Optical modulation system and optical modulation method

Abstract

Optical modulation method including providing at least one optical device configured for modulating at least one optical electromagnetic wave provided to and transmitted through the at least one optical device, providing the at least one optical signal electromagnetic wave from at least one first light source to the at least one optical device, the at least one optical signal electromagnetic wave having at least one operation wavelength to be modulated by the at least one optical device; providing a photo-excitation electromagnetic wave from the at least one first light source or from at least one second optical source to the at least one optical device at a pump light intensity to displace in wavelength the resonance wavelengths and the resonance dips in the transmission spectrum to optically modulate the transmitted intensity of the at least one optical signal electromagnetic wave at the at least one operation wavelength.

Description

[0001] P4298PC00

[0002] OPTICAL MODULATION SYSTEM AND OPTICAL MODULATION METHOD

[0003] FIELD OF THE INVENTION

[0004] The present invention relates to an optical system and more particularly to an optical system for optical modulation or for optical switching. The present invention relates to a method for optical modulation or optical switching.

[0005] BACKGROUND

[0006] Tunable metasurfaces are of great importance in the fields of optics and photonics due to their ability to manipulate electromagnetic waves across a wide range of frequencies. Unlike traditional static optical elements, tunable metasurfaces offer flexibility in dynamic (real-time) control of properties such as phase, amplitude, and polarization of light. The mechanisms of tunability in active metasurfaces generally involve external stimuli such as electrical, optical, mechanical, or thermal inputs that alter the material’s optical properties. Electro-optic tuning is primarily achieved by integrating materials with high electro-optic coefficients, such as liquid crystals, lll-V semiconductors or lithium niobate (LN), into the metasurface design. Optical tuning, instead, is typically achieved by exploiting nonlinear optical effects, such as the Kerr effect, or photo-induced processes, such as hot carrier generation in plasmonic metals or free carrier generation in semiconductors.

[0007] Thermo-optical and photo-thermal nonlinearities have been widely explored recently for their potential in tuning optical responses in nanostructures and metasurfaces. Indeed, metasurfaces exploiting Mie resonances in high-refractive-index dielectric materials, such as silicon, can confine light efficiently. This leads to strong field enhancements within the nanoresonators. This is particularly valuable in enabling nonlinear optical phenomena in silicon, which would otherwise be too weak in the bulk material.

[0008] This capability to modulate light dynamically can be applied to advanced photonic functionalities such as high-speed optical switching, beam steering, and polarization control. In recent works exploring photo-thermal and thermo-optical nonlinearities, the focus has predominantly been on steady-state nonlinear behavior in silicon-based metasurfaces and nanostructures, rather than dynamic modulation.

[0009] These studies have demonstrated impressive changes of the optical properties through both photo-thermal effects, where absorbed light induces heating, and thermo-optical effects, where temperature changes modify the refractive index. P4298PC00

[0010] For example, silicon nanostructures have been shown to alter scattering and transmission intensities under continuous-wave (CW) excitation, with effective nonlinear indices n2 orders of magnitude higher than bulk silicon (i.e, n = n₀ + n₂I where I is the excitation intensity).

[0011] Recently, the studies introduced bound states in the continuum (BIC) in silicon metasurfaces to enable thermo-optical bistability, and optimize hysteresis width and switching power, suggesting a path for energy-efficient optical computing and non-reciprocity using silicon-based metasurfaces.

[0012] However, while steady-state studies have achieved significant breakthroughs, transient modulation through thermo-optical and photo-thermal nonlinearities has been thought to be inherently limited by the thermal response time of the system.

[0013] This limitation is especially pronounced for photo-thermal modulation, since it relies on actual heating of the material (a process inherently slower than electronic or all-optical effects). Most metasurfaces and nanostructures investigated for their thermo-optical responses, such as those supporting high-Q resonances, are bound by the timescales required for heat diffusion, limiting their application in scenarios requiring fast modulation speeds.

[0014] Notably, prior to the present work, no solution had demonstrated optical switching on submicrosecond timescales (MHz-range modulation speeds) using purely thermal effects, due to this presumed thermal speed limit.

[0015] The optical system and method of the present disclosure address the above-mentioned inconveniences, and provides an alternative optical system and method to those currently proposed in the state-of-the-art.

[0016] SUMMARY

[0017] According to one aspect of the present invention, an optical modulation method is provided.

[0018] The optical modulation method may include providing at least one optical device configured for modulating at least one optical electromagnetic wave provided to and transmitted through the at least one optical device. The at least one optical device may include at least one support substrate and / or layer supporting at least one dielectric metasurface comprising an array of elements configured to generate at least one or a plurality of dielectric metasurface resonances each having a resonance wavelength producing a resonance dip in the transmission spectrum of the at least one optical device. The optical modulation method may P4298PC00

[0019] include providing the at least one optical signal electromagnetic wave from at least one first light source to the at least one optical device, the at least one optical signal electromagnetic wave having at least one operation wavelength to be modulated by the at least one optical device. The optical modulation method may include providing a photo-excitation electromagnetic wave from the at least one first light source or from at least one second optical source to the at least one optical device at a pump light intensity to displace in wavelength the resonance wavelengths and the resonance dips in the transmission spectrum to optically modulate the transmitted intensity of the at least one optical signal electromagnetic wave at the at least one operation wavelength.

[0020] The present invention also concerns an optical modulation system.

[0021] The optical modulation system may include at least one optical device configured to modulate at least one optical signal electromagnetic wave provided to and transmitted through the at least one optical device; the at least one optical device may include at least one support substrate and / or layer supporting at least one dielectric metasurface comprising an array of elements configured to generate at least one or a plurality of dielectric metasurface resonances each having a resonance wavelength producing a resonance dip in the transmission spectrum of the at least one optical device. The optical modulation system may include a first light source configured to generate and provide the at least one optical signal electromagnetic wave, the at least one optical signal electromagnetic wave having at least one operation wavelength to be modulated by the at least one optical device, and the first light source is configured to generate and provide a photo-excitation electromagnetic wave for provision to the at least one optical modulation device at a pump light intensity value to displace in wavelength the resonance wavelengths and the resonance dips to optically modulate the transmitted intensity of the at least one optical signal electromagnetic wave at the at least one operation wavelength, wherein the at least one optical signal electromagnetic wave and the photo-excitation electromagnetic wave have the same wavelength to permit single-wavelength or single-band operation; or may include a first light source configured to generate and provide the at least one optical signal electromagnetic wave, the at least one optical signal electromagnetic wave having at least one operation wavelength to be modulated by the at least one optical modulation device, and a second light source configured to generate and provide a photo-excitation electromagnetic wave for provision to the at least one optical device at a pump light intensity value to displace in wavelength the resonance wavelengths and the resonance dips to optically modulate the transmitted intensity of the at least one optical signal electromagnetic wave at the at least one operation wavelength, wherein the at least P4298PC00

[0022] one optical signal electromagnetic wave and the photo-excitation electromagnetic wave have different wavelengths to permit dual-wavelength or dual-band operation.

[0023] Other advantageous features are found in the dependent claims.

[0024] The optical modulation method and / or system provides rapid modulation by, for example, exploiting thermo-optical nonlinearities. Thermo-optical nonlinearities can, for example, decouple the rise and fall times of the transmission signal from the underlying thermal dynamics. By, for example, aligning the signal wavelength relative to the metasurface’s resonances (e.g. just off-resonance), the optical rise / fall times can be made much shorter than the thermal heating / cooling times. This decoupling of optical and thermal dynamics allows modulation speeds in the hundreds of kHz, far beyond what conventional thermo-optic devices allow. Such capabilities are highly valuable for applications requiring ultrafast and reconfigurable optical modulation, including optical coding, high-speed signal processing, data encryption, and dynamic displays.

[0025] The ability to tailor transient responses by choosing the spectral detuning of the operating wavelength relative to a metasurface resonance alignment further enhances the potential for energy-efficient and scalable photonic systems in advanced computing and telecommunication technologies.

[0026] These and other objects, features and advantages of the present invention and the manner of realizing them will become more apparent, and the invention itself will best be understood from a study of the following description with reference to the attached drawings showing some preferred embodiments of the invention.

[0027] BRIEF DESCRIPTION OF THE DRAWINGS

[0028] The accompanying drawings, which are incorporated herein and constitute part of this specification, illustrate the presently preferred embodiments of the invention, and together with the general description given above and the detailed description given below, serve to explain features of the invention. Like reference numerals may refer to like parts throughout the several views. Each embodiment herein may be used in combination with any other embodiment(s) described herein. Also, the images are simplified for illustration purposes and may not be depicted to scale.

[0029] Figures 1A and 1B schematically show exemplary optical systems according to the present disclosure. P4298PC00

[0030] Figures 2A to 2D show optical properties of an amorphous silicon (a-Si) metasurface. Figure 2A is a schematic illustration of a-Si metasurface on an exemplary Fused Silica substrate (P, D, and H denote the periodicity, diameter, and height of the disks of the metasurface, respectively). Figure 2B is a schematic illustration of (upper) the modulated CW laser signal, (middle) the temperature evolution in time, and (lower) differential transient transmission, AT / T, of the metasurface. Figure 2C shows the transmission spectra of fabricated and simulated metasurfaces. The inset shows a SEM image of the fabricated metasurface with P of 380 nm, D of 290 nm, and H of 100 nm. Figure 2D shows the measured real part, n, and imaginary part, k, of the refractive indices of a-Si at 20°C, 70°C, 120°C, 170°C, and 220°C.

[0031] Figures 3A to 3D show measured and simulated thermo-optical nonlinearities (TONL) in steady-state. Figure 3A shows measured transmission spectra of the metasurface under different pump intensities. The legend specifies the measured temperatures corresponding to the pump intensities by Raman thermometry. The semi-transparent regions specify the probe wavelengths of Figure 3C. Figure 3B shows simulated transmission spectra of the metasurface under different pump intensities. The semi-transparent regions specify the probe wavelengths of Figure 3D. Figure 3C shows measured pump intensity-dependent transmission of the metasurface at the probe wavelengths of 488nm, 750nm, 800nm, and 815nm. Upper x-axis shows the measured temperatures corresponding to the pump intensities. Figure 3D shows the simulated pump intensity (temperature)-dependent transmission of the metasurface at the probe wavelengths of 488 nm, 777 nm, 800 nm, and 813 nm.

[0032] Figures 4A to 4I show measured and simulated transient thermo-optical nonlinearities (TONL) at resonance (800nm). Figure 4A is a schematic illustration of the metasurface with the pump beams of 0.75 (inner), 1.5 (middle), and 2.25 (outer)μm in radius used in Figure 4B and the pump intensities of 1.1 (blue), 2.2 (red), and 3.3 (yellow) mW / μm2in Figure 4F with the radius of 1.5 mW / μm2. In all measurements, the probe size was 0.75 μm in radius. Figure 4B shows measured normalised ΔT / T of the metasurface at 800nm probe for the 1.5, 3, and 4.5pm (488 nm) pump beam diameters at 2.2 mW / μm2. The inset shows the nonnormalised transmission, AT / T, of the same cases. Figure 4C shows the simulated normalised ΔT / T of the 3 by 3, 7 by 7, and 11 by 11 array of nanodisks at 800 nm probe while pumping at 488 nm at 2 mW / μm2. Figure 4D shows the simulated transient (upper) and normalised transient (lower) temperatures of the 3 by 3, 7 by 7, and 11 by 11 array of nanodisks at 2 mW / μm2pump intensity. Figure 4E shows the measured τopt,heat in Figure 4B and calculated Tth.heat in Figure 4D versus pump diameter. Figure 4F shows the measured normalised ΔT / T of the metasurface P4298PC00

[0033] at 800nm probe for 1.1 mW / μm2, 2.2 mW / μm2, and 3.3 mW / μm2intensity 488nm 3 pm in diameter pump beams. The inset shows AT / T of the same cases. Figure 4G shows the simulated normalised ΔT / T of the 7 by 7 array of nanodisks for the 1 mW / μm2, 2 mW / μm2, and 3 mW / μm2488nm pump intensities at 800 nm probe wavelength. Figure 4H shows simulated transient (upper) and normalised transient (lower) temperatures of the 7 by 7 array of nanodisks for the 1 mW / μm2, 2 mW / μm2, and 3 mW / μm2. Figure 4I shows the measured τopt,heat and calculated Tth, heat versus pump intensity diameter.

[0034] Figures 5A to 5F show measured and simulated transient TONL at near resonance probing. Figure 5A shows the transmission spectrum of the metasurface with an electric dipole (ED) resonance at 770nm and the spectral positions of the pump and probe wavelengths of 488nm and 785 nm, respectively. Figure 5B shows measured normalised ΔT / T (upper) and normalised temperature (lower) of the metasurface, for 1.1 mW / μm2, and 3.3 mW / μm2488nm pump intensities at 785 nm probe wavelength. Figure 5C shows simulated normalised ΔT / T of the 7 by 7 array of nanodisks for the 1 mW / μm2(blue), and 3 mW / μm2(yellow) 488nm pump intensities at 785 nm probe wavelength. Figure 5D shows the measured pump intensity-dependent transmission of the metasurface at the pump and probe wavelengths of 488 and 785nm, respectively. Upper x-axis shows the measured temperatures corresponding to the pump intensities. The arrows illustrate the gradual change in transmission at 1.1 and 3.3 mW / μm2in Figure 5B. Figure 5E shows the simulated AT / T at 785 nm (upper) for the laser turned off at 300ns at 3 mW / μm2pump intensity with 0.55 absorption at 488nm and (lower) for the laser turned off at 125 ns at 3 mW / μm2pump intensity with unity absorption at 488nm. Figure 5F shows the simulated transient transmission at 785 nm for the modulated 488nm laser at 1 MHz where laser-on time equals 125 ns at 3 mW / μm2intensity with unity absorption at 488 nm. Figure 5G shows measured pump intensity-dependent transmission of the metasurface at the probe wavelength of 785 nm for the pump wavelengths of 488 nm and 785 nm.

[0035] Figure 6A shows a measured transmission spectra map of the metasurface with the disk diameter range from 240 to 300 nm (100 nm thickness and 380nm periodicity) for the wavelength range from 500 to 900nm. The dashed lines specify the spectral positions of the magnetic dipole (MD) and electric dipole (ED) resonances. Figure 6B shows a simulated transmission spectra map of the metasurface with the disk diameter range from 240 to 300 nm (100 nm thickness and 380nm periodicity) for the wavelength range from 500 to 900 nm. Figure 6C shows normalized magnetic field profile at the wavelength of 700 nm and the diameter of 290 nm. Figure 6D shows normalized electric field profile at the wavelength of 800 nm and the diameter of 290 nm. P4298PC00

[0036] The elements 17, for example, the nano-disks 17 may have a diameter and / or width that provides and / or generates at least one electric and / or at least one magnetic resonance in the wavelength range of 500nm to 2500nm, as indicated by Figures 10A, 10C and 10D.

[0037] Figure 7A is a schematic of a home-built microscope, and Figure 7B is a schematic of an optical setup for the steady-state and the transient measurements.

[0038] Figure 8A shows Raman spectra from a-Si metasurface under different pump intensities and corresponding measured temperatures. Figure 8B shows Raman spectrum of a-Si film showing Gaussian deconvoluted Raman peaks from right to left: LA (ω=312 cm⁻¹), LO (ω=380 cm⁻¹), TO (ω=470 cm⁻¹), 2LA (ω=561 cm⁻¹), 2TO (ω=798 cm⁻¹).

[0039] Figure 9A shows the refractive index (n) and extinction coefficient (k) as functions of wavelength at various temperatures (20°C, 100°C, 150°C, 200°C, 250°C and 450°C) taken from reference No.63 (see below). Figures 9B and 9C respectively show the real and imaginary part of the thermo-optic coefficients (dn / dT and dk / dT) for each temperature separation. The average coefficients (computed excluding 450°C) are shown as dashed black lines. Figures 9C and 9D respectively show the predicted and measured refractive index (n) and extinction coefficient (k) at 450°C as a function of wavelengths.

