes in the vanadium oxide suggest that this modulation is accomplished by a dielectric-matching condition rather than plasmon coupling through the bilayer film. The results of this switching, including the wavelength dependence, are qualitatively reproduced by a transfer matrix model. The prospects for effecting a similar modulation on a much faster time scale by using ultrafast laser pulses to trigger the semiconductor-to-metal transition are also discussed.


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## Body

## 1. Introduction

Ever since its initial description in a much-cited letter by Ebbesen et al. [1], the phenomenon of extraordinary
optical transmission (EOT) has generated intense interest regarding both
the fundamental physics of the transmission mechanism and potential
applications.  In brief, the EOT effect refers to the observations that (i)
light transmission through periodic arrays of subwavelength holes in opaque
thin films can be much larger than the combined transmission for isolated holes
predicted by standard diffraction theory [2], and (ii)
the spectral profile of the transmission follows a sequence of dips and peaks peculiar to the metal and the detailed geometry of the hole array. This effect has been described predominantly in terms of light waves coupled to collective oscillations of the
free electrons (surface plasmons), which bear the SPP acronym—surface plasmon polaritons.Numerous applications of EOT
have been proposed and, in some cases, reduced to practice. Specific
applications of subwavelength holes [3] include SPP-activated
lithographic masks, bright point sources, SPP couplers/decouplers, near-field
optical storage heads, molecular sensors, and so on. Recent work [4] has shown that the electroluminescence
efficiency of an organic light-emitting diode (OLED) can be significantly
enhanced by use of an perforated anode, which allows for light emission from
both the back and the front of the device. Control of the EOT through a hole
array could make it possible, for example, to modulate selectively in
wavelength and time the light generated by an OLED or other light sources, or
propagation in a waveguide, in effect serving as a subwavelength optical
switch. However, we are aware of only two previous reports on schemes for postfabrication
modulation of the EOT at visible and near-infrared wavelengths, and both involve
varying the refractive index of the input side dielectric. Moreover, both would
be difficult to implement in the kinds of applications described here. In one
case, the authors [5] used different index-matching
liquids to vary the degree of asymmetry between the dielectric layer above a perforated
gold film and the quartz substrate. The other scheme [6] entailed sandwiching a layer
of liquid crystal between a transparent indium-tin-oxide electrode and a perforated
chromium film on quartz, then varying the applied electric field. Ultrafast
switching of THz signals through metallic subwavelength hole arrays has
recently been treated elsewhere [7].Here we review another
recently demonstrated method to control the amount of light transmitted through
perforated double-layer thin films on transparent substrates [8, 9]. The structures consist of an
optically opaque metal film (silver or gold) on top of a vanadium dioxide (VO2)
film deposited on a glass (SiO2) substrate, with a periodic array of
subwavelength holes penetrating the double layer. The intensity of transmitted
light is controlled by means of a reversible semiconductor-to-metal phase
transition (SMT), thermally induced in the VO2 layer, which undergoes
drastic changes in its electrical and optical properties. Much to our initial
surprise, these structures exhibit larger optical transmission with the
VO2 layer in the metallic state as compared to transmission in the
semiconducting state—quite the
opposite of the well-known behavior of plain (i.e., no over layer, no
holes) VO2 films of any thickness. This reverse optical switching can be understood in terms of a simple model that takes into account the losses
due to leaky evanescent waves in the plane of the VO2 layer and
diffuse scattering from the holes at the entrance and exit apertures. Numerical
simulations based on the transfer matrix formalism for photonic crystals
provide semiquantitative support for the experimental findings.


