A double-sided achromatic superlens based on phase load balancing and a design method thereof

Abstract

The application discloses a double-sided achromatic superlens based on phase load balancing and a design method, and belongs to the technical field of micro-nano optics and computational imaging. The superlens comprises a transparent low-refractive substrate, a first structure layer located on the incident surface of the substrate and a second structure layer located on the emitting surface of the substrate; the first structure layer is a non-periodic phase type Fresnel zone plate, which is used for providing a basic focusing phase and pre-bending incident parallel light to the inside of the substrate; the second structure layer is an isotropic cylindrical nano column arranged in a square lattice, which is used for providing a residual focusing phase and a wide-band chromatic aberration compensation phase. Through the double-sided phase distribution balancing logic, the light deflection pressure is shared together, combined with the full-path scalar diffraction model, super-atom response calculation and end-to-end deep learning optimization, the bottleneck of low-refractive material in high-NA achromatic application is completely solved, and the micro-nano processing technology of large area and low cost is compatible.

Description

Technical Field

[0001] This invention belongs to the field of micro-nano optics and computational imaging, specifically relating to a double-sided achromatic superlens based on phase load equalization and its design method. Background Technology

[0002] Traditional achromatic superlenses often use high-refractive-index materials (such as TiO2 or GaN) and are typically single-layer structures. In practical applications, polymer materials offer more flexible processing options and significant advantages in terms of process resolution and cost.

[0003] However, existing low-refractive-index medium single-layer superlenses have the following main drawbacks: Limited phase deflection capability: In low refractive index media, the phase modulation range of a single-layer metasurface unit is narrow, making it difficult to provide the large gradient phase required to achieve high numerical aperture (NA), resulting in extremely low edge efficiency of large-aperture lenses.

[0004] Dispersion compensation is difficult: phase difference compensation in a wide band requires a huge time delay reserve, and a single-layer structure can hardly achieve full-band achromatic aberration while ensuring high NA. Summary of the Invention

[0005] To address the issues of insufficient phase gradient and severe chromatic aberration over a wide band when using low-refractive-index media to realize large-aperture, high numerical aperture (NA) metalenses, this application designs a double-sided achromatic metalens and its design method based on phase load balancing. By using double-sided phase distribution balancing logic, the light deflection pressure is shared by both sides, and combined with end-to-end training, a metasurface lens with both high NA and achromatic performance is achieved.

[0006] A double-sided achromatic superlens based on phase load equalization, comprising: Transparent low-refractive-index substrate; The first structural layer, disposed on the incident surface of the transparent low-refractive-index substrate, is a non-periodic phase-type Fresnel zone plate, used to provide a basic focusing phase and pre-deflect the incident parallel light into the interior of the substrate; The second structural layer, disposed on the exit surface of the transparent low-refractive-index substrate, is an isotropic cylindrical nanopillar arranged in a square lattice, used to provide the remaining focusing phase and broadband chromatic aberration compensation phase. The target total phase distribution of the superlens satisfy: r is the radial coordinate, λ is the working wavelength, and f is the target focal length of the superlens; The task is split into two parts through end-to-end training: ; The basic focusing phase provided by the first structural layer is The sum of the residual focusing phase and chromatic aberration compensation phase provided by the second structural layer is .

[0007] Preferably, the transparent low-refractive-index substrate is made of polymer material with a refractive index n=1.45, a substrate thickness h=1mm, and an overall effective light transmission aperture D=2cm for the lens.

[0008] Preferably, the first structural layer adopts an 8-step binary optical structure to approximate continuous phase, and its maximum microstructure height is... Where n is the refractive index of the transparent low-refractive-index substrate, The design center wavelength is given; where m is the index of the half-wave zone, taken as a positive integer, and the radial radius of the m-th half-wave zone is given. satisfy: ,in The primary focal length shared by the first structural layer.

[0009] Preferably, the lattice period of the second structural layer satisfies the subwavelength condition to suppress higher-order diffraction in the working band; the height of the nanopillar is configured to satisfy the maximum group delay required for the wide-band chromatic aberration compensation; the diameter of the nanopillar gradually varies according to its spatial position within a preset range to provide a local phase modulation range covering 0-2π.

[0010] Preferably, the lattice period of the second structural layer is 300nm~500nm, the height of the nanopillars is 1μm~3μm, and the diameter of the nanopillars is 50nm~250nm.

