Strong Modulation of Absorption and Third-Harmonic Generation in

Resonant Metasurfaces based on VO

Margherita Marni and Domenico de Ceglia

Department of Information Engineering, University of Padova, Italy

Keywords: Metasurfaces, Nonlinear Optics, Harmonic Generation, Nanoantennas, Tunable Devices, Nanophotonics,

Phase-change Materials.

Abstract: Control of linear and nonlinear optical signals is of key importance in a variety of applications, including

signal processing, optical computing and energy harvesting, to name just a few. Optical modulation and

switching, and more generally tunability in photonic devices, are usually achieved in the visible and near-

infrared range by carrier injection, chemical or mechanical activation, or by deploying materials with large

electro-optic or optical nonlinear coefficients. However, these mechanisms are inherently weak and therefore

require intense control signals in order to produce significant modulation effects. Here we adopt a

nanophotonic solution in which a resonant film of a volatile phase-change material, vanadium dioxide, is

inserted between an array of antennas and a metallic backplane. Our design takes advantage of (i) the large

refractive-index change of VO

at its insulator-to-metal transition and (ii) the field enhancements available

when the Fabry-Pérot resonance of the film and the plasmonic resonance of the antennas are exited. In

response to the VO

phase transition, not only does our metasurface provide a strong and broadband

modulation of linear absorption and reflection but it also shows a drastic variation of third-harmonic

generation, with a conversion-efficiency contrast higher than three orders of magnitude.

1 INTRODUCTION

Metasurfaces and their constituent metamolecules,

i.e., nanoantennas, are able to control light-matter

interactions at the nanoscale (Yu et al., 2011).

Amplitude, phase and polarization of light can be

manipulated at will by properly designing these

nanostructures. Dynamic control of metasurfaces’

functionalities holds the promise to unlock a wide

variety of new opportunities for highly compact

photonic devices, capable of modulating, beaming

and switching light. Here we discuss the modulation

properties of a plasmonic metasurface that

incorporates vanadium dioxide. This phase-change

material is particularly attracting for the design of

low-power tunable devices because it exhibits an

abrupt and reversible change of its complex refractive

index at the relatively low temperature of 68 °C. So

far, a number of designs of VO

-based metasurfaces

has been investigated. The design strategies to

achieve tunability at optical frequencies are based on

the use of either planar structures (Kats et al., 2013;

Kats et al., 2012; Kocer et al., 2015), in which one of

the films is made of VO

, or patterned nanostructures

(i.e., metasurfaces), typically designed with hybrid

-metal resonators – see, for example (Zhu et al.,

2017). The metasurface proposed here is configured

as a perfect absorber, known as Salisbury screen at

microwave frequency, with a thin film of VO

sandwiched between a two-dimensional array of

plasmonic antennas and a metallic substrate that acts

as a mirror. In this configuration, the metasurface

provides two types of resonances: Fabry-Pérot (FP)

resonances with field localization in the VO

film;

antenna resonances (AR), with the field highly

confined around the plasmonic antennas. Thanks to

the coupling of these two resonances, high absorption

is achieved in a broad band of near-infrared

wavelengths, when VO

is in its insulating phase. On

the other hand, when VO

switches to the metallic

phase, for temperatures larger than 68 °C , the

metasurface tends to reflect light more efficiently,

and therefore absorption drops significantly.

In addition, we have investigated the modulation

of third-harmonic generation (THG) due to the cubic

nonlinearity of VO

. If the pump signal at the

fundamental wavelength is tuned at the AR of the

metasurface, a large contrast of third-harmonic

Marni, M. and de Ceglia, D.

Strong Modulation of Absorption and Third-Harmonic Generation in Resonant Metasurfaces based on VO2.

DOI: 10.5220/0010340000400045

In Proceedings of the 9th International Conference on Photonics, Optics and Laser Technology (PHOTOPTICS 2021), pages 40-45

ISBN: 978-989-758-492-3

conversion efficiency is obtained in response to the

insulator-to-metal transition.