## 2. The Extraordinary Transmission Effect and the Semiconductor-to-Metal Transition

Many authors [5, 10–13] have elaborated on the
initial explanation (given in [1]) that the excitation
of surface-plasmon polaritons (SPPs) at either or both metal-dielectric
interfaces mediates the EOT effect. A small group of researchers had previously
dismissed the role of SPPs and put forth a model of nonresonant generation and
interference of composite diffracted evanescent waves (CDEWs) [14]; however, a more recent
exchange of articles,[15–19], comments [20, 21], and responses to comments [22, 23] between proponents of the SPP and CDEW
models has led to a tacit consensus that surface plasmons must be involved in
the extraordinary transmission at visible and near-infrared wavelengths. Indeed, most workers in this
field now regard the excitation of propagating SPP modes as the dominant mechanism
for mediating the EOT effect in metal films perforated by periodic arrays of subwavelength
apertures. Recent studies [24, 25] have also identified another, albeit weaker, contribution to
the observed transmission, namely, the localized surface-plasmon resonances [26] (LSPRs) that originate on the metallic ridge of each aperture.
Revealing the role of the LSPRs may in fact has provided the concrete evidence
to explain why hole arrays in good metals such as gold and silver invariably
exhibit the largest EOT effects [24]. Other researchers [27–29] have interpreted the EOT effect in a purely
phenomenological fashion—in terms of Fano-type
spectral profiles, which result from the interference of two distinct contributions:
a resonant channel (e.g., SPPs and/or
other surface modes) and nonresonant scattering—and accounted for
the observed spectral shapes without explicitly specifying the nature of the
resonant channel.TheEOT spectra exhibit very
sharp minima in the transmission profiles. These minima have routinely been
attributed to the nonresonant Wood’s anomaly for diffraction gratings [30], which amounts to the
disappearance of a diffracted order as it becomes tangent to the plane of the
grating. The spectral positions of the minima are known as Rayleigh
wavelengths. At normal incidence, the first-order Rayleigh wavelength coincides
with the grating spacing [31].ConcerningVO2 and its semiconductor-to-metal transition (SMT), it is a first-order phase
transition, and occurs at a critical temperature Tc≈67°C, from a high-temperature metallic phase
to a low-temperature semiconducting phase. Above Tc, VO2 has a tetragonal rutile structure and exhibits metallic character; of particular  interest here is the relatively high
optical opacity, especially in the infrared (IR) wavelength range. Below Tc,
the dimerization and tilting of the V-V pair result in a monoclinic unit cell
and the opening of a narrow band-gap [32]; in this phase, the film is
markedly more transparent than it is in the metallic phase (Figure 3(d)). The
precise mechanism of the phase transition has long been a topic of controversy;
whether the SMT is driven by electron correlations or by the band-gap
opening (for a review, see [33]). In fact, a recent
theoretical study [34] concludes that an interplay
of charge and lattice degrees of freedom initiates and drives the SMT. Both components
of the transition (lattice and electronic) take place in less than 100 fs,
which makes VO2 a candidate for applications in fast optical
switching [35]. The presence of a thermal
hysteresis (Figure 3(d)), which is attributed to variations in the
phase-equilibrium temperatures for film grains of different sizes [36], allows for potential
applications in memory devices and optical data storage.


