Asymmetric optical nonlinear metasurfaces, nonreciprocal transmission systems and their applications combining equivalent zero-refractive-index media and continuum bound states

Abstract

The present invention relates to an asymmetric optical nonlinear metasurface, a nonreciprocal transmission system, and its applications, that combines an equivalent zero-refractive-index medium and a continuous domain bound state. The metasurface comprises a silicon plate with a plurality of equally spaced pores arranged horizontally and vertically on the surface of the plate. The pores have a circular outer contour, and their depth is less than the thickness of the plate. By adjusting any one or more structural parameters of the plate's thickness, pore depth, pore radius, and pore spacing, the metasurface's band structure forms a triple degenerate point at the Γ point in the Brillouin zone. The present invention combines the high-Q characteristics of a quasi-BIM with the zero-refractive-index characteristics near the triple degenerate point, greatly enhancing the system's nonlinear effects and thus enabling wide-range nonreciprocal transmission at low pump intensities.

Description

Technical Field

[0001] The present invention relates to the technical field of non-reciprocal transmission, and in particular to an asymmetric optical nonlinear metasurface combining an equivalent zero-refractive-index medium and a continuous domain bound state, a non-reciprocal transmission system, and applications thereof. Background Art

[0002] Nonreciprocal devices and systems are crucial in a variety of fields, including optical communications, radar, light detection and ranging, nonlinear signal processing, and integrated photonic circuits. In recent years, nonlinear-induced nonreciprocity has attracted widespread attention due to its advantages, such as requiring no external magnetic field bias and relatively simple structure. However, achieving significant nonreciprocal transmission remains challenging. The main reason for this is that the nonlinear coefficients of most materials are small, requiring high operating powers to achieve the desired nonreciprocal response, which greatly limits the practical application of this technology. Summary of the Invention

[0003] The purpose of the present invention is to overcome the defects of the prior art and provide an asymmetric optical nonlinear metasurface, a non-reciprocal transmission system and its application that combines an equivalent zero-refractive index medium and a continuous domain bound state, so as to solve the problem that the existing non-reciprocal transmission requires a higher working power to achieve the ideal non-reciprocal response due to the small nonlinear coefficient of the material, which limits its practical application.

[0004] The technical solution to achieve the above purpose is:

[0005] The present invention provides an asymmetric optical nonlinear metasurface combining an equivalent zero-refractive index medium and a continuous domain bound state, comprising a silicon plate, wherein a plurality of pores are evenly spaced on the silicon plate, the pores being evenly spaced in the horizontal and vertical directions on the surface of the silicon plate, the outer contour of the pores being circular, and the depth of the pores being less than the thickness of the silicon plate;

[0006] By adjusting any one or more structural parameters of the thickness of the silicon plate, the depth of the pores, the radius of the pores and the spacing of the pores, the band structure of the metasurface forms a triple degenerate point at the Γ point in the Brillouin zone.

[0007] A further improvement of the asymmetric optical nonlinear metasurface combining an equivalent zero-refractive index medium and a continuous domain bound state of the present invention is that the silicon plate has an upper surface and a lower surface arranged opposite to each other;

[0008] The air holes are provided on the upper surface of the silicon plate;

[0009] The upper surface of the silicon plate forms a first port, and the lower surface of the silicon plate forms a second port.

[0010] A further improvement of the asymmetric optical nonlinear metasurface combining an equivalent zero-refractive index medium and a continuous domain bound state in the present invention is that the arrangement direction of the pores is consistent with the thickness direction of the silicon plate.

[0011] A further improvement of the asymmetric optical nonlinear metasurface combining an equivalent zero-refractive index medium and a continuous domain bound state is that the relationship between the dielectric constant of the silicon plate and the local electric field intensity is:

[0012] ε=ε lin +X (3) |E| 2 ,

[0013] Where ε represents the dielectric constant, ε lin represents the linear dielectric constant, X (3) is the third-order nonlinear coefficient, and E is the local electric field intensity.

