Dielectric metasurface reverse optimization method based on space coupling mode theory

Abstract

The invention discloses a medium metasurface reverse optimization method based on a space coupling mode theory, and relates to the field of optics, and the method comprises the following steps: building a cut-off waveguide array based on a metasurface, calculating a guided mode and a propagation constant of each waveguide according to the cut-off waveguide array, and coupling adjacent waveguides through a coupling matrix, a waveguide array is obtained; an input light field is coupled into a waveguide array, propagation of light in waveguides is simulated based on a spatial coupling mode theory model, and near-field intensity distribution is converted into far-field intensity distribution by using a Rayleigh-Sommerfeld diffraction theory; and calculating the difference between the target intensity and the far-field intensity through a loss function, evaluating the effect of the current metasurface design, and gradually adjusting the geometric parameters of the waveguide unit through an optimization algorithm. According to the method, the problems of efficient modeling and optimization in metasurface design are solved through the space coupling mode theoretical model.

Description

Technical Field

[0001] The present invention relates to the field of optics, and in particular to a method for inverse optimization of a dielectric metasurface based on spatial coupled mode theory. Background Art

[0002] Metasurfaces are usually composed of a large number of sub-wavelength scatterers, whose shapes and sizes need to be precisely optimized to achieve specific optical functions. To this end, a variety of design methods have been proposed with the aim of reducing computational costs while maintaining high accuracy. In order to accurately predict optical responses and achieve high-performance designs, researchers have developed a metasurface inverse design method based on full-wave simulation. This design process usually includes two steps: forward and backward. The forward problem uses a Maxwell equations solver to predict the scattering behavior of the meta-unit, while the backward problem optimizes the design of the metasurface based on its performance through numerical optimization techniques.

[0003] Full-wave simulations have high accuracy and can accurately predict the phase and amplitude response of any metasurface without making any assumptions about the geometry and layout of the element units; however, full-wave simulations are computationally expensive, and the computational burden quickly becomes unbearable as the size of the metasurface increases; to address this issue, many methods have been proposed to reduce the computational cost.

[0004] Among them, the widely used "local periodicity" approximation (LPA) assumes that the geometric changes of the meta-unit are small in the local range, so its optical response can be approximated by the scattered field of a single meta-unit; in this case, the response of the meta-unit is assumed to be the same as the response of its infinitely periodic array replica, which can be conveniently simulated using the finite-difference time-domain (FDTD) or rigorous coupled wave analysis (RCWA) algorithm; by selecting the meta-unit with the smallest local phase error, the layout of the entire metasurface can be designed relatively easily; although the LPA method has a very fast calculation speed, the accuracy will be significantly reduced in scenarios where large phase gradients (such as high numerical aperture lenses) need to be processed; recently, a design method based on temporal coupled mode theory (TCMT) has been proposed, which models the metasurface meta-unit as a tiny resonator and analytically calculates its coupling relationship to achieve fast and accurate numerical design; however, this method is only applicable to resonance-based metasurface design, and is not applicable to dielectric metasurface design that needs to consider guided mode propagation.

[0005] Currently, no effective solution has been proposed for the problems in the related technologies. Summary of the invention

[0006] In response to the problems in the related technology, the present invention proposes a dielectric metasurface inverse optimization method based on spatial coupled mode theory to overcome the above-mentioned technical problems existing in the existing related technology.

[0007] To this end, the specific technical solution adopted by the present invention is as follows:

[0008] A dielectric metasurface inverse optimization method based on spatial coupled mode theory, the optimization method comprising the following steps:

[0009] S1. Create a truncated waveguide array based on the metasurface, calculate the guided mode and propagation constant of each waveguide according to the truncated waveguide array, and couple adjacent waveguides using a coupling matrix to obtain a waveguide array;

[0010] S2, coupling the input light field into the waveguide array, simulating the propagation of light in the waveguide based on the spatial coupled mode theory model, and converting the near-field intensity distribution into the far-field intensity distribution using the Rayleigh-Sommerfeld diffraction theory;

[0011] S3. The difference between the target intensity and the far-field intensity is calculated through the loss function to evaluate the effect of the current metasurface design, and the geometric parameters of the waveguide unit are gradually adjusted through the optimization algorithm.