[0040] Figures 10A and 10B respectively show real and imaginary parts of the average thermo-optical coefficient of amorphous silicon (a-Si) as functions of wavelength. Figures 10C and 10D respectively show temperature dependence of the refractive index (n) and extinction coefficient (k) of amorphous silicon (a-Si) across different wavelengths. The solid lines represent the measured values at 20°C, 70°C, 120°C, 170°C, and 220°C, while the dashed lines show the interpolated values for 35°C and the extrapolated values for higher temperatures (250°C to 600°C).

[0041] Figure 11 shows the measured pump intensity-dependent transmission of the metasurface at the probe wavelength of 785 nm for the pump wavelengths of 488 nm and 785 nm as a function of normalised pump intensity.

[0042] Figure 12 shows transient transmission depends on the resonance center. This can be employed for optical coding and computing, or screen pixels. Figure 12 shows a transient optical response of metasurfaces probed at 800 nm with resonances at 785, 790, 795, 800, 805, and 810 nm. The first state represents the system in the absence of the pump laser (488 P4298PC00

[0043] nm, 3 mW / μm2). The second state occurs immediately after the pump laser is turned off. The third and fourth states illustrate how metasurfaces with different resonances exhibit distinct relaxation dynamics overtime. Modulation occurs within 600 ns, enabling operation in the MHz regime. This rapid modulation is made possible by thermo-optical nonlinearities, which decouple the rise and fall times of the transmission signal from the underlying thermal dynamics. Such capabilities are highly valuable for applications requiring ultrafast and reconfigurable optical modulation, including optical coding, high-speed signal processing, data encryption, and dynamic displays as well as counterfeiting related applications. The ability to tailor transient responses by leveraging resonance alignment further enhances the potential for energy-efficient and scalable photonic systems in advanced computing and telecommunication technologies.

[0044] BRIEF DESCRIPTION OF THE SEVERAL EMBODIMENTS

[0045] Figures 1A and 1B schematically show exemplary optical systems according to the present disclosure.

[0046] The optical system 1 is, for example, optical system for optical modulation and / or optical switching. The optical system 1 is, for example, an optical modulation system and / or an optical switching system.

[0047] The optical system 1 includes, for example, at least one optical device 3 and at least one light source 5, 7.

[0048] The optical device 3 is configured to optically process at least one or a plurality of optical electromagnetic waves 9. The optical device 3 is, for example, an optical modulation device 3 configured to optically modulate the at least one or the plurality of optical electromagnetic waves 9.

[0049] The optical electromagnetic wave(s) 9 is, for example, provided to and transmitted through the optical modulation device 3. The optical electromagnetic wave 9 is, for example, an optical signal wave to be operated on and / or processed by the system 1 and / or optical device 3.

[0050] The optical device 3 includes, for example, at least one support substrate and / or layer 11 supporting at least one dielectric metasurface 15.

[0051] The dielectric metasurface 15 comprises, for example, a dielectric material having a high thermo-optical coefficient and a high refractive index. Exemplary materials include at least one P4298PC00

[0052] of: Amorphous silicon (a-Si: H, a-Si), Crystalline silicon (c-Si), Polycrystalline silicon, Germanium (Ge), Gallium Arsenide (GaAs), Gallium Phosphide (GaP), AIGaAs, and Tellurium (Te).

[0053] In an exemplary embodiment detailed below, the dielectric metasurface is or comprises an amorphous silicon metasurface 15. The amorphous silicon metasurface 15 comprises at least one array of elements 17, for example, nano-disks 17 configured to generate one or more at least one dielectric metasurface resonances. The or each dielectric metasurface resonance has a resonance wavelength and produces, for example, a resonance inflection or dip in a characteristic spectrum or transmission spectrum of the optical device 3.

[0054] The resonance dip comprises, for example, a portion of the transmission spectrum in which the transmission value decreases to a minimum value (or at least one minimum value) of the dip with increasing wavelength value and increases from the minimum value with increasing wavelength value.

[0055] In an exemplary embodiment, the amorphous silicon metasurface 15 and / or the array of nanodisks 17 are, for example, configured to generate at least one magnetic dipole (MD) Mie resonance having at least one or a magnetic dipole resonance wavelength MD producing a magnetic dipole resonance dip in the transmission spectrum of the optical device 3 (see, for example, Figure 2C). The amorphous silicon metasurface 15 and / or the array of nano-disks 17 are, for example, configured to generate at least one electric dipole (ED) Mie resonance having at least one or an electric dipole resonance wavelength ED producing an electric dipole resonance dip in the transmission spectrum of the optical device 3 (see, for example, Figure 2C).

[0056] The electric dipole Mie resonance (or Mie-type resonance) generated by the array of nanodisks 17 is, for example, an electric dipole formed by electric field confinement and / or enhancement inside the nano-disks 17 of the amorphous silicon metasurface 15. The magnetic dipole Mie resonance (or Mie-type resonance) generated by the array of nano-disks 17 is, for example, a magnetic dipole formed by magnetic field confinement and / or enhancement inside the nano-disks 17 of the amorphous silicon metasurface 15.

[0057] The optical device 3 includes the support substrate and / or layer 11 that comprises, for example, silicon oxide, and includes for example a plurality of nano-pillars PL extending from the support substrate and / or layer 11. The nanopillars PL or each nanopillar PL includes for P4298PC00

[0058] example at least one nano-disk 17. The nanopillars PL or each nanopillar PL and each nanodisk 17 comprises, for example, amorphous silicon, or a non-crystalline form of silicon.

[0059] In an exemplary embodiment, the amorphous silicon metasurface 15 and the array of nanodisks 17 are configured to generate a plurality of resonance dips in the transmission spectrum for example, a first resonance dip and a second resonance dip; or first, second and third resonance dips. These dips are, for example, produced by the electric dipole and at least one further electric or magnetic resonance mode, for example, an electric quadrupole, or an electric quadrupole and an electric octupole or a magnetic dipole and an electric quadrupole. For example, an alternating series of electric and magnetic modes. For example, at least an electric dipole, a magnetic dipole, an electric quadrupole, a magnetic quadrupole; and so forth.

[0060] The optical signal electromagnetic wave 9 has at least one wavelength or operation wavelength o to be manipulated or operated on by the optical modulation device. The optical signal electromagnetic wave 9 has at least one operation wavelength o to be, for example, modulated and / or switched by the optical device 3.

[0061] The operation wavelength o is, for example, set to include or to be at a wavelength at which a transmission intensity, transmission coefficient and / or transmission amount at that wavelength is changed by a temperature-induced displacement in wavelength of the dielectric metasurface resonance.

[0062] The operation wavelength o may include or be, for example, a wavelength at a resonance wavelength of at least one dielectric metasurface resonance, a wavelength that is longer than a resonance wavelength of at least one dielectric metasurface resonance, or a wavelength that is longer than a resonance wavelength of at least one dielectric metasurface resonance. The operation wavelength o is set based on whether a maximum change in transmission is to be provided, a monotonic change in transmission is to be provided, or a non-monotonic change in transmission is to be provided.

[0063] The operation wavelength o may, for example, include or be at least one of: the electric dipole resonance wavelength ED, the magnetic dipole resonance wavelength MD, a wavelength longer than the electric dipole resonance wavelength ED, a wavelength longer than the magnetic dipole resonance wavelength MD, a wavelength shorter than the electric dipole resonance wavelength ED, and a wavelength shorter than the magnetic dipole resonance wavelength MD (see, for example, Figures 3Aand 3B). P4298PC00

[0064] The optimal detuning (shorter or longer than the resonance) depends on the resonance linewidth. The shorter or longer wavelength value of the operation wavelength o is, for example, dependent on the linewidth of the resonances. The shorter wavelength value may, for example, be in a range of 30nm offset from the dielectric metasurface resonance, for example, 23 nm in the exemplary embodiment shown in Figure 3A. The longer wavelength value may, for example, be in a range of 30nm offset from the dielectric metasurface resonance, for example, 15 nm in the exemplary embodiment shown in Figure 3A.

[0065] As mentioned, the array of nano-disks 17 includes a plurality of nano-disks 17, and the nanodisks 17 or each nano-disk 17 has a diameter and / or width that is sub-wavelength at the operation wavelength o. The diameter and / or width extends, for example, in a direction (substantially) perpendicular to a direction of extension of the nanopillar PL from the supporting substrate or layer 11.

[0066] For example, a nano-disk 17 of about 200-300 nm in diameter (with about 100 nm height) will support MD and ED Mie resonances in the 500-900 nm wavelength range. Each nano-pillar (disk) height is also sub-wavelength relative to the operation wavelength. Each nano-disk 17 may have, for example, a diameter between 200nm and 300nm to support a (at least one) magnetic dipole Mie resonance and (at least one) an electric dipole Mie resonance in the wavelength range of 500nm to 900nm.

[0067] Each nano-pillar extends, for example, a distance from the support substrate and / or layer 11 that is sub-wavelength at the at least one operation wavelength o.

[0068] The nano-disks 17 are, for example, periodically arranged (or substantially periodically arranged) on the optical device 3. The periodic separation of the nano-disks is, for example, sub-wavelength at the operation wavelength o.

[0069] The amorphous silicon metasurface 15 and the array of nano-disks 17 may, for example, be configured to provide near-unity light absorption (> 90% light absorption) at a wavelength of the photo-excitation electromagnetic wave 9. This advantageously permits to provide faster optical modulation, as detailed further below.

[0070] In alternative exemplary embodiments, the amorphous silicon metasurface 15 is configured to generate at least one dielectric metasurface resonance that include at least one of a quasi- P4298PC00

[0071] bound state in the continuum (q-BIC), a surface lattice resonance (SLR), a guided-mode resonances (GMR), a higher-order Mie mode (e.g., quadrupolar or anapole states), and a hybrid or coupled resonance. These modes can be created by adapting the shape and spacing of the individual elements / resonators of the metasurface 15. For example, by breaking the symmetry of the geometry of the shape / structure used in the metasurface 15, for example by alternating a disk diameter to include for example larger / smaller disks (q-BIC), or for example by placing the individual elements / resonators at a spacing that creates the first diffraction order of the grating parallel to the interface of the substrate 11 and spectrally matching one of the resonances of the individual resonators (SLRs).

[0072] In an exemplary embodiment (see, for example, Figure 1B), the optical system 1 may include, a light source or first light source 5 configured to generate and provide the optical signal electromagnetic wave 9, and configured to generate and provide at least one photo-excitation electromagnetic wave 19 and / or pump / optical excitation light 19 for provision to the optical device 3. The optical signal electromagnetic wave 9 and the photo-excitation electromagnetic wave 19 have, for example, the same wavelength. This permits single-wavelength or singleband operation of the optical system 1.

[0073] The photo-excitation electromagnetic wave19 may, for example, be provided directly from the light source 5 to the optical device 3, or provided indirectly via at least one or a plurality of optical components (not shown in Figures 1A and 1B). The optical components may, for example, comprise elements configured to direct and / or guide the photo-excitation electromagnetic 19, and may include, for example, at least one of an optical reflector, a lens, and an optical waveguide.

[0074] The first light source 5 is configured to generate and provide the photo-excitation electromagnetic wave 19, for provision to the optical device 3, at a pump light intensity or intensity value that displaces the or each dielectric metasurface resonance in wavelength. The pump light intensity or intensity value displaces the resonance dips in wavelength to optically modulate the transmitted intensity of the optical signal electromagnetic wave 9 at the operation wavelength o (or at least one operation wavelength o).

[0075] The first light source 5 comprises, for example, at least one laser. P4298PC00

[0076] The magnetic and electric dipole resonance wavelengths MD, ED and / or the resonance dips are, for example, displaced in wavelength to optically modulate the transmitted intensity of the optical signal electromagnetic wave 9 at the operation wavelength or wavelengths o.

[0077] In an alternative embodiment (see, for example, Figure 1 A), the system 1 includes at least the first light source 5 and at least a second light source 7. The first light source 5 is configured to generate and provide the optical signal electromagnetic wave 9, and the second light source is configured to generate and provide the photo-excitation electromagnetic wave 19 for provision to the optical device 3. The optical signal electromagnetic wave 9 and the photoexcitation electromagnetic wave 19 have, for example, different wavelengths. This permits dual-wavelength or dual-band operation of the system 1.

[0078] The photo-excitation electromagnetic wave 19 is, for example, provided at a pump light intensity that displaces the or each dielectric metasurface resonance in wavelength and / or displaces the resonance dips in wavelength to optically modulate the transmitted intensity of the optical signal electromagnetic wave 9 at the operation wavelength o (or at least one operation wavelength o). The magnetic and electric dipole resonance wavelengths MD, ED and / or the resonance dips are, for example, displaced in wavelength to optically modulate the transmitted intensity of the optical signal electromagnetic wave 9 at the operation wavelength or wavelengths o.

[0079] The pump light intensity displaces in wavelength the dielectric metasurface resonance (for example, the magnetic and electric dipole resonance wavelengths MD, ED) and the resonance dips in the transmission spectrum by photothermal heating displacement of the dielectric metasurface resonance (for example, of the magnetic dipole Mie resonance and / or the electric dipole Mie resonance) by the photo-excitation electromagnetic wave 9. The photoexcitation electromagnetic wave 9 and / or the pump light intensity provides thermal energy through absorption of the photo-excitation electromagnetic wave 9 and pump light by the material of the optical device 3, that is, by the support substrate and / or layer 11 and / or the amorphous silicon metasurface 15. The received thermal energy influences the dielectric metasurface resonance and / or the dipoles to displace the above-mentioned spectral wavelength displacement.

[0080] The first light source 5 comprises, for example, at least one laser. The second light source 7 comprises, for example, at least one of a laser, and a broadband light source such as a LED or lamp. P4298PC00

[0081] A first pump light intensity value of the photo-excitation electromagnetic wave 19 may, for example, be changed to a second pump light intensity value (different to the first pump light intensity value) to displace in wavelength the dielectric metasurface resonance (for example, of the magnetic dipole Mie resonance and / or the electric dipole Mie resonance) and the resonance dip(s) to optically modulate the transmitted intensity of the optical signal electromagnetic wave 9 at the operation wavelength or wavelength o. The first pump light intensity value may, for example, be lower than or greater than the second pump light intensity value. The first pump light intensity value or the second pump light intensity value may, for example, be zero in value (absence of pump light) in certain exemplary embodiments.

[0082] Optical modulation of the transmitted intensity of the optical signal electromagnetic wave 9 at the operation wavelength or wavelengths o can be performed by the provision and removal / modification of the pump light and the photo-excitation electromagnetic wave 19. This can be cyclically repeated to imprint a modulation signal on the optical signal electromagnetic wave 9.

[0083] Optical switching at the operation wavelength (or wavelengths) o may be implemented in this manner. The provision of the pump light and / or the photo-excitation electromagnetic wave 19 optically modulates the transmitted intensity of the optical signal electromagnetic wave 9 at the operation wavelength or wavelengths o. This modulates and changes the transmitted intensity. This modulation can, for example, provide optical switching at the operation wavelength or wavelengths o. The transmitted intensity may change to or change from a lower value that is considered an off-state of the switch.

[0084] Optical switching back to the initial state of the system or optical device 3 (prior to the provision (or removal / modification) of the pump light and / or the photo-excitation electromagnetic wave 19) can, for example, be attained by removing (or providing) the pump light and / or the photoexcitation electromagnetic wave 19.

[0085] This can, for example, be done by switching off the light source 5,7 or blocking / obscuring the provision of the pump light and / or the photo-excitation electromagnetic wave 19 to the optical device 3. The removal can, for example be at least partial. This permits switching and the provision of reconfigurable switching.