[0014] A further improvement of the asymmetric optical nonlinear metasurface combining an equivalent zero-refractive-index medium and a continuous domain bound state in the present invention is that the outer contour of the silicon plate is square.

[0015] The present invention also provides a non-reciprocal transmission system formed by an asymmetric optical nonlinear metasurface combining an equivalent zero-refractive index medium and a continuous domain bound state, comprising:

[0016] A light source emitting module is used to emit incident light toward the upper surface or lower surface of the silicon plate, wherein the frequency of the incident light emitted by the light source emitting module is equal to or close to the frequency corresponding to the triple degenerate point of the Dirac cone formed by the band structure of the metasurface at the Γ point in the Brillouin zone.

[0017] A further improvement of the non-reciprocal transmission system of the present invention is that the incident angle of the incident light emitted by the light source emission module is adjustable, and the Q factor of the quasi-continuum bound state can be adjusted by adjusting the incident angle of the incident light.

[0018] A further improvement of the non-reciprocal transmission system of the present invention is that the rate of change of the refractive index of the silicon plate with the incident light intensity is:

[0019]

[0020] Where dn represents the change in the material's refractive index, dI represents the change in the incident light intensity, ε represents the dielectric constant, μ represents the magnetic permeability, and dε represents the change in the material's dielectric constant.

[0021] The present invention further provides an application of a non-reciprocal transmission system in the field of optical communication, radar detection, optical detection, optical ranging, nonlinear signal processing or integrated photonic circuits.

[0022] The beneficial effects of the present invention combining an asymmetric optical nonlinear metasurface, a nonreciprocal transmission system and its application with an equivalent zero-refractive-index medium and a continuous domain bound state are as follows:

[0023] The present invention provides an asymmetric optical nonlinear metasurface that combines an effective zero-refractive index medium and a bound state of a continuous medium, and utilizes the strong nonlinear properties of the zero-refractive index material and the high quality factor properties of the quasi-BIC to enhance the nonlinear effect and realize nonreciprocal transmission.

[0024] The metasurface and non-reciprocal system of the present invention combine the high Q characteristics of quasi-BIM with the zero refractive index characteristics near the triple degeneracy point, greatly enhancing the nonlinear effect of the system, thereby realizing a wide range of non-reciprocal transmission at low pump intensity.

[0025] The present invention combines quasi-BIM with ZIM for the first time to enhance nonlinear effects, which is of great significance for applications involving nonlinear effects. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 This is a schematic diagram of the structure of the asymmetric optical nonlinear metasurface of the present invention that combines an equivalent zero-refractive-index medium and a continuous domain bound state.

[0027] Figure 2 for Figure 1 Schematic diagram of the structure of a single unit cell in the metasurface shown.

[0028] Figure 3 This is a graph of the energy band structure along Γ-X and Γ-Y near the Γ point of the asymmetric optical nonlinear metasurface and the non-reciprocal system combining an equivalent zero-refractive index medium and a continuous domain bound state of the present invention.

[0029] Figure 4 This is a Q factor curve diagram of the asymmetric optical nonlinear metasurface and nonreciprocal system combining an equivalent zero-refractive index medium and a continuous domain bound state near the Γ point along Γ-X and Γ-Y.

[0030] Figure 5 This is a graph of the equivalent dielectric constant (left vertical axis) and magnetic permeability (right vertical axis) of energy band 1 of the asymmetric optical nonlinear metasurface and non-reciprocal system combining an equivalent zero-refractive index medium and a continuous domain bound state in the present invention.

[0031] Figure 6 This is a graph of the equivalent dielectric constant (left vertical axis) and magnetic permeability (right vertical axis) of energy band 6 of the asymmetric optical nonlinear metasurface and non-reciprocal system combining an equivalent zero-refractive index medium and a continuous domain bound state in the present invention.