## 3. Experimental Method and Results

Two types of structures investigated
in [8, 9] were: (i) hole array in Ag−on−VO2 double layer on glass (Figure 1(b)); (ii) hole array in
Au−on−VO2 on glass (Figure 1(b)); (iii) hole array in VO2 film on glass (Figure 1(c)); (iv)  plain VO2 film on glass.
All the VO2 layers were prepared simultaneously on fused-silica substrates
in a pulsed-laser deposition (PLD) system (KrF excimer laser: λ=248nm, fluence  ≈4J/cm2, repetition rate =25Hz) by ablating a vanadium target in a 12−mTorr O2 atmosphere at 550°C.
The resulting film thickness was 200nm, as determined by Rutherford backscattering spectrometry (RBS). The Ag and Au overlayers were deposited in a
bell-jar thermal evaporator. RBS-measured thicknesses were 160nm for Ag and
230nm for Au. The hole arrays, consisting of 60×60 nominally cylindrical
apertures of 250−nm diameter and 750−nm pitch, were milled down to the
substrates with a focused ion beam (FIB: liquid Ga+ ion source at 30keV, 90−pA beam current). Figure 1(a) shows an FIB micrograph of part of such
an array (structure type (iii)), while Figure 1(d) shows the same array
(different portion) imaged in illumination mode with a scanning near-field
optical microscope (SNOM: λ=532nm, aperture diameter  ≈100nm). It is relevant to note here that the
air-filled holes in this SNOM image appear darker, that is, transmit less than the surrounding VO2 film,
whereas the contrast is reversed in the case of holes in Ag−VO2 (Figure 1(e)) or Au−VO2 double layers (not shown). We shall return to this
observation shortly. Spectral measurements, at normal and oblique incidence,
were performed with collimated white light through an optical fiber and a
micro-objective. The incident-beam spot was slightly smaller than the size of
the array, and the beam divergence was determined to be  ≈1°. The transmission spectrum through each
sample was collected in the zero-diffraction-order (i.e., detected beam collinear with incident beam) by another
micro-objective, stopped down to reduce outgoing-beam divergence to  ≈1°, and coupled to an optical fiber. The fiber
was then fed into a monochromator equipped with a cooled-CCD detector. The
substrates were attached to a resistor-heated sample holder, mounted on a
translation-rotation stage, with a precision thermocouple placed in contact
with the top surface of the sample. The position of the hole array with respect
to the incident beam was monitored in reflection via a CCD camera connected to
a video display.Figure 1
(Color online) (a) FIB micrograph of a hole-array corner. Schematics of the
studied hole arrays in: (b)Ag/AU−VO2 double layers, (c) single VO2 layer. SNOM transmission images (λ=532nm) of hole arrays in: (d) single
VO2 layer (semiconducting phase), (e) Au−VO2 double layer. All perforated structures are on glass substrates.Figure2 presents the main
experimental results of the work in [8]: (i) controlled
switching of the zero-order extraordinary optical transmission (EOT)
through periodic subwavelength structures, and (ii) highly unusual transmission
behavior of the VO2 layer in these structures.
Figure 2(a) shows the transmission spectra for a hole array in a silver-VO2 double layer on glass, at two different temperatures, which correspond to the two phases of the VO2 layer. It is immediately obvious that, for wavelengths
greater than about 600nm, the high-temperature (i.e., VO2 in its metallic phase) transmission dominates.
The transmission contrast in the visible range is rather small, at some points
even slightly in favor of the low-temperature transmission (i.e., VO2 in its
semiconducting phase), since the optical properties of the semiconducting and
metallic phases of VO2 differ considerably only in the IR range, as
evidenced by the spectral dependence of the complex permittivity (Figure 3(c) and inset; data from [37]) and the transmission (Figures
3(a) and 3(b), solid lines). (Figure 2(a), inset) shows the zero-order EOT
intensity as a function of temperature at 800nm. Comparing the shape of this
hysteresis curve to that of a plain VO2 film (Figure 3(d)), it becomes clear why we call our observation reversed optical switching ofVO2.
In all fairness, some credit should go to the air-filled holes, since it is
really the permittivity contrast between the content of the holes (air) and the
surrounding material (VO2) that contributes to the effect, as we
explain later on.Figure 2
(Color online) experimental
zero-order transmission spectra, in eachVO2 phase, for perforated double
