Nonlinear components for wavefront control based on graphene nonlinear metasurfaces

Abstract

The present invention discloses a nonlinear component for wavefront control based on a graphene nonlinear metasurface. The nonlinear component comprises a plurality of periodically distributed metagratings, each comprising a metal substrate provided with a plurality of periodically distributed grooves filled with a dielectric layer, and the dielectric layer covered with periodically distributed graphene ribbons. Independent voltages are applied to the graphene ribbons to control their chemical potential, thereby achieving a nonlinear phase gradient. In the terahertz domain, the present invention provides an improved diffraction law for nonlinear wavefront control based on a graphene nonlinear phase gradient metasurface. This law can overcome the limitations of NGSL for nonlinear wavefront control. By rationally adjusting the chemical potential of graphene through applied voltage, multifunctional control of nonlinear waves, including reflection and beam steering, is achieved, thereby enabling the design of nonlinear components.

Description

Technical Field

[0001] The present invention belongs to the technical field of optical systems, and in particular relates to a nonlinear component for wavefront control based on a graphene nonlinear metasurface. Background Art

[0002] Metasurfaces, composed of engineered planar metaatoms in two-dimensional geometries, have attracted significant interest in recent decades due to their powerful ability to efficiently control the amplitude, phase, and polarization of electromagnetic waves. By designing subwavelength metaatoms, numerous metasurface-based applications have been proposed, including beam splitters, holographic imaging, superlenses, odd-even-correlated diffraction, and angularly asymmetric diffraction. Recently, the concept of metasurfaces has been extended to the nonlinear regime. It provides a paradigm for studying nonlinear optics, as it allows for the creation of stronger nonlinear optical responses at more compact scales beyond the limitations of bulk nonlinear media.

[0003] Nonlinear metasurfaces have demonstrated typical nonlinear effects such as second harmonic generation (SHG), third harmonic generation (THG), and four-wave mixing (FWM). Local field enhancement is achieved in the metasurface paradigm through various resonance mechanisms, such as surface plasmons in plasma metasurfaces, Mie resonances in high-permittivity metasurfaces, and bound states (BICs) in continuous media. Even if the thickness of the object is very thin, the interaction between light and the nonlinear metasurface can be very strong. Therefore, high conversion efficiency with low input intensity can be obtained without the need for phase matching conditions. Although a lot of efforts have been made for nonlinear metasurfaces, most of the reported work to date has focused on improving the efficiency of nonlinear light generation, and few works have studied the wavefront control of the generated nonlinear light, that is, controlling the direction of the generated nonlinear wave. Using traditional methods, it is difficult to simultaneously generate nonlinear light and control its wavefront.

[0004] Therefore, in order to solve the above technical problems, it is necessary to provide a nonlinear component based on graphene nonlinear metasurface for wavefront control. Summary of the Invention

[0005] In view of this, an object of the present invention is to provide a nonlinear component for wavefront control based on a graphene nonlinear metasurface.

[0006] In order to achieve the above-mentioned purpose, the technical solution provided by one embodiment of the present invention is as follows:

[0007] A nonlinear component for wavefront control based on a graphene nonlinear metasurface, the nonlinear component comprising a plurality of periodically distributed metagratings, the metagrating comprising a metal substrate, the metal substrate being provided with a plurality of periodically distributed grooves, the grooves being filled with a dielectric layer, the dielectric layer being covered with periodically distributed graphene ribbons, and independent voltages being applied to the graphene ribbons to control the chemical potential of the graphene ribbons, thereby achieving a nonlinear phase gradient.

[0008] In one embodiment, the material of the metal substrate is gold, and the optical properties of gold are obtained by the Drude model: where f p =2069THz, γ=17.65THz; the material of the dielectric layer is PMMA, and the dielectric constant is 2.25.

[0009] In one embodiment, the metagrating comprises m periodically distributed grooves, a dielectric layer, and a graphene ribbon, wherein the width and depth of the grooves are w and h respectively, the distance between two adjacent grooves is a, and the width of the graphene ribbon is w. g , and w g <w, the total length of the metagrating is p, p=ma, and the voltages applied to the m graphene strips are V1, V2, ..., V m , the phase difference between adjacent grooves is 2π / m.