[0011] A design method for a double-sided achromatic superlens based on phase load equalization includes the following steps: Step S1: Construct a forward physical propagation model. Use angular spectrum theory to establish a full-path scalar diffraction model from the incident wavefront to the focal plane image point. The optical path difference caused by the substrate thickness h is taken into account in the model. Step S2: Superatomic characteristic parameter quantization. The diameter d and height H of the nanopillars in the second structural layer are used as variables to be optimized. Full-wave electromagnetic simulation is employed to perform element-level electromagnetic simulation, establishing the superatomic geometric parameters and complex amplitude response. The mapping relationship, where The complex amplitude transmission response of a nanopillar unit with diameter d and height H at the operating wavelength λ includes information on amplitude transmittance and phase delay. Step S3: Define a multi-criteria loss function, which simultaneously includes a point spread function morphology approximation term and a diffraction efficiency energy evaluation term; Step S4: Gradient descent optimization. Calculate the back gradient using automatic differentiation technology. Iteratively update the structural parameters of the full-aperture superatoms using a gradient-based automatic differentiation optimization algorithm or a heuristic optimization algorithm. After convergence, output a two-dimensional map of the spatial distribution of the superatoms across the entire aperture range.

[0012] Preferably, the forward physics propagation model in step S1 specifically includes: Step S11: The incident light field is modulated by the first structural layer to obtain the complex amplitude of the outgoing wavefront. ;in The initial complex amplitude distribution of the light field incident on the first structural layer is given by x and y, which are the abscissa and ordinate of the rectangular coordinate system in the lens aperture plane; 0 is the position coordinate of the incident surface where the first structural layer is located along the optical axis. Step S12: Calculate the propagation of the light field inside the substrate using the angular spectral transfer method to obtain the complex amplitude distribution propagating to the incident surface of the second structural layer. h is the position coordinate of the exit surface where the second structural layer is located in the optical axis direction, corresponding to the substrate thickness; Step S13: The light field is modulated by the second structural layer to obtain the final output light field. The complex amplitude distribution of the emitted light field modulated by the second structural layer; Step S14: Calculate the complex amplitude distribution of the modulated light field as it propagates freely to the focal plane. And obtain the focal plane light intensity distribution. .

[0013] Preferably, the unit electromagnetic simulation conditions in step S2 are as follows: periodic boundary conditions are used on the horizontal plane, and perfectly matched layer absorption boundary is used in the beam propagation direction; the incident light is a broadband light source covering a wide wavelength range of 400nm~650nm, and non-polarized or orthogonal linearly polarized state is used as the excitation source, with the incident angle range scanning from 0° to the maximum refraction tilt angle corresponding to the lens edge.

[0014] Preferably, the multi-criteria loss function is: Among them, wavelength set , Let be the actual point spread function. Let λ be the ideal Airy spot diffusion function, Efficiency(λ) be the single-wavelength focusing efficiency, and γ be the weighting coefficient. The weight coefficient γ has a value range of [0.1, 0.8]. In the initial stage of optimization, it is set to 0.1~0.2, and in the convergence smoothing period, it is gradually increased to 0.5-0.8.

[0015] Preferably, the optimization parameters in step S4 are: an initial learning rate of 0.05 combined with a cosine annealing decay strategy, a maximum number of iterations of 2000, and a convergence threshold of the change in the loss function over 100 consecutive iterations. And the Strell ratio of each sampling wavelength .

[0016] The fabrication method for the double-sided achromatic superlens based on the above-mentioned phase load equalization includes the following steps: Step P1, Substrate Pretreatment: Double-sided grinding and polishing are performed on a 1mm thick photosensitive substrate to ensure that the surface roughness reaches the nanometer level; Step P2, Front Exposure: Using ultraviolet grayscale lithography or two-photon polymerization technology, a depth profile of a non-periodic Fresnel zone plate is defined on the incident surface of the substrate. Step P3, Backside Tracking Alignment: Flip the substrate and use the body alignment marks preset on the edge of the substrate to achieve spatial alignment of the second structural layer relative to the first structural layer, with an alignment accuracy of less than 800nm; Step P4, Backside Exposure: Expose and define the subwavelength nanopillar array on the emitting surface of the substrate; Step P5, Unified Development: Place the double-sided exposed substrate in the matching developer solution for single or step development.