layers in: (a) Ag−VO2, with (inset) its reverse hysteresis at λ=800nm (normalized to the
highest transmission in the metallic phase of the VO2 layer; upward/downward
arrow denotes the heating/cooling part of the thermal cycle; cf, regular hysteresis in Figure 3(d)),
(b) Au−VO2, (c) demonstration of the spectral splitting of
the Wood’s anomaly minima with deviation from the normal (0°) angle of
incidence (lower/upper set of three curves corresponds to the semiconducting/metallic
phase of the VO2 layer in the Ag−VO2 hole array).(Color online) experimental
zero-order transmission spectra for single plain (i.e., no holes) and perforated layers in: (a) semiconductingVO2, (b) metallic VO2. Wavelength dispersion of the (c) real and
(inset) imaginary parts of the VO2 dielectric function, in each phase
(data extracted from [24]), (d) Regular hysteresis at λ=800nm for the plain-VO2 case (normalized to the highest transmission in the semiconducting phase of the
VO2 layer; downward/upward arrow denotes the heating/cooling part of
the thermal cycle; cf, reverse
hysteresis in (Figure 2(a) inset).
(a)(b)(c)(d)The controlled switching of
the zero-order EOT in the near-IR range stands out even more prominently in the
case of a perforated gold-VO2 double layer on glass (Figure 2(b))—for example, the
high-temperature transmission at 800nm exceeds the low-temperature
transmission by more than a decade. The SNOM image (Figure 1(e)) clearly shows that virtually no light can pass through the intact film and that all the detected light must have traveled through the holes. Similar images were obtained for
the hole arrays in Ag−VO2−SiO2. The overall magnitude of
the zero-order EOT through the gold−VO2−SiO2 structure is
smaller than the magnitude in the corresponding phase of the silver−VO2−SiO2 structure, most likely because of the larger metal-layer thickness [38] and smaller effective hole
diameter [39] for the gold-structure with
respect to the silver structure. The relative sharpness of the maximum transmission
peak for the gold−VO2 structure might also be related to hole size: smaller
holes, being less efficient scatterers of surface modes into far-field light,
diminish the radiative damping and hence increase the lifetime of these modes,
which in turn reduces the width of the peak [40]. In any case, the key
observation for both types of structures remains that EOT in the metallic phase
of VO2 is further enhanced over EOT in the semiconducting phase.As noted above, at normal
incidence, the first-order Rayleigh wavelength coincides with the grating
spacing, or in this case, with the hole spacing in the array [31]. The sharp normal-incidence
minima for our samples occur close to 750nm (Figures 2(a) and 2(b)), which
corresponds to the nominal lattice spacing for our hole arrays. As the
incidence angle is increased, the Rayleigh wavelengths for grazing orders should
become longer on one side of the sample normal and become shorter on the other
side [31]. Consequently, we expect the
sharp minimum at λ(R) to split into two separate minima: one occurring at λ(R−)<λ(R), and
the other at λ(R+)>λ(R). Indeed, our experimental observations confirm
this prediction. Figure 2(c) shows the doubling of the normal-incidence Wood’s
anomaly as the sample plane is rotated with respect to the incident-detected-beam
axis. The polarization of the incident light was such that the electric field
would oscillate parallel to the rows (or columns) of the Ag−VO2−SiO2 hole array. Both the high- and low-temperature phases exhibit two sharp dips in
each of their transmission curves for nonzero angles of incidence. For
instance, the zero-order transmission at incidence angle of 2° has one dip at
730nm and another one at 760nm, as opposed to a single dip at 750nm for the
zero-order transmission at 0°. In addition, we find once again that the EOT in
the high-temperature state—for all pairs of
curves—is further
enhanced over the EOT in the low-temperature state.Returning to the reverse-switching
effect, the following explanation has been proposed. Since the metal film(Ag or Au) is optically thick, none of the incident light can traverse the nonperforated
double-layer structure (Figure 1(e), black regions). Therefore, transmission
can only occur through the holes in the metal layer, in the form of evanescent
waves generated by diffraction of the incident light at the metal-air interface
and mediated by surface-plasmon polaritons.The waves that emanate from the holes in the metal overlayer undergo additional scattering and must then travel through the perforatedVO2 layer, where they become leaky