[0012] Furthermore, the guided mode of the waveguide includes: the electric field distribution and magnetic field distribution of the light wave in the waveguide, wherein:

[0013] The calculation formula for the electric field distribution of light waves in the waveguide is:

[0014]

[0015] Where E(x,y,z) t represents the electric field distribution in the waveguide; represents the transverse electric field component of mode i; u i (z) represents the amplitude of mode i at position z; x and y represent spatial coordinates; z represents the longitudinal coordinate; t represents the transverse coordinate; N represents the total number of waveguides in the waveguide array;

[0016] The calculation formula for the magnetic field distribution of light waves in the waveguide is:

[0017]

[0018] Where H(x,y,z) t represents the magnetic field distribution in the waveguide; represents the transverse magnetic field component of mode i; u i (z) represents the amplitude of mode i at position z; x and y represent spatial coordinates; z represents the longitudinal coordinate; t represents the transverse coordinate; and N represents the total number of waveguides in the waveguide array.

[0019] Furthermore, the coupling matrix calculation formula is:

[0020]

[0021] Where C represents the coupling matrix of the coupling strength between waveguides; U(z) represents the coefficient vector, U(z)=[u1(z),u2(z),...u N (z)]; K represents the coupling coefficient matrix, which is used to describe the coupling relationship between modes; B represents the diagonal matrix of the phase change characteristics during the propagation process, and its diagonal elements B ii =β i β i represents the propagation constant of mode i.

[0022] Furthermore, the element c of the coupling matrix C pm The calculation formula is:

[0023]

[0024] In the formula, c pm Represents the element value of the coupling matrix C; The unit vector representing the z longitudinal coordinate direction; represents the transverse electric field component of mode p; represents the transverse magnetic field component of mode m; x and y represent spatial coordinates; z represents the longitudinal coordinate; and t represents the transverse direction.

[0025] Furthermore, the input light field is coupled into the truncated waveguide array, and the propagation of light in the waveguide is simulated based on the spatial coupled mode theory model, and then the near-field intensity distribution is converted into the far-field intensity distribution using the Rayleigh-Sommerfeld diffraction theory, which includes the following steps:

[0026] S21, decomposing the incident electromagnetic field to obtain the waveguide mode components of the input light field;

[0027] S22, calculating the initial mode amplitude of each waveguide based on the waveguide mode component of the input light field;

[0028] S23. Use the spatial coupled mode theory model to simulate the propagation process of the light field in the waveguide, and allow the modes of adjacent waveguides to interact with each other. When the light field propagates to the end of the waveguide, couple the light field to the free space to obtain the near-field intensity distribution of the metasurface at the waveguide exit.

[0029] S24. The near-field intensity distribution is propagated to the focal plane through the Rayleigh-Sommerfeld diffraction theory, and the far-field intensity distribution of the metasurface is calculated to obtain the far-field intensity distribution of the metasurface.

[0030] Furthermore, the calculation formula for the initial mode amplitude is:

[0031]

[0032] In the formula, u i(0) represents the initial mode amplitude of mode i; E incident represents the input electromagnetic field; c represents the speed of light in vacuum; represents the transverse electric field component of mode i; n0 represents the refractive index of free space; represents the effective refractive index of mode i; t represents the transverse direction.

[0033] Furthermore, the calculation formula of the far-field intensity distribution of the metasurface is:

[0034]

[0035] In the formula, E far (x, y) represents the far-field intensity distribution of the metasurface; (x, y) represents the electric field intensity E on the far-field plane far (x, y) represents the position of the near-field plane; (x', y') represents the electric field strength E on the near-field plane near The position of (x′, y′); r represents the distance between the near-field source point (x', y') and the observation point (x, y) in the far field; λ represents the wavelength; E near (x′, y′) represents the near-field intensity distribution at the waveguide outlet; j represents the imaginary unit; x' and y' represent the electric field intensity E on the near-field plane near (x′, y′) is the spatial coordinate of the location; x and y represent the electric field intensity E on the far field plane far (x, y) are the spatial coordinates of the location; z represents the vertical coordinate.

[0036] Furthermore, the difference between the target intensity and the far-field intensity is calculated by the loss function to evaluate the effect of the current metasurface design, and the geometric parameters of the waveguide unit are gradually adjusted by the optimization algorithm so that the far-field intensity distribution is consistent with the target intensity distribution. The following steps are included:

[0037] S31, using the loss function, calculating the difference between the target intensity and the far-field intensity;

[0038] S32, based on the forward simulation, using the automatic differentiation framework, calculate the gradient of the loss function with respect to the waveguide width;

[0039] S33, adjusting the geometric dimensions of the waveguide unit by back propagation and using the optimization algorithm of the metasurface parameters, and calculating the optimized metasurface waveguide width;

[0040] S34. Based on the optimized metasurface waveguide width, a far-field intensity distribution consistent with the target intensity distribution is obtained.