[0086] The optical system 1 includes, for example, pump light intensity determination means 21. P4298PC00

[0087] The pump light intensity determination means 21 is configured to determine or set a light intensity of the photo-excitation electromagnetic wave 19 to be provided to the optical device 3. The pump light intensity determination means 21, can, for example, be included in the first or second light source 5,7 to directly set and / or adjust the light intensity outputted by the first or second light source 5,7. The pump light intensity determination means 21 comprises in this case an internal control device or system that permits to vary the output power of the light source. In an exemplary embodiment, the light source comprises an adjustable output power laser.

[0088] Alternatively or additionally, pump light intensity determination means 21 can be located externally to the first or second light source 5, 7 to modify the light intensity outputted by the first or second light source 5, 7. The pump light intensity determination means 21 is, for example, located between the first or second light source 5, 7 and the optical device 3. The pump light intensity determination means 21 may, for example, comprise at least one optical filter, for example, at least one neutral density filter.

[0089] The pump light intensity determination means 21 and the provided light intensity advantageously permits to decouple (i) a thermal response time for a temperature change from (ii) an optical response time for an optical transmission change of the optical device 3, as explained further below in relation to Figure 4H that shows that Tth.heat and Tth.cooi remain constant for different pump intensities, and in Figure 4F one interestingly observes that τopt,heat, and Topt.cooi vary significantly with the pump intensity, Topt, heat decreasing from about 6 ps to about 0.5 ps when the intensity increases from 1.1 mW / μm2to 3.3 mW / μm2(Fig. 4I). This provides a thermo-optical non-linear response of the optical device 3 to permit faster optical modulation. The pump light intensity determination means 21 is, for example, configured to provide the photo-excitation electromagnetic wave 19 with a pump light intensity > 0.14mW per square micron, or greater than 1.1 mW per square micron. The desired resonance wavelength shift is also a factor in setting or determining the pump light intensity provided.

[0090] The optical system 1 may, for example, include a beam diameter, width or area determination means 23. The beam diameter, width or area determination means 23 is, for example, configured to set and / or determine a beam diameter, width or area of the photo-excitation electromagnetic wave 19 to be provided to the optical device 3. The beam diameter, width or area determination means 23 comprises, for example, at least one or a plurality of optical apertures or diaphragms. The optical aperture or diaphragm may, for example, be an adjustable aperture or diaphragm to change the beam diameter, width or area. The beam P4298PC00

[0091] diameter, width or area determination means 23 may, for example, be located between the first or second light source 5, 7 and the optical device 3.

[0092] The beam diameter, width or area determination means 23 and the resulting beam permit to decouple (i) a thermal response time for a temperature change from (ii) an optical response time for an optical transmission change of the optical device 3 thus providing a non-linear thermo-optical response of the optical device 3. As discussed further below, the Inventors show that while Tth.heat becomes slower for larger arrays, τopt,heat remains approximately constant (Fig. 4E). The increased temperatures at larger beam diameters, caused by collective heating, amplify thermo-optical nonlinear responses in ΔT / T, enhancing transmission dynamics and decoupling them from thermal dynamics This advantageously permits faster optical modulation by the at least one optical modulation device.

[0093] The beam diameter, width or area determination means 23 is, for example, configured to provide the photo-excitation electromagnetic wave 19 with a beam diameter or width < 100 microns, or < 50 microns, or < 25 microns, or < 10 microns, or less than 2.25 microns.

[0094] The optical system 1 includes, for example, at least one light source modulation device 25 configured to modulate the photo-excitation electromagnetic wave 19. In an exemplary embodiment, the light source modulation device 25 may comprise, for example, an electronic modulation device including a function generator or a waveform generator to produce a modulation signal that controls the electrical power provided to the laser (via, for example, a modulation control circuit) to turn the laser on and off. The light source modulation device 25 may alternatively comprise at least one of an optical chopper, an optical shutter, an acousticoptic modulator and an electro-optic modulator.

[0095] The modulated photo-excitation electromagnetic wave 19 provides, for example, modulated pump light irradiation to the optical device 3 in which the pump light is provided and nonprovided in an alternative manner. The modulated photo-excitation electromagnetic wave 19 has a modulation frequency and a modulation cycle. The pump light is, for example, provided during a first time duration of the modulation cycle and non-provided during a second time duration of the modulation cycle.

[0096] The light source modulation device 25 is, for example, configured to set the first time duration of the modulation cycle to be different than the second time duration of the modulation cycle. The light source modulation device 25 is, for example, configured to set the first time duration P4298PC00

[0097] of the modulation cycle to be less than the second time duration of the modulation cycle. This permits to decouple the heating duration and the cooling duration of the amorphous silicon nano-disks 17 and / or the metasurface 15 to increase the optical modulation rate of the transmitted intensity of the optical signal electromagnetic wave 9 at the operation wavelength AO compared to a modulation cycle having equal first and second time durations, as explained further below.

[0098] The optical system 1 may include, for example, at least one optical detector 27 configured to detect the transmitted electromagnetic wave 29 transmitted by the optical device 3 and to detect the optical signal electromagnetic wave 9 and / or modulated optical signal electromagnetic wave 9 transmitted through the optical device 3. The optical detector 27 may, for example, comprise an optical spectrum analyzer; or at least one spectrometer and at least one photodetector, CMOS device or CCD device.

[0099] In an alternative embodiment, the at least one optical detector 27 is located relative to the optical device 3 to detect the electromagnetic wave 29 as a reflected electromagnetic wave reflected by the optical device 3 and to detect the optical signal electromagnetic wave 9 and / or modulated optical signal electromagnetic wave 9 reflected by the optical device 3.

[0100] The optical system 1 may include, for example, processing means 31, for example, a computer for processing the data and / or signal detected by the optical detector 27.

[0101] The optical system 1 is configured to carry out an optical modulation method or optical switching method as now further described.

[0102] The optical modulation method includes providing the optical modulation device 3, and providing the at least one optical signal electromagnetic wave 9 from the first light source 5 (or operation wavelength light source) to the optical device 3.

[0103] As mentioned above, the optical signal electromagnetic wave 9 has at least one operation wavelength Xo to be modulated by the optical device 3.

[0104] The method includes providing the photo-excitation electromagnetic wave 19 from the first light source 5 (the first light source 5 is an optical pump light source and an operation wavelength light source). Alternatively, the photo-excitation electromagnetic wave 19 is provided from a second optical source 7. P4298PC00

[0105] The photo-excitation electromagnetic wave 19 is provided to the optical device 3 and / or the amorphous silicon metasurface at a pump light intensity or pump intensity value that displaces in wavelength the dielectric metasurface resonance wavelength, for example, the magnetic and electric dipole resonance wavelengths and displaces the resonance dips in the transmission spectrum (produced by, for example, the at least one electric dipole ED and the at least one magnetic dipole MD) to optically modulate the transmitted intensity of the optical signal electromagnetic wave 9 at the at least one operation wavelength o.

[0106] The pump light intensity of the photo-excitation electromagnetic wave displaces in wavelength the magnetic and / or electric dipole resonance wavelengths and the resonance dips in the transmission spectrum by photothermal heating displacement of the at least one magnetic dipole Mie resonance and / or the at least one electric dipole Mie resonance.

[0107] As mentioned, the first light source 5 may provide the optical signal electromagnetic wave 9 and the photo-excitation electromagnetic wave 19. The optical signal electromagnetic wave 9 and the photo-excitation electromagnetic wave 19 may thus have the same wavelength to permit single-wavelength or single-band operation.

[0108] The first light source 5 may provide the optical signal electromagnetic wave 9 and is an operation wavelength light source, and the second light source 7 may provide the photoexcitation electromagnetic wave 19 and is an optical pump light source. The optical signal electromagnetic wave 9 and the photo-excitation electromagnetic wave 19 have different wavelengths to permit dual-wavelength or dual-band operation.

[0109] The photo-excitation electromagnetic wave 19 can be changed from a first pump light intensity value to a second pump light intensity value (different to the first pump light intensity value) to displace in wavelength the magnetic and / or electric dipole resonance wavelengths and the resonance dips to optically modulate the transmitted intensity of the optical signal electromagnetic wave 9 at the at least one operation wavelength o.

[0110] A first pump light intensity value of the photo-excitation electromagnetic wave 19 may, for example, be changed to a second pump light intensity value (different to the first pump light intensity value) to displace in wavelength the dielectric metasurface resonance, for example of the magnetic dipole Mie resonance and / or the electric dipole Mie resonance, and the P4298PC00

[0111] resonance dip(s) to optically modulate the transmitted intensity of the optical signal electromagnetic wave 9 at the operation wavelength or wavelengths o.

[0112] The first pump light intensity value may, for example, be lower than or greater than the second pump light intensity value. The first pump light intensity value or the second pump light intensity value may, for example, be zero in value (absence of pump light) in certain exemplary embodiments.

[0113] As previously mentioned, optical modulation of the transmitted intensity of the optical signal electromagnetic wave 9 at the operation wavelength or wavelengths o can thus be performed by the provision and removal / modification of the pump light and the photo-excitation electromagnetic wave 19. This can be cyclically repeated to imprint a modulation signal on the optical signal electromagnetic wave 9.

[0114] Optical switching at the operation wavelength (or wavelengths) o may be implemented in this manner. The provision of the pump light and / or the photo-excitation electromagnetic wave 19 optically modulates the transmitted intensity of the optical signal electromagnetic wave 9 at the operation wavelength or wavelengths o. This modulates and changes the transmitted intensity. This modulation can, for example, provide optical switching at the operation wavelength or wavelengths o. The transmitted intensity may change to or change from a lower value that is considered an off-state of the switch.

[0115] Optical switching back to the initial state of the system or optical device 3 (prior to the provision (or removal / modification) of the pump light and / or the photo-excitation electromagnetic wave 19) can, for example, be attained by removing (or providing) the pump light and / or the photoexcitation electromagnetic wave 19.

[0116] This can, for example, be done by switching off the light source 5,7 or blocking / obscuring the provision of the pump light and / or the photo-excitation electromagnetic wave 19 to the optical device 3. The removal can, for example be at least partial. This permits switching and the provision of reconfigurable switching.

[0117] The photo-excitation electromagnetic wave 19 displaces the resonance dips in the transmission spectrum produced by the at least one electric dipole (ED) and the at least one magnetic dipole (MD). P4298PC00

[0118] The operation wavelength o to be modulated may include or have a wavelength (see, for example, Figure 3A) at, for example, at least one of:

[0119] the electric dipole resonance wavelength ED,

[0120] the magnetic dipole resonance wavelength MD,

[0121] a wavelength oL longer than the electric dipole resonance wavelength ED,

[0122] a wavelength oL longer than the magnetic dipole resonance wavelength MD,

[0123] a wavelength os shorter than the electric dipole resonance wavelength ED, and a wavelength os shorter than the magnetic dipole resonance wavelength MD.

[0124] While the optical method is described in relation to the exemplary embodiment of the magnetic dipole Mie resonance and / or the electric dipole Mie resonance, the dielectric metasurface resonance may be any one of the other dielectric metasurface resonances mentioned previously above.

[0125] As previously mentioned, the optical signal electromagnetic wave 9 is manipulated or operated on by the optical device 3 at (at least) the operation wavelength o, this wavelength being modulated and / or switched by the optical device 3.

[0126] The optical signal electromagnetic wave 9 having an operation wavelength os at a wavelength shorter than the electric dipole resonance wavelength ED (and / or the magnetic dipole resonance wavelength MD) provides, for example, a monotonic and / or non-linear change in the transmitted intensity of the optical signal electromagnetic wave 9 at the operation wavelength os (see, for example, Figures 3C and 3D).

[0127] The optical signal electromagnetic wave 9 having an operation wavelength or at the electric dipole resonance wavelength ED (and / or at the magnetic dipole resonance wavelength MD) provides, for example, a monotonic and / or non-linear change in the transmitted intensity of the optical signal electromagnetic wave 9 at the operation wavelength or (see, for example, Figures 3C and 3D).

[0128] The optical signal electromagnetic wave 9 having an operation wavelength oL at a wavelength longer than the electric dipole resonance wavelength ED (and / or the magnetic dipole resonance wavelength MD) provides a non-monotonic and / or non-linear change in the transmitted intensity of the optical signal electromagnetic wave 9 at the operation wavelength oL. The pump light intensity displaces the electric dipole Mie resonance (and / or the at least P4298PC00

[0129] one magnetic dipole Mie resonance) by photothermal heating to longer wavelengths and across the operation wavelength oL to provide the non-monotonic and / or non-linear change in the transmitted intensity of the optical signal electromagnetic wave 9 at the operation wavelength oL (see, for example, Figures 3C and 3D).

[0130] Optical modulation of the optical signal electromagnetic wave 9 may be obtained by modulating the photo-excitation electromagnetic wave 19 to provide a modulated photoexcitation electromagnetic wave to the optical device 3. The modulated photo-excitation electromagnetic wave 19 is provided or generated using the previously described light source modulation device 25.

[0131] The modulated photo-excitation electromagnetic wave 19 has a modulation frequency and modulation cycle. The pump light is, for example, provided during a first time duration of the modulation cycle and non-provided during a second time duration of the modulation cycle.

[0132] The modulated photo-excitation electromagnetic wave provides, for example, modulated pump light irradiation to the optical device 3 in which the pump light is provided and nonprovided in an alternative manner at the modulation frequency.

[0133] In an exemplary embodiment, the modulated photo-excitation electromagnetic wave 19 is provided to the optical device 3 with a beam diameter, width or area that decouples a thermal response time for a temperature change from an optical response time for an optical transmission change of the of the optical device 3 to provide a non-linear thermo-optical response of the optical device 3. This permits faster optical modulation by the optical device 3. The beam diameter, width or area determination means 23 is configured to provide such a beam diameter, width or area.

[0134] In an exemplary embodiment, the photo-excitation electromagnetic wave 19 and / or the modulated photo-excitation electromagnetic wave 19 is, for example, provided to the optical device 3 with a beam diameter or width < 100 microns, or < 50 microns, or < 25 microns, or < 10 microns, or less than 2.25 microns.

[0135] In an exemplary embodiment, the modulated photo-excitation electromagnetic wave 19 may be provided to the optical device 3 with a pump light intensity that decouples a thermal response time for a temperature change from an optical response time for an optical P4298PC00

[0136] transmission change of the optical device 3 to provide a thermo-optical non-linear response of the optical device 3 and / or the metasurface 15. This permits faster optical modulation by the optical device 3.

[0137] The pump light intensity determination means 21 is, for example, used to determine the pump light intensity provided to the optical device 3.

[0138] The photo-excitation electromagnetic wave 19 and / or the modulated photo-excitation electromagnetic wave 19 is, for example, provided with a pump light intensity > 0.14mW per square micron, or greater than 1.1 mW per square micron.

[0139] In an exemplary embodiment, the optical signal electromagnetic wave 9 may have an operation wavelength oL at a wavelength longer than the electric dipole resonance wavelength ED (or the magnetic dipole resonance wavelength MD) to provides a nonmonotonic and / or non-linear change in the transmitted intensity of the optical signal electromagnetic wave 9 at the operation wavelength oL. The modulated photo-excitation electromagnetic wave 19 is, for example, provided to the optical device 3 with a pump light intensity that (i) during the first time duration of the modulation cycle, displaces in wavelength the electric dipole Mie resonance (or the magnetic dipole resonance wavelength MD) to longer wavelengths and across the operation wavelength oLto a longer wavelength than the operation wavelength oL; and that (ii) during the second time duration of the modulation cycle, displaces in wavelength the electric dipole Mie resonance (or the magnetic dipole resonance wavelength MD) to shorter wavelengths and across the operation wavelength oL to a shorter wavelength than the operation wavelength oL to modulate the transmitted intensity of the optical signal electromagnetic wave 9 at the operation wavelength oL at a higher frequency than a modulation frequency of the modulated photo-excitation electromagnetic wave 19.