[0010] In one embodiment, the value of m is 2-5.

[0011] In one embodiment, in the nonlinear component:

[0012] When m = 2, the phase difference between adjacent grooves is π, and the chemical potentials of the two graphene ribbons are 0.268 eV and 0.160 eV respectively;

[0013] When m = 3, the phase difference between adjacent grooves is 2π / 3, and the chemical potentials of the three graphene ribbons are 0.290 eV, 0.218 eV, and 0.120 eV, respectively;

[0014] When m = 4, the phase difference between adjacent grooves is π / 2, and the chemical potentials of the four graphene ribbons are 0.338 eV, 0.266 eV, 0.206 eV, and 0.120 eV, respectively;

[0015] When m=5, the phase difference between adjacent grooves is 2π / 5, and the chemical potentials of the five graphene ribbons are 0.444 eV, 0.340 eV, 0.278 eV, 0.212 eV and 0.120 eV, respectively.

[0016] In one embodiment, in the nonlinear component:

[0017] When m=2, the width of the groove is w=6μm, the depth of the groove is h=7μm, the distance between two adjacent grooves is a=10μm, the total length of the metagrating is 20μm, and the width of the graphene ribbon is w g =2μm;

[0018] When m=3, the width of the groove is w=5μm, the depth of the groove is h=7μm, the distance between two adjacent grooves is a=6.67μm, the total length of the metagrating is 20μm, and the width of the graphene ribbon is w g =2μm;

[0019] When m=4, the width of the groove is w=4μm, the depth of the groove is h=7μm, the distance between two adjacent grooves is a=5μm, the total length of the metagrating is 20μm, and the width of the graphene ribbon is w g =2μm;

[0020] When m=5, the width of the groove is w=3μm, the depth of the groove is h=7μm, the distance between two adjacent grooves is a=4μm, the total length of the metagrating is 20μm, and the width of the graphene ribbon is w g =2μm.

[0021] In one embodiment, the incident light of the nonlinear component is FF light, and the reflected light is THG wave.

[0022] In one embodiment, the incident angle of the incident light is θ i , the reflection angle of the reflected light is θ r , and satisfy:

[0023]

[0024] in, k0=2π / λ, n is the diffraction order, G=2π / p, q=3, and the phase gradient is

[0025] In one embodiment, the reflection angle is θ r =arsin(λ FF / 3p), λ FF is the wavelength of the incident light.

[0026] In one embodiment, the wavelength λ of the incident light FF The input intensity is 10KW / cm 2 .

[0027] In one embodiment, the incident angle θ of the incident light i Less than the critical angle θ c When the reflected light is diffracted into two diffraction orders n = 0 and n = 1, the incident angle θ of the incident light is i Greater than the critical angle θc When , the reflected light is diffracted into two diffraction orders n = 1 and n = 2.

[0028] The present invention has the following beneficial effects:

[0029] The present invention provides an improved diffraction law for nonlinear wavefront control based on a graphene-based nonlinear phase gradient metasurface in the terahertz domain, which can break through the limitations of NGSL for nonlinear wavefront control.

[0030] By rationally adjusting the chemical potential of graphene through applied voltage, multifunctional control of nonlinear waves, including reflection and beam control, is achieved, thereby realizing the design of nonlinear components. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments recorded in this application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0032] Figure 1 Schematic diagram of the structure of a metagrating (unit cell) in the nonlinear component of the present invention;

[0033] Figure 2a The optical properties (amplitude and phase) of THG waves and the chemical potential (E f ) curve graph;

[0034] Figure 2b The magnetic field distribution diagram of the reflected THG wave when m = 2;

[0035] Figure 2c The isofrequency curves of the incident angle and the reflection angle when m = 2;

[0036] Figure 2d The relationship between the incident angle and the reflection angle when m = 2;

[0037] Figure 3 The magnetic field of THG wave under different incident angles of FF light when m=2 (H y ) simulation diagram;