evanescent waves, that is, waves that lose intensity as they propagate [41]. The VO2 acts as a lossy
medium: the waves penetrate the side walls of the air-filled holes and leak into the plane of the VO2 layer, where partial absorption occurs. As
a result, this leakage channels a portion of the light away from the zero-order
transmission path and thus renders it undetected in the far field. The amount
of light that penetrates into the VO2 material between the holes
depends on the optical constants of metallic or semiconducting VO2 and, in particular, on the permittivity contrast between the hole content (air)
and its surroundings (VO2). Lower permittivity contrast reduces both
the leakage into the VO2 layer and the nonforward (diffuse) scattering
from the holes at the air and glass interfaces [42]; conversely, higher permittivity contrast increases those losses.In the visible range (e.g., up to500nm), the complex permittivities of the two phases of VO2 (Figure 3(c) and inset) exhibit similar trends and values, so the transmission contrast
between the two phases remains relatively low in this wavelength range (Figures
2(a), 2(b) and 3(a), 3(b)). In the near-IR range, however, the permittivity of
metallic VO2 differs significantly from its semiconducting
counterpart; for example, at 850nmε(VO2−met)=2.67+2.98i,
while ε(VO2−semi) = 8.17+2.65i. Therefore, because the permittivity
contrast between the interior (air) and the exterior (VO2) of the
holes is lower in the case of metallic VO2, the zero-order
high-temperature transmission receives an enhancement over the zero-order
low-temperature transmission.In order to bring out the
significance of theVO2 layer for the metallic-phase enhancement of
the EOT in Ag−VO2−SiO2 and Au−VO2−SiO2 structures, the optical properties of a hole array in VO2 on glass (Figure 1(c)), that is, without a good-metal overlayer, were also examined [9]. It must be noted that
transmission observed through this type of structure is not extraordinary,
in the sense used thus far, owing to the insufficient opacity of the VO2 layer. Figure 3(a) compares the zero-order transmission, in the semiconducting
phase, through the hole array (dotted line) and through a nonperforated area
nearby (solid line). The hole array transmits less than the intact film
throughout the wavelength range because the array serves as a diffraction
grating that diverts some of the incident power into nonzero diffracted orders,
which propagate out of the detector path and consequently do not contribute to
the zero-order transmission. Similarly to the loss mechanisms discussed above,
a portion of the diffracted field becomes trapped as leaky waves in the plane
of the VO2 layer, while some of the light that persists in the zero
order inside the holes undergoes additional diffuse scattering at the glass interface.
Also, since direct transmission through the partially transparent VO2 film overwhelms the transmission emerging from the holes, the holes appear
darker than their surroundings in the SNOM image of low-temperature
transmission through a VO2 array (Figure 1(d)), as mentioned earlier.Figure3(b) presents the
corresponding transmission curves for the metallic phase of the VO2 layer. Here, something intriguing happens in the near-IR range: in spite of
diffraction effects, the zero-order transmission through the hole array (dotted
line) exceeds the direct transmission through the flat film (solid line). This
observation also pertains to the above argument that the air-filled holes, when
surrounded by metallic-VO2, tend to channel the light along the forward direction by reducing the losses due to leaky waves and nonforward
scattering, all to the benefit of the detected zero-order transmission. Part of
the light traversing the perforated film passes through air-filled holes
instead of passing through
VO2 material, and so it avoids the absorption and reflection that
befall all the light traversing the flat VO2 film.
Ultimately, in the metallic-VO2 case, the zero-order transmission through
the hole array prevails over the direct transmission through the nonperforated
film.A major point in this
qualitative explanation is that theholy films with nanoscale
dimensions, with or without the metal, result in a very large effective interfacial
area for the transmitted photons. This effect is a direct property of the
ability to construct these nanoscale structures.