2 DESCRIPTION OF THE

METASURFACE

The tunable absorber metasurface, reported in Figure

1, is composed of a substrate made of gold, a thin-

film layer of VO

and an array of gold antennas with

a cross shape. The design has been made so that the

structure is insensitive to the input polarization, with

each antenna resonating near 𝜆1.55 μm. The

antenna has a square cross-section with size

30x30 nm and the length of the cross arms is

145 nm. The antenna length has been designed by

maximizing, at 1.55 μm, the average field-

enhancement calculated in the rods volume. The

period of the unit cell is 300 nm in both the 𝑥 and 𝑦

directions, so that the metasurface shows only zero-th

order reflection at normal incidence, at both the pump

and the third-harmonic (TH) wavelengths.

Figure 1: Schematics of the tunable metasurface under

investigation. The structure is illuminated at normal

incidence with a near-infrared source (red arrow). The TH

signal is radiated back towards the source (blue arrow).

The simulations have been performed using

COMSOL, both in the linear and nonlinear regime.

Gold has been modelled with the Lorentz-Drude

dispersion of (Rakić et al., 1998). For VO

in the

insulator phase (𝑇68 °C) and metallic phase (𝑇

68 °C), we have used the datasets made available in

(Wan et al., 2019). The metasurface is illuminated

with a plane wave at normal incidence, linearly-

polarized along the y-direction. Linear and

nonlinear spectra are calculated by using the layer

thickness of VO

, 𝑡





, as a free parameter that

varies between 40 nm and 140 nm . In our

structure, the VO

film acts as spacer between the

antenna array and the backplane mirror, as in the

Salisbury screen absorber configuration.

3 RESULTS AND DISCUSSION

3.1 Linear Response and Modulation of

Absorption

The metasurface supports two types of resonances,

namely, FP resonances and AR. The AR has been

designed at 1.55 μm in absence of the VO

film and

the gold backplane, and assuming a glass substrate

(index 1.5). It is reasonable to expect an absorption

peak near this wavelength, with strong field

localization around the antennas. In addition, since

there is a gold slab under the VO

layer, according to

the image theorem, we can expect that our structure

shows absorption peaks when the FP resonances of

the film are excited, specifically when 𝜆





4𝑛





𝑡





/𝑚, where 𝑚1,2,… is the FP resonance

order and 𝑛





is the VO

refractive index. At

wavelengths near the AR and FP resonances, the

metasurface behaves as a strong absorber. In Figure

2, we show the absorption spectrum in the linear

regime for a VO

thickness equal to 80 nm.

Figure 2: Calculated absorption spectrum as function of

wavelength in insulator (blue line) and metal (red line) state

of VO

when the VO

thickness is 80𝑛𝑚.

One can note the broadband enhanced absorption

effect associated with the excitation of the FP

resonance and the AR. Furthermore, there is a strong

difference between the spectra in the insulator and

metal states of VO

. In particular, in a broadband

region, from 1 to 2 μm, the structure switches from a

high absorption state, with maximum peaks close to

100%, to a low absorption state, with an average

Strong Modulation of Absorption and Third-Harmonic Generation in Resonant Metasurfaces based on VO2

absorption of approximately 40% in the same

wavelength range. The interesting and

counterintuitive aspect to observe is that the structure

is very absorptive when the VO

is in the insulator

phase, while it becomes a more efficient reflector

when VO

switches to the metallic state.

Figure 3: Absorption color map of the tunable absorber

metasurface as a function of wavelength and VO

thickness.

In (a) VO

is in its insulator state, in (b) VO

is in its metal

state. In (a) the dashed lines follow the FP and AR

resonances according to model in Eq. (1).