[0140] In an exemplary embodiment, the amorphous silicon metasurface 15 and the array of nanodisks 17 are configured to generate a plurality of resonance dips in the transmission spectrum for example, a first resonance dip and a second resonance dip; or first, second and third resonance dips. These dips are, for example, produced by the electric dipole and at least one further electric or magnetic resonance mode, for example, an electric quadrupole, or an electric quadrupole and an electric octupole or a magnetic dipole and an electric quadrupole. For example, an alternating series of electric and magnetic modes. For example, at least an electric dipole, a magnetic dipole, an electric quadrupole, a magnetic quadrupole; and so forth. P4298PC00

[0141] The amorphous silicon metasurface 15 and the array of nano-disks 17 are, for example, configured to generate the plurality of resonance dips in the transmission spectrum produced by the magnetic dipole and higher order magnetic resonance modes, to generate the plurality of resonance dips in the transmission spectrum produced by the electric dipole and higher order electric resonance modes.

[0142] The modulated photo-excitation electromagnetic wave 19 is, for example, provided to the optical device 3 with a pump light intensity that (i) during the first time duration of the modulation cycle, displaces in wavelength at least the above-mentioned first and second resonance dips (or first and further higher order resonance dips), to longer wavelengths and across the operation wavelength oL to a longer wavelength than the operation wavelength oL; and that (ii) during the second time duration of the modulation cycle, displaces in wavelength at least the first and further higher order resonance dips to shorter wavelengths and across the operation wavelength oL to a shorter wavelength than the operation wavelength oL to modulate the transmitted intensity of the optical signal electromagnetic wave 9 at the operation wavelength oL at a higher frequency than a modulation frequency of the modulated photo-excitation electromagnetic wave 19.

[0143] This can be done using the magnetic dipole and higher order magnetic resonance modes to obtain a higher optical modulation frequency than the modulated photo-excitation electromagnetic wave 19. This can be done using the electric dipole and higher order electric resonance modes to obtain a higher optical modulation frequency than the modulated photoexcitation electromagnetic wave 19. As mentioned, these modes may, for example, alternate between electric and magnetic resonance modes.

[0144] The modulated photo-excitation electromagnetic wave 19 is provided by modulating a light output frequency of the first light source 5 or the second optical source 7 using the light source modulation device 25.

[0145] The pump light of the modulated photo-excitation electromagnetic wave 19 is provided for heating during the first time duration of the modulation cycle and non-provided for cooling during the second time duration of the modulation cycle. P4298PC00

[0146] In an exemplary embodiment, the first time duration of the modulation cycle may, for example, be less than the second time duration of the modulation cycle to decouple the heating duration and the cooling duration of the amorphous silicon nano-disks 17 and / or the metasurface 15 to increase the optical modulation rate of the transmitted intensity of the optical signal electromagnetic wave 9 at the operation wavelength oL compared to a modulation cycle having equal first and second time durations.

[0147] The second time duration of the modulation cycle may correspond, for example, to a cooling duration of the amorphous silicon nano-disks 17 and / or the metasurface 15 that displaces in wavelength the electric (and / or magnetic) dipole Mie resonance to shorter wavelengths and across the operation wavelength oL to a shorter wavelength than the operation wavelength oL.

[0148] Alternatively, the second time duration of the modulation cycle may correspond, for example, to a cooling duration of the amorphous silicon nano-disks 17 and / or the metasurface 15 that displaces in wavelength the electric (and / or magnetic) dipole Mie resonance to shorter wavelengths and to the operation wavelength oL located at the (electric) dipole resonance wavelength ED, MD.

[0149] The photo-excitation electromagnetic wave 19 may, for example, have a wavelength at which light absorption by the amorphous silicon nano-disks 17 and / or the metasurface 15 minimizes a ratio of the first time duration to second time duration. This permits flash heating of the amorphous silicon nano-disks 17 and / or the metasurface 15, and permits to increase the optical modulation rate.

[0150] Further details, analysis and explanations of exemplary embodiments of the optical system and optical methods of present disclosure are now provided below in relation to electric-dipole Mie resonances and magnetic-dipole Mie resonances. Transient and steady-state effects are presented, and large thermo-optical resonance shifts are demonstrated, as well nonmonotonic transmission dynamics, and decoupling of the optical and thermal response times.

[0151] As mentioned, thermo-optical nonlinearities (TONL) in metasurfaces enable dynamic control of optical properties like transmission, reflection, and absorption through external stimuli such as laser irradiation or temperature. As slow thermal dynamics are expected to ultimately limit modulation speeds, research has primarily focused on steady-state effects. In this disclosure, the Inventors investigate photo-driven TONL in amorphous silicon (a-Si) metasurfaces 15 both P4298PC00

[0152] under steady-state and, most importantly, dynamic conditions (50 kHz modulation) using a 488 nm continuous-wave pump laser. First, the Inventors show that a non-monotonic change in the steady-state transmission occurs at wavelengths longer than the electric-dipole resonance (800 nm). In particular, at 815 nm transmission first decreases by 30% and then increases by 30% as the laser intensity is raised to 5 mW / pm.

[0153] Next, the Inventors demonstrate that TONL decouple the thermal and optical characteristic times, the latter being up to 7 times shorter in the tested conditions (i.e τopt= 0.5μs vs τth= 3.5μs). Most remarkably, the Inventors experimentally demonstrate that the combination of these two effects enables optical modulation at twice the speed (100 kHz) of the excitation laser modulation. The Inventors finally show how to achieve all-optical transmission modulation at MHz speeds with large amplitudes (85%). Overall, these results show that photo-driven TONL produce large and fully reversible transmission modulation in dielectric metasurfaces with fast and adjustable speeds. Therefore, they open completely new opportunities toward exploiting TONL in dynamically reconfigurable systems, from optical switching to wavefront manipulation.

[0154] In this disclosure, the Inventors investigate photo-driven TONL in amorphous silicon (a-Si) metasurfaces both under steady-state and, most importantly, dynamic conditions (50 kHz modulation) using a 488 nm continuous-wave pump laser. The Inventors show that TONL produce large (up to 470%), nonlinear, and fully reversible changes of visible to near-infrared transmission, with both the sign (i.e., increase or decrease) and intensity dependence determined by the wavelength position relative to the electric-dipole resonance (800 nm). Noticeably, a non-monotonic response is reported at off-resonance condition (815 nm), transmission first decreasing by 30% and then increasing by 30% as the laser intensity is raised to 5 mW / pm. Most importantly, the Inventors reveal a decoupling of the thermal and optical characteristic times that combined with the non-monotonic response, enables optical modulation at twice the speed (100 kHz) of the excitation laser modulation. Finally, the Inventors show how TONL can be exploited to achieve MHz transmission modulation speeds with large modulation amplitudes (85%), paving the way for all-optical modulation devices. Overall, these results highlight that photo-driven TONL in dielectric metasurfaces open completely new opportunities toward dynamically reconfigurable systems, from optical switching to wavefront manipulation.

[0155] The Inventors investigate the photo-thermo-optical response and nonlinear dynamics of amorphous silicon (a-Si) metasurfaces (Figure 2A), demonstrating their unique capability to decouple thermal and optical characteristic timescale as well as their potential for P4298PC00

[0156] photothermally-driven transmission modulation, both in terms of amplitude and speed. The Inventors designed and fabricated high-Q electric dipole resonant metasurfaces and characterized their transmission spectrum, T(λ), under both steady-state and modulated (50 kHz) photo-excitation using a CW 488nm laser with variable intensity and beam size. Under steady-state irradiation, the Inventors demonstrate large, nonlinear, and fully reversible changes in T(λ), with both the sign (i.e., increase or decrease) and intensity dependence determined by the wavelength position relative to resonance. On resonance (i.e. 800 nm), a monotonic increase of T from 0.09 to 0.51 (about 470% experimental, about 1360% theoretical) is obtained under 5 mW / pm2 irradiation. Strikingly, at 815 nm (red-shifted from resonance), a non-monotonic response is reported, with T first decreasing from to 0.22 (-31% at 1.5 mW / pm2) and then increasing to 0.41 (+29% at 5 mW / pm2). For modulated irradiation, the Inventors further show that thermo-optical non-linearities (TONL) uniquely decouple the system’s thermal response time (Tth) from its optical response time (τopt) ((Fig. 2B)). For example, with a beam diameter of 3 pm, exciting approximately 7 by 7 a-Si nanoresonators, the heating dynamics exhibit Tth, heat (the time interval between 10% and 90% of the temperature change) about 3.5 ps, while the transmission, T(t), response time decreases with increasing excitation intensity, reaching τopt,heat (the time interval between 10% and 90% of the transmission change) about 0.5 ps at 3.3 mW / μm2. Most remarkably, the Inventors demonstrate that the combination of non-monotonic T(t) response and decoupled Toptcan lead to a doubling of the optical modulation frequency (100 kHz) with respect to the photothermal modulation frequency (50 kHz) while preserving a large modulation amplitude (30% experimental, 85% theoretical). Finally, the Inventors discuss how Tth / i-opt decoupling can also enable photo-thermo-optical modulation speeds exceeding 1 MHz. The experimental findings are in excellent agreement with a Multiphysics COMSOL model, which incorporates newly measured, temperature-dependent refractive index (n) and extinction coefficient (k) data for a-Si over 20-220°C. Overall, these results highlight that photo-driven TONL in dielectric metasurfaces open completely new opportunities toward dynamically reconfigurable systems, including optical switching devices and wavefront manipulation components, such as beam steering and metalenses.

[0157] Concerning the optical properties of the a-Si metasurface 15, the Inventors designed and fabricated a-Si metasurfaces 15 consisting of an array of nanodisks 17 with diameters(D) ranging from 200 nm to 300 nm, a thickness (t) of 100 nm and a periodicity (P ) of 380 nm. The experimental transmission spectrum of the metasurface with nanodisks of 290 nm diameter (Fig. 2C) is characterized by two pronounced dips around 695 nm and 800 nm, in good agreement with the simulated results. The resonance at 695 nm is attributed to the magnetic dipole (MD) mode, while the resonance at 800 nm corresponds to the electric dipole P4298PC00

[0158] (ED) mode. The Inventors provide detailed field profiles for both the MD and ED resonances in Figures 6A to 6D, illustrating the field confinement and mode distributions at these resonant wavelengths. The quality factor (Q-factor) of the experimental electric dipole resonance at 800 nm is about 50, reflecting the metasurface’s ability to achieve strong light confinement and offering good possibility for optical modulation. This is made possible by the good quality of the fabricated nanodisk array (see inset of Figure 2C). While there is a close agreement between the simulated and measured spectra, slight deviations are likely due to small fabrication imperfections or unaccounted material loss in the simulations.

[0159] Nonetheless, both the experimental and simulated data confirm the strong resonant behavior of the metasurface within the visible to near-infrared spectrum, showcasing its potential for applications in optical modulation.

[0160] To further explore the thermo-optic properties of the metasurface, the temperature dependence of the refractive index of an a-Si thin film (100 nm thick) is measured by ellipsometry using an external heater to vary the sample temperature from 20°C to 220°C (Fig.

[0161] 2D). The measurement shows that across the visible and near-infrared wavelength range, a-Si thermo-optical coefficient is dispersive and can be negative or positive depending on the wavelength (see Fig. 10Ato 10D), differently from previously assumed constant values across the spectrum. The real (n) and imaginary (k) parts of the refractive index of a-Si exhibit a more pronounced increase in the spectral window between 650 nm and 850 nm as the temperature increases. In an exemplary embodiment, resonance(s) may, for example, be provided in this range.

[0162] This temperature dependence reflects the thermo-optic effect in a-Si, which can be exploited to dynamically tune the metasurface’s optical properties under varying thermal conditions. Notably, the measured thermo-optical coefficient, derived from the variation of the refractive index (n) with temperature, exhibits a maximum ( about 4x10'4K'1) at about 800nm, coinciding with the exemplary ED resonance provided in an exemplary embodiment herein (see Fig.

[0163] 10A). This alignment between the peak thermo-optical coefficient and the ED resonance highlights the metasurface 15 as an ideal platform for exploring thermo-optical effects. The strong field confinement at the ED resonance further amplifies the temperature-induced refractive index changes, making it particularly suited for dynamic tuning of optical properties via thermal modulation. Note that our measurements reveal that the real part of the thermo-optical coefficient of a-Si is 0 at about 480nm, which makes this spectral region important for applications requiring high stability against temperature changes. P4298PC00

[0164] Concerning TONL in steady-state optical response, to explore the impact of TONL on the steady-state transmission spectrum of a-Si metasurfaces, the Inventors perform a series of transmission measurements under varying photoexcitation intensities (Figure 3). A 488 nm continuous wave (CW) laser is used as pump to photoexcite / heat the metasurface, which has an absorption of about 0.55 at this wavelength. Instead, a low-intensity, CW white light source is utilized as the probe to measure the transmission spectra across the visible / near-infrared spectrum, allowing us to quantify the change of the metasurface’s optical transmission in realtime at selected probe wavelengths. Further details of the experimental setup, including a diagram, are provided below. Taking advantage of the pump CW laser, the Inventors also use calibrated Raman thermometry to measure the temperature of the metasurface 15 in-situ during the experiments (comprehensive details are provided further below).

[0165] Figure 3A displays the measured transmission spectra of the metasurface 15 as a function of pump laser intensity (3 pm beam diameter), with the corresponding temperatures ranging from 20°C to 500°C. As the pump intensity increases, the transmission dips associated with the magnetic dipole (MD) at around 695 nm and the electric dipole (ED) at around 800 nm red shift and become less pronounced. Notably, the ED resonance experiences a larger shift (about 40 nm) than the MD resonance (about 22 nm), which can be attributed to two main reasons. First, the thermo-optical coefficient of a-Si is higher in the spectral region of the ED resonance than at the MD resonance position, leading to a greater refractive index change with temperature near 800 nm. Second, the ED mode exhibits a higher field enhancement and Q-factor than the MD, resulting in stronger light-matter interactions and greater sensitivity to temperature-induced refractive index changes. This enhanced field confinement can induce larger shifts in the ED resonance as the metasurface 15 heats up. When cooling the sample (after exposure to the maximum pump intensity), the transmission spectrum returns to its initial state, indicating that the applied pump intensity can reversibly tune the metasurface’s optical properties without permanent modifications of the materials, such as laser-induced crystallization or oxidation of a-Si. To model the temperature-dependent response of the metasurface, the Inventors first extrapolated the a-Si experimental refractive index data beyond 220°C using an approach that validated against available literature for other materials. Simulations are in excellent agreement with the experimental data, capturing the trends in transmission modulation with increasing laser intensity (see Figure 3B).

[0166] To assess the existence and magnitude of nonlinear variations in the transmitted signal due to thermo optical effects, particularly near the ED resonance at 800 nm, the Inventors analyze the evolution of transmission at selected wavelengths. The pump intensity-dependent transmission at four probe wavelengths (488 nm, 750 nm, 800 nm, and 815 nm) is plotted in P4298PC00

[0167] Figure 3C, clearly showing a nonlinear response of the metasurface at wavelengths around the ED resonance. For the 488 nm probe, which is far from resonance, there is minimal change in transmission, indicating that the thermo-optical effect is less pronounced at this wavelength because of the low thermo-optical coefficient of a-Si and the flat spectrum. In contrast, at 750 nm (left of resonance) and 800 nm (on resonance), there is a significant negative and positive nonlinear change in the transmission as the pump intensity increases, respectively. The nonlinearity is particularly strong at 800 nm, where the ED resonance occurs, leading to a sharp increase in transmission with increasing pump intensity, reaching up to about 470% AT / T, (from 0.09 to 0.51) at about 5.6mW / μm2intensity. At 815 nm probe wavelength, one also observes a unique behavior: transmission first decreases from 0.32 to 0.22 (-30% at about 1.5 mW / μm2) and then increases, reaching the initial value at about 3 mW / μm2and then raising up to 0.42 (+30%) for pump a pump intensity of about 5 mW / μm2, eventually plateauing at higher intensities. Numerical simulations confirm the trends observed in experiments, with significant transmission modulation occurring near the resonant wavelengths (777 nm, 800 nm, and 813 nm). In comparison, the off-resonance wavelength (488 nm) remains largely unaffected (Fig. 3D). The good agreement between experimental and simulated results demonstrates the accuracy of the material and electromagnetic models in capturing TONL of the metasurface. Based on the calculations, with improvements in the fabrication, up to 1360% AT / T (from 0.05 to 0.73) is possible thanks to a gigantic TONL at the resonance wavelength of 800 nm.