[0038] Figure 4a The optical properties (amplitude and phase) of THG waves and the chemical potential of graphene (E f ) curve graph;

[0039] Figure 4b The magnetic field distribution diagram of the reflected THG wave when m = 3;

[0040] Figure 4c The isofrequency curves of the incident angle and the reflection angle when m = 3;

[0041] Figure 4d The relationship between the incident angle and the reflection angle when m = 3;

[0042] Figure 5 The magnetic field of THG wave under different incident angles of FF light when m=3 (H y ) simulation diagram;

[0043] Figure 6 The diffraction efficiency curves of THG light at two diffraction orders of n=0 and n=2 when m=2, 3, 4, and 5;

[0044] Figure 7 The magnetic field of the THG wave with the incident angle of FF light of ±30° when m=3 (H y ) simulation diagram;

[0045] Figure 8 The magnetic field (H) of the THG wave with the FF light incident angle of 0° when m=1, 2, 3 y )Simulation diagram. DETAILED DESCRIPTION

[0046] In order to enable those skilled in the art to better understand the technical solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0047] Inspired by the concept of phase gradient metasurfaces (PGMs) in linear optics, PGMs in nonlinear optics have been theoretically proposed and experimentally demonstrated, which provides a feasible means for wavefront control of generated nonlinear light. Specifically, taking third harmonic generation (THG) as an example, the designed nonlinear PGMs can not only generate THG but also introduce abrupt phase shifts into THG. It can completely cover 2π. As an analogy to the linear case, nonlinear abrupt phase shifts will generate additional momentum This leads to the nonlinear generalized Snell's law (NGSL), namely:

[0048]

[0049] in, k0 = 2π / λ is the wave vector of the incident fundamental frequency (FF) in free space, The symmetry of momentum space is broken, so in order to maintain momentum conservation, the THG must bend accordingly. For example, beam control of nonlinear light is experimentally realized in nonlinear metasurfaces, or asymmetric transmission in optical nonlinear metasurfaces is experimentally observed based on NGSL. NGSL has become the cornerstone of arbitrary control of nonlinear wavefronts, but it is only applicable to FF light with an incident angle below the critical angle defined by Equation (1), with θ r =90°, that is, θ c =1-ξ / (3k0). Similar to the linear case, when the incident angle is higher than the critical angle, NGSL will not be able to predict the reflection or refraction angle of nonlinear light. Therefore, there are significant limitations to the complete control of nonlinear wavefronts.

[0050] This paper re-examines the NGSL by designing and studying graphene-based nonlinear PGMs that can produce a pronounced THG effect. Essentially, all designed nonlinear PGMs are periodic structures with spatially repeated supercells along the interface. For such structures, grating-based diffraction effects from reciprocal lattice vectors should be considered. Recent advances in linear PGMs have shown that higher-order diffraction occurs when the incident angle exceeds a critical threshold. Inspired by this advance, we will study reflective nonlinear PGMs and show that the NGSL is indeed incorrect for FFs with incident angles exceeding the critical angle. We will propose an improved diffraction law involving reciprocal lattice vectors that can fully describe the diffraction behavior of the generated nonlinear waves. This diffraction law provides more opportunities for manipulating the propagation of nonlinear light and allows one to achieve many interesting effects. To illustrate, we design a nonlinear PGM-based retroreflector that can guide the generated nonlinear light back to the original direction of the incident FF light. Furthermore, taking advantage of the tunable properties of graphene ribbons, a tunable nonlinear PGM is designed and investigated, which can guide the reflection of the generated THG in multiple directions by simply changing the periodic arrangement of the applied external voltage.

[0051] The present invention discloses a nonlinear component, comprising a plurality of periodically distributed meta-gratings. Figure 1 As shown, the metagrating includes a metal substrate 10, on which are provided a number of periodically distributed grooves, the grooves are filled with a dielectric layer 20, and the dielectric layer 20 is covered with periodically distributed graphene ribbons 30. Independent voltages are applied to the graphene ribbons to control the chemical potential of the graphene ribbons, thereby realizing a nonlinear phase gradient.