[0032] Figure 7The linear transmission spectra of energy band 1 under different incident angles are obtained by combining an asymmetric optical nonlinear metasurface and a nonreciprocal system with an equivalent zero-refractive-index medium and a continuous domain bound state according to the present invention.

[0033] Figure 8 The linear transmission spectra of energy band 6 at different incident angles are obtained by combining an asymmetric optical nonlinear metasurface and a nonreciprocal system with an equivalent zero-refractive-index medium and a continuous domain bound state according to the present invention.

[0034] Figure 9 and Figure 10 The scattering intensities of five main multi-dipoles of the asymmetric optical nonlinear metasurface and the non-reciprocal system near-zero quasi-BIC and ordinary quasi-BIC combined with the equivalent zero refractive index medium and continuous domain bound state of the present invention.

[0035] Figure 11 The present invention combines an asymmetric optical nonlinear metasurface and a nonreciprocal system with an equivalent zero-refractive-index medium and a continuous domain bound state to obtain a nonlinear transmission spectrum of energy band 1 at a fixed incident angle of 1 degree.

[0036] Figure 12 The present invention combines an asymmetric optical nonlinear metasurface and a nonreciprocal system with an equivalent zero-refractive-index medium and a continuous domain bound state to obtain a nonlinear transmission spectrum of band 6 at a fixed incident angle of 5 degrees.

[0037] Figure 13 This is a relationship diagram between the transmittance and light intensity of energy band 1 excited from port 1 and port 2 of the asymmetric optical nonlinear metasurface and nonreciprocal system combined with an equivalent zero-refractive index medium and a continuous domain bound state in the present invention.

[0038] Figure 14 This is a relationship diagram between the transmittance and light intensity of energy band 6 excited from port 1 and port 2 of the asymmetric optical nonlinear metasurface and nonreciprocal system combined with an equivalent zero-refractive index medium and a continuous domain bound state in the present invention. DETAILED DESCRIPTION

[0039] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0040] See Figure 1The present invention provides an asymmetric optical nonlinear metasurface, a non-reciprocal transmission system and its application that combines an equivalent zero-refractive index medium and a continuous domain bound state. First, a square silicon plate with circular air holes is designed. Silicon exhibits inherent third-order nonlinearity. Secondly, by retaining an unprocessed layer of a certain thickness (that is, the bottom of the air hole does not penetrate the lower surface of the silicon plate), the out-of-plane symmetry of the metasurface is broken and structural asymmetry is introduced. Then, through fine adjustment of the structural parameters, the band structure forms a triple degenerate point at the Γ point in the Brillouin zone, realizing the equivalent zero refractive index of the metasurface. Under oblique incidence, the BIC is transformed into a quasi-BIC. The Q factor of the quasi-BIC can be adjusted by changing the incident angle. The high Q factor of the quasi-BIC can greatly enhance the local electric field intensity, thereby enhancing the nonlinear effect and minimizing the intensity required to trigger these nonlinear phenomena. The present invention combines the high Q characteristics of the quasi-BIC with the zero refractive index characteristics near the triple degenerate point, greatly enhancing the nonlinear effect of the system, thereby realizing a large range of non-reciprocal transmission at low pump intensity. The following describes the asymmetric optical nonlinear metasurface, nonreciprocal transmission system and its applications in combination with an equivalent zero-refractive-index medium and a continuous domain bound state according to the present invention with reference to the accompanying drawings.

[0041] First, the English abbreviations involved in the present invention are explained.

[0042] BICs (Bound states in the continuum) are special electromagnetic eigenstates whose frequencies lie within the radiation continuum but are completely localized. A notable feature of BICs is their theoretically infinite quality factor (Q factor), even though they exist in the continuous spectrum. Although perfect BICs are very unique, they cannot be excited by incident waves due to their infinite Q factor. Importantly, by introducing external perturbations or adjusting system parameters, true BICs will collapse into sharp Fano resonances with ultra-high Q factors, which are called quasi-bound states in the continuum (quasi-BICs).