## 4. Numerical Simulations

Numerical simulations of the zero-order transmission spectra through all four types of experimental structures were undertaken to see if they would reproduce the general features observed in the experiments of [8, 9] (Figure 4). The
computational scheme stems from a numerical method for modeling the properties
of one- and two-dimensional patterned photonic crystal slabs. All of our simulations
use the optical constants of VO2 as extracted from [37] and plotted in Figure 3(c);
the optical constants of Ag and Au were taken from [43]. The well-known transfer matrix
formalism was employed [44]: (i) the piecewise complex
permittivity within each layer is represented by a Fourier decomposition in
terms of reciprocal square lattice vectors; (ii) the solution of Maxwell’s equations
in each layer is decomposed into sets of eigenvectors propagating along the
normal to the slab, in both directions; (iii) transfer matrices connect the amplitudes of partial waves at different
planar slices of the slab inside the same layer; (iv) interface matrices connect the amplitudes
across successive layers of the slab by imposing continuity conditions on the
tangential (i.e., inplane) components of the electric and magnetic fields at the interface; (v) material matrices convert the partial-wave amplitudes at a given
point into inplane components of electric and magnetic fields at this point.(Color online) numerical simulations of zero-order transmission, using the transfer matrix formalism (see text) and theVO2 dielectric function in Figure 3(c). Single plain (i.e., no holes) and perforated VO2 layers on glass: (a) semiconducting phase, (b) metallic phase. Perforated double layers on
glass, in each VO2 phase: (c) Ag−VO2, (d) Au−VO2.
(a)(b)(c)(d)In essence, this method
constructs a totaltransfer matrix that connects the field amplitudes at different dielectric planes. The first task in this scheme is to perform Fourier transformations of the two-dimensional periodic dielectric function, ε→(r→),
for the reciprocal lattice vectors, G→,
assuming the function is only dependent on x and y as
(1)εG→G→'=1S∫ε(r→)exp⁡[i(G→'−G→)r→]dxdy,G→=(2πgxdx,2πgydy),gx=gy=0,±1,±2,…,±gmax⁡,
where dx and dy are the periods along x- and y-axis, and each
layer is assumed to have translational invariance along z-axis. The numerical calculation implements this integral over a
finite subset of the reciprocal vectors, with Ng=(2gx,max⁡+1)(2gy,max⁡+1) elements. This Fourier decomposition can be
evaluated so that the order of convergence is smaller than 10−3.
Next, the solution of Maxwell’s equations is written as a Fourier decomposition
into a sum of plane waves:
(2)E→(x,y,z,t)=EG→exp⁡(ikx,G→x+iky,G→y)exp⁡(iKz−iωt).
Here, kx,G→ is defined as kx,G→=kx+Gx,
where kx(=ω/csin⁡θcos⁡φ) is the x−component
of the incoming wavevector, k→.
Maxwell’s equations become the eigenvalue-eigenvector problem solving 2Ng linear equations for inplane electric
components Ex,G and Ey,G.
It can be written in a compact form as
(3)(N)−1ME//→=K2E//→.
The M and N are 2Ng×2Ng matrices that explicitly consist of the
components of the wavevectors and reciprocal lattice vectors. Then, the
eigenvalue K that is an element of a
diagonal matrix and the corresponding eigenvector E//→ can be computed.At this point, two kinds of
transfer matrices need to be formulated. Thelayer matrix (the first kind) allows us to compute the amplitude vector
from z to z + L as follows:
(4)A→(z+L)=TL→A→(z),TL→=(exp⁡[iKL]00exp⁡[−iKL]).
The interface matrix represents the amplitude transfer across the
interface between two adjacent layers of the slab. From the boundary condition
of tangential components of electric and magnetic fields at the interface, the
interface matrix is calculated as
(5)T→b,a=F→b−1F→a,F→=(E→//E→//cωCE→//K−cωCE→//K),
where C is a 2Ng×2Ng matrix composed of the matrix N.
Now, we can set up a total transfer matrix that describes the change of input
amplitude through an entire layered-system as follows:
(6)A→out=T→totA→in,
with
(7)T→tot=Tb,aNTLNTaNaN−1⋯TL1Ta1,a0,
where N runs through the number of different layers. (e.g., in the
bilayer case, the total transfer matrix comprises two layer matrices and three
interface matrices.) From knowledge of the total transfer matrix and given a
frequency of incoming light, the reflection, absorption, and transmission can
be computed from the output electromagnetic field components. The computation
is then repeated throughout the whole spectral range.Despite several
simplifications to the model, such as square instead of circular apertures, the
simulation results show good semiquantitative agreement with the corresponding
experimental findings. For example, Figures4(a) and 4(b) supports the above
discussion regarding the zero-order transmission through a VO2 hole
array as compared to the transmission through a flat VO2 film. In
particular, the simulated curves for the metallic phase (Figure 4(b)) show the characteristic cross-over in the near-IR region, where the perforated metallic−VO2 film transmits more per unit area thanthe nonperforated (plain) film. The simulations also corroborate the key experimental observation
of this work, namely, that the EOT through subwavelength hole arrays in Ag−VO2−SiO2 (Figure 4(c)) and Ag−VO2−SiO2 (Figure 4(d)) structures exhibits
a pronounced enhancement in the near-IR range for the metallic over the
semiconducting phase of the VO2 layer. Even though the calculated
spectra differ somewhat in shapes and absolute magnitudes from the corresponding
experimental curves, the simulations unequivocally demonstrate the effect of reverse
optical switching.