[0052] Specifically, the material of the metal substrate 10 in this embodiment is gold (Au), and its optical properties are obtained by the Drude model: where f p= 2069 THz, γ = 17.65 THz. The material of the dielectric layer 20 is PMMA, and the dielectric constant is 2.25. In order to introduce a non - linear phase shift along the phase gradient metasurface (PGM), different voltages are applied to the graphene strips 30.

[0053] Since the graphene strips 30 do not contact the metal grating, the chemical potential of the m graphene strips can be independently controlled by applying different voltages (V1, V2,..., V m )). The width and depth of the groove are w and h respectively, and the width of the graphene strip is w g < w. The distance between two adjacent grooves is a, so the period of the metagrating is p = ma.

[0054] The grooves involved in the non - linear metasurface can effectively enhance the interaction between light and graphene strips, so it is of great significance for improving the conversion efficiency of the third - harmonic and expanding the phase coverage range of the designed non - linear phase gradient. In addition, the grooves can effectively avoid the wave coupling between metagrating, so that higher - order diffraction can be easily observed in the PGM. Note that within the considered terahertz (THz) operating frequency range, only graphene is regarded as the non - linear material in this invention, because the third - order non - linear coefficients of gold and PMMA are much smaller than that of graphene and can be ignored. The linear conductivity of graphene (i.e., σ g ) can be expressed by the Drude model, where the relaxation time τ is set to 10 -13 s -1 . The designed graphene - based non - linear metasurface can be fabricated by transferring the prepared single - layer graphene strips onto the metal grating filled with PMMA. In this invention, the third - harmonic generation (THG) is taken as an example for discussion.

[0055] Considering the transverse magnetic wave (TM) polarized fundamental frequency (FF) light (i.e., only the magnetic field along the y - direction) usually incident from air to the PGM, due to photon interaction, the graphene strips immediately generate THG signals, and most of the generated non - linear light will enter the grooves except for a small amount of radiation into air. Then, the THG undergoes multiple reflections between the top and bottom of the grooves and finally reflects back into air. The phase of the THG radiated from each groove consists of three parts: (i) the cumulative phase of the THG propagating in the groove, (ii) the abrupt phase caused by the graphene layer, (iii) the additional phase of multiple reflections between the top and bottom of the groove. Therefore, the phase difference between two adjacent grooves (i.e., ) is mainly determined by the graphene strips with different chemical potentials. When When , the abrupt phase shift completely covers 2π, and a continuous THG wave can be generated. The abrupt phase shift required for THG can be obtained by designing the appropriate chemical potential of each graphene strip by applying different voltages to the graphene strips. In the metagrating, V1, V2, ..., V m Once the abrupt phase shift of the THG wave is introduced along the interface of the designed metasurface, for an angle of θ i The incident FF light, the reflection angle θ of THG r It is not determined by the NGSL equation (Equation (1)). Instead, it is determined by the following equation:

[0056]

[0057] Where G = 2π / p, n is the diffraction order, q = 3 in THG, and the phase gradient is Formula (1) corresponds to the diffraction order n = 0 in formula (1). According to formula (1), when θ i >θ c When , the reflected THG wave has no diffraction channel to radiate into free space; however, according to equation (2), the THG wave can couple to higher orders and radiate outward as a propagating wave.

[0058] In order to verify the above theory, we take the nonlinear PGM with m=2 as an example. FF = 60 μm, groove distance a = 10 μm, groove depth h = 7 μm, groove width w = 6 μm, graphene ribbon width w g = 2μm. In this case, G = 3k0, ξ = 3k0, which means that the critical angle of the n = 0 diffraction order is θ c = 0°, in order to present THG in the designed PGM, COMSOL Multiphysics was used to model the nonlinear graphene. Simulation, E FF and E TH is the electric field of the local linear FF light and the generated THG light, σ (3) is the third-order nonlinear surface conductivity of graphene. THG radiation can be obtained through simulation. During the simulation, if not stated, the intensity of the incident FF light is set to 10kW / cm 2 .