[0043] Zero-index metamaterials (ZIMs) are materials characterized by extreme electromagnetic parameters, where the dielectric constant and / or magnetic permeability are close to zero. In ZIMs, all fields are uniform regardless of the shape and size of the sample, effectively generating light of infinite wavelength. This unique property has been shown to significantly enhance optical nonlinearities. ZIMs show great potential in optical nonlinearity. In practical applications, effective ZIMs can be realized using photonic crystals with accidental degeneracy at the Γ point (Dirac cone dispersion).

[0044] See Figure 1 , shows the structural diagram of the asymmetric optical nonlinear metasurface of the present invention that combines the equivalent zero refractive index medium and the continuous domain bound state. Figure 1 , the present invention describes an asymmetric optical nonlinear metasurface that combines an equivalent zero-refractive-index medium and a continuous domain bound state.

[0045] like Figure 1 As shown, the asymmetric optical nonlinear metasurface combining an equivalent zero-refractive index medium and a continuous domain bound state of the present invention includes a silicon plate 11, and a plurality of pores 12 are evenly spaced on the silicon plate 11. The pores 12 are evenly spaced in the horizontal and vertical directions on the surface of the silicon plate 11. The outer contour of the pores 12 is circular, and the depth of the pores 12 is less than the thickness of the silicon plate 11. By adjusting any one or more structural parameters of the thickness of the silicon plate 11, the depth of the pores 12, the radius of the pores 12, and the spacing of the pores 12, the band structure of the metasurface forms a triple degenerate point at the Γ point in the Brillouin zone.

[0046] The pores 12 are periodically arranged on the surface of the silicon plate 11. The spacing between two adjacent pores 12 is the distance between the centers of the two pores 12. The pores 12 are arranged in multiple rows along the horizontal and vertical directions on the surface of the silicon plate 11, with the centers of the pores 12 in the same row located on the same straight line.

[0047] Furthermore, the silicon plate 11 has an upper surface and a lower surface arranged opposite to each other; the air hole 12 is provided on the upper surface of the silicon plate 11; the upper surface of the silicon plate 11 forms a first port 1, and the lower surface of the silicon plate 11 forms a second port 2.

[0048] The incident wave (or incident light) may be incident from the first port 1 or the second port 2 .

[0049] Furthermore, the arrangement direction of the pores 12 is consistent with the thickness direction of the silicon plate 11 .

[0050] Furthermore, the relationship between the dielectric constant of the silicon plate 11 and the local electric field strength is:

[0051] ε=ε lin +X (3) |E| 2 ,

[0052] Where ε represents the dielectric constant, ε lin represents the linear dielectric constant, ε lin =12.11,X (3) is the third-order nonlinear coefficient, X (3) =2.8×10 -18 m 2 / V 2 (m and V denote meters and volts, respectively), and E is the local electric field strength.

[0053] Furthermore, the outer contour of the silicon plate 11 is square, preferably square.

[0054] The thickness of the silicon plate 11 of the present invention is t, the depth of the pores 12 is d, and the remaining thickness of the lower surface of the silicon plate 11 is td. The out-of-plane symmetry on the silicon plate 11 is broken to achieve non-reciprocal nonlinear effects.

[0055] The present invention also provides a non-reciprocal transmission system formed by an asymmetric optical nonlinear metasurface combining an equivalent zero-refractive index medium and a continuous domain bound state, comprising:

[0056] The light source emission module is used to emit incident light toward the upper surface or lower surface of the silicon plate. The frequency of the incident light emitted by the light source emission module is equal to or close to the frequency corresponding to the triple degenerate point of the Dirac cone formed by the band structure of the metasurface at the Γ point in the Brillouin zone.

[0057] Furthermore, the incident angle of the incident light emitted by the light source module is adjustable, and by adjusting the incident angle of the incident light, the Q factor of the quasi-continuum bound state can be adjusted. When adjusting the Q factor of the quasi-BIC, the Q factor is adjusted as high as possible. A high Q factor can greatly enhance the local electric field strength E, thereby strengthening nonlinear effects and minimizing the intensity required to trigger these nonlinear phenomena.

