Achromatic polarization multiplexing superlens and hybrid inverse design method thereof

Abstract

The application relates to the field of micro-nano optical technology and discloses an achromatic polarization multiplexing superlens and a hybrid reverse design method thereof. The achromatic polarization multiplexing superlens comprises a sapphire substrate and a cross-shaped silicon dielectric column array, and a unit is regulated by four geometric parameters of X and Y direction arm lengths and transverse and longitudinal arm widths. The hybrid reverse design method is based on RCWA to establish a multi-wavelength TE / TM polarization multiplexing transmission response library, define TE achromatic focusing phase, TM vortex phase and group delay targets, search for global dispersion compensation parameters by using a particle swarm algorithm, screen matching units, and generate an initial structure layout; then, according to unit multiplexing transmission responses and a propagation model, output plane light fields are calculated, TE focal fields and TM vortex fields are evaluated, and when the evaluation does not meet preset conditions, light field deviations caused by non-periodic arrangement coupling errors and a propagation model approximation are corrected in combination with accompanying optimization. The application can realize TE achromatic focusing and TM vortex light output in a single layer mid-infrared device.

Description

Technical Field

[0001] This invention relates to the field of micro-nano optics technology, and more specifically to an achromatic polarization multiplexing superlens and its hybrid reverse design method. The hybrid reverse design method is used to design superlenses that combine high focusing efficiency and multifunctional multiplexing in the mid-infrared band. Background Technology

[0002] Mid-infrared light field manipulation plays a crucial role in thermal imaging, molecular fingerprint spectroscopy analysis, and free-space optical communication. Among these, achromatic lenses are the core components ensuring high-quality imaging across a wide wavelength range. Currently, traditional mid-infrared optical systems largely rely on high-refractive-index materials such as germanium and zinc selenide, typically requiring the stacking of multiple lenses to correct chromatic aberration. However, this traditional optical architecture is bulky and heavy, and it is difficult to integrate multiple light field manipulation functions onto a single device, failing to meet the demands of modern optical systems for lightweight design, miniaturization, and high integration.

[0003] Metasurfaces are planar optical devices composed of subwavelength artificial microstructures. They offer high design freedom and integration, enabling flexible manipulation of the amplitude, phase, and polarization state of light waves at the subwavelength scale, thus finding wide application in multidimensional optical field manipulation. Among them, achromatic metalenses, utilizing the dispersion compensation mechanism of micro / nano structures, can achieve predetermined focusing functions over a wide wavelength range, making them an important candidate to replace traditional infrared refractive lenses. Compared to traditional multi-level diffractive lenses, metalenses not only offer advantages in planarity and lightweight design but also facilitate large-scale manufacturing using semiconductor processes.

[0004] Building upon this foundation, by further incorporating polarization multiplexing functionality into achromatic superlenses, different optical field manipulation functions can be achieved within the same device for different polarization states. For example, focusing can be achieved under transverse electric (TE) polarization incidence, while vortex light output can be achieved under transverse magnetic (TM) polarization incidence, thereby further enhancing the device's functional integration and application value. Therefore, achromatic polarization multiplexing superlenses have promising application prospects in mid-infrared integrated imaging, spectral detection, and information transmission.

[0005] However, existing achromatic superlenses, especially those with polarization multiplexing capabilities, still have the following design problems that need to be solved: First, traditional forward design methods based on cell library matching usually ignore the near-field electromagnetic coupling effect between aperiodic structural cells, which can easily lead to a decrease in focusing efficiency and insufficient dispersion compensation accuracy when dealing with large numerical apertures or complex phase distributions. Second, while gradient-based adjoint optimization methods can correct physical errors to some extent, their optimization results are usually related to how closely the initial structure approximates the target response. When the initial structure deviates significantly from the target phase, target group delay, or target optical field distribution, the optimization process may encounter problems such as reduced convergence speed, parameter update oscillations, or convergence to an undesirable local solution. Therefore, in multi-wavelength, multi-functional design tasks, a high-quality initial structure is required as the starting point for optimization.

[0006] Therefore, proposing a hybrid inverse design method that can obtain high-quality initial structures through global search and perform full-field fine optimization by combining physical gradients has important practical significance. Summary of the Invention

[0007] In view of this, the present invention provides an achromatic polarization multiplexed superlens and its hybrid reverse design method. The aim is to achieve TE polarization achromatic focusing and TM polarization vortex light output in the same single-layer mid-infrared superlens by using a multi-parameter complex transmission response library of a cross-shaped silicon dielectric pillar unit, particle swarm optimization, and propagation model evaluation. The TE polarization focusing performance and TM polarization vortex light field quality of the initial structural layout are evaluated based on the propagation model. When both the focusing performance conditions of the TE polarization channel and the vortex light field quality conditions of the TM polarization channel meet preset conditions, the initial structural layout is output. When either condition is not met, the initial structural layout is used as a starting point for adjoint optimization correction to correct near-field electromagnetic coupling errors caused by aperiodic arrangement and optical field deviations caused by propagation model approximation, thereby improving the design feasibility and optical field control quality of multi-wavelength, multi-polarization multiplexed superlens.

[0008] To achieve the above objectives, the present invention adopts the following technical solution: In a first aspect, the present invention provides a hybrid reverse design method for an achromatic polarization multiplexing superlens, comprising the following steps: The first step is to establish a parameterized model of a cross-shaped silicon dielectric pillar unit, which includes four geometric parameters: arm length along the X direction, arm length along the Y direction, width of the horizontal arm along the X direction, and width of the vertical arm along the Y direction. Under a preset set of working wavelengths and two polarization states, TE and TM, the four geometric parameters are scanned based on the rigorous coupled-wave analysis (RCWA) method to obtain the complex transmission response corresponding to different geometric parameters, and a response database between geometric parameters and transmission phase, transmission amplitude, and group delay is established. The second step is to define the phase distribution of the achromatic focused target in the TE polarization channel and the phase distribution of the achromatic vortex target in the TM polarization channel, and determine the target group delay distribution based on the target phase change relationship under different working wavelengths. The third step involves constructing a matching error function based on the response database, target phase distribution, and target swarm delay distribution; using the particle swarm algorithm to search for global dispersion compensation parameters; and selecting the cross-shaped silicon dielectric pillar unit with the smallest matching error at each sampling position of the full aperture of the superlens to generate the initial structural layout. The fourth step involves constructing the complex amplitude distribution of the superlens exit surface based on the complex transmission response of each unit in the initial structural layout, and calculating the light field distribution at the target output surface using a propagation model to evaluate the focusing performance of the TE polarization channel and the vortex light field quality of the TM polarization channel. The evaluation results from the propagation model are used to determine whether preset conditions are met, including the focusing performance conditions of the TE polarization channel and the vortex light field quality conditions of the TM polarization channel. If met, the initial structural layout is output; otherwise, the initial structural layout is used as the starting structure for adjoint optimization correction, and the corrected structural layout is output.

[0009] In one specific implementation, the response database is obtained through RCWA parameter scanning, the operating wavelengths of which include 3.5μm, 4.0μm, and 4.5μm, the lattice period of the cross-shaped silicon dielectric pillar unit is 1.8μm to 2.2μm, and the height is 4.0μm to 6.0μm; the values ​​of the four geometric parameters are all in the range of 0.5μm to 1.5μm, and the response database includes at least the transmission amplitude, transmission phase, and group delay response under TE polarization and TM polarization.