[0041] Furthermore, the loss function is calculated as:

[0042] L=||I far -I target|| 2 ;

[0043] Where L represents the difference between the target intensity and the far-field intensity; I far Indicates the far-field output intensity; I target Indicates the target strength;

[0044] Among them, the far-field output intensity I far The calculation formula is:

[0045] I far =f(w1,w2,...w n |E in );

[0046] In the formula, I far Indicates the far-field output intensity; w1, w2, ... w n represents the waveguide width of the metasurface; E in represents the input electric field incident on the metasurface.

[0047] Furthermore, the optimization algorithm calculation formula of the supersurface parameters is:

[0048] w opt =argmin w ||f(E in )-I target ||;

[0049] In the formula, w opt represents the waveguide width of the optimized metasurface; I target Indicates target strength; E in represents the input electric field incident on the metasurface; w = (w1, w2, ... w n ) represents the geometric parameter vector of the metasurface design.

[0050] The beneficial effects of the present invention are:

[0051] The present invention uses a spatial coupled mode theory model, which far exceeds the traditional full-wave simulation in terms of computational efficiency. It can significantly reduce the calculation time while ensuring accuracy, thereby greatly improving the design efficiency. Secondly, compared with the local period approximation (LPA) method, the present invention can accurately consider the coupling effect between adjacent element units, thereby significantly improving the prediction accuracy and reliability in the design of complex optical systems. Especially in application scenarios such as high numerical aperture lenses, multi-wavelength focusing, and coma suppression, the spatial coupled mode theory shows excellent performance. In addition, the spatial coupled mode theory can cope with light field design under arbitrary incident conditions, breaking through the limitations of traditional methods on incident conditions, and greatly enhancing the flexibility and adaptability of the design. Through memory optimization, the spatial coupled mode theory also realizes efficient calculation of large-scale metasurfaces, greatly reducing memory usage, and providing strong support for the design and simulation of large-area metasurfaces. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0053] Figure 1 is a flow chart of a dielectric metasurface inverse optimization method based on spatial coupled mode theory according to an embodiment of the present invention;

[0054] Figure 2 It is a flow chart of a spatial coupled mode theory (SCMT) model in a dielectric metasurface inverse optimization method based on spatial coupled mode theory according to an embodiment of the present invention;

[0055] Figure 3 It is a hybrid architecture diagram of a spatial coupled mode theory (SCMT) model in a dielectric metasurface inverse optimization method based on spatial coupled mode theory according to an embodiment of the present invention;

[0056] Figure 4 This is a comparison diagram of the focal efficiency of SCMT and LPA for a high numerical aperture (NA) lens design in a dielectric metasurface inverse optimization method based on spatial coupled mode theory according to an embodiment of the present invention;

[0057] Figure 5 This is a comparison diagram of the focal efficiency of SCMT and LPA in a multi-wavelength lens design in a dielectric metasurface inverse optimization method based on spatial coupled mode theory according to an embodiment of the present invention;

[0058] Figure 6This is a comparison diagram of the side view and light intensity distribution of a lens optimized using SCMT at different incident angles in a dielectric metasurface inverse optimization method based on spatial coupled mode theory according to an embodiment of the present invention. DETAILED DESCRIPTION

[0059] To further illustrate each embodiment, the present invention provides drawings, which are part of the disclosure of the present invention and are mainly used to illustrate the embodiments. They can be used in conjunction with the relevant descriptions in the specification to explain the operating principles of the embodiments. With reference to these contents, ordinary technicians in this field should be able to understand other possible implementation methods and advantages of the present invention.

[0060] According to an embodiment of the present invention, a dielectric metasurface inverse optimization method based on spatial coupled mode theory is provided.

[0061] The present invention is further described with reference to the accompanying drawings and specific embodiments. Figure 1 As shown, according to the inverse optimization method of dielectric metasurface based on spatial coupled mode theory according to an embodiment of the present invention, the optimization method comprises the following steps:

[0062] S1. Create a truncated waveguide array based on the metasurface, calculate the guided mode and propagation constant of each waveguide according to the truncated waveguide array, and use the coupling matrix to couple adjacent waveguides to obtain a waveguide array.