For VO

is in its insulator state, there are two

absorption peaks, at 𝜆



1.13 μm and at 𝜆





1.67 μm, corresponding to the FP resonance and to

the AR, respectively. It is interesting to notice that the

AR appears at a longer wavelength with respect to the

designed wavelength of 1.55 μm. In fact, the system

is made by two coupled resonators (FP and AR), and

the two resonances tend to split and repel each other

when coupling is stronger, leading to the typical

anticrossing effect of coupled oscillators. In order to

highlight this behavior, we have calculated the

absorption spectra for different values of VO

thickness. The results of this analysis are presented in

Figure 3. When VO

is in the insulator state, the

metasurface response can be modelled as a two

coupled oscillator system, with resonance frequencies

given by (Novotny, 2010):

𝜔

,



𝜔





𝜔









𝜔





𝜔







4Γ



𝜔



𝜔











(1)

where 𝜔



and 𝜔



are the FP and AR resonance

frequencies in absence of mutual coupling,

respectively, whereas Γ is the anticrossing frequency

splitting. Here 𝜔



2𝜋𝑐/𝜆



is the frequency of the

first-order FP resonance and 𝜔



2𝜋𝑐/1.55𝜇𝑚 is

the frequency of the uncoupled AR (Γ0). A good

agreement with the numerically-calculated

absorption peaks is obtained when the mutual

coupling is Γ≅0.26 𝜔



, as depicted in Figure 3(a),

in which the dashed curves are retrieved by using Eq.

(1). The anticrossing due to coupling produced a

broadband absorption for wavelength from 1 to 2 μm

and for a broad range of 𝑡





values. The AR weakly

depends on 𝑡



, and it is strongly blue-shifted when

undergoes the phase transition. The AR is

completely quenched when the VO

film becomes

metallic – see Figure 3(b).

Figure 4: Reflection contrast R





, on a dB color

scale, for varying 𝜆 and 𝑡





. The dashed lines follow the

FP and AR resonances according to model in Eq. (1).

A better idea of the tunability performances is

provided by the modulation depth of reflectance,

which is a metrics that can be retrieved

experimentally. When VO

changes phase from

insulator to metallic, the metasurface switches from a

virtually perfect absorber [see Figure 2 and Figure

3(a)] to a good mirror [see Figure 3(b)]. The

reflectance contrast, defined as R





, where

/

is the reflectance for VO

in the

PHOTOPTICS 2021 - 9th International Conference on Photonics, Optics and Laser Technology

insulator/metal state, is mapped in Figure 4 for

varying wavelength and VO

film thickness. Thanks

to the anticrossing of the AR and FP resonance an

average ~15 dB contrast is obtained in a large

bandwidth in the near infrared, with a peak of 20 dB

at 𝜆~1.6 μm with a thickness of VO

of 85 nm.

Figure 5: Field enhancement spatial calculated as the ratio

between local electric field and incident one E

, when VO

is in insulator state with a VO

film thickness equal to

80nm. (a) FE calculated at the AR wavelength. (b) same as

(a) at the FP resonance wavelength.

Another important aspect of the problem is the

behavior of the field enhancement (FE), calculated as

the ratio between the amplitude of the local electric

field and the amplitude of the incident electric field.

Figure 4 compares the FE spatial distribution when

the structure is under FP and AR resonance

conditions. It is clear that the FE at the AR

wavelength is higher than that calculated at the FP

resonance. Figure 5(a) indicates that the localization

and the electric-field mainly concerns the area around

the antenna. On the other hand, Figure 5(b) shows that

the FE is distributed throughout the volume of the

when the FP is excited. When the VO

passes in

its metal state, the FE decreases by ~90% for the AR

and by ~70% for the FP resonance.