[0010] In one specific implementation scheme, the phase distribution of the achromatic focusing target in the TE polarization channel is as follows: ； The achromatic vortex target phase distribution of the TM polarization channel is as follows: ； in, This represents the radial distance from the corresponding unit position within the superlens plane to the center of the lens. To design the focal length, Let be the angular frequency of the incident light. It is the speed of light in a vacuum. Let be the topological charge number of the vortex beam. This represents the azimuth angle of the corresponding unit position within the superlens plane.

[0011] In one specific implementation scheme, after obtaining the initial structural layout, the scheme further includes an adjoint optimization correction step based on the full-wave electromagnetic field and multidimensional geometric gradient; in the adjoint optimization correction step, the mathematical model of the full-wave electromagnetic field and multidimensional geometric gradient is based on the Lorentz reciprocity theorem, and the quality factor is... For geometric parameters The derivative is: ; in, Represents the quality factor in relation to geometric parameters The derivative of Indicates the geometric parameters of the cross-shaped silicon dielectric pillar unit; For the positive incident field at position and wavelength Electric field distribution under, For the accompanying electric field distribution, For position The dielectric constant distribution at that location, Indicates the dielectric constant distribution with respect to geometric parameters The partial derivatives, For the volume of the simulation region, This indicates taking the real part.

[0012] In one specific implementation, the accompanying optimization and correction steps include: The three-dimensional sensitivity field calculated in the accompanying optimization correction step is mean-compressed along the device thickness direction to obtain a two-dimensional gradient distribution, the calculation formula of which is: ; in, The compressed two-dimensional gradient distribution For a three-dimensional sensitivity field, The height of the cross-shaped silicon dielectric pillar unit. , and Spatial coordinates; For the two-dimensional gradient distribution Two-dimensional spline interpolation is performed to obtain a continuous two-dimensional gradient function. ; For the four geometric parameters of the cross-shaped silicon dielectric pillar unit, samples are taken according to their corresponding boundary positions, and the parameter update amount is calculated.

[0013] In a specific feasible implementation, in the accompanying optimization correction step, corresponding quality factors are constructed based on the TE polarization target and the TM polarization target, respectively, and a weighted joint objective function is formed. In the k-th iteration, the joint objective function is: ; in, and They represent the first The quality factors corresponding to the TE polarization target and the TM polarization target at the next iteration. and Let each represent the corresponding dynamic weight, and satisfy the following conditions: .

[0014] In one specific implementation scheme, the dynamic weights are adaptively adjusted based on the performance indicators of the polarization channel corresponding to the previous state; wherein, the optimal initial structural layout output by the particle swarm optimization algorithm is defined as the 0th iteration state; when At that time, the dynamic weights are determined based on the performance indicators corresponding to the TE polarization channel and the TM polarization channel in the 0th iteration state; when At that time, the dynamic weight is based on the first The performance indicators corresponding to the TE polarization channel and TM polarization channel are determined in the next iteration state; the calculation formula for the dynamic weight is: ; ; in, The iteration number is greater than or equal to 1; when hour, and These represent the performance indicators corresponding to the TE polarization channel and the TM polarization channel in the 0th iteration state, respectively; when hour, and They represent the first Performance metrics for the TE polarization channel and TM polarization channel in the next iteration state; It is a small positive number greater than 0, used to avoid the denominator being zero and to improve the numerical stability of weight calculation.

[0015] In one specific feasible implementation, the performance metrics Defined as the first The normalized focusing efficiency of the TE polarization channel within the target focal region in the next iteration state is calculated using the following formula: ; in, Indicates the first The electric field distribution of the TE polarization channel on the output surface in the next iteration state. This represents the region of focal integration centered on the theoretical focus. Indicates the statistical region of the output surface; The performance indicators Defined as the first The normalized matching degree between the output mode field of the TM polarization channel and the target vortex mode field in the next iteration is calculated using the following formula: ; in, Indicates the first The actual electric field distribution of the TM polarization channel on the output surface in the next iteration state. This represents the complex amplitude distribution of the target vortex mode field. This indicates the conjugate operation.

[0016] In one specific implementation, after calculating the parameter update amount, the parameter update amount is normalized to obtain a normalized parameter update amount; the normalized parameter update amount is used for the iterative update of geometric parameters in the accompanying optimization correction step.

[0017] Secondly, an achromatic polarization multiplexing superlens, designed using the aforementioned hybrid reverse design method, includes: Sapphire substrate; and Multiple cross-shaped silicon dielectric pillar units are formed on the upper surface of the sapphire substrate; The multiple cross-shaped silicon dielectric pillar units are arranged at equal intervals according to a square lattice to form a metasurface array; The geometric parameters of the cross-shaped silicon dielectric pillar unit include the arm length along the X direction. Arm length along the Y direction Width of the transverse arm along the X direction and the width of the longitudinal arm along the Y direction ; The spacing between the centers of adjacent units in both the X and Y directions is equal to the lattice period. The lattice period The determination is based on a comprehensive consideration of the device's operating wavelength, unit structure size range, phase modulation requirements, and focusing performance requirements.

[0018] Compared with existing technologies, the achromatic polarization multiplexing superlens and its hybrid reverse design method described in this invention generate an initial structural layout using an RCWA unit complex transmission response library and a particle swarm optimization (PSO) algorithm for global search. The initial structural layout is then output based on the propagation model evaluation results. Alternatively, starting from this initial structural layout, local corrections are made by combining adjoint optimization, three-dimensional sensitivity field thickness direction compression, and two-dimensional spline interpolation. This achieves the collaborative design of mid-infrared broadband achromatic polarization multiplexing superlenses and has the following beneficial effects: 1. This invention uses the RCWA unit complex transmission response library and particle swarm optimization algorithm to search for global dispersion compensation parameters. Under multi-wavelength conditions, it simultaneously considers target phase matching and target swarm delay matching, thereby obtaining an initial structural layout constrained by the unit complex transmission response, target phase, and target swarm delay. Compared to using random or empirical structures as the starting point for optimization, this initial structural layout already possesses an initial optical response close to the target wavefront and target dispersion response before entering the propagation model evaluation or accompanying optimization correction. Therefore, it can provide a physically realizable starting structure for subsequent correction steps, helping to reduce the sensitivity of the local optimization process to random initial conditions and narrowing the search range for subsequent parameter corrections.

[0019] 2. This invention uses a cross-shaped silicon dielectric pillar unit with four geometric parameters. Compared with the traditional simple rectangular or cuboid structure, it has a higher degree of freedom in phase adjustment and a stronger dispersion compensation capability. It can achieve differentiated optical field control for the two polarization states of TE and TM, thereby realizing the polarization multiplexing function of TE achromatic focusing and TM vortex light output on a single device.