[0059] We first consider the THG from the designed PGM with the same graphene ribbon to reveal the relationship between the optical properties of the generated THG wave (including amplitude and phase) and the chemical potential of the graphene ribbon. The results are shown in Figure 2. Figure 2a As shown, the incident wave is a TM polarized plane wave. When the applied chemical potential is E f1 = 0.268eV (point B1) and E f2=0.160eV (point A1), the two units obtain a nonlinear phase difference of π, thereby achieving a sudden phase shift (2π / m) when m=2. Figure 2b The corresponding magnetic field distribution is shown, which clearly reveals the phase difference of the reflected THG waves in the two units. Using these two units, a nonlinear PGM with m = 2 can be designed.

[0060] To reveal the diffraction process, Figure 2c The isofrequency curve based on formula (2) is shown. When the incident angle is lower than the critical angle, that is, θ i <0°, the reflected THG wave is controlled by NGSL, that is, n = 0; when the incident angle exceeds the critical angle, that is, θ i >0°, the reflected THG wave will follow the diffraction order n=2. Specular reflection (n=1) always exists. In theory, the THG reflection angle of each diffraction order can be accurately calculated using formula (2). The relationship between the reflection angle of the THG wave and the incident angle is as follows: Figure 2d As shown, the simulation results (solid points) are consistent with the calculation results (solid line) based on formula (2).

[0061] In order to verify the proposed diffraction law, Figure 3 (a) to (f) show the numerical simulation magnetic field (H) of the THG wave of the FF Gaussian beam with different incident angles. y ) mode. As mentioned above, for θ i <0°, below the critical angle, the THG wave will be mainly the diffraction orders of n=0 and n=1, Figure 3 (a) to (c) are the incident angles θ i = -15°, -30°, -60°, except for the mirror reflection, the abnormal reflection or radiation of THG wave is mainly the n = 0 diffraction order in all cases, and the corresponding reflection angles are θ r =47.8°, 30°, 7.7°, the result is consistent with Figure 2d The calculation results are consistent with those in . i >0°, above the critical angle, Figure 3 (d) to (f) are the incident angles θ i =15°,θ i =30°,θ i =60°, the reflection angle of THG wave is mainly n=2 diffraction order, and the corresponding reflection angles are θ r =-47.8°, θ r =-30°,θ r =-7.7°, which is consistent with Figure 2d In addition, for specular reflection, Figure 2d The simulation results in are also in good agreement with the calculation results.

[0062] In principle, the diffraction law modified by formula (2) is applicable to the case where m is an arbitrary value. The present invention involves and demonstrates the case where m is 2 to 5, and the results obtained are almost the same, except that there are differences in the diffraction efficiency of THG in each channel (this will be discussed later). Here we take the case of m = 3 as an example. In order to maintain consistency, the phase gradient of the THG wave remains unchanged, that is, ξ = 3k0. The total length of the metagrating p = 20μm, the groove distance a = 6.67μm, the groove depth h = 7μm, the groove width w = 5μm, and the width of the graphene ribbon w g = 2μm. The phase difference between two adjacent units is 2π / 3, which can also be achieved by designing a suitable chemical potential. Figure 4a The functional relationship between the amplitude and phase of the reflected THG wave and the chemical potential of graphene when the incident FF light is normal is shown. The chemical potential corresponding to the phase difference of 2π / 3 is E f1 =0.290eV (point C2), E f2 = 0.218 eV (point B2) and E f3 =0.120eV (point A2). Figure 4b The corresponding magnetic field distributions are shown, clearly revealing the phase differences of the reflected THG waves in the three cells.

[0063] Since ξ=3k0, the critical angle of the metasurface is also θ when m=3 c =0°. For θ i <0°, the reflected THG wave will be diffracted into two diffraction orders, namely Figure 4c n=0 and n=1 in θ i >0°, the reflected THG wave is diffracted into two diffraction orders, namely Figure 4c n=1 and n=2 in . Figure 2c and Figure 4c It can be seen that the diffraction rules for m = 2 and m = 3 are the same. Therefore, the relationship between the reflection angle and the incident angle of the THG wave is the same for m = 2 and m = 3. Figure 2d and Figure 4d shown.