[0017] The advantages and effects of this application are as follows: This application presents a double-sided achromatic superlens and its design method based on phase load equalization. Through the deep coupling of "large-scale geometric phase" and "subwavelength dispersion compensation," diffraction-limited imaging with a large aperture of 2 cm and a numerical aperture of 0.8 is achieved at an ultra-thin thickness of 1 mm, completely solving the bottleneck of low refractive index materials in high-NA achromatic applications. Furthermore, the polymer substrate used in this invention is highly compatible with micro / nano fabrication processes such as nanoimprint lithography and ultraviolet lithography, meeting the demands for large-area, low-cost mass production.

[0018] The above description is only an overview of the technical solution of this application. In order to better understand the technical means of this application and implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, the preferred embodiments of this application are described in detail below with reference to the accompanying drawings.

[0019] The above and other objects, advantages and features of this application will become more apparent to those skilled in the art from the following detailed description of specific embodiments in conjunction with the accompanying drawings. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of this application 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 some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In all drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn to scale.

[0021] Figure 1 This is a schematic diagram of the structure of the first structural layer (Fresnel zone plate); Figure 2 This is a schematic diagram of the second structural layer (metasurface nanopillar array); Figure 3 This is a schematic diagram of the overall structure of the double-sided achromatic superlens based on phase load equalization of the present invention; Figure 4 This is a flowchart of the end-to-end reverse design method of the present invention. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. In the following description, specific details such as specific configurations and components are provided merely to help fully understand the embodiments of this application. Therefore, those skilled in the art should understand that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of this application. In addition, for clarity and brevity, descriptions of known functions and structures are omitted in the embodiments.

[0023] It should be understood that the phrase "an embodiment" or "this embodiment" throughout the specification means that a specific feature, structure, or characteristic related to the embodiment is included in at least one embodiment of this application. Therefore, "an embodiment" or "this embodiment" appearing throughout the specification does not necessarily refer to the same embodiment. Furthermore, these specific features, structures, or characteristics can be combined in any suitable manner in one or more embodiments.

[0024] Furthermore, reference numerals and / or letters may be repeated in different examples within this application. Such repetition is for the purpose of simplification and clarity and does not in itself indicate a relationship between the various embodiments and / or settings discussed.

[0025] In this article, the term "and / or" is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can mean: A exists alone, B exists alone, and A and B exist simultaneously. The term " / and" in this article describes another type of relationship between related objects, indicating that two relationships can exist. For example, A / and B can mean: A exists alone, and A and B exist alone. In addition, the character " / " in this article generally indicates that the related objects before and after it are in an "or" relationship.

[0026] In this article, the term "at least one" is merely a description of the relationship between related objects, indicating that there can be three relationships. For example, "at least one of A and B" can mean: A exists alone, A and B exist simultaneously, or B exists alone.

[0027] It should also be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion. Example

[0028] This embodiment mainly introduces a double-sided achromatic superlens based on phase load balancing, the core feature of which lies in utilizing the double-sided structure to jointly bear the pressure of large-angle light deflection. For example... Figure 3 As shown, Figure 3 This is a schematic diagram of the overall structure of the double-sided achromatic superlens based on phase load equalization of the present invention; the intersection is the Achromatic Focus. The physical structure of the lens consists of a transparent substrate and functional layers on both sides.

[0029] I. Overall Structure and Physical Parameters This embodiment proposes a double-sided achromatic superlens based on phase load equalization. Its core feature lies in utilizing the double-sided structure to jointly bear the pressure of large-angle light deflection. The physical structure of this lens consists of a transparent substrate and functional layers on both sides: Transparent substrate: Utilizing a low-refractive-index polymer material (such as PMMA) with a refractive index n=1.45, substrate thickness h=1mm, and an overall effective light-transmitting aperture D=2cm for the lens. This type of polymer material not only possesses excellent optical transmittance but also exhibits extremely high fidelity in micro / nano patterning and potential for miniaturization resolution (e.g., using high-fidelity implosion miniaturization processes), enabling stable fabrication of feature sizes at the tens of nanometer scale. This material is highly compatible with micro / nano fabrication processes such as nanoimprint lithography, ultraviolet lithography, electron beam lithography, and two-photon polymerization, thus perfectly supporting the precision fabrication of high aspect ratio nanopillar arrays with a minimum exit surface diameter of 50nm, meeting the demands for large-area, low-cost mass production.

[0030] Please refer to Figure 1 The first structural layer (SideA), located at the incident plane of the substrate, is a non-periodic phase-type Fresnel zone plate (FZP). To achieve... Full-phase modulation, its maximum microstructure height (in (For the design center wavelength). An 8-step binary optical structure is used to approximate continuous phase. The aperiodicity of the ring band is specifically manifested in the gradual narrowing of the ring width as the radial distance increases. The radial radius of the m-th half-wave zone. satisfy: ,in The primary focal length shared by SideA.