[0020] 3. In the accompanying optimization and correction process, this invention compresses the three-dimensional sensitivity field along the device thickness direction into a two-dimensional gradient distribution, and obtains a continuous gradient function through two-dimensional spline interpolation. Then, it extracts the corresponding geometric parameter update amounts based on the boundary positions of the arm length and arm width of the cross-shaped silicon dielectric pillar unit. Thus, the three-dimensional electromagnetic field sensitivity information can be converted into parameter gradients corresponding to the two-dimensional layout geometric parameters, reducing the sensitivity to mesh discretization and local field fluctuations when directly using local three-dimensional mesh point information for parameter updates, thereby helping to improve the stability of parameter updates during the accompanying optimization and correction process.

[0021] 4. The superlens of the present invention operates in the mid-infrared atmospheric window of 3.5μm to 4.5μm, and uses a combination of silicon and sapphire materials. It has low absorption loss and high refractive index contrast, and is compatible with semiconductor micro-nano processing technology. It has the potential for miniaturization, integration and mass production. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0023] Figure 1 This is an overall flowchart of a hybrid reverse design method for an achromatic polarization multiplexing superlens provided in an embodiment of the present invention; Figure 2This is a schematic diagram of the cross-shaped silicon dielectric pillar unit structure and array arrangement in an embodiment of the present invention, wherein, Figure 2 (a) is a three-dimensional structural diagram of a cross-shaped silicon dielectric pillar unit disposed on a sapphire substrate. Figure 2 (b) is a schematic diagram of the array arrangement of multiple cross-shaped silicon dielectric pillar units arranged in a square lattice; 1 in the figure is a sapphire substrate and 2 is a cross-shaped silicon dielectric pillar unit; Figure 3 This is a schematic diagram of the principle of three-dimensional sensitivity field compression along the thickness direction and two-dimensional interpolation mapping in an embodiment of the present invention; 3 in the figure is the three-dimensional sensitivity field, 4 is the compression process along the thickness direction of the device, and 5 is the two-dimensional gradient mapping plane; Figure 4 This is a phase and transmission amplitude response diagram obtained by scanning the cross-shaped silicon dielectric pillar unit based on RCWA parameters in an embodiment of the present invention, wherein... Figure 4 (a) is the transmission phase response diagram of the TE polarization channel. Figure 4 (b) shows the transmission amplitude response diagram of the TE polarization channel. Figure 4 (c) is the transmission phase response diagram of the TM polarization channel. Figure 4 (d) is the transmission amplitude response diagram of the TM polarization channel; Figure 5 This is a fitness convergence curve of the particle swarm optimization process in an embodiment of the present invention. Figure 6 The normalized focal field distribution of the TE polarization channel at 3.5 μm, 4.0 μm, and 4.5 μm is obtained based on the RCWA unit complex transmission response and propagation model. Figure 6 (a) Figure 6 (b) and Figure 6 (c) Corresponding to operating wavelengths of 3.5μm, 4.0μm and 4.5μm respectively; Figure 7 The normalized vortex optical field distribution of the TM polarization channel at 3.5 μm, 4.0 μm, and 4.5 μm is obtained based on the RCWA unit complex transmission response and propagation model. Figure 7 (a) Figure 7 (b) and Figure 7 (c) Corresponding to working wavelengths of 3.5μm, 4.0μm and 4.5μm respectively. Detailed Implementation

[0024] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0025] The achromatic polarization multiplexing superlens described in this invention, such as Figure 2 As shown, it includes a sapphire substrate 1 and a plurality of cross-shaped silicon dielectric pillar units 2 formed on the upper surface of the sapphire substrate 1; the plurality of cross-shaped silicon dielectric pillar units 2 are arranged at equal intervals according to a square lattice to form a metasurface array.

[0026] Here, "multiple" refers to the number of cross-shaped silicon dielectric pillar units required to constitute a two-dimensional metasurface array, rather than a single cross-shaped silicon dielectric pillar unit; for example, it could be... An array consisting of cross-shaped silicon dielectric pillar units, wherein and All are integers greater than or equal to 2. The specific number of the cross-shaped silicon dielectric pillar units is determined based on the aperture size of the superlens, the lattice period, and the target focal length.

[0027] The equally spaced square lattice arrangement means that the center points of each cross-shaped silicon dielectric pillar unit form a square grid within the plane of the sapphire substrate 1, and the spacing between the centers of adjacent units in the X and Y directions is equal to the lattice period. The lattice period Based on a comprehensive consideration of the device's operating wavelength, unit cell size range, phase modulation requirements, and focusing performance requirements, the preferred setting is a range that allows the metasurface array to primarily maintain zero-order diffraction propagation and suppress higher-order diffraction within the operating wavelength range, ensuring sufficient arrangement density and phase sampling accuracy between adjacent units. Furthermore, the lattice period... When the lattice period P is too large, it can easily introduce higher-order diffraction and reduce wavefront reconstruction accuracy, thereby affecting focusing efficiency and achromatic performance; when the lattice period P is too small, it may increase electromagnetic coupling between adjacent units and increase processing difficulty. Therefore, in this invention, the lattice period P is... The array period parameters are determined to balance fabrication feasibility, unit control capability, and device focusing performance.

[0028] In one alternative embodiment, the cross-shaped silicon dielectric pillar array can be formed on the sapphire substrate 1 using electron beam lithography and inductively coupled plasma etching processes. The fabrication process can be implemented using conventional micro / nano fabrication techniques in the art, therefore, the fabrication process will not be described in detail or further limited.

[0029] The achromatic polarization multiplexing superlens described in this invention operates in the mid-infrared band (3.5μm–4.5μm) and possesses polarization multiplexing characteristics. It can converge incident TE polarized light to form an achromatic focal point and convert incident TM polarized light into an achromatic vortex beam. The topological charge of the vortex beam can be set according to the target vortex mode; in one specific embodiment, it can be... .

[0030] This invention further provides a hybrid reverse design method for the above-mentioned achromatic polarization multiplexing superlens, such as... Figure 1 As shown, the method includes the following steps: The first step is to generate a global initial layout based on the particle swarm optimization algorithm.

[0031] First, the geometric parameters of the cross-shaped silicon dielectric pillar unit are scanned to establish a database corresponding to the geometric parameters and optical responses. The geometric parameters are denoted as follows: in, Let X be the arm length along the X direction. Let the arm length be along the Y direction. The width of the transverse arm along the X direction. The width of the longitudinal arm along the Y direction. The optical response includes at least the transmission phase and group delay.

[0032] In this embodiment, the group delay is determined by the relationship between the transmission phase and the angular frequency, which can be expressed as: in, Indicates group delay, Indicates the transmission phase. It represents angular frequency.

[0033] Under discrete wavelength simulation conditions, the group delay can also be approximated by the transmission phase difference at adjacent frequency points.

[0034] After establishing the database, the target phase distribution under different polarization channels is defined respectively.

[0035] The target phase of the TE polarization channel is the achromatic focusing target phase; The target phase of the TM polarization channel is the achromatic vortex target phase.

[0036] The phase distribution of the achromatic focused target in the TE polarization channel can be expressed as: The phase distribution of the achromatic vortex target in the TM polarization channel can be expressed as: in, This represents the radial distance from the corresponding unit position within the superlens plane to the center of the lens. To design the focal length, Let be the angular frequency of the incident light. It is the speed of light in a vacuum. Let be the topological charge number of the vortex beam. This represents the azimuth angle of the corresponding unit position within the superlens plane.