[0064] To verify the diffraction when m=3, Figure 5 (a) to (f) show the numerical simulation magnetic field (H) of the THG wave of the FF Gaussian beam with different incident angles when m = 3. y ) mode. For θ i <0°, below the critical angle, the THG wave will be mainly the diffraction orders of n=0 and n=1, Figure 5 (a) to (c) are the incident angles θ i = -15°, -30°, -60°, the reflected THG wave is diffracted into n = 0 and n = 1 diffraction orders, and the corresponding reflection angles are θr =47.8°, 30°, 7.7°, the result is consistent with Figure 4d The calculation results are consistent with those in . i >0°, above the critical angle, Figure 5 (d) to (f) are the incident angles θ i =15°,θ i =30°,θ i =60°, the reflected THG wave is diffracted into n=1 and n=2 diffraction orders, and the corresponding reflection angles are θ r =-47.8°, θ r =-30°,θ r =-7.7°, which is consistent with Figure 4d In addition, for specular reflection, Figure 4d The simulation results in are also in good agreement with the calculation results.

[0065] In addition, for the diffraction efficiency (ie, conversion efficiency) in each channel, especially for n=0 and n=2 diffraction orders, the diffraction efficiency is related to m. The diffraction efficiency is defined as C eff =P TH / P FF , where P FF is the input power of the incident wave, P TH is the output power of the reflected THG wave of each diffraction channel. Figure 6 (a) to (d) are the diffraction efficiencies of THG light at n = 0 and n = 2 when m = 2, 3, 4, and 5, respectively. In all cases, the input intensity of the incident FF light is 10 KW / cm 2 Where m = 2 is a special case because the designed nonlinear PGM has mirror plane symmetry. Therefore, the diffraction response of the THG light has angular symmetry for full incidence (refer to Figure 6 For m33, this mirror symmetry is broken, resulting in an angularly asymmetric response (see Figure 6 In the simulation and calculation, for m = 4, the groove distance a = 5 μm, the groove depth h = 7 μm, the groove width w = 4 μm, and the width of the graphene ribbon w g = 2 μm, in order to obtain the required nonlinear phase difference π / 2 between adjacent units, the chemical potentials of the graphene ribbons are E f1 =0.338eV, E f2 =0.266eV, E f3 =0.206eV and E f4 = 0.120 eV. For m = 5, the groove distance a = 4 μm, the groove depth h = 7 μm, the groove width w = 3 μm, and the width of the graphene ribbon w g= 2 μm, in order to obtain the required nonlinear phase difference of 2π / 5 between adjacent units, the chemical potentials of the graphene ribbons are E f1 =0.444eV, E f2 =0.340eV, E f3 =0.278eV, E f4 = 0.212eV and E f5 =0.120eV.

[0066] As m increases, the conversion efficiency of the n=2 diffraction order gradually decreases and eventually becomes small. The physical mechanism of this asymmetric THG conversion is mainly due to the multiple reflection effect in the higher-order diffraction. Note that the n=0 diffraction order is the lowest diffraction order, while n=2 is a higher order. Similar to the results in the linear PGM, the THG in the n=0 diffraction order undergoes one round trip in the groove, while for higher-order diffraction (i.e., the n=2 diffraction order), the THG undergoes multiple reflections and round trips in the groove (L=m-n+1). This means that the round trip is related to m, especially L=1 (m=2) and L=2 (m=3). Due to the ohmic losses of gold and graphene, more round trips in high-order diffraction result in more energy dissipation. Therefore, for m=2, the diffraction response is symmetrical because the round trips of the n=0 and n=2 orders are the same. For m = 3, the round trip distances are L = 1 (n = 0) and L = 2 (n = 3), respectively. Thus, the THG efficiency for waves incident above the critical angle is lower than for waves incident below the critical angle. Furthermore, the degree of asymmetric response becomes more severe as m increases.