[0031] Please refer to Figure 2 The second structural layer (Side B) is located at the exit surface of the substrate and consists of isotropic cylindrical nanopillars (to achieve polarization-independent focusing) arranged in a tetragonal lattice. To satisfy the Nyquist sampling theorem and suppress higher-order diffraction, the lattice period is set at... Between. The height of the nanopillars is fixed (the value ranges from...). The value of the nanopillar diameter is used as an optimization variable for spatial variation, ranging from 50 nm to 250 nm, and the scanning step size is set to 5 nm to establish a high-precision superatomic spectrum mapping.

[0032] II. Phase Allocation and Load Balancing Logic Since the target focal length in this embodiment is f=0.75cm, corresponding to a numerical aperture (NA) of 0.8, a single-sided structure cannot provide sufficient phase gradient in a low refractive index medium of 1.45. This invention achieves high NA focusing through the following phase load equalization logic: Let the total phase distribution of the target be total. The total phase distribution of an ideally achromatic focused target Must meet: ; The task is split into two parts through end-to-end training: ; The first structural layer provides the basic focusing phase. The incident parallel light is pre-deflected into the substrate; after the light propagates through a 1mm substrate, the second structural layer provides the remaining focusing phase based on the light's arrival position. and wideband chromatic aberration compensation phase In the design process, the first step is to perform primary phase allocation on the first structural layer (SideA). Under the constraints of processing resolution and physical modulation characteristics of low-refractive-index materials, the critical focal length that achieves the maximum beam deflection angle while maintaining high diffraction efficiency is calculated and selected, thereby constructing a non-periodic Fresnel zone plate structure. This layer acts as a primary phase modulator, significantly pre-deflecting the incident parallel light and guiding it into the substrate. Subsequently, the second structural layer (SideB) located on the exit surface is used as a fine-tuning mechanism. After the light propagates through a 1mm thick substrate, the second structural layer provides the remaining focusing phase fine-tuning and wide-band chromatic aberration compensation phase based on the phase deviation at the light field's arrival position. Through this dual-sided phase-sharing mechanism, the local phase gradient of each micro / nano structure layer within the full aperture is controlled within the effective modulation range of the low-refractive-index medium, effectively solving the problem of diffraction efficiency attenuation caused by excessive phase gradients at the edges of large-aperture lenses, and significantly improving the overall imaging quality.

[0033] This invention employs an all-path scalar diffraction model to describe the physical process of light field traveling from the incident plane through a double-layer microstructure to the focal plane. This model not only accounts for the phase change caused by spatial geometry but also rigorously considers the propagation path difference caused by the thick substrate and the field coupling effect between the two layers. The specific calculation process is as follows: 1. Modulation of incident light field with the first structural layer (SideA) Suppose a broadband collimated plane light beam is incident perpendicularly along the positive z-axis, with a wavelength of... The initial complex amplitude distribution is When light passes through the area located When the first structural layer (FZP) is applied, phase modulation is applied to it. The complex amplitude transmittance function of Side A is: .

[0034] Complex amplitude of the outgoing wavefront modulated by SideA Represented as: ; 2. Field propagation and optical path difference compensation inside the substrate (dual-field coupling core) After the light field exits from Side A, it needs to pass through a transparent substrate of thickness h and refractive index n to reach Side B. This model uses the angular spectral transfer method to calculate this free propagation process.

[0035] First, a two-dimensional Fourier transform is performed on the emitted light field of SideA, decomposing it into a superposition of different spatial frequencies (plane light waves): ; in, , These are spatial frequency components.

[0036] In a medium with refractive index n, the angular spectral transfer function after propagation distance h Phase delay and optical path difference caused by the substrate were taken into account: ; Note: This item strictly describes the optical path difference caused by the increased physical path of oblique rays in the substrate.

[0037] Propagation to the SideB incident surface (i.e. Complex amplitude distribution for: ; 3. Modulation and secondary coupling of the second structural layer (SideB) The metasurface array at Side B finely modulates the complex wavefront arriving at that location. Let the complex amplitude response function of the local superatoms at Side B be... The final emitted light field after SideB modulation for:

[0038] 4. Free space propagation to the focal plane The modulated light field is then processed again using angular spectrum theory, from... The focal plane propagates into the air. The angular spectral transfer function at this point uses the air refractive index. Complex amplitude distribution on the focal plane The final representation is:

[0039] Through the rigorous interlayer coupling calculations described above, the model can accurately predict the point spread function (PSF) and its light intensity distribution on the focal plane under different structural parameters. This provides a physical basis for subsequent end-to-end optimization.