[0037] Subsequently, based on the target phase distribution and the target group delay distribution, a fitness function is constructed to characterize the degree of matching between the optical response of the candidate cross-shaped silicon dielectric pillar unit and the target requirements.

[0038] The particle swarm optimization (PSO) algorithm is used to search for the optimal global dispersion compensation parameters across the entire aperture range to generate an initial structure distribution that meets the achromatic requirements. The global dispersion compensation parameters refer to a set of parameters to be optimized at each operating wavelength to correct the overall target phase distribution; their dimension corresponds to the number of operating wavelengths. Specifically, the search space for the PSO algorithm is first constructed based on the cross-shaped silicon dielectric pillar cell database obtained from parameter scanning. The position vector of each particle... This represents a set of candidate global dispersion compensation parameters, which in one embodiment can be written as: ,in, Indicates the first Global phase compensation parameters at each operating wavelength Indicates the number of operating wavelengths; velocity vector This represents the update step size of the particle in the parameter space. For a given particle position vector... First in The sampling location and the first At each operating wavelength, the basic target phase is calculated according to the aforementioned target phase distribution formula, and combined with... The compensation parameters corresponding to the working wavelength are used to obtain the target phase at the sampling position under the working wavelength; then, based on the ratio of the target phase difference to the angular frequency interval at the corresponding angular frequency points of adjacent working wavelengths, the corresponding target group delay is approximately obtained.

[0039] Subsequently, for each candidate cross-shaped silicon dielectric pillar cell in the database, the phase error between its phase response and the target phase, and the group delay error between its group delay response and the target group delay are calculated, and a weighted matching error function is constructed. In one embodiment, the first... Candidate cells at each sampling location The matching error can be expressed as: in, Indicates the first At the sampling location, the first The matching error of each candidate unit. Indicates the sampling location number. Indicates the candidate unit number; Indicates the first The candidate unit in the th The encapsulation phase error between the phase response at each sampling location and the target phase; Indicates the first The candidate unit in the th The group delay response at each sampling location Indicates the first Target group delay at each sampling location; This represents the group delay normalization factor, used to make the group delay error term dimensionless. Preferably, The maximum absolute value of the target group delay at all sampling locations within the current design band can be taken, i.e., the maximum value of each... The largest of the absolute values; when this maximum value is too small or close to zero, the larger of the average of the absolute values ​​of the target group delay at all sampling locations and the preset lower limit value can also be taken as the value. . and Let represent the weighting coefficients of the phase error term and the group delay error term, respectively. Both are non-negative and preferably satisfy . + =1. and To balance the contributions of phase matching accuracy and group delay matching accuracy to the matching error, its specific value can be tuned through conventional numerical experiments based on the average magnitude of the two types of error terms in the initial iteration phase. In an optional embodiment, when achromatic performance is emphasized more, it can be appropriately increased. When greater emphasis is placed on the accuracy of target wavefront matching, it can be appropriately increased. .

[0040] In one embodiment, the wrapping phase difference and the minimum phase difference can be defined as: in, Indicates that candidate unit m is in the th order. Phase response at each sampling location Indicates the first The target phase at each sampling location; This represents the principal value of the complex argument, and its range is (- , Because phase quantities have Due to its periodicity, the aforementioned wrapping phase difference is used to characterize the phase matching error, in order to avoid phase crossing errors during direct subtraction. The boundary conditions lead to an overestimation of the error.

[0041] For each sampling position, the candidate unit with the smallest matching error is selected, and the combination of geometric parameters corresponding to this candidate unit is used as the initial geometric parameters for that sampling position. After completing the above matching for all sampling positions across the entire aperture, a candidate initial structural layout corresponding to the particle's current position vector is generated. The candidate initial structural layout is determined by the set of initial geometric parameters at each sampling position across the entire aperture. In each iteration of the particle swarm optimization algorithm, each particle corresponds to a candidate initial structural layout, and the overall matching performance of different candidate initial structural layouts is evaluated using a fitness function.

[0042] In one specific implementation, the fitness function of the particle swarm optimization algorithm can be expressed as: in, Let be the fitness function of the particle swarm optimization algorithm. This represents the total number of sampling locations across the entire aperture. and These are the weighting coefficients for the phase error term and the group delay error term, respectively. , and satisfy ; To select candidate units in the first The encapsulation phase error between the phase response at each sampling location and the target phase This is the group delay response corresponding to the candidate cell. For the first Target group delay at each sampling location This is the group delay normalization factor. The method for determining the weighting coefficient is as follows: First, statistically analyze the average phase error and the average normalized group delay error of all candidate cross-shaped silicon dielectric pillar cells in the parameter scanning database at the full-aperture sampling positions. Let the number of candidate cells in the parameter scanning database be... , No. The candidate unit in the th The phase error term and the normalized group delay term at each sampling position are as follows: The average phase error and the average normalized group delay error are respectively: in, The number of candidate units in the database is scanned for parameters. Number the candidate units. Indicates the first The candidate unit in the th The encapsulation phase error between the phase response at each sampling location and the target phase Indicates to , Calculate the arithmetic mean of all error terms within the range.

[0043] In one alternative implementation, the weighting coefficients are determined by normalization according to the reciprocal of the average error order, and the calculation formula is as follows: in, It is a small positive number greater than 0, used to avoid the denominator being zero; and These are the bias coefficients for the phase error term and the group delay error term, respectively, both of which are positive. When the design objective has no special bias, we can take... At this point, the weighting coefficients are inversely proportional to the average magnitude of the corresponding errors, ensuring a balance between the contributions of the phase error term and the group delay error term to the fitness function; when the design objective places greater emphasis on achromatic performance, a weighting coefficient of 100% can be adopted. To increase the contribution of the group delay error term to the fitness function; when the design objective focuses more on the target wavefront phase matching accuracy, it can be taken as follows: This is to increase the contribution of the phase error term to the fitness function. As can be seen from the above formula, , And satisfy In one specific embodiment, it is possible to adopt , .

[0044] The rules for updating the velocity and position of particles can be expressed as: in, and Let these represent the position vector and velocity vector of the i-th particle in the k-th iteration, respectively. This represents the individual optimal position of the particle. This represents the current global optimal position of all particles. Indicates inertia weight, and Represents the learning factor. and This represents a random number within the range [0,1]. The inertia weight... The learning factor is used to balance global search capability and local convergence capability, and its preferred value range is 0.4 to 0.9; and The value used to adjust the degree to which particles approach their individual optimal position and the global optimal position is preferably in the range of 1.0 to 2.5. In one specific embodiment, a value of 1.0 to 2.5 can be used. =0.7, = =1.5. The number of particles, the maximum number of iterations, and the termination condition can be set through conventional numerical experiments based on the number of working wavelengths, the number of sampling positions, and the dimension of the search space; for example, the number of particles can be 10 to 50, and the maximum number of iterations can be 20 to 200. After multiple rounds of iteration, the candidate initial structure layout corresponding to the particle with the optimal fitness function is selected as the optimal initial structure layout, and this optimal initial structure layout can be used as the starting structure for subsequent propagation model evaluation or accompanying optimization correction.