[0058] Furthermore, the refractive index of the incident light passing through the silicon plate changes with the incident light intensity as follows:

[0059]

[0060] Among them, dn represents the change of the refractive index of the material, dI represents the change of the incident light intensity, ε represents the dielectric constant, μ represents the magnetic permeability, and dε represents the change of the dielectric constant of the material. Mainly depends on X (3) ,From this we can see that the smaller the dielectric constant, the greater the change of the refractive index with the incident light intensity, which shows that ZIM can produce stronger nonlinear optical properties.

[0061] The present invention further provides an application of a non-reciprocal transmission system in the field of optical communication, radar detection, optical detection, optical ranging, nonlinear signal processing or integrated photonic circuits.

[0062] The principle of the present invention is described below with reference to the experimental results of a specific example.

[0063] The silicon plate structure used in the experiment can be found in Figure 1 The thickness of the silicon plate is t = 798nm, the radius of the pores is r = 197nm, the depth of the pores is d = 570nm, and the interval or period of the pores is a = 724.5nm. Theoretically, the larger the length and width of the silicon plate, the better. The length and width of the silicon plate used in the experiment is 6a. Figure 2As shown, the silicon plate can be regarded as consisting of many primitive cells, each of which is a square with a length and a width of period a.

[0064] Silicon exhibits a third-order nonlinear effect, that is, the relationship between its dielectric constant and the local electric field strength is ε = ε lin +X (3) |E| 2 , where ε lin =12.11 is the linear dielectric constant, X (3) =2.8×10 -18 m 2 / V2 is the third-order nonlinear coefficient, and E is the local electric field strength. In order to utilize the nonlinear effect to achieve nonreciprocity, the out-of-plane symmetry is broken, so that the remaining silicon layer with a thickness of td is not perforated.

[0065] The completely destructive interference between the double degenerate dipole mode radiated by the photonic crystal slab and the Fabry-Pérot mode forms the FW-BIC. Figure 3 The band structures of Γ-X and Γ-Y near the Γ point are shown. Bands 1-3 near the Γ point consist of three degenerate modes with nearly linear dispersion and form an accidental Dirac cone at a frequency of 163.88 THz. The modal distribution of bands 1-3 and band 6 in the xy cross section at the Γ point (H z )like Figure 3 As shown in the inset, the three degenerate modes at the Γ-point are classified into a pair of dipole modes and a quadrupole mode. Figure 4 The Q factors along Γ-X and Γ-Y near the Γ point are shown, indicating the presence of BICs at the Γ points of bands 1 and 6.

[0066] The effective electromagnetic parameters are calculated using the boundary effective medium method. This method relies on calculating the average eigenstate field (E, H) on the boundary of a single unit cell and calculating the constitutive relations D = εE and B = μH. The equivalent dielectric constant (left axis) and magnetic permeability (right axis) of energy band 1 and energy band 6 obtained by inversion are shown as follows: Figure 5 and Figure 6 The results show that the structure has a refractive index close to zero at and near the Dirac point frequency. Figure 5 The vertical dashed line indicates the frequency of 163.83 THz, where the effective permittivity is 0.35 and the effective permeability is -0.001. Figure 6 The vertical dashed line in the middle represents the frequency of 176.26 THz, where the effective dielectric constant is -10.64 and the effective permeability is -0.007. Next, we analyze ε = ε lin +X (3) |E| 2 and The mechanism of quasi-BIC and zero refractive index enhancement of nonlinearity is obtained. The high Q factor of quasi-BIC can greatly enhance the local electric field intensity E, thereby increasing the change of dielectric constant and enhancing the nonlinear effect. In addition, the rate of change of refractive index with incident light intensity is in Mainly depends on X (3) From the formula, we can see that the smaller the dielectric constant, the greater the change of the refractive index with the incident light intensity, which shows that ZIM can produce stronger nonlinear optical properties.