[0063] It should be noted that the spatial coupled mode theory (SCMT) model considers the dielectric metasurface as an array of truncated waveguides, each of which can support a single guided mode, which defines the electric and magnetic field distributions of the light wave in the waveguide. These distributions can be expressed as the basis functions of the waveguide mode, and the guided mode has a transverse component. and the propagation constant β.

[0064] Specifically, the guided mode of the waveguide includes: the electric field distribution and magnetic field distribution of the light wave in the waveguide, wherein:

[0065] The calculation formula for the electric field distribution of light waves in the waveguide is:

[0066]

[0067] Where E(x,y,z) t represents the electric field distribution in the waveguide; represents the transverse electric field component of mode i; u i (z) represents the amplitude of mode i at z; x and y represent spatial coordinates, i.e., the positions on the waveguide cross section; z represents the longitudinal coordinate, i.e., the longitudinal position of light propagating in the waveguide; t represents the transverse direction, i.e., it is used to emphasize that the electric field and the magnetic field are transverse components; N represents the total number of waveguides in the waveguide array;

[0068] The calculation formula for the magnetic field distribution of light waves in the waveguide is:

[0069]

[0070] Where H(x,y,z) t represents the magnetic field distribution in the waveguide; represents the transverse magnetic field component of mode i; u i (z) represents the amplitude of mode i at z; x and y represent spatial coordinates, i.e., the positions on the waveguide cross section; z represents the longitudinal coordinate, i.e., the longitudinal position of light propagating in the waveguide; t represents the transverse direction, i.e., it is used to emphasize that the electric field and the magnetic field are transverse components; N represents the total number of waveguides in the waveguide array.

[0071] It should be noted that the mutual coupling between adjacent waveguides is described by the coupling matrix C, which can capture the near-field interaction between adjacent waveguides. The elements of the coupling matrix represent the coupling strength between the mode in a waveguide and the mode in its adjacent waveguide. The coupling effect is accurately described as the overlap integral of the electric and magnetic fields between the modes. The element c of the coupling matrix C is pm Represents the modal overlap between the electric field (E field) of mode p and the magnetic field (H field) of mode m.

[0072] Specifically, the coupling matrix calculation formula is:

[0073]

[0074] Where C represents the coupling matrix of the coupling strength between waveguides; U(z) represents the coefficient vector, U(z)=[u1(z),u2(z),...u N (z)]; K represents the coupling coefficient matrix, which is used to describe the coupling relationship between modes; B represents the diagonal matrix of the phase change characteristics during the propagation process, and its diagonal elements B ii =β i β i represents the propagation constant of mode i.

[0075] Specifically, the element c of the coupling matrix C is pm The calculation formula is:

[0076]

[0077] In the formula, c pm Represents the element value of the coupling matrix C; The unit vector representing the z longitudinal coordinate direction; represents the transverse electric field component of mode p; represents the transverse magnetic field component of mode m; x and y represent spatial coordinates, i.e., the positions on the waveguide cross section; z represents the longitudinal coordinate, i.e., the longitudinal position of light propagating in the waveguide; t represents the transverse direction, i.e., it is used to emphasize that the electric field and magnetic field are transverse components.

[0078] S2. Couple the input light field into the waveguide array, simulate the propagation of light in the waveguide based on the spatial coupled mode theory model, and use the Rayleigh-Sommerfeld diffraction theory to convert the near-field intensity distribution into the far-field intensity distribution.

[0079] It should be noted that coupling the input light field into the waveguide array is used to simulate the propagation of light in the metasurface and the final far-field intensity distribution. It is also to calculate the near-field distribution in the waveguide given the input electromagnetic field and convert it into the far-field intensity distribution in free space.

[0080] It should be noted that the input light field is coupled into the waveguide array, and the propagation of light in the waveguide is simulated by the spatial coupled mode theory model, and the near-field distribution of the metasurface is restored at the waveguide outlet; then, the near-field is propagated to the focal plane through the Rayleigh-Sommerfeld diffraction theory to generate the far-field intensity distribution.

[0081] It should be noted that the coupling of the input field is achieved by decomposing the incident electromagnetic field into waveguide modes; this coupling is achieved by decomposing the incident field into waveguide modes, and the initial mode amplitude of each waveguide is determined by the various mode components of the input field.