[0045] In one optional implementation, after obtaining the optimal initial structural layout, a mathematical model of the full-wave electromagnetic field and multidimensional geometric gradient can be established, and the geometric parameters of the cross-shaped silicon dielectric pillar unit can be iteratively optimized under the constraint of the full-wave electromagnetic field. The mathematical model is based on the Lorentz reciprocity theorem and the quality factor. For geometric parameters The derivative can be expressed as: in, Represents the quality factor in relation to geometric parameters The derivative of Indicates the geometric parameters of the cross-shaped silicon dielectric pillar unit; For the positive incident field at position and wavelength Electric field distribution under, For the accompanying electric field distribution, For position The dielectric constant distribution at that location, Indicates the dielectric constant distribution with respect to geometric parameters The partial derivatives, For the volume of the simulation region, This indicates taking the real part.

[0046] To facilitate the mapping of three-dimensional electromagnetic field information to two-dimensional geometric parameter updates, this invention defines the local overlap between the forward incident field and the adjoint field at a spatial location as the three-dimensional sensitivity field. For a given operating wavelength and polarization target, the three-dimensional sensitivity field can be expressed as: in, Represents the three-dimensional sensitivity field. Indicates the spatial position of the normal incident field. and wavelength Electric field distribution under, This represents the electric field distribution associated with the objective function. This indicates taking the real part. For multi-wavelength or multi-polarization joint targets, the three-dimensional sensitivity fields under different operating wavelengths and different polarization targets can be weighted and superimposed according to the corresponding weights in the joint objective function to obtain a comprehensive three-dimensional sensitivity field for updating geometric parameters.

[0047] Based on the aforementioned three-dimensional sensitivity field, the quality factor affects the geometric parameters. The derivative can be equivalently expressed as the integral relationship between the three-dimensional sensitivity field and the dielectric constant perturbation term over the simulation region, i.e.: Therefore, the full-wave electromagnetic field and multidimensional geometric gradient modeling process not only obtains the derivative of the quality factor with respect to the geometric parameters, but also provides a three-dimensional sensitivity field for subsequent thickness direction compression and two-dimensional gradient mapping.

[0048] For the four geometric parameters of the cross-shaped silicon dielectric pillar unit, calculate respectively. Thus, respectively obtain and and The corresponding gradient information is used for subsequent parameter updates.

[0049] Gradient mapping is performed based on compression along the device thickness direction and two-dimensional spline interpolation. For example... Figure 3 As shown, 3 represents the three-dimensional sensitivity field calculated from the forward incident field and the adjoint field, 4 represents the compression process along the device thickness direction, and 5 represents the two-dimensional gradient mapping plane. For a cross-shaped silicon dielectric pillar unit with height H, the three-dimensional sensitivity field is uniformly compressed along the device thickness direction to obtain a two-dimensional gradient distribution, the calculation formula of which is: in, This is a two-dimensional gradient distribution obtained after compression along the thickness direction of the device. The three-dimensional sensitivity field is calculated based on the forward incident field and the adjoint field. The height of the cross-shaped silicon dielectric pillar unit. , and Let be the spatial coordinates. The above formula is used to calculate the two-dimensional gradient distribution after compression in the thickness direction, while the three-dimensional sensitivity field... It is calculated from the positive incident field and the adjoint field in the process of modeling the full-wave electromagnetic field and multidimensional geometric gradient.

[0050] It should be noted that the adjustable geometric parameters of the cross-shaped silicon dielectric pillar unit mainly include the arm length and arm width parameters in the plane, while the sensitivity field obtained from the full-wave electromagnetic field calculation is a three-dimensional spatial distribution. If the sensitivity value of a certain height section or a local three-dimensional grid point is directly selected as the basis for updating the geometric parameters, the parameter update amount is easily affected by local grid discrepancies, local field strength fluctuations, and the non-uniformity of the field distribution near the sidewalls of high aspect ratio structures. Therefore, this embodiment first performs mean compression on the three-dimensional sensitivity field along the thickness direction of the device to obtain a two-dimensional gradient distribution corresponding to the planar layout. Then, a continuous two-dimensional gradient function is obtained through two-dimensional spline interpolation, and the gradient update amount is extracted at the boundary positions corresponding to the arm length and arm width. Through the above processing, a correspondence can be formed between the three-dimensional electromagnetic field sensitivity information and the two-dimensional geometric processing parameters, thereby improving the consistency and stability of the subsequent geometric parameter update process.

[0051] Subsequently, a two-dimensional spline interpolation function is established on the two-dimensional gradient plane of the entire device aperture obtained by compression along the device thickness direction, resulting in a continuous two-dimensional gradient function for extracting gradient values ​​at arbitrary spatial locations. For each cross-shaped silicon dielectric pillar unit, preferably, the two-dimensional spline interpolation function is called in the corresponding planar projection region and its adjacent local regions, sampling is performed at the boundary positions corresponding to the four geometric parameters of the unit, and the parameter update is calculated accordingly. By first establishing a continuous gradient function on the entire device plane and then extracting gradient values ​​for the local boundaries of each unit, both the overall continuity of the gradient field and the accuracy of the local geometric update of the unit can be taken into account.

[0052] Among them, the arm length along the X direction The gradient update is obtained by averaging the interpolated gradients at the two ends of the cross-shaped structure in the X direction; the arm length along the Y direction... The gradient update amount is obtained by averaging the interpolated gradients at the two ends of the cross-shaped structure in the Y direction; the width of the horizontal arm along the X direction The gradient update amount is obtained by averaging the interpolated gradients at the upper and lower boundaries of the horizontal arm; the width of the vertical arm along the Y direction The gradient update amount is obtained by the average interpolated gradient at the left and right boundaries of the vertical arm.

[0053] In one alternative implementation, the gradient update amounts corresponding to the above four parameters can be expressed as follows: in, and Respectively represent and and The corresponding gradient update amount, The coordinates of the unit center are It is a continuous gradient function obtained by two-dimensional spline interpolation.

[0054] To reduce the impact of differences in the magnitude of gradients of different parameters on the stability of subsequent parameter updates, the aforementioned gradient update amounts can be normalized. In one optional implementation, the normalization factor can be expressed as: in, It is a small positive number greater than 0, used to avoid the normalization factor becoming too large when the maximum gradient magnitude is close to zero.

[0055] Correspondingly, the normalized parameter update amounts are as follows: The normalized parameter update amount , , and Used for iterative updates of geometric parameters in subsequent optimization steps.

[0056] Geometric parameter update based on multi-objective constraints. Quality factors are constructed according to the TE and TM polarization objectives, respectively, forming a weighted joint objective function. To balance the optimization performance of the two polarization channels, the joint objective function in the k-th iteration can be expressed as: in, and They represent the first The quality factors corresponding to the TE polarization target and the TM polarization target at the next iteration. and Let each represent a corresponding dynamic weight, and satisfy the following conditions: In one optional implementation, the dynamic weights are adaptively adjusted based on the performance metrics of the polarization channels corresponding to the previous state. To clarify the determination method of the dynamic weights in the first iteration, the optimal initial structural layout output by the particle swarm optimization algorithm is defined as the 0th iteration state. Before entering the first geometric parameter update, a forward simulation is performed on the optimal initial structural layout to calculate the performance metrics of the TE polarization channels and TM polarization channels in the initial state. and .when At that time, the dynamic weight is based on and Determined; when At that time, the dynamic weight is based on the first The performance metrics after the next iteration are determined. Their calculation formula can be uniformly expressed as: Where k is the iteration number greater than or equal to 1; when hour, and These represent the optimal initial structural layout. and ;when hour, and They represent the first Performance metrics for the TE polarization channel and TM polarization channel after the next iteration; It is a small positive number greater than 0, used to avoid the denominator being zero and to improve the numerical stability of the weight calculation. Preferably, when and When all performance metrics are normalized to the [0,1] interval, Desirable In one specific embodiment, it is preferable to . The specific value can be set through conventional numerical experiments based on the order of magnitude of the performance index. Its value should be significantly smaller than the normal variation of the performance index to avoid having a dominant influence on the dynamic weight allocation result. As shown in the above formula, the polarization channel with the lower performance index will receive a larger weight in the current iteration, thereby achieving a balanced optimization of the dual-channel performance.