## 5. Prospects for All-Optical Modulation of the EOT

Since the electronic response
of the plasmonic material in these structures is fast on the femtosecond time
scale, it is logical to ask whether the EOT can likewise be modulated on an
ultrafast time scale. Experiments by Cavalleri et al. onVO2 films show that hole doping initiated by a
femtosecond laser pulse can initiate the SMT on a time scale of a few hundred
femtoseconds [45]. The details of the ultrafast response, however, are dependent on the thickness
of the film. More recent X-ray studies seem to indicate that for 800nm
incident laser light, the turn-on response of the film is extremely fast for
film thicknesses of 70nm or less, but diffusive after that [46]. This ultrafast response depth is, of course, a function of the excitation
wavelength, and it is possible that a laser wavelength with greater penetration
depth in VO2 could achieve ultrafast SMT initiation for thicker
films. The response time also appears to be a function of fluence, with
important dynamical features showing a differentiated response below the 100−fs
time scale [47].The more challenging question for ultrafast modulation is whether or not theSMT can be turned off on a fast time scale. Evidence so far indicates that the return from metallic to the semiconducting phase occurs on nanosecond or sub-nanosecond time scales,
governed essentially by thermal diffusivity [48, 49]. While
the metallic state relaxes on a sub-picosecond time scale for near-threshold
densities of photo-initiated electron-hole pairs, the relaxation times increase
significantly with increasing electron-hole plasma density, even for rather
thin VO2 films on diamond substrates [50]. In the case of the bilayer plasmonic structures embodied in our
hole arrays, however, it is possible that the thermal conductivity of the metal
would significantly assist the cooling transition back to the semiconducting
state. Hence the question of possible ultrafast turn-on and turn-off of
plasmonic effects remains an open question.


## 6. Conclusions

In generic terms, the future
of optoelectronic devices relies on the ability to manipulate light on a subwavelength
scale, where diffraction-limited optical elements lose their utility. Here we have
reviewed a novel way to control theextraordinary optical transmission through subwavelength hole arrays in structures composed of a VO2 thin film sandwiched between an opaque metal layer and a transparent substrate.
While the control mechanism here is the thermally induced
semiconductor-to-metal transition of VO2, but the transition can
take place on a sub-picosecond time scale if triggered by a laser pulse, which
opens the possibility for ultrafast switching devices. Furthermore, the present
work has uncovered a counterintuitive trend in the near-IR transmission
properties of the perforated VO2 layer when compared to a continuous
VO2 film of the same thickness, namely, reverse optical switching,
whereby the zero-order transmitted intensity from perforated Ag−VO2 or Au−VO2 double layers on glass is in fact considerably higher
during the metallic phase of the VO2 than it is during the
semiconducting phase. A simple heuristic model is sufficient to account
qualitatively for this effect, based on the idea that the losses in the zero-order
transmission are caused by evanescent waves that leak into the VO2 layer, in addition to diffuse scattering at the entrance and exit apertures.
The magnitude of these increases with higher permittivity contrast between the
interior and the exterior of the holes. The role of metallic VO2 in
further enhancing the EOT from perforated silver or gold films has been emphasized
by comparing measurements on perforated and nonperforated areas of the same VO2 film, which showed that the zero-order high-temperature transmission through a
VO2 hole array can exceed the direct transmission through the flat film.



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