[0082] Specifically, the input light field is coupled into the truncated waveguide array, and the propagation of light in the waveguide is simulated based on the spatial coupled mode theory model, and then the near-field intensity distribution is converted into the far-field intensity distribution using the Rayleigh-Sommerfeld diffraction theory, which includes the following steps:

[0083] S21, decomposing the incident electromagnetic field to obtain the waveguide mode components of the input light field;

[0084] S22, calculating the initial mode amplitude of each waveguide based on the waveguide mode component of the input light field;

[0085] S23. Use the spatial coupled mode theory model to simulate the propagation process of the light field in the waveguide, and allow the modes of adjacent waveguides to interact with each other. When the light field propagates to the end of the waveguide, couple the light field to the free space to obtain the near-field intensity distribution of the metasurface at the waveguide exit.

[0086] S24. The near-field intensity distribution is propagated to the focal plane through the Rayleigh-Sommerfeld diffraction theory, and the far-field intensity distribution of the metasurface is calculated to obtain the far-field intensity distribution of the metasurface.

[0087] Specifically, the calculation formula for the initial mode amplitude is:

[0088]

[0089] In the formula, u i (0) represents the initial mode amplitude of mode i; E incident represents the input electromagnetic field; c represents the speed of light in vacuum; represents the transverse electric field component of mode i; n0 represents the refractive index of free space; represents the effective refractive index of mode i; t represents the transverse direction, which is used to emphasize that the electric field and the magnetic field are transverse components.

[0090] Specifically, the calculation formula for the far-field intensity distribution of the metasurface is:

[0091]

[0092] In the formula, E far (x, y) represents the far-field intensity distribution of the metasurface; (x, y) represents the electric field intensity E on the far-field plane far (x, y) represents the position of the near-field plane; (x', y') represents the electric field strength E on the near-field plane near The position of (x′, y′); r represents the distance between the near-field source point (x', y') and the observation point (x, y) in the far field; λ represents the wavelength; E near (x′, y′) represents the near-field intensity distribution at the waveguide outlet; j represents the imaginary unit; x' and y' represent the electric field intensity E on the near-field plane near (x′, y′) is the spatial coordinate of the location; x and y represent the electric field intensity E on the far field plane far (x, y) represents the spatial coordinates of the position; z represents the longitudinal coordinate, that is, the longitudinal position of the light propagating in the waveguide.

[0093] S3. The difference between the target intensity and the far-field intensity is calculated through the loss function to evaluate the effect of the current metasurface design, and the geometric parameters of the waveguide unit are gradually adjusted through the optimization algorithm.

[0094] It should be noted that based on the forward simulation, the geometric dimensions of the waveguide unit are adjusted through the optimization algorithm so that the far-field intensity distribution is as close to the target distribution as possible. By using the automatic differentiation framework, the calculation graph is automatically generated after the forward model calculation is completed, and the gradient of the loss function with respect to all input parameters can be calculated. Through back propagation, the hyperparameters of the metasurface can be updated using the optimizer.

[0095] Specifically, the difference between the target intensity and the far-field intensity is calculated by the loss function to evaluate the effect of the current metasurface design, and the geometric parameters of the waveguide unit are gradually adjusted by the optimization algorithm so that the far-field intensity distribution is consistent with the target intensity distribution, including the following steps:

[0096] S31, using the loss function, calculating the difference between the target intensity and the far-field intensity;

[0097] S32, based on the forward simulation, using the automatic differentiation framework, calculate the gradient of the loss function with respect to the waveguide width;

[0098] S33, adjusting the geometric dimensions of the waveguide unit by back propagation and using the optimization algorithm of the metasurface parameters, and calculating the optimized metasurface waveguide width;

[0099] S34. Based on the optimized metasurface waveguide width, a far-field intensity distribution consistent with the target intensity distribution is obtained.

[0100] Specifically, the calculation formula of the loss function is:

[0101] L=||I far -I target || 2 ;

[0102] Where L represents the difference between the target intensity and the far-field intensity; I far Indicates the far-field output intensity; I target Indicates the target strength;

[0103] Among them, the far-field output intensity I far The calculation formula is:

[0104] I far =f(w1,w2,…w n |E in );

[0105] In the formula, I far Indicates the far-field output intensity; w1, w2, … w n represents the waveguide width of the metasurface; E in represents the input electric field incident on the metasurface.