[0057] In one alternative implementation, the performance metrics Defined as the first The normalized focusing efficiency of the TE polarization channel within the target focal region in the next iteration state is calculated using the following formula: ; in, Indicates the first The electric field distribution of the TE polarization channel on the output surface in the next iteration state. This represents the region of focal integration centered on the theoretical focus. Indicates the statistical region of the output surface; The performance indicators Defined as the first The normalized matching degree between the output mode field of the TM polarization channel and the target vortex mode field in the next iteration is calculated using the following formula: ; in, Indicates the first The actual electric field distribution of the TM polarization channel on the output surface in the next iteration state. This represents the complex amplitude distribution of the target vortex mode field. This indicates the conjugate operation.

[0058] After obtaining the joint objective function, the geometric parameters of the cross-shaped silicon dielectric pillar unit are iteratively updated based on the aforementioned normalized parameter update amount. In one optional embodiment, a moving asymptote-like optimization method can be used to update the parameter vector; in another optional embodiment, a gradient ascent update can also be used, the expression of which can be expressed as: in, and They represent the first Second and third The geometric parameter vector at the next iteration Indicates the first The update step size in the next iteration. In one optional implementation, the initial step size is first determined based on the maximum absolute value of each component of the normalized parameter update vector at the 0th iteration, combined with the maximum allowable geometric change in a single iteration. It can be represented as: in, This represents the first normalized parameter update vector at the 0th iteration. There are several components, where 𝜉 is a small positive number greater than 0, used to avoid the denominator being zero; This represents the maximum allowable geometric change in a single iteration, determined based on the machining scale and process resolution of the geometric parameters. Preferably, it is the smaller of 5%–10% of the minimum machining dimension and 1%–5% of the initial value of the corresponding geometric parameters. In a specific embodiment, when the maximum allowable geometric change in a single iteration is 0.01 μm, it can be taken as... =0.01μm.

[0059] When using an adaptive step size, first calculate the first... The relative improvement of the joint objective function in each iteration can be expressed as: The step size is then updated based on the relative improvement, which can be expressed as: in, This represents the step size increment factor. This represents the step size reduction factor. and These represent the preset maximum step size and the preset minimum step size, respectively. This indicates that the joint objective function improves the threshold. and The method for determining the parameter values ​​is as follows: within a preset candidate range, through several trial iterations of the initial structure, the parameter combination that allows the joint objective function to maintain an upward trend and whose parameter updates do not exhibit significant oscillations is selected as the final value; preferably, Take a value of 1.05 to 1.50. The value can be taken as 0.50 to 0.95. In one specific embodiment, the values ​​can be taken as follows: =1.20、 =0.80. The aforementioned and Based on the initial step size, the preferred values ​​are respectively taken as follows: 2 to 5 times and 0.1 to 0.5 times; in one specific embodiment, it can be taken as 2 to 5 times and 0.1 to 0.5 times; =0.05μm, =0.001μm. The improved threshold. The objective function is determined based on its normalized magnitude and the average improvement during the trial iterations, preferably ranging from 5% to 20% of the average relative improvement during the trial iterations. When the joint objective function has been normalized to the [0,1] interval... Preferred selection In one specific embodiment, it is preferable to .

[0060] The process of calculating the three-dimensional sensitivity field, mapping the two-dimensional gradient, and updating the geometric parameters is repeated until the joint objective function satisfies the preset convergence condition. In one optional implementation, the convergence condition can be defined as continuous... The absolute value of the change in the joint objective function in the next iteration satisfies: in, This indicates the preset convergence threshold. This represents the number of iterations that continuously satisfy the convergence condition. and The objective function can be set through conventional numerical experiments based on its magnitude, optimization stability requirements, and computational cost; when the joint objective function has been normalized to the [0,1] interval, Preferred selection , Preferably, the value is 3 to 10, and in a specific embodiment, it can be 3 to 10. = , =5. By changing the set of working wavelengths, the weights of the objective function, and the convergence constraints in the reverse design method, the design of multi-wavelength, multi-functional superlenses can be achieved.

[0061] Example 1 This embodiment presents the reverse design process of an achromatic polarization multiplexing superlens. The goal of this design is to achieve achromatic focusing under TE polarization incident conditions and vortex light output under TM polarization incident conditions. The superlens consists of a cross-shaped silicon dielectric pillar unit array and a sapphire substrate, as shown below. Figure 2 (a) and Figure 2 As shown in (b), the anisotropy of the cross-shaped structure is beneficial for achieving differentiated control of the two polarization states, TE and TM.

[0062] In this embodiment, the geometric parameters of the cross-shaped silicon dielectric pillar unit are determined comprehensively based on the operating wavelength, material refractive index, phase modulation range, fabrication feasibility, and the requirement to suppress higher-order diffraction. For a mid-infrared achromatic polarization multiplexing superlens with an operating wavelength of 3.5 μm to 4.5 μm, the lattice period is preferably 1.8 μm to 2.2 μm, making the lattice period approximately 0.45 to 0.55 times the central operating wavelength, thus balancing phase sampling density, fabrication feasibility, and reducing the impact of higher-order diffraction on device performance. The height of the cross-shaped silicon dielectric pillar unit is preferably 4.0 μm to 6.0 μm to ensure sufficient phase modulation depth and transmission modulation capability in the mid-infrared band. The arm length along the X direction, the arm length along the Y direction, the width of the horizontal arm along the X direction, and the width of the vertical arm along the Y direction of the cross-shaped silicon dielectric pillar unit can be parametrically scanned within the range of 0.5 μm to 1.5 μm, and selected based on phase response, group delay response, and transmission efficiency.

[0063] To characterize the aspect ratio of a cross-shaped silicon dielectric pillar cell, this invention defines the ratio of cell height to minimum lateral feature width as the aspect ratio, expressed as: in, Indicates aspect ratio. Indicates the height of the cross-shaped silicon dielectric pillar unit. and These represent the width of the transverse arm along the X direction and the width of the longitudinal arm along the Y direction, respectively. When H = 5.0 μm, and... and When the depth-to-width ratio varies within the range of 0.5μm to 1.5μm, the aspect ratio of the cross-shaped silicon dielectric pillar unit is approximately 3.3 to 10, and therefore can be regarded as a high aspect ratio micro / nano structure.