[0168] Concerning TONL in transient optical response, to investigate the transient TONL in a-Si metasurface, the Inventors performed time-resolved measurements and simulations under various pump and probe conditions (Fig. 4A). The transient response was measured by probing the metasurface at the resonance wavelength (Fig. 4) and near resonance wavelength (Fig. 5) while pumping it with the 488 nm continuous wave (CW) laser using different beam sizes and intensity levels. The 488 nm CW pump laser was modulated at 50 kHz, with a transient modulation time of about 2 ns, which is much faster than the heating and cooling times of the metasurface. As such, this modulation does not influence the measured transient dynamics, allowing the Inventors to capture the thermo-optical response of the system accurately. The details of the AT / T setup can be found further below. The resulting AT / T dynamics provide insight into the interaction between optical heating and the time evolution of the metasurface’s refractive index, highlighting the role of transient TONL in modulating light transmission.

[0169] Figure 4B shows the experimentally measured normalised ΔT / T at 800 nm probe wavelength (i.e. at the ED resonance) for three different pump beam radii (small 0.75 pm, medium 1.5 P4298PC00

[0170] pm, and large 2.25 pm) but constant pump intensity of 2.2 mW / μm2. Transmission is instead probed in a central region with a constant diameter of 1.5 pm, equivalent to approximately 3 by 3 meta-atoms. Increasing the pump beam diameter while keeping the intensity unchanged in the probed region allows us to assess the impact of collective heating effects on transient TONL. In fact, the constant intensity ensures that light absorption and heat dissipation in each meta-atom (i.e. self-heating) are the same in all measurements. On the other hand, illuminating more meta-atoms (larger beam) results in a larger contribution of heat diffusion (i.e. collective heating) onto the final temperature of the meta-atoms in the central region (details of the configuration are provided further below). In agreement with the steady-state results (Figure 3C), for all beam sizes ΔT / T increases during the " Laser On" phase and decreases when the laser is turned off. Notably, while the characteristic time of the optical signal in the " Laser On" phase (τopt,heat), i.e. during heating, is approximately constant, the characteristic time during the " Laser Off' phase (τopt,cooi), i.e. cooling, depends on the beam size, smaller beams leading to faster changes in transmission. Additionally, as shown in the inset of Fig. 3b, the amplitude of AT / T increases with the beam diameter. These observations depend on the elevated temperatures caused by the increase in collective heating effects with the beam diameter.

[0171] The Inventors also performed COMSOL simulations to model the AT / T response of metasurfaces consisting of 3 by 3, 7 by 7, and 11 by 11 arrays of nanodisks and mimic the effect of increasing beam diameters (Fig. 3c) (see below for the details of the simulations). These also show that larger arrays (corresponding to larger beams) exhibit slower transient responses due to the more distributed collective heating effects and higher temperatures (Fig.

[0172] 4D). With the model, the Inventors also compute the temperature evolution of each system and the associated thermal characteristic time (Tth) for heating and cooling. One obtains Tth.heat equal to 1.5, 3.5 and 4.5 ps, and Tth.cooi equal to 1.4, 3.2 and 5.6 ps for 3 by 3, 7 by 7, and 11 by 11 array of nanodisks 17, respectively.

[0173] Interestingly, while Tth.heat becomes slower for larger arrays, τopt,heat remains approximately constant and equal to about 1.5 ps, as observed in experiments (Fig. 4E). The increased temperatures at larger beam diameters, caused by collective heating, amplify thermo-optical nonlinear responses in ΔT / T, enhancing transmission dynamics and decoupling them from thermal dynamics. Small differences between the calculated and measured characteristic times of the transmission modulation can arise from the unaccounted cold nanoresonators around the heated region or a minor mismatch in the thermal parameters of the materials. P4298PC00

[0174] Overall, these results confirm the critical role of beam size in modulating the transient optical response of the metasurface.

[0175] The influence of pump intensity on the transient response is shown in Figure 4F, which illustrates the normalised ΔT / T at low (1.1 mW / pm2), medium (2.2 mW / pm2), and high (3.3 mW / pm2) laser intensity levels. The inset of Figure 4F shows AT / T, providing insight into the amplitude changes under different intensity conditions. As expected, higher pump intensities result in stronger modulation, i.e. a larger change in transmission as a consequence of elevated temperatures (Fig. 4D), confirming the strong thermo-optical nonlinear effect in the metasurface.

[0176] Contrary to the case of increasing beam size, Figure 4H shows that Tth, heat and Tth.cooi remain constant for different pump intensities, as shown also in previous works. Specifically, they are equal to 3.5 ps and 3.2ps, respectively. However, in Figure 4F one interestingly observes that Topt.heat, and τopt,coolvary significantly with the pump intensity, τopt,heatdecreasing from about 6 ps to about 0.5 ps when the intensity increases from 1.1 mW / μm2to 3.3 mW / μm2(Fig. 4I). This apparent discrepancy is a unique consequence of the TONL on AT / T.

[0177] Although the thermal response of the metasurface 15 (heating and cooling rates) remains unaffected by the pump intensity, TONL accelerate the effect on AT / T, resulting in a much faster modulation of the signal at higher intensities. The Inventors confirmed the experimental result with numerical simulations, achieving excellent agreement regarding transient times and magnitudes (Fig. 4G). This further highlights how TONL can decouple the thermal response from the transient optical behavior, creating a situation where optical modulation speeds do not directly correspond to the thermal dynamics of the system.

[0178] The Inventors finally consider the case where one probes the transient response of the metasurface 15 at a wavelength that is red-shifted compared to the ED resonance mode for which a non-monotonic evolution of the transmission signal with incident intensity was observed in steady-state (Figure 5D). Because of experimental limitations (available bandpass filters), the Inventors used a metasurface comparable to that presented above but with the ED resonance at 770nm (nanodisk D of 280 nm, P of 380 nm, and t of 100nm) and probed it at 785nm (Fig. 4a).

[0179] Figure 5B, shows the normalized AT / T for 1.1 mW / μm2and 3.3 mW / μm2pump intensities. A markedly different response from that observed on-resonance (Fig. 4F) is obtained. Most strikingly, there exist clear variations in both the characteristic times and the shape of AT / T P4298PC00

[0180] with pump intensity, highlighting the profound influence of TONL on the transient response. At 1.1 mW / μm2transmission monotonically decreases. Indeed, upon photothermal heating the resonance redshifts (about 12 nm), eventually matching the probe wavelength, which thus reaches the minimum transmission value (Fig. 5D). Once the laser is turned off, the resonance shifts back to its initial position resulting in a monotonic increase in the transmission. At 3.3 mW / μm2, however, as time passes and temperature increases further, the resonance redshifts beyond the probe wavelength, reaching about 30nm shift at steady-state. When the resonance center becomes more red-shifted than the probe wavelength, transmission increases again.

[0181] One thus observes that when the laser is turned on, transmission shows an extremely fast dip (about 300 ns), followed by rapid recovery to the initial transmission value (i.e. zero differential transmission). When the laser is turned off, the system similarly exhibits a fast dip in transmission and a quick recovery. This trend can be better understood by considering Figure 5D, acquired in steady state.

[0182] During a dynamic modulation with the 488 nm CW laser, the transmission signal evolves in time along the curve, up to 1.1 mW / μm2(3.3 mW / μm2) pump intensity, with non-uniform speed due to the non-linear change in temperature. For 3.3 mW / μm2pump intensity, the final transmission has the same amplitude as the initial one, as observed by the recovery of AT / T in Figure 5D.

[0183] Overall, in this particular condition one observes that while the laser is modulated at 50kHz, the transmission signal is effectively modulated at twice this speed, i.e. 100kHz. The Inventors emphasize that this complex optical behavior is not mirrored by the thermal response, as Figure 5B shows that the temperature monotonically increases when the laser is on and decreases after it is turned off. This discrepancy between the optical and thermal responses confirms that the system is no longer linear and is governed by highly complex nonlinearities that effectively decouple the transient optical response from the underlying thermal dynamics.

[0184] In Figure 5C, the Inventors present simulated normalized AT / T for a 7 by 7 nanodisk array, resonant at 770 nm, at 785 nm as in the experimental conditions. The simulations closely replicate the measured behavior, confirming that the transient optical modulation is governed by both the intensity of the pump laser and the resonant properties of the metasurface.

[0185] Overall, TONL introduces a decoupling of thermal and optical dynamics and the resonant nature of the metasurface introduces non-monotonic evolutions of the optical signal with P4298PC00

[0186] temperatures. Together, they generate unique and non-intuitive behaviors in the metasurface transient optical properties, further reinforcing the importance of TONL in driving advanced optical modulation effects.

[0187] Toward understanding the limits of modulation speed in the studied system, the Inventors focused on the control of the laser on and laser off phases. Indeed, although above an effective doubling of the modulation speed is demonstrated, one observes that the transmission recovery time during the laser-off phase increases with increasing incident power. The upper panel in Figure 5E shows the calculated transient transmission when the laser is turned off after 300 ns, instead of 10 ps, for a pump intensity of 3 mW / μm2. The initial sharp drop in transmission (from 0.6 to 0.1 corresponds to about 85% change in T) follows the behavior reported in Figure 5B to 5C for the high pump intensity case (laser on phase). However, when the laser is turned off, the cooling dynamic follows the evolution observed for the low pump intensity case (laser off phase). This is due to the fact that the cooling process is governed solely by the temperature reached at 300ns, irrespective of the illumination intensity used.

[0188] The temperature at the minimum of AT / T is the same for the high and low pump intensity cases, as it corresponds to the shift of the ED resonance to the probe wavelength. However, the heating rate and thus the time it takes to reach this temperature strongly depends on the used intensity. This behavior effectively decouples the heating and cooling rates, enabling faster modulation. The modulation speed, therefore, becomes even faster than what would be expected from traditional thermo-optical switches.

[0189] Finally, the Inventors also consider the case in which absorption of the metasurface at 488 nm is unity instead of 0.55 as in our experiments (Fig. 5E lower panel). As just discussed, a higher heating rate further accelerates the optical modulation rate resulting in the minimum transmission occurring at just 125 ns. Moreover, thanks to the flash heating, the heated area is more localized resulting in faster cooling and recovery of the transmission when the laser is turned off compared to the case of absorption is equal to 0.55. This unique behavior opens the possibility for operating the metasurface in the MHz range with very high modulation depths (Fig. 5F), making it significantly more efficient than conventional thermo-optical switches, which are typically constrained by slower thermal response times. By leveraging this fast modulation mechanism, we demonstrate that TONL in a-Si metasurfaces has the potential to break the typical limitations of thermal-based modulation, offering much faster switching capabilities. P4298PC00

[0190] Concerning a comparison between the dual and single band operations, when using the 488 nm laser for photothermally heating the metasurface (Figure 5A), the pump wavelength is spectrally far from any resonance, corresponding to dual-band operation. Consequently, absorption at the pump wavelength remains essentially constant with temperature and, as the pump intensity increases, the steady-state temperature of the metasurface increases as well (Fig. 5D). Therefore, the observed steady-state and dynamic transmission changes are purely due to TONL at the probe wavelength. In contrast, when using a 785 nm pump laser (Figure 5A), close to the electric dipole (ED) resonance of the metasurface 15, the system operates in a single-band mode, where both thermo-optical and photo-thermal nonlinearities must be considered. As shown in Figure 5G, at low pump intensities, transmission decreases as the metasurface heats up but not as much as with 488 nm pumping because of the much lower absorption at 785 nm. As the pump intensity increases, the photo-thermal nonlinearity becomes more pronounced, resulting in an enhanced nonlinear response (see Fig. 11). Eventually, the evolution of the transmission with pump intensity follows the same shape as with 488 nm excitation but with a non-linear stretching of the x-axis due to the non-linear change in absorbed power. The interaction between the heating effects and the resonance properties of the metasurface thus causes the transmission to behave in a more complex manner compared to the dual-band operation.

[0191] The present disclosure reveals novel insights into the transient and steady-state TONL in a-Si metasurfaces, building on existing literature primarily focused on steady-state nonlinear optical effects. The results highlight the unique ability of a-Si metasurfaces to exhibit nonlinear and non-monotonic transmission changes and to decouple the transient optical response from the slower thermal dynamics of the system. These two effects, driven by TONL, eventually enable high-speed transmission modulation while benefiting from the resonant nature of the system to achieve large modulation amplitudes.

[0192] The role of collective heating was also explored in the experiments, particularly by varying the pump beam size and intensity. It is found that smaller beams induce faster thermal responses due to more localized heating, while larger beams result in slower responses due to the increase of collective heating effects. This behavior is consistent with the predictions of earlier work, where the spatial distribution of heat plays a significant role in determining the overall optical response of the metasurface. More importantly, the elevated temperatures thanks to the enhanced collective heating in larger beams trigger higher TONL which results in acceleration in optical response compared to the thermal response of the system. Furthermore, it is showed that increasing the pump beam intensity, fora given beam size, can P4298PC00

[0193] dramatically accelerate the optical response time, while leaving the thermal response time unaltered. This provides a simple and direct way to control the dynamics of the optical response of the metasurface.

[0194] The use of Raman thermometry for in-situ temperature measurements is also worth final consideration. Raman thermometry is indeed a highly effective method for measuring the temperature of silicon materials. Monocrystalline silicon (c-Si) displays a pronounced and distinct Raman peak, which arises from the interaction of light with phonon modes. The temperature of Si nanoparticles can thus be determined based on the linewidth broadening of the Raman peak or its spectral shift as well as from the reduction in the anti-Stokes / Stokes signal ratio. However, it has been observed that Mie resonances, present in both metals and semiconductors, can have a significant impact on the Raman scattering spectrum. Specifically, they can affect the linewidth of the spectral peaks as well as alter the anti-Stokes / Stokes ratio, with the latter being influenced by the Purcell effect. To mitigate the impact of Mie resonances, the Inventors employed a 488 nm pump laser to induce the Raman signal, as the spectrum of the metasurface at this wavelength lacks Mie-like resonances and remains almost flat.

[0195] Due to the broadened and more chaotic Raman signal in amorphous materials, there have been fewer attempts in the literature to apply Raman thermometry to amorphous silicon. In the present approach, the Inventors decompose the Raman peaks to isolate the intensity and central positions of each vibrational mode of a-Si. This reveals several vibrational peaks, including a distinct transverse optical phonon mode at 470 cm’1(see below). As showed through the excellent agreement of experiments and simulations, the anti-Stokes / Stokes ratio of this mode can be used to reliably measure the local a-Si temperature during the experiments.

[0196] Overall, high-speed all-optical photonic devices are attracting growing interest, and the present findings provide new guidelines on how to exploit TONL towards rapid modulation. The ability of a-Si metasurfaces to decouple the transient optical response from thermal dynamics presents a new avenue for developing fast, tunable optical modulators, switches, and sensors.