[0067] Through simulation experiments, the transmission spectra of band 1 and band 6 at different incident angles are obtained as follows Figure 7 and Figure 8 As shown. Under normal incidence (θ = 0°), BIC has a vanishing linewidth, which means infinite Q factor, marked by a black dotted circle. As the incident angle θ gradually increases, the linewidth of the transmission spectrum increases significantly. In order to gain a deeper understanding of the spectral response of the two different quasi-BIC modes, the scattered power of different multipoles of the two quasi-BIC modes in the Cartesian coordinate system is calculated based on the multipole scattering theory. According to the general multipole scattering theory, the total intensity of the scattered power can be defined as

[0068]

[0069] Among them, P, M, T, Q αβ and M αβ They are electric dipole (ED), magnetic dipole (MD), toroidal dipole (TD), electric quadrupole (EQ) and magnetic quadrupole (MQ). Based on this theory, Figure 9 and Figure 10 The scattering powers of different multipole moments induced in the metasurface under the excitation of near-zero quasi-BIC and ordinary quasi-BIC are shown respectively. Figure 9 As shown in Figure 2, the EQ moment (cyan line) mainly contributes to the near-zero quasi-BIC. In contrast, the ordinary quasi-BIC is mainly caused by the MQ resonance, because the contribution of the MQ moment (magenta line) is dominant, as shown in Figure 2. Figure 10 The field distributions of near-zero quasi-BIC and ordinary quasi-BIC are shown as follows. Figure 9 and Figure 10 As shown in the illustration.

[0070] According to the temporal coupled-mode theory (TCMT), a two-port Fano resonator with negligible intrinsic loss is described as:

[0071]

[0072] Where a is the resonance amplitude, ω0 is the resonance frequency, γ is the attenuation rate, and κ i is the coupling coefficient between the resonator and the first port, is the signal entering the resonator from the first port, is the signal leaving the resonator from the first port, r B is the background reflection coefficient, t B is the background transmission coefficient. B ,t B This refers to the system's response when moving away from the Fano resonance. Furthermore, this model includes the Lorentz oscillator as a special case of the Fano resonator. The attenuation rate can be decomposed into γ = γ1 + γ2, where γ1 and γ2 are the attenuation rates of radiation radiated to the port.

[0073] Formula 3 requires additional conditions:

[0074]

[0075] Derived from energy conservation and time reversal symmetry, it can be easily obtained from Equations 3 and 4 that the transmission coefficient of the system is:

[0076]

[0077] Where, T B =|t B | 2 , x=(ω0-ω) / γ is the detuning factor of the resonator, ω is the driving frequency, and is the characteristic parameter of the resonator. represents the detuning from the resonant frequency where transmission is zero. The minus sign in Equation 5 corresponds to the case where the frequency of the transmission zero is lower than the resonant frequency, indicating that the frequency of the transmission zero is lower than the transmission maximum. The plus sign is the dual case where the transmission zero of the resonator is located at a frequency higher than the resonant frequency. The inventors define the asymmetry coefficient of different ports as (k can also be defined as the ratio of the field strengths excited by different ports), then Equation 5 can be rewritten as:

[0078]

[0079] If the resonant cavity is symmetrical, then κ = 1 and This suggests that the asymmetric effect is through the factor Scaling the transmission without affecting its line shape. Considering that the maximum transmission rate of a symmetric Fano resonator is 1, the asymmetry imposes the following constraints on the transmission of the Fano resonator:

[0080]

[0081] As a direct consequence of time reversal symmetry, this equation applies to any lossless linear structure, whether it is a Fano resonator or not. For Fano resonators, Equation 6 also applies to the lossy case, which can be intuitively explained as increasing the loss reduces the maximum transmission compared to the lossless case. By substituting the resonator's intrinsic decay rate γ for loss Adding γ to the above, we can obtain a rigorous proof similar to the lossless case. Now, consider the third-order nonlinearity ε = ε in the Fano resonator lin +X (3) |E| 2 The nonlinearity causes the resonant frequency of the resonator to shift