[0106] Specifically, the optimization algorithm calculation formula for the supersurface parameters is:

[0107] w opt =argmin w ||f(E in )-I target ||;

[0108] In the formula, w opt represents the waveguide width of the optimized metasurface; I target Indicates target strength; E in represents the input electric field incident on the metasurface; w = (w1, w2, ... w n ) represents the geometric parameter vector of the metasurface design.

[0109] In summary, the present invention includes the establishment of a spatial coupled mode theoretical model, the construction of a forward solver, the definition of optimization targets, and gradient optimization; wherein, the spatial coupled mode theoretical model comprehensively describes the near-field coupling effect between adjacent elements of the metasurface by accurately calculating the coupling coefficient between waveguides; in this model, the input field is first coupled to the guided mode of each element, and then the propagation process of the light field inside the element is simulated, while allowing the modes between adjacent elements to interact; when the light field propagates to the end of the waveguide, it is coupled back to the free space, and with the help of the Rayleigh-Sommerfeld diffraction theory, the far-field distribution of the metasurface is further derived; in the inverse design link, the optimization target is determined by setting a loss function, which aims to quantify the difference between the target far-field intensity of the metasurface and the actual calculated intensity; in order to effectively adjust the structural parameters of the element to minimize the loss, the present invention adopts an automatic differentiation framework to calculate the gradient of the loss function to the waveguide width, and performs gradient optimization based on the optimization algorithm.

[0110] like Figure 3 FIG. 1 is a hybrid architecture diagram of the spatial coupled mode theory (SCMT) model according to an embodiment of the present invention; the forward solver of the hybrid architecture is regarded as a nonlinear function, and its output is the near-field E out , the input is the waveguide width ω and the incident field E in β S is the propagation constant array of each waveguide; the matrix B is a diagonal matrix, and β is its diagonal element; C represents the coupling matrix of the coupling strength between waveguides; K represents the coupling coefficient matrix, which is used to describe the coupling relationship between modes; β is calculated by pre-training the neural network i , c ij , k ij , which can effectively improve efficiency and support the calculation of width gradients; the mode propagation in the waveguide is differentially calculated by the Euler method, which can effectively save memory; β i represents the propagation constant of mode i; c ij represents the modal overlap between the electric field (E field) of mode i and the magnetic field (H field) of mode j in the coupling matrix C; k ij Represents the elements in the coupling coefficient matrix K.

[0111] In order to facilitate understanding of the above technical solutions of the present invention, the working principle or operation mode of the present invention in the actual process is described in detail below.

[0112] In order to verify the effectiveness of the present invention, the method of the present invention was simulated in three application scenarios: high numerical aperture (NA) lens, multi-wavelength lens, and coma suppression lens, and compared with the most popular full-wave simulation (FDTD) and LPA methods.

[0113] The experimental simulation contents are as follows:

[0114] For high numerical aperture (NA) lenses, their edges have rapidly changing phase profiles, which reduces the accuracy of the LPA method; based on the superlens designed by the LPA method, the SCMT method is used to improve the focusing efficiency of the radial superlens with a numerical aperture of NA=0.8 and a wavelength of 650nm; the metasurface is composed of titanium dioxide (TiO2) square waveguides, and the waveguide array is placed on a silicon dioxide (SiO2) substrate with a period of 400nm; the height of each waveguide is 800nm, and the width ranges from 160nm to 380nm.

[0115] like Figure 4 , which is a comparison diagram of the focus efficiency of SCMT and LPA of the high numerical aperture (NA) lens design described in an embodiment of the present invention, wherein after SCMT optimization, the focus efficiency is increased from 35% to 40%.

[0116] Similar to large numerical aperture (NA) lenses, superlenses that focus multi-wavelength light also reduce the accuracy of the LPA method; a superlens that supports simultaneous focusing of two wavelengths (650nm and 450nm) is designed using both SCMT and LPA methods; the NA is 0.4, the metasurface is composed of titanium dioxide (TiO2) square waveguides, the substrate is silicon dioxide (SiO2), and the period is 280nm; the height of the waveguide is 800nm, and the width ranges from 80nm to 240nm.

[0117] like Figure 5 As shown, it is a comparison diagram of the focus efficiency of the multi-wavelength lens design SCMT and LPA according to an embodiment of the present invention, wherein the efficiency of the lens designed by SCMT at 650nm is slightly lower than that of LPA, but at 450nm, its efficiency is much higher than that of LPA.