[0040] III. For the end-to-end design flow, please refer to [link / reference]. Figure 4This invention employs an end-to-end optimization algorithm to reverse-engineer the subwavelength superatoms of the second structural layer. The specific steps are as follows: Step 1: Construct a forward physical propagation model. A full-path scalar diffraction model from the incident wavefront to the focal plane image point is established using angular spectrum theory, taking into account the optical path difference caused by the substrate thickness h.

[0041] Step 2: Superatomic Characteristic Parameter Quantization. The diameter *d* and height *H* of the superatoms (nanopillars) in the second structural layer are used as variables to be optimized, and their mapping relationship with the complex amplitude response *T(d,H,λ)* is established. UnitCell electromagnetic simulation is performed using full-wave electromagnetic simulation methods (including but not limited to rigorous coupled-wave analysis (RCWA), finite element method (FEM), or finite-difference time-domain method (FDTD)). Periodic boundary conditions (PBC) are applied on the horizontal plane (xy plane) to satisfy the local periodic approximation of the metasurface design; a perfectly matched layer (PML) absorbing boundary is applied in the beam propagation direction (z-axis). Considering the pre-deflection effect of the first structural layer (SideA), the light field reaching SideB has a certain spatial distribution and tilt angle. Therefore, the incident light conditions are set as follows: a broadband light source covering a wide wavelength range of 400nm-650nm; considering the isotropy of cylindrical superatoms, non-polarized or orthogonally linearly polarized states are used as excitation sources; the incident angle range is scanned from normal incidence (0°) to the maximum refraction tilt angle corresponding to the lens edge (e.g., 0°-25°) to establish a comprehensive response database that includes the incident angle dimension.

[0042] By extracting the S-transmission parameters of the transmission surface through simulation, the complex amplitude response of the superatom under different geometric parameters and operating wavelengths was calculated. Where |t| is the amplitude transmittance, For phase delay. Within the selected physical parameter scan space (e.g., period). Height H traversal traversal of diameter d The verification data show that the synergistic effect of intrinsic mode resonance and propagation phase effect in superatomic structures can achieve complete [symbol / propagation] at the center wavelength (e.g., 532 nm). It features phase modulation coverage and provides an ultra-long group delay to compensate for SideA geometric dispersion. Simultaneously, it maintains high transmission efficiency for most parameter combinations across the entire 400nm-650nm wavelength range. Maintain above 80%.

[0043] Step 3: To achieve wide-band achromaticity while maintaining high diffraction efficiency, this invention constructs a multi-criteria loss function that incorporates morphological approximation and energy evaluation. In gradient descent optimization, the following objective function is minimized:

[0044] Among them, wavelength set This loss function aims to enforce the actual point spread function at different wavelengths ( It closely approximates the ideal value in spatial location and shape, while maximizing the energy utilization rate of the beam. Specific definitions and constraints are as follows: 1. Ideal point spread function : The light field distribution of ideal achromatic focusing should strictly conform to the Airy disk diffraction-limited model in an aberration-free system. For any radial coordinate on the target focal plane... Its physical expression is defined as:

[0045] in, The central peak light intensity, It is a first-order Bessel function of the first kind. The overall effective aperture of the lens, Set the focal length for the target. This reference function mathematically anchors the focal point of all test wavelengths to be on the same physical plane with no center offset.

[0046] 2. Calculation method of efficiency term The efficiency term is introduced to prevent the neural network from converging to a physically meaningless solution with "high morphological similarity but extremely low transmittance" during backpropagation. In this embodiment, the focusing efficiency (diffraction efficiency) of a single wavelength is defined as: the radius of the theoretical Airy disk main lobe (i.e., the radius of the first dark ring) on ​​the actual focal plane. The ratio of the optical power within the incident light source to the total incident optical power is calculated using the following formula:

[0047] 3. Weighting coefficients The value and basis Weighting coefficient It is used to balance the magnitude difference between "achromatic aberration control" (norm 2 squared difference) and "light energy utilization" (efficiency term).