[0064] In one specific embodiment, the height of the cross-shaped silicon dielectric pillar unit is set to 5.0 μm, and the lattice period is set to 2.0 μm. These values ​​are within the aforementioned preferred range, which can balance the phase modulation capability in the mid-infrared band, the structural transmission efficiency, and the feasibility of micro-nano fabrication. To obtain the transmittance and phase response data of the cross-shaped silicon dielectric pillar unit in the mid-infrared band, a parametric scan is performed in the wavelength range of 3.5 μm to 4.5 μm and the geometric size range of 0.5 μm to 1.5 μm, thereby establishing the correspondence between geometric parameters and optical response.

[0065] At P=2.0μm, H=5.0μm, = Under the condition of 0.5μm, for and Representative RCWA scans were performed in the range of 0.5 μm to 1.5 μm, and the results are as follows: Figure 4 As shown. Figure 4 This indicates that at 3.5 μm, 4.0 μm, and 4.5 μm, the transmission amplitude of the cross-shaped silicon dielectric pillar unit remains at a high level overall, and the phase response coverage is close to 2. The TE polarization response mainly varies with... The TM polarization response mainly varies with The change indicates that the cross-shaped silicon dielectric pillar unit has the ability to control polarization differences. Figure 4 This is an example of a two-dimensional slice of a four-parameter response database, during the complete design process. and It is also used as an adjustable parameter in the screening process.

[0066] In other alternative embodiments, when the operating wavelength remains between 3.5 μm and 4.5 μm, the lattice period can be selected within the range of 1.8 μm to 2.2 μm, and the height of the cross-shaped silicon dielectric pillar unit can be selected within the range of 4.0 μm to 6.0 μm. For combinations of different heights and lattice periods, the correspondence between geometric parameters and optical response can be re-established according to the parameter scanning, particle swarm optimization algorithm initial layout generation, and accompanying optimization update process described in this invention, and a structural layout that meets the requirements of TE polarization achromatic focusing and TM polarization vortex light output can be obtained. Therefore, this invention is not limited to a single numerical embodiment with a height of 5.0 μm and a lattice period of 2.0 μm.

[0067] The reverse design method first utilizes a particle swarm optimization (PSO) algorithm to generate the optimal initial structural layout. Specifically, the PSO algorithm optimizes global dispersion compensation parameters to compensate the target phase distribution across all operating wavelengths, and approximates the target group delay based on the target phase difference at adjacent operating wavelengths. Subsequently, by comparing the matching errors between the phase response and group delay response of candidate cross-shaped silicon dielectric pillar cells in the database and the target values, the geometric parameter combination with the minimum matching error is selected for each sampling position, thereby generating candidate initial structural layouts corresponding to each particle. After particle swarm iteration, the candidate initial structural layout corresponding to the particle with the optimal fitness function is selected as the optimal initial structural layout. Its fitness convergence process is as follows: Figure 5 As shown.

[0068] It should be noted that the optimal initial structural layout is not randomly generated, but rather selected based on the RCWA unit complex transmission response library, the target phase distribution, the target group delay distribution, and the matching error function. For each sampling position within the full aperture of the superlens, candidate cross-shaped silicon dielectric pillar units are selected based on the matching error between their phase response, group delay response, and target response. The particle swarm optimization algorithm further searches for global dispersion compensation parameters to reduce the overall phase matching error and group delay matching error across the entire aperture. Therefore, the optimal initial structural layout already possesses an initial optical response close to the target wavefront and target dispersion response before entering the adjoint optimization correction, and can serve as a physically realizable starting point for subsequent local optimization.

[0069] Subsequently, based on the RCWA complex transmission response of each unit in the optimal initial structural layout, the complex amplitude distribution of the superlens's exit surface is constructed, and the optical field distribution at the target output surface is calculated using a propagation model. Evaluations are conducted for three operating wavelengths: 3.5 μm, 4.0 μm, and 4.5 μm. The superlens is designed with a diameter of 30 μm (i.e., a design radius of 15 μm) and a focal length of 27 μm, corresponding to a numerical aperture of approximately 0.49.

[0070] In one alternative implementation, the propagation model may be an angular spectrum propagation model or an equivalent scalar diffraction propagation model. Let the complex amplitude distribution at the exit surface of the superlens be... Its two-dimensional Fourier transform is The propagation distance is The complex amplitude distribution at the target output surface can be expressed as: in, , and These are the transverse wave vector components, and These represent the two-dimensional Fourier transform and the two-dimensional inverse Fourier transform, respectively; the light intensity distribution at the target output surface can be represented by... get.

[0071] To evaluate the broadband achromatic control capability of this design method, the output optical field obtained based on the complex transmission response and propagation model of the RCWA unit was analyzed. The calculation results are as follows: Figure 6 and Figure 7 As shown, the TE polarization channel forms a focused spot near the design focal point at all three wavelengths, while the TM polarization channel forms a vortex light field with a dark center and a ring-shaped intensity distribution at the corresponding wavelength.

[0072] In this embodiment, the preset conditions are used to determine whether the initial structural layout can be used as the output structural layout. The preset conditions include the focusing performance conditions of the TE polarization channel and the vortex optical field quality conditions of the TM polarization channel. The focusing performance conditions of the TE polarization channel include: at working wavelengths of 3.5μm, 4.0μm, and 4.5μm, the focused spot at the target output surface is located near the designed focal point, the focal position deviation is not greater than a preset focal deviation threshold, and the focusing efficiency in the focal integration region is not less than a preset focusing efficiency threshold. The vortex optical field quality conditions of the TM polarization channel include: at working wavelengths of 3.5μm, 4.0μm, and 4.5μm, a dark center annular optical field corresponding to the target topological charge number is formed at the target output surface, the ratio of the average light intensity of the central dark spot region to the annular peak light intensity is not greater than a preset dark center threshold, and the normalized matching degree between the output optical field and the target vortex mode field is not less than a preset matching degree threshold. The preset focus deviation threshold, preset focus efficiency threshold, preset dark center threshold, and preset matching degree threshold are evaluation criteria pre-set before performing propagation model evaluation. Their values ​​can be determined according to device design tolerance, processing tolerance, system optical path allowable deviation, or application requirements. When both the focusing performance conditions of the TE polarization channel and the vortex optical field quality conditions of the TM polarization channel are met, the initial structural layout is used as the output structural layout. When any condition is not met, the initial structural layout is used as the starting structure for the accompanying optimization correction, and the four geometric parameters of the cross-shaped silicon dielectric pillar unit are further corrected. The accompanying optimization correction is used to correct the near-field electromagnetic coupling error caused by aperiodic arrangement and the optical field deviation caused by propagation model approximation, and can be implemented by combining three-dimensional sensitivity field thickness direction compression, two-dimensional spline interpolation, and boundary sampling parameter update methods.