[0082]

[0083] where ω 0,lin is the resonant frequency in the linear (low intensity) state, |a0| 2 is a characteristic quantity of the resonator in units of energy. In principle, nonlinearity also affects the decay rate γ and the coupling coefficient κ between the resonator and the port. i ; however, for perturbations involving only the real part of the dielectric constant, these effects are usually neglected because γ and κ i is mainly determined by the modal distribution, which is less affected by nonlinearity than the resonant frequency. This allows Equation 5 to be applied to the nonlinear case, if 0 is replaced by the expression in Equation 8. The remaining parameters γ, T bg and k are calculated in the linear regime. Therefore, Equations 6 and 7 also hold in the nonlinear case. In the linear case, the parameter κ that determines the boundary is still an asymmetric factor. Therefore, all the above derivations based on TCMT can be applied to the nonlinear case.

[0084] Having examined the linear properties of the metasurface above, we now consider nonlinear effects. Increasing the input intensity increases the dielectric constant due to Kerr nonlinearity, which in turn causes the resonant frequency to decrease. Because the resonant cavity is asymmetric, this frequency shift is different when excited from opposite sides. Figure 7 and Figure 8 Given a fixed incident light intensity (I0 = 0.04 MW / cm 2 ) and the relationship between transmittance and incident light frequency at different incident angles, where the blue line and the red line represent port 1 (above the metasurface, such as Figure 1 as shown) and port 2 (below the metasurface, as Figure 1 The gray line is the linear contrast. Figure 11 and Figure 12 Corresponding to the first and sixth energy bands respectively. In order to keep the Q factor the same in the two cases, the inventors obtained Figure 4 Choose the appropriate incident angle from the Q factor curve, Figure 11The incident angle is 1 degree, Figure 12 The incident angle is 5 degrees. The dotted line indicates the position of the transmission peak. The results show that the transmission peak position in the nonlinear case shifts to the left compared to the linear case, indicating a decrease in the resonant frequency. The blue and red arrows indicate the resonant frequency shifts for incident signals from Port 1 and Port 2, respectively. Due to the asymmetric structure, the resonant frequency shifts differ between the two ports. Figure 11 The difference in the offset between the two ports corresponds to the near-zero quasi-BIC case and is much larger than Figure 12 The common quasi-BIC situation.

[0085] For bands 1 and 6, Figure 13 and Figure 14 The relationship between the transmittance and the incident intensity at fixed incident angle and frequency is shown, where the blue and red lines represent the incident angles at port 1 and port 2, respectively. The non-reciprocal intensity range (NRIR) is defined as the ratio between I1 and I2 that results in the same transmission intensity when incident from opposite directions. NRIR is equal to k or k -1 , depending on whether k>1 or k<1. In particular, NRIR=max{k,k -1 Substituting k in} into formula 7, the result is An NRIR of 1 indicates that a system has the same response from opposite directions, so there is no isolation. The NRIR is always equal to the linear electromagnetic asymmetry. The same Q factor is controlled in both cases, with the NRIRs of bands 1 and 6 being 7.1 and 1.4 respectively. Figure 13 The equivalent refractive index is close to zero at the incident frequency, so its NRIR is approximately Figure 14 The right picture shows the incident light intensity I0 = 0.04 MW / cm 2 The mode distribution (H z ), where the blue and yellow arrows represent the incident light at port 1 and port 2, respectively. Figure 13 From the mode distribution diagram, it can be seen that the transmitted field incident on port 2 is much weaker than that on port 1. Figure 14 The transmitted fields incident on port 1 and port 2 are almost the same. The results show that the combination of ZIM and quasi-BIC can produce a huge nonlinear optical effect.