[0048] 4. Core physical constraints for eliminating color difference Light intensity centroid coincidence constraint: The requirement is to obtain the centroid coordinates of the actual light spot intensity at each wavelength within a wide wavelength range of 400nm-650nm. The drift is extremely small. The maximum lateral color difference (LCA) must meet the following requirements. (Half height, full width).

[0049] One of the criteria for stopping optimization is the ratio of the actual peak light intensity to the ideal aberration-free peak light intensity at each wavelength. All values ​​must be greater than 0.8, meaning that the diffraction-limited imaging standard is met across the entire wavelength range.

[0050] Value range and basis: In actual training, The value range is set to [0.1, 0.8]. In the initial optimization phase, A smaller value (e.g., 0.1~0.2) is chosen to prioritize driving the superatomic array to generate the correct phase gradient to ensure the achromatic PSF overlap; once the loss function enters a convergence plateau, a dynamic learning rate strategy is adopted to... The step size is increased to 0.5~0.8, which forces the algorithm to screen for combinations of superatomic geometric parameters with intrinsic high transmittance in the solution space, thereby achieving a balance between high NA and high efficiency.

[0051] Step 4: Gradient Descent Optimization. Calculate the backpropagation gradient using automatic differentiation techniques, and iteratively update the structural parameters of the full-aperture hyperatom using a gradient-based automatic differentiation optimization algorithm or a heuristic optimization algorithm such as the Adam optimizer. The initial learning rate is set to 0.05, combined with a cosine annealing decay strategy. The maximum number of iterations is set to 2000, and the convergence threshold is set to the change in the loss function over 100 consecutive iterations. And the Strell ratio of each sampling wavelength satisfies To balance computational power consumption and spectral resolution, in Within the target band, six discrete wavelength nodes are selected with a step size of 50 nm as training sampling points. Although the optimization is based on discrete wavelengths, thanks to the smooth and monotonic geometric dispersion characteristics of the first structural layer and the physical continuity of the polymer material in the second structural layer that conforms to the Cauchy dispersion law, the phase delay between adjacent discrete nodes can be automatically interpolated with high precision. This ensures the lens's continuous achromatic focusing capability across the entire band in terms of physical mechanism. After the algorithm converges, it outputs a two-dimensional spectrum of the superatomic spatial distribution across the entire aperture range.

[0052] IV. Working Principle and Beneficial Effects In this embodiment, when multi-wavelength mixed light is incident, the Fresnel structure of the first layer first works with the substrate to complete approximately 40%-60% of the deflection task. After the light enters the second layer, the superatomic array, determined by end-to-end training, is finely adjusted according to local phase requirements, and the intrinsic dispersion of the superatoms is used to cancel the geometric dispersion of the Fresnel structure. Through this deep coupling of "large-scale geometric phase" and "subwavelength dispersion compensation," this invention achieves diffraction-limited imaging with a large aperture of 2cm at an ultra-thin thickness of 1mm, completely solving the bottleneck of low refractive index materials in high-NA achromatic applications.

[0053] This invention utilizes the self-photosensitive properties of the substrate material to achieve a double-sided structure through the following process: Substrate pretreatment: The photosensitive substrate with a thickness of 1mm is subjected to double-sided grinding and polishing to ensure that the surface roughness reaches the nanometer level.

[0054] Side A: Using ultraviolet grayscale lithography or two-photon polymerization, chemical cross-linking or degradation is induced directly inside or on the surface of the substrate incident on the substrate to define the depth profile of a non-periodic Fresnel zone plate. Because it is bulk lithography, multi-step or continuous phase morphology can be directly achieved by controlling the exposure dose.

[0055] Backside tracking alignment: Flip the substrate and use the body alignment marks preset on the edge of the substrate to achieve spatial alignment of SideB relative to SideA through the backside optical system, with an alignment accuracy of less than 800nm.

[0056] Side-B exposure: Direct exposure of the subwavelength nanopillar array on the exit surface. By precisely controlling the exposure depth, it is ensured that the nanopillar height H achieves the designed dispersion compensation.

[0057] Unified development: The substrate after double-sided exposure is placed in the matching developer for single or step development, directly dissolving the uncrosslinked (positive adhesive characteristics) or degraded (negative adhesive characteristics) bulk material.