[0118] A single-layer metasurface lens with less coma is a better choice, which requires accurate modeling of plane waves with different incident angles, which cannot be achieved by the LPA method; by using the SCMT model to equally maximize the focal intensity for different incident angles, a single-layer metal lens can be designed.

[0119] like Figure 6 As shown, a side view of a lens optimized using SCMT and a comparison diagram of light intensity distribution at different incident angles described in an embodiment of the present invention can perfectly focus a vertically incident plane wave. However, as the incident angle increases, coma also increases. In contrast, the lens optimized using SCMT significantly suppresses coma when the incident angle is plus or minus 40 degrees.

[0120] In summary, with the help of the above-mentioned technical scheme of the present invention, the present invention, through the spatial coupled mode theoretical model, is far more computationally efficient than the traditional full-wave simulation, can significantly reduce the calculation time while ensuring accuracy, and greatly improves the design efficiency; secondly, compared with the local periodic approximation (LPA) method, the present invention can accurately consider the coupling effect between adjacent element units, thereby significantly improving the prediction accuracy and reliability in the design of complex optical systems; especially in application scenarios such as high numerical aperture lenses, multi-wavelength focusing, and coma suppression, the spatial coupled mode theory shows excellent performance; in addition, the spatial coupled mode theory can cope with the light field design of arbitrary incident conditions, breaking through the limitations of traditional methods on incident conditions, and greatly enhancing the flexibility and adaptability of the design; through memory optimization, the spatial coupled mode theory also realizes efficient calculation of large-scale metasurfaces, greatly reducing memory usage, and providing strong support for the design and simulation of large-area metasurfaces.

[0121] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A dielectric metasurface inverse optimization method based on spatial coupled mode theory, characterized in that: The optimization method includes the following steps: S1. Create a truncated waveguide array based on the metasurface, calculate the guided mode and propagation constant of each waveguide according to the truncated waveguide array, and couple adjacent waveguides using a coupling matrix to obtain a waveguide array; S2, coupling the input light field into the waveguide array, simulating the propagation of light in the waveguide based on the spatial coupled mode theory model, and converting the near-field intensity distribution into the far-field intensity distribution using the Rayleigh-Sommerfeld diffraction theory; S3. The difference between the target intensity and the far-field intensity is calculated through the loss function to evaluate the effect of the current metasurface design, and the geometric parameters of the waveguide unit are gradually adjusted through the optimization algorithm.

2. According to claim 1, a dielectric metasurface inverse optimization method based on spatial coupled mode theory is characterized in that: The guided mode of the waveguide includes: the electric field distribution and magnetic field distribution of the light wave in the waveguide, wherein: The calculation formula for the electric field distribution of light waves in the waveguide is: Where E(x,y,z) t represents the electric field distribution in the waveguide; represents the transverse electric field component of mode i; u i (z) represents the amplitude of mode i at position z; x and y represent spatial coordinates; z represents the longitudinal coordinate; t represents the transverse coordinate; N represents the total number of waveguides in the waveguide array; The calculation formula for the magnetic field distribution of light waves in the waveguide is: Where H(x,y,z) t represents the magnetic field distribution in the waveguide; represents the transverse magnetic field component of mode i; u i (z) represents the amplitude of mode i at position z; x and y represent spatial coordinates; z represents the longitudinal coordinate; t represents the transverse coordinate; and N represents the total number of waveguides in the waveguide array.

3. The method for inverse optimization of dielectric metasurface based on spatial coupled mode theory according to claim 1, characterized in that: The coupling matrix calculation formula is: Where C represents the coupling matrix of the coupling strength between waveguides; U(z) represents the coefficient vector, U(z)=[u1(z),u2(z),...u N (z)]; K represents the coupling coefficient matrix, which is used to describe the coupling relationship between modes; B represents the diagonal matrix of the phase change characteristics during the propagation process, and its diagonal elements B ii =β i β i represents the propagation constant of mode i.

4. The method for inverse optimization of dielectric metasurface based on spatial coupled mode theory according to claim 3, characterized in that: The element c of the coupling matrix C pm The calculation formula is: In the formula, c pm Represents the element value of the coupling matrix C; The unit vector representing the z longitudinal coordinate direction; represents the transverse electric field component of mode p; represents the transverse magnetic field component of mode m; x and y represent spatial coordinates; z represents the longitudinal coordinate; and t represents the transverse direction.