[0197] To further enhance the transient nonlinearities and modulation rates, one can modulate higher Q factor resonances such as q-BIC or surface lattice resonances (SLR), as well as pumping the system at wavelengths with near-unity absorption or utilizing the concept of thermo-optical bistability. Furthermore, by exploiting nonlinear changes in the absorption rate of the pump P4298PC00

[0198] beam, the modulation rates can be further enhanced, and complex dynamic responses can be engineered. Moreover, the excellent agreement between the present experimental results and COMSOL simulations reinforces the robustness of the TONL mechanism in a-Si metasurfaces, further supporting their potential for high-performance applications in telecommunications and optical computing.

[0199] In conclusion, this disclosure provides a comprehensive exploration of both steady-state and transient TONL in a-Si metasurfaces. The novel decoupling of optical and thermal responses opens up new possibilities for achieving ultrafast optical modulation, surpassing the limitations imposed by thermal dynamics in traditional metasurface systems. This work represents a significant step forward in understanding and harnessing TONL for advanced photonic applications.

[0200] Concerning sample preparation, the metasurface samples were fabricated on a 550 pm thick fused silica substrate. A 100 nm thick layer of amorphous silicon (a-Si) was deposited onto the substrate 11 using plasma-enhanced chemical vapor deposition (PECVD) at 550°C. This deposition technique ensures a uniform a-Si layer with well-controlled thickness, which is critical for the metasurface’s optical performance. Electron beam lithography (EBL-Raith EBPG5000+) was employed to pattern the a-Si nanodisks 17. A 120 nm thick ZEP 520A resist was spin-coated onto the a-Si layer and subsequently patterned using EBL to define the nanodisk structures. After developing the resist, the patterned ZEP resist served as a mask for the etching process. The a-Si nanodisks were then etched into the substrate using argon ion beam etching (Veeco Nexus IBE350). The back surface of the chips was also etched by IBE to remove the deposited a-Si at the back surface of the chips. After the etching process, the remaining ZEP resist was removed by soaking the samples in acetone. To ensure the complete removal of any residual organic material, the samples were subjected to a final low-power microwave plasma cleaning (Tepla-300), which further cleaned the surface without affecting the nanodisk structures.

[0201] Concerning setups, steady-state measurements (Fig.2B, Fig.3, and Fig.5D): The experimental setup used for spectral, Raman, and AT / T measurements is a custom-built system designed to enable precise control and visualization of the metasurface sample. The setup includes a microscopy section to visually inspect the sample, which utilizes a high numerical aperture (NA 0.8) 100x objective and a CMOS camera. The halogen lamp (OSL2IR-Thorlabs) is used for the transmission measurements. The system is coupled with an Andor Shamrock 750 spectrometer body equipped with an iDus 420 CCD camera for spectral measurements. The system is equipped with a 488 nm OBIS LX laser, which can be digitally modulated up to 150 P4298PC00

[0202] MHz. This laser serves as the primary pump source for many of the experiments, including Raman and AT / T measurements. Additionally, a 785 nm laser is integrated into the setup for non-degenerate (single-band) measurements, allowing us to explore the metasurface’s behavior under different excitation wavelengths. For Raman and steady-state transmission measurements, the 488 nm pump laser is filtered using a series of cut-off filters to remove any unwanted pump light. The spectrometer is configured with a high line number grating to increase the spectral resolution, ensuring that even subtle shifts in the Raman spectra are captured with high precision.

[0203] It is worth noting that AT / T is defined as (T(A, intensity) - To(A)) / To(A) where To(A) is the unperturbed room temperature transmission.

[0204] Concerning transient measurements (Fig.4 and Fig.5A), AT / T measurements are conducted using a commercial time-correlated single photon counting (TCSPC) system (PicoQuant Hydraharp 400) coupled with a silicon single-photon avalanche diode (Si SPAD- Micro Photon Devices PDM Series) detector, providing a time resolution of approximately 20 ps. (NA 0.8) 100x objective is used in these measurements. In these measurements, the 488 nm laser was modulated at 50 kHz using a square wave trigger signal (% 50 duty cycle) (TTi TG320), which serves as a synchronization signal for the TCSPC module. To selectively probe specific spectral regions of transmitted white light, narrow bandwidth (about 3 nm in FWHM) bandpass filters were employed, isolating the wavelengths of interest for detailed analysis. It is worth noting that AT / T is defined as (T(A, time) - To(A)) / To(A).

[0205] Concerning COMSOL modelling of the TONL, all simulations were performed by using the Finite Element Method (FEM) based commercial software COMSOL Multiphysics (COMSOL Multiphysics 6.2).

[0206] Concerning transient photo-thermal heating simulations (Fig.4D and Fig.4E), the simulated structures were modeled in close agreement with the experimental geometric parameters (t=100 nm, D=290 nm P=380 nm). A 3D model was built with 3 by 3, 7 by 7, and 11 by 11 arrays of a-Si nanopillars supported on SiO2to mimic the area irradiated with the pump laser beam as we changed the beam diameter from 1 to 3 pm. Each structure was placed in a 400nm thick air layer of refractive index 1, lying on the surface of a 400 nm thick SiO2background medium layer, with both dimensions along the vertical direction. The lateral dimensions of the simulated domain were varied with the size of the array simulated. The simulation domain was truncated by exploiting 300 nm thick Infinite Element Domains (IEDs) in all of the spatial directions. The nanopillar’s optical properties were described by using the P4298PC00

[0207] temperature-dependent refractive indices we measured by ellipsometry. A monochromatic plane wave at normal incidence from above was utilized to excite the metasurface. The wavelength of the input light was set to the wavelength corresponding to the pump laser. Laser power was varied in the simulations to match the experimental conditions. The laser illumination was switched on for 10 ps and subsequently switched off to study the heating and cooling dynamics of the illuminated metasurface region. Maxwell’s equations were then solved in the transient frequency domain for the total field at the excitation wavelength. The resistive losses could then be evaluated from the model through the volume integral in the subdomain of concern. With the resistive losses calculated from electromagnetic simulation, the resultant temperature dynamics were simulated with a 3D heat transfer model. The nanoparticle array and SiO2substrate were set as heat sources, with heat dissipated according to the integration of resistive losses. The ambient temperature was set at 20°C and the average temperatures of the simulated particles are considered in the study. The Inventors also considered the influence of temperature increase on the heat conductivity and electric permittivity of the materials.

[0208] Concerning the metasurface unit cell simulations at elevated temperatures (Fig.3B), the metasurface unit cell simulation (Electromagnetic Waves, Frequency Domain) at different temperatures was done by using the measured n and k dataset at different temperatures. Due to the limitation of ellipsometry, we extrapolated the n and k at higher than 220°C (see below).

[0209] Later, the Inventors mapped the transient temperatures to the perturbed transmission using the abovementioned simulations and obtained AT / T simulations for the specific cases in the study.

[0210] In relation to Raman thermometry, the Inventors employed Raman spectroscopy to measure the local temperature of the metasurface, adapting a method previously used for crystalline silicon (c-Si) to amorphous silicon (a-Si). Unlike c-Si, a-Si exhibits a more complex and broadened Raman spectrum due to the amorphous nature of its phonon modes. The most pronounced phonon mode in a-Si appears at approximately 470 cm-1, corresponding to the transverse optical (TO) phonon mode. To determine the local temperature of the metasurface, the Inventors fitted Gaussian functions to the measured Raman spectrum to accurately identify the center and amplitude of the 470 cm-1TO mode. The amplitude of this mode was then used to calculate the temperature. Specifically, we applied the same temperature calculation model that utilizes the intensity ratio of the Stokes and anti-Stokes Raman peaks. The equation used is: P4298PC00

[0211]

[0212] (1)-

[0213] where IA and Is are the intensities of Anti-Stokes and Stokes Raman signals, respectively, ks is the Boltzman constant, h is the Planck constant, copis the frequency of the phonon mode, and T is the temperature.

[0214] Figure 6A shows the measured transmission spectra map of the metasurface 15 as a function of disk diameter and wavelength. It reveals resonant features that shift with changes in the disk diameter, indicating how the optical resonance of the structure is influenced by variations in geometry. As can be seen, while the ED mode is very sensitive to the change in the diameter, the MD mode is rather stationary. Fig. 6B presents the simulated transmission spectra under the same conditions, providing a comparison with the measured data.

[0215] The close agreement between the measured and simulated results validates the accuracy of the simulation model, allowing for further insights into the behavior of the metasurface.

[0216] As shown in Fig. 6C, the normalized magnetic field (|H| / |H0|) is concentrated at the lower part of the disk at a wavelength of 700nm for a disk diameter of 290nm. This behavior indicates the formation of a magnetic dipole, which is characterized by the strong confinement of the magnetic field and the loop-like current flow within the structure. Panel d shows the normalized electric field (|E| / |E0|) at a wavelength of 800 nm for a disk diameter of 290 nm. The enhanced electric fields are localized inside the disk, forming a dipole-like distribution.

[0217] Figure 7A is a schematic of the home-built microscope, and Figure 7B is a schematic of the optical setup of the steady-state and the transient measurements.

[0218] The experimental setup used for spectral, Raman, and transient measurements is a custom built system specifically designed to provide precise control and detailed observation of metasurface samples. It integrates multiple components to facilitate the analysis of the optical properties of the metasurfaces. The setup includes a high-resolution microscopy section that utilizes a high numerical aperture (NA 0.8) 100x objective lens, which, combined with a CMOS camera, enables visualization of the sample surface. To ensure consistent illumination during transmission measurements, a halogen lamp (OSL2IR-Thorlabs) is employed, providing stable and controllable lighting conditions. P4298PC00

[0219] For spectral measurements, the system is equipped with an Andor Shamrock 750 spectrometer, paired with an iDus 420 CCD camera, allowing for high-resolution (down to 0.05 nm in spectrum) capture of transmission spectra. To achieve enhanced spectral resolution, a high line number grating is used in the spectrometer, making it possible to detect even subtle shifts in the Raman spectra, which are critical for analyzing changes in the optical properties of the metasurface.

[0220] The experimental setup also features a 488 nm OBIS LX laser that is the primary pump source for most of the experiments, including Raman, steady-state and transient transmission measurements. This laser can digitally modulate up to 150 MHz, providing precise control over the excitation conditions. Additionally, a 785 nm CW laser is integrated into the system, allowing for non-degenerate measurements that help explore the metasurface’s behavior under different excitation wavelengths. During steady state and transient measurements, the 488 nm laser is used with a series of notch filters (NF488-15-Thorlabs) to remove any unwanted pump light, ensuring the accuracy of the recorded spectral data.

[0221] Transient transmission measurements, as illustrated in Figures 4 and 5A, are performed using a time-correlated single photon counting (TCSPC) system. This system, based on a PicoQuant Hydraharp 400 unit coupled with a silicon single-photon avalanche diode (Si SPAD), provides a time resolution of approximately 20 ps, making it ideal for capturing rapid changes in transmission. The 488 nm laser is modulated at 50 kHz using a square wave trigger signal, which synchronizes the laser pulses with the TCSPC module, allowing for precise timing during transient measurements. Narrow bandwidth bandpass filters, 3nm FWHM, (2xNF488-15, FBH808-3, FBH785-3 / Thorlabs) are employed to isolate specific spectral regions of the transmitted white light, enabling targeted analysis of changes in transmission at selected wavelengths.

[0222] The experimental setup, as shown in Figure 7B, includes detailed arrangements of components such as the laser input, the microscope section, and the collection system. It shows the excitation and detection aperture which we used for the experiments in Figure 4A. During this experiment, the excitation and detection aperture co-centered on the sample plane. While the Inventors keep the detection aperture at about 1.5 pm size on the image plane, the Inventors changed the excitation aperture from about 1.5 pm to about 4.5 pm, gradually. It also shows how light is directed through the microscope and into either the spectrometer or the SPAD detector, depending on the type of measurement being conducted. Figure 5B further details the arrangement used for transient measurements, emphasizing the integration of the TCSPC system and the various filters used for precise spectral analysis. This setup allows for P4298PC00

[0223] an in-depth investigation of the thermo-optical properties of the metasurfaces under both steady-state and transient conditions. By combining high-resolution spectral tools with timecorrelation measurements, the system enables comprehensive studies of the dynamic responses of metasurfaces to changes in pump intensity and wavelength. This setup is particularly valuable for exploring the unique behaviors induced by thermo-optical nonlinearity, offering insights into the rapid modulation capabilities of a-Si metasurfaces.

[0224] Figures 8A and 8B show the results of Raman spectroscopy conducted on amorphous silicon (a-Si) metasurfaces under different experimental conditions. In Figure 8A, Raman spectra are presented for the metasurface subjected to various pump intensities, ranging from 30 μW / μm2to 5 mW / μm2, with corresponding local temperatures from approximately 20°C to 460°C. As the pump intensity increases, the temperature of the metasurface rises, affecting the Raman spectral features. These spectra reveal the broad nature of the phonon modes in a-Si, which is typical due to the amorphous structure of the material. The most prominent feature is the transverse optical (TO) phonon mode around 470 cm-1, which is indicative of the a-Si’s phonon behavior.

[0225] Figure 8B displays a Gaussian deconvolution of the Raman spectrum for a thin a-Si film, identifying several key phonon modes. These include the longitudinal acoustic (LA) mode at 312 cm-1, the longitudinal optical (LO) mode at 380 cm-1, and the TO mode at 470 cm-1, along with second-order modes such as 2LA at 561 cm-1and 2TO at 798 cm-1. This deconvolution allows for a more precise understanding of the contributions of various phonon modes to the overall Raman spectrum of a-Si. Note that the literature indicates that the intensity ratio between the TA and TO modes, the full width at half maximum of the modes, and their central wavenumber are influenced by factors such as the growth method, growth temperature, doping levels, and hydrogen content.

[0226] Raman spectroscopy in this study serves as a method for determining the local temperature of the a-Si metasurface, adapted from techniques used for crystalline silicon (c-Si). Unlike c-Si, a-Si’s Raman spectrum is more complex due to the disordered structure, resulting in broader peaks. The TO mode, which is the most pronounced at around 470 cm-1, is central to these temperature measurements. To accurately quantify the temperature, the researchers used a Gaussian fitting method to determine the center and amplitude of the TO mode peak. They then employed a temperature calculation model based on the intensity ratio of Stokes and anti-Stokes Raman signals [3]. The relationship is described by the formula P4298PC00

[0227]

[0228] IA / IS= exp(ℏωp / kBT)

[0229] where IA and Is are the intensities of the anti-Stokes and Stokes signals, h is the reduced Planck constant, copis the phonon frequency, 470 cm-1, ks is the Boltzmann constant, and T is the temperature in Kelvin. This method provides a direct and precise way to monitor temperature changes in the metasurface as a function of applied pump power, enabling the study of thermo-optical effects in a-Si metasurfaces.

[0230] Figure 9A to 9F provide a detailed analysis of the thermo-optic behavior of crystalline silicon (c-Si) across a range of temperatures and wavelengths, as well as the extrapolation of optical properties to higher temperatures (up to 450°C). This analysis is critical for understanding the temperature dependence of optical constants, which is essential for applications in optics, photonics, and materials science.

[0231] In this analysis, the Inventors use the measured values of n and k at 20°C, 100°C, 150°C, 200°C, and 250°C by Vuye et al. [Reference 63] (Fig. 9A and 9B, respectively). The thermo-optical coefficients were computed for each temperature separation (e.g., 20°C to 100°C, 100°C to 150°C), providing insight into the thermal sensitivity of the material’s optical properties over different intervals (Figures 9C and 9D). Additionally, average thermo-optic coefficients were calculated across all separations, generalizing how n and k vary with temperature.