[0067] The diffraction law proposed in this invention and the efficiency response of THG in each diffraction order provide a way to design nonlinear devices with fascinating functions. In particular, in the PGM design, the graphene used is electrically tunable, which greatly facilitates the design of tunable devices simply by changing the chemical potential of graphene. For illustration, the present invention designs a nonlinear retroreflector, which means that the reflected THG wave can be redirected back to its original direction, i.e., θ r =-θ i The function of nonlinear retroreflection is demonstrated with m=2. The geometric parameters of the designed nonlinear retroreflector are set as a=10μm, w=6μm and w g =2μm, p=λ TH = 20 μm, the nonlinear phase gradient is ξ = 3k0. According to formula (2), when the incident wave λ FF =60μm, the angle is ±30°, and nonlinear retroreflection can be achieved. In order to obtain nonlinear retroreflection, the chemical potential of the graphene ribbon is selected to be E f1 =0.268eV and E f2 = 0.160eV, to produce a nonlinear phase difference π. In order to reveal the performance of this designed nonlinear retroreflector, Figure 7(a) and (b) show the simulated reflection field of THG wave respectively. It is clear that when θ i =-30°, the reflection angle of the THG wave is θ r =30°(refer to Figure 7 (a)). Similarly, for θ i =30°, the reflection angle of THG wave is θ r =-30°(Ref. Figure 7 (b)).

[0068] In addition, by utilizing the electrically tunable properties of graphene, it is possible to design tunable devices that can control the generated THG in multiple directions simply by changing the chemical potential of graphene. Based on formula (2), for the incident FF light, the emission direction of the generated THG wave is θ r =arsin(λ FF / 3p). By adjusting the size of p, the emission direction of the generated THG can be controlled. Because the phase coverage of 2π in the entire metagrating is achieved by m units, in traditional designs, it is difficult to change the size of the metagrating once the PGM configuration is fixed. However, in this design using graphene, it becomes very convenient to simply arrange and combine different voltages applied to the graphene ribbon.

[0069] For example, the geometric parameters are selected as a=10 μm, h=7 μm, w=6 μm and w g =2μm. When the same voltage is applied to all graphene ribbons (the chemical potential of the graphene ribbon is E f =0.100eV), there is no phase gradient along the metasurface. Then, the THG wave will be reflected by following Snell’s law, i.e., θ r =θ i =0°, such as Figure 8 As shown in (a), the applied voltage has the characteristics of "AAAAAA" arrangement. When two different voltages (E f1 =0.268eV and E f2 = 0.160eV) to achieve a phase gradient ξ = 3k0, at which time p = 2a = 20μm, and the reflection angle of the THG wave is θ r =90°, such as Figure 8 As shown in (b), in this case, the arrangement of applied voltages becomes "ABABAB". When three different voltages are periodically applied to the graphene ribbon, namely E f1 =0.270eV, E f2 =0.202eV and E f3 = 0.100eV, the nonlinear phase difference between adjacent units is 2π / 3, the phase gradient is ξ = 2k0, p = 3a = 30μm, and the reflection angle of the THG wave is θ r=41.8°, such as Figure 8 As shown in (c), in this case, the arrangement of applied voltages is "ABCABC." This results in a tunable device for wavefront control. Furthermore, as m increases, the pixels of the PGM become very small when the width a enters the deep subwavelength scale. By applying voltage permutations and combinations in the nonlinear metasurface, nonlinear wavefront control can be flexibly performed.

[0070] It can be seen from the above technical solutions that the present invention has the following advantages:

[0071] The present invention provides an improved diffraction law for nonlinear wavefront control based on a graphene-based nonlinear phase gradient metasurface in the terahertz domain, which can break through the limitations of NGSL for nonlinear wavefront control.

[0072] By rationally adjusting the chemical potential of graphene through applied voltage, multifunctional control of nonlinear waves, including reflection and beam control, is achieved, thereby realizing the design of nonlinear components.

[0073] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above and that the invention can be embodied in other specific forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be considered in all respects as illustrative and non-restrictive, and the scope of the invention is defined by the appended claims, not the foregoing description, and all variations within the meaning and range of equivalents of the claims are intended to be included therein. Any reference sign in a claim should not be construed as limiting the claim to which it relates.