3.2 Nonlinear Response and

Modulation of Third Harmonic

Generation

We now focus on the nonlinear response of the

metasurface that originates from the cubic

nonlinearity of VO

. We assume an isotropic 𝝌

𝟑

tensor so that the induced nonlinear polarization at the

TH wavelength is:

𝑃





3𝜔



𝜖



𝜒







𝐸







𝜔



𝐸







𝜔



𝐸







𝜔



𝐸



𝜔,

(2)

where 𝑖,𝑗,𝑘 are the Cartesian coordinates, 𝜖



the

vacuum permittivity and 𝜒







the third-order

nonlinear susceptibility of VO

. Here we assume that

𝜒







10





when VO

is in the insulator

state and 𝜒







3.1610





when VO

is in

the metal state. The increase of 𝜒







that accompanies

the insulator-to-metal transition has been

experimentally observed in (Petrov, Yakovlev, &

Squier, 2002), where third-harmonic generation from

a VO

film measured as a function of pump irradiance

and temperature. In our nonlinear simulations, the

structure is pumped at normal incidence with a y-

Figure 6: Color map of THG conversion efficiency as a

function of pump wavelength and VO

thickness. (a) VO

is in insulator state, and (b) VO

is in metal state.

Strong Modulation of Absorption and Third-Harmonic Generation in Resonant Metasurfaces based on VO2

polarized plane wave with intensity I_0=1 GW/cm^2

and wavelength in the near-infrared, in the

wavelength range where the FP and AR resonances

occur. The conversion efficiency of TH generation is

calculated as η_THG=P^3ω/P^ω, where P^3ω is the

power of the reflected TH signal and P^ω is the

incident power. In Figure 6, η_THG is mapped as a

function of pump wavelength and VO2 film

thickness.

With VO

in the insulator phase, a maximum peak

of THG is observed when the pump wavelength is

tuned at the AR, while no feature is associated with

the FP resonance [Figure 6(a)]. Even though the 𝜒







increases when VO

switches in the metallic state,

THG efficiency drops significantly near the AR

wavelength and only a shallow peak appears near the

FP resonance [Figure 6(b)]. These results are in

agreement with the Fermi’s golden rule, which

predicts that the THG conversion efficiency scales as

(Vincenti et al., 2014):

𝜂



∝

𝜒













(3)

In response to the VO

transition, on one hand 𝜒







increases by a factor ~3, on the other hand the FE

drops by 90% on the AR resonance and 70% on the

FP. As a result of this FE drop, the conversion

efficiency is significantly inhibited in the VO

metallic state. A better picture of this effect can be

observed in Figure 7, where cross sections of the

color maps of Figure 6 are plotted for 𝑡





80 nm.

When the pump is tuned on the AR wavelength, the

drop of reflected THG is of about three orders of

magnitude (30 dB), due to the high sensitivity of THG

to the FE.

Figure 7: Color map of THG conversion efficiency as a

function of pump wavelength and VO

thickness. (a) VO

is in insulator state, and (b) VO

is in metal state.

4 CONCLUSIONS

We have studied a tunable metasurface that exploits

the insulator-to-metal transition of VO

. The structure

has been designed as a tunable absorber/mirror in the

Salisbury configuration, with the VO

film acting as

a tunable spacer between a metallic backplane and an

array of metallic antennas. Our results indicate that a

deep modulation of linear spectra – absorption and

reflection – are obtained if the structure is judiciously

designed so that Fabry-Pérot and antenna resonances

are mutually coupled. A reflectance contrast of ~15

dB is found in a broad bandwidth in the near-infrared

range. An even stronger modulation effect is

predicted for the reflected third-harmonic generation.

The conversion efficiency of this nonlinear process

drops by ~30 dB when the metasurface is pumped

near the antenna resonance.

ACKNOWLEDGEMENTS

The authors acknowledge the project “Internet of

Things: Sviluppi Metodologici, Tecnologici E

Applicativi”, cofunded (2018–2022) by the Italian

Ministry of Education, Universities and Research

(MIUR) under the aegis of the “Fondo per il

finanziamento dei dipartimenti universitari di

eccellenza” initiative (Law 232/2016). The work was

partially sponsored by the RDECOM-Atlantic, US

Army Research Office, and Office of Naval Research

Global.

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Strong Modulation of Absorption and Third-Harmonic Generation in Resonant Metasurfaces based on VO2