[0232] As can be seen in Figures 9C and 9D, the thermo-optical coefficients of c-Si do not differentiate between the different temperature ranges and are pretty close to the average thermo-optical coefficient. Therefore, to estimate the optical properties at 450°C, the Inventors employ the approach using the average thermo-optic coefficient to linearly extrapolate the higher temperatures n and k values. The Inventors predict n and k at 450°C starting from their values at 20°C. These calculated values are then compared with the actual measured data at 450°C, allowing us to assess the accuracy and reliability of the prediction (Figures 9E and 9F). The comparison between predicted and measured values at 450°C showed the effectiveness of using average-based thermo-optic coefficients for high-temperature predictions. This analysis demonstrates the utility of using thermo-optic coefficients for predicting high-temperature optical behavior when direct measurements are not available. P4298PC00

[0233] Later, the Inventors applied the same approach to compute the n an k values of a-Si at elevated temperatures. To achieve this, the Inventors first computed the average thermo-optical coefficients, which are dn / dK and dk / dK, as can be seen in Figures 10A and 10B, respectively. These coefficients were derived from measurements of n and k at various temperatures (20°C, 70°C, 120°C, 170°C, and 220°C) and wavelengths, as shown in Figures 10C and 10D, respectively. Using these coefficients, we extrapolated the optical constants to higher temperatures, up to 600°C, starting from the measured values at lower temperatures. This comprehensive dataset provides a detailed view of how the refractive index and extinction coefficient change over a broad temperature range, thus enabling better modeling and design of optical systems that operate in varying thermal environments.

[0234] Figure 11 shows how the transmission varies as a function of the normalized pump intensity for off-resonance (resonance center of 770nm and pump wavelength of 488nm) and near resonance (resonance center of 770nm and pump wavelength of 785nm) excitations. The Inventors are confident that both curves reach approximately the same temperature (around 450°C) at their peak transmissions, as they are nearly identical at this point. By normalizing the x-axis of each curve to its respective range, one can directly compare the evolution of transmission relative to the percentage change in normalized power. This approach enables to observe how transmission varies as the system approaches the same final temperature across both cases. Notably, the data reveals different trends for the two excitation wavelengths, reflecting the distinct interactions of each wavelength with the metasurface’s resonant properties. In particular, at 785 nm, the amount of absorbed power depends on the shift of the resonance itself.

[0235] The word “about” as used herein means the identified value plus / minus 5%.

[0236] While the invention has been disclosed with reference to certain preferred embodiments, numerous modifications, alterations, and changes to the described embodiments, and equivalents thereof, are possible without departing from the scope of the invention. Accordingly, it is intended that the invention not be limited to the described embodiments, and be given the broadest reasonable interpretation in accordance with the language of the appended claims. P4298PC00

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[0317] The disclosure of each one of the above references is hereby incorporated herein by reference in its entirety for all purposes.

Claims

P4298PC00CLAIMS1. Optical modulation method including:- providing at least one optical modulation device (3) configured for modulating at least one optical electromagnetic wave (9) provided to and transmitted through the at least one optical modulation device (3);the at least one optical modulation device (3) including at least one support substrate and / or layer (11) supporting an amorphous silicon metasurface (15), the amorphous silicon metasurface (15) comprising an array of nano-disks (17) configured to generate at least one magnetic dipole Mie resonance having a magnetic dipole resonance wavelength ( MD) producing a magnetic dipole resonance dip in the transmission spectrum of the at least one optical modulation device (3) and configured to generate at least one electric dipole Mie resonance having an electric dipole resonance wavelength ( ED) producing an electric dipole resonance dip in the transmission spectrum;- providing the at least one optical signal electromagnetic wave (9) from at least one first light source (5) to the at least one optical modulation device (3), the at least one optical signal electromagnetic wave (9) having at least one operation wavelength ( o) to be modulated by the at least one optical modulation device (3),wherein the at least one operation wavelength ( o) to be modulated includes at least one of: the electric dipole resonance wavelength ( ED),the magnetic dipole resonance wavelength ( MD),a wavelength ( oL) longer than the electric dipole resonance wavelength ( ED),a wavelength ( oL) longer than the magnetic dipole resonance wavelength ( MD), a wavelength ( os) shorter than the electric dipole resonance wavelength ( ED), and a wavelength ( os) shorter than the magnetic dipole resonance wavelength ( MD);- providing a photo-excitation electromagnetic wave (19) from the at least one first light source (5) or from at least one second optical source (7) to the at least one optical modulation device (3) at a pump light intensity to displace in wavelength the magnetic and electric dipole resonance wavelengths ( ED, MD) and the resonance dips in the transmission spectrum to optically modulate the transmitted intensity of the at least one optical signal electromagnetic wave (9) at the at least one operation wavelength ( o).P4298PC002. The method according to claim 1, wherein the at least one first light source (5) provides the at least one optical signal electromagnetic wave (9) and the photo-excitation electromagnetic wave (19), and the at least one optical signal electromagnetic wave (9) and the photoexcitation electromagnetic wave (19) have the same wavelength to permit single-wavelength or single-band operation.

3. The method according to claim 1, wherein the at least one first light source (5) provides the at least one optical signal electromagnetic wave (9), and the at least one second light source (7) provides the photo-excitation electromagnetic wave (19), wherein the at least one optical signal electromagnetic wave (9) and the photo-excitation electromagnetic wave (19) have different wavelengths to permit dual-wavelength or dual-band operation.

4. The method according to any one of the previous claims, wherein the pump light intensity of the photo-excitation electromagnetic wave displaces in wavelength the magnetic and electric dipole resonance wavelengths ( ED, MD) and the resonance dips in the transmission spectrum by photothermal heating displacement of the at least one magnetic dipole (MD) Mie resonance and / or of the at least one electric dipole (ED) Mie resonance.

5. The method according to any one of the previous claims, wherein the at least one optical signal electromagnetic wave (9) has an operation wavelength ( o) at a wavelength ( os) shorter than the electric dipole resonance wavelength ( ED) to provide a monotonic and nonlinear change in the transmitted intensity of the at least one optical signal electromagnetic wave (9) at the at least one operation wavelength ( o).

6. The method according to any one of the previous claims 1 to 4, wherein the at least one optical signal electromagnetic wave (9) has an operation wavelength ( o) at a wavelength ( os) shorter than the magnetic dipole resonance wavelength ( MD) to provide a monotonic and non-linear change in the transmitted intensity of the at least one optical signal electromagnetic wave (9) at the at least one operation wavelength ( o).

7. The method according to any one of the previous claims 1 to 4, wherein the at least one optical signal electromagnetic wave (9) has an operation wavelength ( o) at the electric dipole resonance wavelength ( ED) to provide a monotonic and non-linear change in the transmitted intensity of the at least one optical signal electromagnetic wave (9) at the at least one operation wavelength ( o).P4298PC008. The method according to any one of the previous claims 1 to 4, wherein the at least one optical signal electromagnetic wave (9) has an operation wavelength ( o) at the magnetic dipole resonance wavelength ( MD) to provide a monotonic and non-linear change in the transmitted intensity of the at least one optical signal electromagnetic wave (9) at the at least one operation wavelength ( o).

9. The method according to any one of the previous claims 1 to 4, wherein the at least one optical signal electromagnetic wave (9) has an operation wavelength ( o) at a wavelength ( oL) longer than the electric dipole resonance wavelength ( ED) to provide a non-monotonic and non-linear change in the transmitted intensity of the at least one optical signal electromagnetic wave (9) at the at least one operation wavelength ( o).

10. The method according to the previous claim, wherein the pump light intensity displaces the at least one electric dipole Mie resonance by photothermal heating to longer wavelengths and across the at least one operation wavelength ( o) to provide the non-monotonic change and non-linear in the transmitted intensity of the at least one optical signal electromagnetic wave (9) at the at least one operation wavelength ( o).

11. The method according to any one of the previous claims 1 to 4, wherein the at least one optical signal electromagnetic wave (9) has an operation wavelength ( o) at a wavelength ( oL) longer than the magnetic dipole resonance wavelength ( ED) to provide a nonmonotonic and non-linear change in the transmitted intensity of the at least one optical signal electromagnetic wave (9) at the at least one operation wavelength ( o).

12. The method according to the previous claim, wherein the pump light intensity displaces the at least one magnetic dipole Mie resonance by photothermal heating to longer wavelengths and across the at least one operation wavelength ( o) to provide the nonmonotonic change and non-linear in the transmitted intensity of the at least one optical signal electromagnetic wave (9) at the at least one operation wavelength ( o).

13. The method according to any one of the previous claims, wherein the photo-excitation electromagnetic wave (19) is a modulated photo-excitation electromagnetic wave having a modulation frequency and modulation cycle, wherein the pump light is provided during a first time duration of the modulation cycle and non-provided during a second time duration of the modulation cycle.P4298PC0014. The method according to the previous claim, wherein the modulated photo-excitation electromagnetic wave (19) is provided to the at least one optical modulation device (3) with a beam diameter, width or area that decouples a thermal response time for a temperature change from an optical response time for an optical transmission change of the of the at least one optical modulation device (3) to provide a non-linear thermo-optical response of the at least one optical modulation device (3) to permit faster optical modulation by the at least one optical modulation device (3).

15. The method according to any one of the previous claims, wherein the photo-excitation electromagnetic wave or modulated photo-excitation electromagnetic wave (19) is provided to the at least one optical modulation device (3) with a beam diameter or width less than 2.25 microns.

16. The method according to any one of the previous claims 13 to 15, wherein the modulated photo-excitation electromagnetic wave is provided to the at least one optical modulation device (3) with a pump light intensity that decouples a thermal response time for a temperature change from an optical response time for an optical transmission change of the at least one optical modulation device (3) to provide a thermo-optical non-linear response of the at least one optical modulation device (3) to permit faster optical modulation by the at least one optical modulation device (3).

17. The method according to any one of the previous claims, wherein the photo-excitation electromagnetic wave (19) or the modulated photo-excitation electromagnetic wave is provided to the at least one optical modulation device (3) with a pump light intensity greater than 1.1 mW per square micron.

18. The method according to the previous claim 9 or 10, wherein the photo-excitation electromagnetic wave (19) is a modulated photo-excitation electromagnetic wave having a modulation frequency and modulation cycle, wherein the pump light is provided during a first time duration of the modulation cycle and non-provided during a second time duration of the modulation cycle, andthe modulated photo-excitation electromagnetic wave is provided to the at least one optical modulation device (3) with a pump light intensity that, during the first time duration of the modulation cycle, displaces in wavelength the at least one electric dipole Mie resonance to longer wavelengths and across the at least one operation wavelength ( o) to a longer wavelength than the at least one operation wavelength ( o); and that, during the second timeP4298PC00duration of the modulation cycle, displaces in wavelength the at least one electric dipole Mie resonance to shorter wavelengths and across the at least one operation wavelength ( o) to a shorter wavelength than the at least one operation wavelength ( o) to modulate the transmitted intensity of the at least one optical signal electromagnetic wave (9) at the at least one operation wavelength ( o) at a higher frequency than a modulation frequency of the modulated photo-excitation electromagnetic wave (19).

19. The method according to the previous claim, wherein the modulated photo-excitation electromagnetic wave (19) is provided by modulating a light output frequency of the at least one first light source (5) or the least one second optical source (7).

20. The method according to the previous claim 11 or 12, wherein the photo-excitation electromagnetic wave (19) is a modulated photo-excitation electromagnetic wave having a modulation frequency and modulation cycle, wherein the pump light is provided during a first time duration of the modulation cycle and non-provided during a second time duration of the modulation cycle, andthe modulated photo-excitation electromagnetic wave is provided to the at least one optical modulation device (3) with a pump light intensity that, during the first time duration of the modulation cycle, displaces in wavelength the at least one magnetic dipole Mie resonance to longer wavelengths and across the at least one operation wavelength ( o) to a longer wavelength than the at least one operation wavelength ( o); and that, during the second time duration of the modulation cycle, displaces in wavelength the at least one magnetic dipole Mie resonance to shorter wavelengths and across the at least one operation wavelength ( o) to a shorter wavelength than the at least one operation wavelength ( o) to modulate the transmitted intensity of the at least one optical signal electromagnetic wave (9) at the at least one operation wavelength ( o) at a higher frequency than a modulation frequency of the modulated photo-excitation electromagnetic wave (19).

21. The method according to any one of the previous claims 6 to 20, wherein the photoexcitation electromagnetic wave (19) is a modulated photo-excitation electromagnetic wave having a modulation frequency and modulation cycle, wherein the pump light is provided for heating during a first time duration of the modulation cycle and non-provided for cooling during a second time duration of the modulation cycle, andwherein the first time duration of the modulation cycle is less than the second time duration of the modulation cycle to decouple the heating duration and the cooling duration of the amorphous silicon nano-disks (17) and / or the metasurface (15) to increase the opticalP4298PC00modulation rate of the transmitted intensity of the at least one optical signal electromagnetic wave (9) at the at least one operation wavelength ( o) compared to a modulation cycle having equal first and second time durations.

22. The method according to the previous claim, wherein the second time duration of the modulation cycle corresponds to a cooling duration of the amorphous silicon nano-disks (17) and / or the metasurface (15) that displaces in wavelength the at least one electric dipole Mie resonance or magnetic dipole Mie resonance to shorter wavelengths and across the at least one operation wavelength ( o) to a shorter wavelength than the at least one operation wavelength ( o).

23. The method according to the previous claim 21, wherein the second time duration of the modulation cycle corresponds to a cooling duration of the amorphous silicon nano-disks (17) and / or the metasurface (15) that displaces in wavelength the at least one electric dipole Mie resonance or magnetic dipole Mie to shorter wavelengths and to the at least one operation wavelength ( o) located at the electric dipole resonance wavelength ( ED).

24. The method according to any one of the previous claims 21 to 23, wherein the photoexcitation electromagnetic wave (19) has a wavelength at which light absorption by the amorphous silicon nano-disks (17) and / or the metasurface (15) minimizes a ratio of the first time duration to second time duration to permit flash heating of the amorphous silicon nanodisks (17) and / or the metasurface (15) and increase the optical modulation rate.

25. The method according to any one of the previous claims, wherein the amorphous silicon metasurface (15) and the array of nano-disks (17) are configured to provide near unity light absorption at a wavelength of the photo-excitation electromagnetic wave (19).

26. The method according to any one of the previous claims, wherein the at least one electric dipole Mie resonance generated by the array of nano-disks (17) is an electric dipole formed by an electric field confinement and / or enhancement inside the nano-disks (17) of the amorphous silicon metasurface (15), and the at least one magnetic dipole Mie resonance generated by the array of nano-disks (17) is a magnetic dipole formed by a magnetic field confinement and / or enhancement inside the nano-disks (17) of the amorphous silicon metasurface (15).P4298PC0027. The method according to any one of the previous claims, wherein the array of nano-disks (17) includes a plurality of nano-disks (17), wherein each nano-disk (17) has a diameter and / or width that is sub-wavelength at the at least one operation wavelength ( o).

28. The method according to any one of the previous claims, wherein the array of nano-disks (17) includes a plurality of nano-disks (17), wherein each nano-disk (17) has a diameter and / or width between 200nm and 300nm to provide at least one magnetic dipole Mie resonance and at least one electric dipole Mie resonance in the wavelength range of 500nm to 900nm.

29. The method according to any one of the previous claims, wherein the array of nano-disks (17) includes a plurality of nanopillars (PL) extending from the at least one support substrate and / or layer (11), wherein each nanopillar (PL) includes at least one nano-disk (17).

30. The method according to the previous claim, wherein each nano-pillar (PL) extends a distance from the at least one support substrate and / or layer (11) that is sub-wavelength at the at least one operation wavelength ( o).

31. The method according to any one of the previous claims, wherein the nano-disks (17) are periodically arranged on the at least one optical modulation device (3).

32. The method according to the previous claim, wherein the periodic separation of the nanodisks (17) is sub-wavelength at the at least one operation wavelength ( o).