[0073] The various embodiments described in this specification are presented in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A hybrid inverse design method of achromatic polarization multiplexed metalens, characterized in that, Includes the following steps: The first step is to establish a parameterized model of a cross-shaped silicon dielectric pillar unit, which includes four geometric parameters: arm length along the X direction, arm length along the Y direction, width of the horizontal arm along the X direction, and width of the vertical arm along the Y direction. Under a preset set of working wavelengths and two polarization states, TE and TM, the four geometric parameters are scanned based on the rigorous coupled-wave analysis (RCWA) method to obtain the complex transmission response corresponding to different geometric parameters, and a response database between geometric parameters and transmission phase, transmission amplitude, and group delay is established. The second step is to define the phase distribution of the achromatic focused target in the TE polarization channel and the phase distribution of the achromatic vortex target in the TM polarization channel, and determine the target group delay distribution based on the target phase change relationship under different working wavelengths. The third step involves constructing a matching error function based on the response database, target phase distribution, and target swarm delay distribution; using the particle swarm algorithm to search for global dispersion compensation parameters; and selecting the cross-shaped silicon dielectric pillar unit with the smallest matching error at each sampling position of the full aperture of the superlens to generate the initial structural layout. The fourth step involves constructing the complex amplitude distribution of the superlens exit surface based on the complex transmission response of each unit in the initial structural layout, and calculating the light field distribution at the target output surface using a propagation model to evaluate the focusing performance of the TE polarization channel and the vortex light field quality of the TM polarization channel. The propagation model evaluation results determine whether the preset conditions are met. The preset conditions include the focusing performance conditions of the TE polarization channel and the vortex optical field quality conditions of the TM polarization channel. If the conditions are met, the initial structural layout is output. Otherwise, the initial structural layout is used as the starting structure for adjoint optimization and correction, and the corrected structural layout is output.

2. The method of claim 1, wherein, The response database is obtained through RCWA parameter scanning. The operating wavelengths of the parameter scanning include 3.5μm, 4.0μm, and 4.5μm. The lattice period of the cross-shaped silicon dielectric pillar unit is 1.8μm to 2.2μm, and the height is 4.0μm to 6.0μm. The values ​​of the four geometric parameters are all in the range of 0.5μm to 1.5μm. The response database includes at least the transmission amplitude, transmission phase, and group delay response under TE polarization and TM polarization.

3. The method of claim 1, wherein, The phase distribution of the achromatic focusing target in the TE polarization channel is as follows: ； The achromatic vortex target phase distribution of the TM polarization channel is as follows: ； wherein, is the radial distance from the corresponding unit position in the plane of the superlens to the center of the lens, is the design focal length, is the angular frequency of the incident light, is the vacuum speed of light; is the topological charge of the vortex beam, is the azimuthal angle of the corresponding unit position in the plane of the superlens.

4. The hybrid reverse design method for an achromatic polarization multiplexing superlens according to claim 1, characterized in that, After obtaining the initial structure layout, a step of accompanying optimization correction based on full-wave electromagnetic field and multi-dimensional geometric gradient is further included; in the step of accompanying optimization correction, a mathematical model of the full-wave electromagnetic field and the multi-dimensional geometric gradient is based on Lorentz reciprocity theorem, and a quality factor The derivative of the geometric parameter is: ； in, Represents the quality factor in relation to geometric parameters The derivative of Indicates the geometric parameters of the cross-shaped silicon dielectric pillar unit; For the positive incident field at position and wavelength Electric field distribution under, For the accompanying electric field distribution, For position The dielectric constant distribution at that location, Indicates the dielectric constant distribution with respect to geometric parameters The partial derivatives, For the volume of the simulation region, This indicates taking the real part.

5. The hybrid reverse design method for an achromatic polarization multiplexing superlens according to claim 4, characterized in that, The accompanying optimization and correction steps include: The three-dimensional sensitivity field is mean-compressed along the device thickness direction to obtain a two-dimensional gradient distribution, the calculation formula of which is: ； in, The compressed two-dimensional gradient distribution For a three-dimensional sensitivity field, The height of the cross-shaped silicon dielectric pillar unit. , and Spatial coordinates; For the two-dimensional gradient distribution Two-dimensional spline interpolation is performed to obtain a continuous two-dimensional gradient function. ; For the four geometric parameters of the cross-shaped silicon dielectric pillar unit, samples are taken according to their corresponding boundary positions, and the parameter update amount is calculated.

6. The hybrid reverse design method for an achromatic polarization multiplexing superlens according to claim 4 or 5, characterized in that, In the accompanying optimization correction step, corresponding quality factors are constructed based on the TE polarization target and the TM polarization target, respectively, and a weighted joint objective function is formed. In the k-th iteration, the joint objective function is: ； in, and They represent the first The quality factors corresponding to the TE polarization target and the TM polarization target at the next iteration. and Let each represent the corresponding dynamic weight, and satisfy the following conditions: .

7. The hybrid reverse design method for an achromatic polarization multiplexing superlens according to claim 6, characterized in that, The dynamic weights are adaptively adjusted based on the performance indicators of the polarization channel corresponding to the previous state; wherein, the optimal initial structure layout output by the particle swarm optimization algorithm is defined as the 0th iteration state; when At that time, the dynamic weights are determined based on the performance indicators corresponding to the TE polarization channel and the TM polarization channel in the 0th iteration state; when At that time, the dynamic weight is based on the first The performance indicators corresponding to the TE polarization channel and TM polarization channel are determined in the next iteration state; the calculation formula for the dynamic weight is: ； ； in, The iteration number is greater than or equal to 1; when hour, and These represent the performance indicators corresponding to the TE polarization channel and the TM polarization channel in the 0th iteration state, respectively; when hour, and They represent the first Performance metrics for the TE polarization channel and TM polarization channel in the next iteration state; It is a small positive number greater than 0, used to avoid the denominator being zero and to improve the numerical stability of weight calculation.

8. The hybrid reverse design method for an achromatic polarization multiplexing superlens according to claim 7, characterized in that, The performance indicators Defined as the first The normalized focusing efficiency of the TE polarization channel within the target focal region in the next iteration state is calculated using the following formula: ； in, Indicates the first The electric field distribution of the TE polarization channel on the output surface in the next iteration state. This represents the region of focal integration centered on the theoretical focus. Indicates the statistical region of the output surface; The performance indicators Defined as the first The normalized matching degree between the output mode field of the TM polarization channel and the target vortex mode field in the next iteration is calculated using the following formula: ； in, Indicates the first The actual electric field distribution of the TM polarization channel on the output surface in the next iteration state. This represents the complex amplitude distribution of the target vortex mode field. This indicates the conjugate operation.

9. The hybrid reverse design method for an achromatic polarization multiplexing superlens according to claim 5, characterized in that, After calculating the parameter update amount, the parameter update amount is normalized to obtain the normalized parameter update amount; the normalized parameter update amount is used for the geometric parameter iterative update in the accompanying optimization correction step.

10. An achromatic polarizing multiplexed superlens, designed by the hybrid reverse design method according to any one of claims 1 to 9, characterized in that, include: Sapphire substrate; as well as Multiple cross-shaped silicon dielectric pillar units are formed on the upper surface of the sapphire substrate; The multiple cross-shaped silicon dielectric pillar units are arranged at equal intervals according to a square lattice to form a metasurface array; The geometric parameters of the cross-shaped silicon dielectric pillar unit include the arm length along the X direction. Arm length along the Y direction Width of the transverse arm along the X direction and the width of the longitudinal arm along the Y direction ; The spacing between the centers of adjacent units in both the X and Y directions is equal to the lattice period. The lattice period The determination is based on a comprehensive consideration of the device's operating wavelength, unit structure size range, phase modulation requirements, and focusing performance requirements.

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