[0058] V. Typical Application Scenarios The double-sided achromatic superlens based on phase load equalization described in this invention benefits from its large aperture, high numerical aperture, and wide-band achromatic characteristics achieved at extremely thin thicknesses. Combined with the intrinsic properties of polymer substrate materials, it can be widely used as a core optical component in the following system-level scenarios: (1) High-density optical interconnect field This invention can be integrated into data centers, high-performance computing, or chip-level high-density optical interconnect interfaces. The superlens, fabricated from a low-refractive-index polymer material, possesses excellent portability and flexible integration potential. Simultaneously, through bifacial phase allocation equalization logic, the local phase gradient of the micro / nano structure within the full aperture is precisely controlled, exhibiting extremely high diffraction efficiency and waveguide coupling functionality. This enables the device to achieve efficient collimation, routing, and low-loss transmission of broadband optical signals at large apertures, significantly improving the integration and communication bandwidth of optical interconnect systems.

[0059] (2) Lightweight AR / VR display module This invention can be applied to near-eye display optical systems for augmented reality (AR) or virtual reality (VR) devices to replace traditional bulky multi-element refractive lens assemblies. This double-sided superlens achieves excellent chromatic aberration compensation with a large aperture and high achromatic lightness (NA) within an extremely thin 1mm thickness. While significantly reducing the overall weight of the head-mounted display and providing an extremely lightweight wearing experience, it overcomes the color edge aberration inherent in wide-spectrum microdisplays. Its powerful achromatic functionality ensures high-fidelity projection of the microdisplay light field, greatly improving the field of view and image clarity of near-eye displays.

[0060] (3) Biomedical imaging system Because the polymer material used in the lens substrate has excellent biocompatibility, this invention is particularly suitable for contact or implantable biomedical imaging devices, such as miniature endoscopes, portable skin microscopes, and subcutaneous tissue imagers. The device's overall structure is lightweight and miniature, making it easily and seamlessly integrated with miniature sensors or fiber optic bundles. Combined with its powerful functionality of achieving diffraction-limited imaging across the entire 400nm–650nm wavelength range, it enables real-time acquisition of high-resolution, color-aberration-free miniaturized medical images while fully ensuring biosafety.

[0061] The above description is merely a preferred embodiment of the present invention and does not limit the scope of protection of the present invention. For those skilled in the art, the present invention can have various modifications and variations. Any changes, modifications, substitutions, integrations, and parameter alterations to these embodiments within the spirit and principles of the present invention, achieved through conventional substitutions or by achieving the same function without departing from the principles and spirit of the present invention, fall within the scope of protection of the present invention.

Claims

1. A double-sided achromatic superlens based on phase load equalization, characterized in that, include: Transparent low-refractive-index substrate; The first structural layer, disposed on the incident surface of the transparent low-refractive-index substrate, is a non-periodic phase-type Fresnel zone plate, used to provide a basic focusing phase and pre-deflect the incident parallel light into the interior of the substrate; The second structural layer, disposed on the exit surface of the transparent low-refractive-index substrate, is an isotropic cylindrical nanopillar arranged in a square lattice, used to provide the remaining focusing phase and broadband chromatic aberration compensation phase. The target total phase distribution of the superlens satisfy: r is the radial coordinate, λ is the working wavelength, and f is the target focal length of the superlens; The task is split into two parts through end-to-end training: ； The basic focusing phase provided by the first structural layer is The sum of the remaining focusing phase and chromatic aberration compensation phase provided by the second structural layer is .

2. A double-sided achromatic superlens based on phase load equalization according to claim 1, characterized in that, The transparent low-refractive-index substrate is made of polymer material with a refractive index n=1.45, a substrate thickness h=1mm, and an overall effective light transmission aperture D=2cm for the lens.

3. A double-sided achromatic superlens based on phase load equalization according to claim 1, characterized in that, The first structural layer adopts an 8-step binary optical structure to approximate continuous phase, and its maximum microstructure height is... Where n is the refractive index of the transparent low-refractive-index substrate, The design center wavelength is given; where m is the index of the half-wave zone, taken as a positive integer, and the radial radius of the m-th half-wave zone is given. satisfy: ,in The primary focal length shared by the first structural layer.

4. A double-sided achromatic superlens based on phase load equalization according to claim 1, characterized in that, The lattice period of the second structural layer satisfies the subwavelength condition to suppress higher-order diffraction in the working band; the height of the nanopillar is configured to satisfy the maximum group delay required for the wide-band chromatic aberration compensation; the diameter of the nanopillar gradually varies according to its spatial position within a preset range to provide a local phase modulation range covering 0-2π.