33. The method according to any one of the previous claims, wherein the at least one optical modulation device (3) includes the at least one support substrate and / or layer (11) that comprises silicon oxide, and a plurality of nano-pillars (PL) extending from the at least one support substrate and / or layer (11), wherein each nanopillar (PL) includes at least one nanodisk (17), and each nanopillar (PL) and each nano-disk (17) comprises amorphous silicon.

34. The method according to any one of claims 1 to 10, wherein the photo-excitation electromagnetic wave is changed from a first pump light intensity value to a second pump light intensity value different to the first pump light intensity value to displace in wavelength the magnetic and electric dipole resonance wavelengths and the resonance dips to optically modulate the transmitted intensity of the at least one optical signal electromagnetic wave (9) at the at least one operation wavelength ( o).P4298PC0035. Optical modulation system (1) including:- at least one optical modulation device (3) configured to modulate at least one optical signal electromagnetic wave (9) provided to and transmitted through the at least one optical modulation device (3);the at least one optical modulation device (3) including at least one support substrate and / or layer (11) supporting an amorphous silicon metasurface (15), the amorphous silicon metasurface (15) comprising an array of nano-disks (17) configured to generate at least one magnetic dipole Mie resonance having a magnetic dipole resonance wavelength ( MD) producing a magnetic dipole resonance dip in a transmission spectrum of the at least one optical modulation device (3) and configured to generate at least one electric dipole Mie resonance having an electric dipole resonance wavelength ( ED) producing an electric dipole resonance dip in the transmission spectrum; and- a first light source (5) configured to generate and provide the at least one optical signal electromagnetic wave (9), the at least one optical signal electromagnetic wave (9) having at least one operation wavelength ( o) to be modulated by the at least one optical modulation device (3), and the first light source (5) is configured to generate and provide a photo-excitation electromagnetic wave (19) for provision to the at least one optical modulation device (3) at a pump light intensity value to displace in wavelength the magnetic and / or electric dipole resonance wavelengths ( MD, ED) and the resonance dips to optically modulate the transmitted intensity of the at least one optical signal electromagnetic wave (9) at the at least one operation wavelength ( o), wherein the at least one optical signal electromagnetic wave (9) and the photo-excitation electromagnetic wave (19) have the same wavelength to permit single-wavelength or single-band operation;or- a first light source (5) configured to generate and provide the at least one optical signal electromagnetic wave (9), the at least one optical signal electromagnetic wave (9) having at least one operation wavelength ( o) to be modulated by the at least one optical modulation device (3), and a second light source (7) configured to generate and provide a photo-excitation electromagnetic wave (19) for provision to the at least one optical modulation device (3) at a pump light intensity value to displace in wavelength the magnetic and electric dipole resonance wavelengths ( MD, ED) and the resonance dips to optically modulate the transmitted intensity of the at least one optical signal electromagnetic wave (9) at the at least one operation wavelength ( o), wherein the at least one optical signal electromagnetic waveP4298PC00(9) and the photo-excitation electromagnetic wave (19) have different wavelengths to permit dual-wavelength or dual-band operation;wherein the at least one operation wavelength ( o) to be modulated includes at least one of: the electric dipole resonance wavelength ( ED),the magnetic dipole resonance wavelength ( MD),a wavelength ( oL) longer than the electric dipole resonance wavelength ( ED),a wavelength ( oL) longer than the magnetic dipole resonance wavelength ( MD), a wavelength ( os) shorter than the electric dipole resonance wavelength ( ED), and a wavelength ( os) shorter than the magnetic dipole resonance wavelength ( MD).

36. The optical modulation system (1) according to the previous claim, wherein the pump light intensity of the photo-excitation electromagnetic wave displaces in wavelength the magnetic and electric dipole resonance wavelengths ( MD, ED) and the resonance dips in the transmission spectrum by photothermal heating displacement of the at least one magnetic dipole Mie resonance and / or of the at least one electric dipole Mie resonance.

37. The optical modulation system (1) according to any one of the previous claims 35 or 36, wherein the at least one optical signal electromagnetic wave (9) having the at least one operation wavelength ( o) at a wavelength ( os) shorter than the electric dipole resonance wavelength ( ED) permits to provide a monotonic and non-linear change in the transmitted intensity of the at least one optical signal electromagnetic wave (9) at the at least one operation wavelength ( o).

38. The optical modulation system (1) according to any one of the previous claims 35 to 36, wherein the at least one optical signal electromagnetic wave (9) having an operation wavelength ( o) at a wavelength ( os) shorter than the magnetic dipole resonance wavelength ( MD) permits to provide a monotonic and non-linear change in the transmitted intensity of the at least one optical signal electromagnetic wave (9) at the at least one operation wavelength ( o).

39. The optical modulation system (1) according to any one of the previous claims 35 to 36, wherein the at least one optical signal electromagnetic wave (9) having the at least one operation wavelength ( o) at the electric dipole resonance wavelength ( ED) permits to provide a monotonic and non-linear change in the transmitted intensity of the at least one optical signal electromagnetic wave (9) at the at least one operation wavelength ( o).P4298PC0040. The optical modulation system (1) according to any one of the previous claims 35 to 36, wherein the at least one optical signal electromagnetic wave (9) having an operation wavelength ( o) at the magnetic dipole resonance wavelength ( MD) permits to provide a monotonic and non-linear change in the transmitted intensity of the at least one optical signal electromagnetic wave (9) at the at least one operation wavelength ( o).

41. The optical modulation system (1) according to any one of the previous claims 35 to 36, wherein the at least one optical signal electromagnetic wave (9) having the at least one operation wavelength ( o) at a wavelength ( oL) longer than the electric dipole resonance wavelength ( ED) permits to provide a non-monotonic and non-linear change in the transmitted intensity of the at least one optical signal electromagnetic wave (9) at the at least one operation wavelength ( o).

42. The optical modulation system (1) according to the previous claim, wherein the pump light intensity displaces the at least one electric dipole Mie resonance by photothermal heating to longer wavelengths and across the at least one operation wavelength ( o) to provide the nonmonotonic change in the transmitted intensity of the at least one optical signal electromagnetic wave (9) at the at least one operation wavelength ( o).

43. The optical modulation system (1) according to any one of the previous claims 35 to 36, wherein the at least one optical signal electromagnetic wave (9) having an operation wavelength ( o) at a wavelength ( oL) longer than the magnetic dipole resonance wavelength ( ED) permits to provide a non-monotonic and non-linear change in the transmitted intensity of the at least one optical signal electromagnetic wave (9) at the at least one operation wavelength ( o).

44. The method according to the previous claim, wherein the pump light intensity displaces the at least one magnetic dipole Mie resonance by photothermal heating to longer wavelengths and across the at least one operation wavelength ( o) to provide the nonmonotonic change and non-linear in the transmitted intensity of the at least one optical signal electromagnetic wave (9) at the at least one operation wavelength ( o).

45. The optical modulation system (1) according to any one of the previous claims 35 to 44, including at least one light source modulation device (25) configured to modulate the photoexcitation electromagnetic wave, the modulated photo-excitation electromagnetic wave havingP4298PC00a modulation frequency and a modulation cycle, wherein the pump light is provided during a first time duration of the modulation cycle and non-provided during a second time duration of the modulation cycle.

46. The optical modulation system (1) according to any one of the previous claims 35 to 45, including beam diameter, width or area determination means (23) configured to set and / or determine a beam diameter, width or area of the photo-excitation electromagnetic wave (19) to be provided to the at least one optical modulation device (3) to decouple a thermal response time for a temperature change from an optical response time for an optical transmission change of the of the at least one optical modulation device (3) to provide a non-linear thermo-optical response of the at least one optical modulation device (3) to permit faster optical modulation by the at least one optical modulation device.

47. The optical modulation system (1) according to the previous claim, wherein the beam diameter, width or area determination means (23) is configured to provide the photo-excitation electromagnetic wave (19) with a beam diameter or width less than 2.25 microns.

48. The optical modulation system (1) according to any one of the previous claims 35 to 47, including pump light intensity determination means (21) configured to determine or set a light intensity of the photo-excitation electromagnetic wave (19) to be provided to the at least one optical modulation device (3) to decouple a thermal response time for a temperature change from an optical response time for an optical transmission change of the at least one optical modulation device (3) to provide a thermo-optical non-linear response of the at least one optical modulation device (3) to permit faster optical modulation by the at least one optical modulation device (3).

49. The optical modulation system (1) according to the previous claim, wherein the pump light intensity determination means (21) is included in the first or second light source (5,7) to set the light intensity outputted by the first or second light source (5,7); and / or is located externally to the first or second light source (5,7) to modify the light intensity outputted by the first or second light source (5,7).

50. The optical modulation system (1) according to the previous claim 48 or 49, wherein the pump light intensity determination means (21) is configured to provide the photo-excitation electromagnetic wave (19) with a pump light intensity greater than 1,1mW per square micron.P4298PC0051. The optical modulation system (1) according to the previous claim 48 to 50, wherein the pump light intensity determination means (21) is configured to change a first pump light intensity value of the photo-excitation electromagnetic wave (19) to a second pump light intensity value different to the first pump light intensity value to displace in wavelength the magnetic and electric dipole resonance wavelengths ( MD, ED) and the resonance dips to optically modulate the transmitted intensity of the at least one optical signal electromagnetic wave (19) at the at least one operation wavelength ( o).

52. The optical modulation system (1) according to any one of the previous claims 45 to 51, wherein the at least one light source modulation device (25) is configured to provide the modulated photo-excitation electromagnetic wave having a modulation frequency and a modulation cycle, and to provide the pump light during a first time duration of the modulation cycle and not provide the pump light during a second time duration of the modulation cycle, and the pump light intensity determination means (21) is configured to provide the modulated photo-excitation electromagnetic wave (19) with a pump light intensity that, during the first time duration of the modulation cycle, displaces in wavelength the at least one electric dipole Mie resonance to longer wavelengths and across the at least one operation wavelength ( o) to a longer wavelength than the at least one operation wavelength ( o); and that, during the second time duration of the modulation cycle, displaces in wavelength the at least one electric dipole Mie resonance to shorter wavelengths and across the at least one operation wavelength ( o) to a shorter wavelength than the at least one operation wavelength ( o) to modulate the transmitted intensity of the at least one optical signal electromagnetic wave (9) at the at least one operation wavelength ( o) at a higher frequency than a modulation frequency of the modulated photo-excitation electromagnetic wave (19).

53. The optical modulation system (1) according to any one of the previous claims 45 to 51, wherein the at least one light source modulation device (25) is configured to provide the modulated photo-excitation electromagnetic wave having a modulation frequency and a modulation cycle, and to provide the pump light during a first time duration of the modulation cycle and not provide the pump light during a second time duration of the modulation cycle, and the pump light intensity determination means (21) is configured to provide the modulated photo-excitation electromagnetic wave (19) with a pump light intensity that, during the first time duration of the modulation cycle, displaces in wavelength the at least one magnetic dipole Mie resonance to longer wavelengths and across the at least one operation wavelength ( o) to a longer wavelength than the at least one operation wavelength ( o); and that, during the second time duration of the modulation cycle, displaces in wavelength the at least oneP4298PC00magnetic dipole Mie resonance to shorter wavelengths and across the at least one operation wavelength ( o) to a shorter wavelength than the at least one operation wavelength ( o) to modulate the transmitted intensity of the at least one optical signal electromagnetic wave (9) at the at least one operation wavelength ( o) at a higher frequency than a modulation frequency of the modulated photo-excitation electromagnetic wave (19).

54. The optical modulation system (1) according to any one of the previous claims 45 to 53, wherein the at least one light source modulation device (25) is configured to set the first time duration of the modulation cycle to be less than the second time duration of the modulation cycle to decouple the heating duration and the cooling duration of the amorphous silicon nanodisks (17) and / or the metasurface (15) to increase the optical modulation rate of the transmitted intensity of the at least one optical signal electromagnetic wave (9) at the at least one operation wavelength ( o) compared to a modulation cycle having equal first and second time durations.

55. The optical modulation system (1) according to the previous claim, wherein the second time duration of the modulation cycle corresponds to a cooling duration of the amorphous silicon nano-disks (17) and / or the metasurface (15) that displaces in wavelength the at least one electric or magnetic dipole Mie resonance to shorter wavelengths and across the at least one operation wavelength ( o) to a shorter wavelength than the at least one operation wavelength ( o).

56. The optical modulation system (1) according to claim 54, wherein the second time duration of the modulation cycle corresponds to a cooling duration of the amorphous silicon nano-disks (17) and / or the metasurface (15) that displaces in wavelength the at least one electric or magnetic dipole Mie resonance to shorter wavelengths and to the at least one operation wavelength ( o) located at the electric or magnetic dipole resonance wavelength ( ED).

57. The optical modulation system (1) according to any one of the previous claims 52 to 56, wherein the photo-excitation electromagnetic wave (19) has a wavelength at which light absorption by the amorphous silicon nano-disks (17) and / or the metasurface (15) minimizes a ratio of the first time duration to second time duration to permit flash heating of the amorphous silicon nano-disks (17) and / or the metasurface (15) and increase the optical modulation rate.P4298PC0058. The optical modulation system (1) according to any one of the previous claims 35 to 57, wherein the amorphous silicon metasurface (15) and the array of nano-disks (17) are configured to provide near unity light absorption at a wavelength of the photo-excitation electromagnetic wave (19).

59. The optical modulation system (1) according to any one of the previous claims 35 to 58, wherein the at least one electric dipole Mie resonance generated by the array of nano-disks (17) is an electric dipole formed by an electric field confinement and / or enhancement inside the nano-disks (17) of the amorphous silicon metasurface (15), and the at least one magnetic dipole Mie resonance generated by the array of nano-disks (17) is a magnetic dipole formed by a magnetic field confinement and / or enhancement inside the nano-disks (17) of the amorphous silicon metasurface (15).

60. The optical modulation system (1) according to any one of the previous claims 35 to 59, wherein the array of nano-disks (17) includes a plurality of nano-disks (17), wherein each nano-disk (17) has a diameter and / or width that is sub-wavelength at the at least one operation wavelength ( o).

61. The optical modulation system (1) according to any one of the previous claims 35 to 60, wherein the array of nano-disks (17) includes a plurality of nano-disks (17), wherein each nano-disk (17) has a diameter and / or width between 200nm and 300nm to provide at least one magnetic dipole Mie resonance and at least one electric dipole Mie resonance in the wavelength range of 500nm to 900nm.

62. The optical modulation system (1) according to any one of the previous claims 35 to 61, wherein the array of nano-disks (17) includes a plurality of nanopillars (PL) extending from the at least one support substrate and / or layer (11 ), wherein each nanopillar (PL) includes at least one nano-disk (17).

63. The optical modulation system (1) according to the previous claim, wherein each nanopillar (PL) extends a distance from the at least one support substrate and / or layer (11) that is sub-wavelength at the at least one operation wavelength ( o).

64. The optical modulation system (1) according to any one of the previous claims 35 to 63, wherein the nano-disks (17) are periodically arranged on the at least one optical modulation device (3).P4298PC0065. The optical modulation system (1) according to the previous claim, wherein the periodic separation of the nano-disks (17) is sub-wavelength at the at least one operation wavelength (Xo).

66. The optical modulation system (1) according to any one of the previous claims 35 to 65, wherein the at least one optical modulation device (3) includes the at least one support substrate and / or layer (11) that comprises silicon oxide, and a plurality of nano-pillars (PL) extending from the at least one support substrate and / or layer (11), wherein each nanopillar (PL) includes at least one nano-disk (17), and each nanopillar (PL) and each nano-disk (17) comprises amorphous silicon.

67. The optical modulation system (1) according to any one of the previous claims 35 to 66, wherein the amorphous silicon metasurface (15) and the array of nano-disks (17) are configured to generate first and second electric Mie resonances having first and second electric resonance wavelengths producing first and second electric resonance dips in the transmission spectrum.

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