[0074] In addition, it should be understood that although this specification is described in terms of implementation methods, not every implementation method contains only one independent technical solution. This narrative method of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment can also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.

Claims

1. A nonlinear component for wavefront control based on a graphene nonlinear metasurface, characterized in that: The nonlinear component includes a plurality of periodically distributed metagratings, the metagrating including a metal substrate, the metal substrate being provided with a plurality of periodically distributed grooves, the grooves being filled with a dielectric layer, the dielectric layer being covered with periodically distributed graphene ribbons, and independent voltages being applied to the graphene ribbons to control the chemical potential of the graphene ribbons, thereby realizing a nonlinear phase gradient; The material of the metal matrix is ​​gold, and the optical properties of gold are obtained by the Drude model: , where f p =2069THz, γ=17.65THz; the material of the dielectric layer is PMMA, with a dielectric constant of 2.25; The metagrating comprises m periodically distributed grooves, a dielectric layer and a graphene strip, wherein the width and depth of the grooves are w and h respectively, the distance between two adjacent grooves is a, and the width of the graphene strip is w. g , and w g <w, the total length of the metagrating is p, p=ma, and the voltages applied to the m graphene strips are V1, V2, ..., V m , the phase difference between adjacent grooves is 2π / m, and the value of m is 2~5.

2. The nonlinear component according to claim 1, characterized in that In the nonlinear components: When m = 2, the phase difference between adjacent grooves is π, and the chemical potentials of the two graphene ribbons are 0.268 eV and 0.160 eV respectively; When m = 3, the phase difference between adjacent grooves is 2π / 3, and the chemical potentials of the three graphene ribbons are 0.290 eV, 0.218 eV, and 0.120 eV, respectively; When m = 4, the phase difference between adjacent grooves is π / 2, and the chemical potentials of the four graphene ribbons are 0.338 eV, 0.266 eV, 0.206 eV, and 0.120 eV, respectively; When m=5, the phase difference between adjacent grooves is 2π / 5, and the chemical potentials of the five graphene ribbons are 0.444eV, 0.340eV, 0.278eV, 0.212eV and 0.120eV, respectively.

3. The nonlinear component according to claim 1, characterized in that In the nonlinear components: When m=2, the width of the groove is w=6μm, the depth of the groove is h=7μm, the distance between two adjacent grooves is a=10μm, the total length of the metagrating is 20μm, and the width of the graphene ribbon is w g =2μm; When m=3, the width of the groove is w=5μm, the depth of the groove is h=7μm, the distance between two adjacent grooves is a=6.67μm, the total length of the metagrating is 20μm, and the width of the graphene ribbon is w g =2μm; When m=4, the width of the groove is w=4μm, the depth of the groove is h=7μm, the distance between two adjacent grooves is a=5μm, the total length of the metagrating is 20μm, and the width of the graphene ribbon is w g =2μm; When m=5, the width of the groove is w=3μm, the depth of the groove is h=7μm, the distance between two adjacent grooves is a=4μm, the total length of the metagrating is 20μm, and the width of the graphene ribbon is w g =2μm.

4. The nonlinear component according to claim 1, characterized in that The incident light of the nonlinear component is FF light, and the reflected light is THG wave.

5. The nonlinear component according to claim 4, characterized in that: The incident angle of the incident light is θ i , the reflection angle of the reflected light is θ r , and satisfy: ； in, , , , n is the diffraction order, G=2π / p, q=3, and the phase gradient is .

6. The nonlinear component according to claim 5, characterized in that: The reflection angle is θ r =arsin(λ FF / 3p) , λ FF is the wavelength of the incident light.

7. The nonlinear component according to claim 4, characterized in that: The wavelength of the incident light λ FF The input intensity is 10KW / cm 2 .

8. The nonlinear component according to claim 5, characterized in that: The incident angle of the incident light θ i Less than critical angle θ c When the reflected light is diffracted into two diffraction orders n=0 and n=1, the incident angle of the incident light is θ i Greater than the critical angle θ c When , the reflected light is diffracted into two diffraction orders n=1 and n=2.

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