5. The method for inverse optimization of dielectric metasurface based on spatial coupled mode theory according to claim 1, characterized in that: The method of coupling the input light field into the truncated waveguide array, simulating the propagation of light in the waveguide based on the spatial coupled mode theory model, and then converting the near-field intensity distribution into the far-field intensity distribution using the Rayleigh-Sommerfeld diffraction theory includes the following steps: S21, decomposing the incident electromagnetic field to obtain the waveguide mode components of the input light field; S22, calculating the initial mode amplitude of each waveguide based on the waveguide mode component of the input light field; S23. Use the spatial coupled mode theory model to simulate the propagation process of the light field in the waveguide, and allow the modes of adjacent waveguides to interact with each other. When the light field propagates to the end of the waveguide, couple the light field to the free space to obtain the near-field intensity distribution of the metasurface at the waveguide exit. S24. The near-field intensity distribution is propagated to the focal plane through the Rayleigh-Sommerfeld diffraction theory, and the far-field intensity distribution of the metasurface is calculated to obtain the far-field intensity distribution of the metasurface.

6. The method for inverse optimization of dielectric metasurface based on spatial coupled mode theory according to claim 5, characterized in that: The calculation formula of the initial mode amplitude is: In the formula, u i (0) represents the initial mode amplitude of mode i; E incident represents the input electromagnetic field; c represents the speed of light in vacuum; represents the transverse electric field component of mode i; n0 represents the refractive index of free space; represents the effective refractive index of mode i; t represents the transverse direction.

7. The method for inverse optimization of dielectric metasurface based on spatial coupled mode theory according to claim 5, characterized in that: The calculation formula of the far-field intensity distribution of the metasurface is: In the formula, E far (x, y) represents the far-field intensity distribution of the metasurface; (x, y) represents the electric field intensity E on the far-field plane far (x, y) represents the position of the near-field plane; (x', y') represents the electric field strength E on the near-field plane near The position of (x′, y′); r represents the distance between the near-field source point (x', y') and the observation point (x, y) in the far field; λ represents the wavelength; E near (x′, y′) represents the near-field intensity distribution at the waveguide outlet; j represents the imaginary unit; x' and y' represent the electric field intensity E on the near-field plane near (x′, y′) is the spatial coordinate of the location; x and y represent the electric field intensity E on the far field plane far (x, y) are the spatial coordinates of the location; z represents the vertical coordinate.

8. The method for inverse optimization of dielectric metasurface based on spatial coupled mode theory according to claim 1, characterized in that: The method of calculating the difference between the target intensity and the far-field intensity by using the loss function to evaluate the effect of the current metasurface design and gradually adjusting the geometric parameters of the waveguide unit by using the optimization algorithm so that the far-field intensity distribution is consistent with the target intensity distribution includes the following steps: S31, using the loss function, calculating the difference between the target intensity and the far-field intensity; S32, based on the forward simulation, using the automatic differentiation framework, calculate the gradient of the loss function with respect to the waveguide width; S33, adjusting the geometric dimensions of the waveguide unit by back propagation and using the optimization algorithm of the metasurface parameters, and calculating the optimized metasurface waveguide width; S34. Based on the optimized metasurface waveguide width, a far-field intensity distribution consistent with the target intensity distribution is obtained.

9. The method for inverse optimization of dielectric metasurface based on spatial coupled mode theory according to claim 8, characterized in that: The calculation formula of the loss function is: L=||I far -I target || 2 ; Where L represents the difference between the target intensity and the far-field intensity; I far Indicates the far-field output intensity; I target Indicates the target strength; Among them, the far-field output intensity I far The calculation formula is: I far =f(w1,w2,...w n |E in ); In the formula, I far Indicates the far-field output intensity; w1, w2, ... w n represents the waveguide width of the metasurface; E in represents the input electric field incident on the metasurface.

10. The method for inverse optimization of dielectric metasurface based on spatial coupled mode theory according to claim 8, characterized in that: The optimization algorithm calculation formula of the super surface parameters is: w opt =argmin w ||f(E in )-I target ||; In the formula, w opt represents the waveguide width of the optimized metasurface; I target Indicates target strength; E in represents the input electric field incident on the metasurface; w = (w1, w2, ... w n ) represents the geometric parameter vector of the metasurface design.

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