[0086] The advantages of this invention include leveraging the strong nonlinear properties of zero-refractive-index materials and the high-quality factor of quasi-BICs to enhance nonlinear effects and achieve nonreciprocal transmission. The theoretical analysis of nonreciprocal transmission induced by nonlinear materials is relatively comprehensive. This overcomes the dependence of traditional nonreciprocal devices on external magnetic fields, simplifying the device structure. A controllable quasi-BIC based on incident angle adjustment enables flexible adjustment of the nonlinear response. The introduction of FW-BIC overcomes the problem of outward radiation loss and improves the system quality factor.

[0087] The present invention has been described in detail above with reference to the embodiments of the accompanying drawings. A person skilled in the art can make various modifications to the present invention based on the above description. Therefore, certain details in the embodiments should not be construed as limiting the present invention. The scope of protection of the present invention shall be determined by the scope defined in the appended claims.

Claims

1. An asymmetric optical nonlinear metasurface combining an equivalent zero-refractive-index medium and a continuous domain bound state, characterized in that: The silicon plate comprises a plurality of pores arranged at equal intervals on the silicon plate, the pores being arranged at equal intervals in the horizontal and vertical directions on the surface of the silicon plate, the outer contour of the pores being circular, and the depth of the pores being less than the thickness of the silicon plate; By adjusting any one or more structural parameters of the thickness of the silicon plate, the depth of the pores, the radius of the pores and the spacing of the pores, the band structure of the metasurface forms a triple degenerate point at the Γ point in the Brillouin zone.

2. The asymmetric optical nonlinear metasurface combining an equivalent zero-refractive-index medium and a continuous domain bound state according to claim 1, characterized in that: The silicon plate has an upper surface and a lower surface that are arranged opposite to each other; The air holes are provided on the upper surface of the silicon plate; The upper surface of the silicon plate forms a first port, and the lower surface of the silicon plate forms a second port.

3. The asymmetric optical nonlinear metasurface combining an equivalent zero-refractive-index medium and a continuous domain bound state according to claim 1, characterized in that: The arrangement direction of the pores is consistent with the thickness direction of the silicon plate.

4. The asymmetric optical nonlinear metasurface combining an equivalent zero-refractive-index medium and a continuous domain bound state according to claim 1, wherein: The relationship between the dielectric constant of the silicon plate and the local electric field strength is: e=e lin +X (3) |E| 2 , Where ε represents the dielectric constant, ε lin represents the linear dielectric constant, X (3) is the third-order nonlinear coefficient, and E is the local electric field intensity.

5. The asymmetric optical nonlinear metasurface combining an equivalent zero-refractive-index medium and a continuous domain bound state according to claim 1, wherein: The outer contour of the silicon plate is square.

6. A non-reciprocal transmission system formed by using the asymmetric optical nonlinear metasurface combining an equivalent zero-refractive index medium and a continuous domain bound state as claimed in claim 1, characterized in that: include: A light source emitting module is used to emit incident light toward the upper surface or lower surface of the silicon plate, wherein the frequency of the incident light emitted by the light source emitting module is equal to or close to the frequency corresponding to the triple degenerate point at the Γ point in the Brillouin zone when the band structure of the metasurface forms a Dirac cone.

7. The non-reciprocal transmission system according to claim 6, wherein: The incident angle of the incident light emitted by the light source emission module is adjustable, and the Q factor of the quasi-continuum bound state can be adjusted by adjusting the incident angle of the incident light.

8. The non-reciprocal transmission system according to claim 6, wherein: The refractive index of the silicon plate changes with the incident light intensity at a rate of: Where dn represents the change in the material's refractive index, dI represents the change in the incident light intensity, ε represents the dielectric constant, μ represents the magnetic permeability, and dε represents the change in the material's dielectric constant.

9. An application of the non-reciprocal transmission system according to claim 6 in the fields of optical communication, radar detection, optical detection, optical ranging, nonlinear signal processing, or integrated photonic circuits.

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