5. A design method for a double-sided achromatic superlens based on phase load equalization, characterized in that, Includes the following steps: Step S1: Construct a forward physical propagation model. Use angular spectrum theory to establish a full-path scalar diffraction model from the incident wavefront to the focal plane image point. The optical path difference caused by the substrate thickness h is taken into account in the model. Step S2: Superatomic characteristic parameter quantization. The diameter d and height H of the nanopillars in the second structural layer are used as variables to be optimized. Full-wave electromagnetic simulation is employed to perform element-level electromagnetic simulation, establishing the superatomic geometric parameters and complex amplitude response. The mapping relationship, where The complex amplitude transmission response of a nanopillar unit with diameter d and height H at the operating wavelength λ includes information on amplitude transmittance and phase delay. Step S3: Define a multi-criteria loss function, which simultaneously includes a point spread function morphology approximation term and a diffraction efficiency energy evaluation term; Step S4: Gradient descent optimization. Calculate the back gradient using automatic differentiation technology. Iteratively update the structural parameters of the full-aperture superatoms using a gradient-based automatic differentiation optimization algorithm or a heuristic optimization algorithm. After convergence, output a two-dimensional map of the spatial distribution of the superatoms across the entire aperture range.

6. The design method of a double-sided achromatic superlens based on phase load equalization according to claim 5, characterized in that, The forward physical propagation model in step S1 specifically includes: Step S11: The incident light field is modulated by the first structural layer to obtain the complex amplitude of the outgoing wavefront. ;in The initial complex amplitude distribution of the light field incident on the first structural layer is given by x and y, which are the abscissa and ordinate of the rectangular coordinate system in the lens aperture plane; 0 is the position coordinate of the incident surface where the first structural layer is located along the optical axis. Step S12: Calculate the propagation of the light field inside the substrate using the angular spectral transfer method to obtain the complex amplitude distribution propagating to the incident surface of the second structural layer. h is the position coordinate of the exit surface where the second structural layer is located in the optical axis direction, corresponding to the substrate thickness; Step S13: The light field is modulated by the second structural layer to obtain the final output light field. ; The complex amplitude distribution of the emitted light field modulated by the second structural layer; Step S14: Calculate the complex amplitude distribution of the modulated light field as it propagates freely to the focal plane. And obtain the focal plane light intensity distribution. .

7. The design method of a double-sided achromatic superlens based on phase load equalization according to claim 5, characterized in that, The unit electromagnetic simulation conditions in step S2 are as follows: periodic boundary conditions are used on the horizontal plane, and perfectly matched layer absorption boundary is used in the beam propagation direction; the incident light is a broadband light source covering a wide wavelength range of 400nm~650nm, and non-polarized or orthogonal linearly polarized state is used as the excitation source, with the incident angle range scanning from 0° to the maximum refraction tilt angle corresponding to the lens edge.

8. The design method of a double-sided achromatic superlens based on phase load equalization according to claim 5, characterized in that, The multi-criteria loss function is: Among them, wavelength set , Let be the actual point spread function. For the ideal Airy spot diffusion function, The single-wavelength focusing efficiency is given by γ, which is a weighting coefficient. The weight coefficient γ has a value range of [0.1, 0.8]. In the initial stage of optimization, it is set to 0.1~0.2, and in the convergence smoothing period, it is gradually increased to 0.5-0.

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9. The design method of a double-sided achromatic superlens based on phase load equalization according to claim 5, characterized in that, The optimization parameters in step S4 are: an initial learning rate of 0.05 combined with a cosine annealing decay strategy, a maximum number of iterations of 2000, and a convergence threshold of the change in the loss function over 100 consecutive iterations. And the Strell ratio of each sampling wavelength .

10. The fabrication method of a double-sided achromatic superlens based on phase load equalization according to claim 1, characterized in that, Includes the following steps: Step P1, Substrate Pretreatment: Double-sided grinding and polishing are performed on a 1mm thick photosensitive substrate to ensure that the surface roughness reaches the nanometer level; Step P2, Front Exposure: Using ultraviolet grayscale lithography or two-photon polymerization technology, a depth profile of a non-periodic Fresnel zone plate is defined on the incident surface of the substrate. Step P3, Backside Tracking Alignment: Flip the substrate and use the body alignment marks preset on the edge of the substrate to achieve spatial alignment of the second structural layer relative to the first structural layer, with an alignment accuracy of less than 800nm; Step P4, Backside Exposure: Expose and define the subwavelength nanopillar array on the emitting surface of the substrate; Step P5, Unified Development: Place the double-sided exposed substrate in the matching developer solution for single or step development.

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