Method for increasing number of multiplexing channels of non-staggered multi-dimensional channel multiplexing metasurface

Abstract

The invention discloses a method for increasing the number of multiplexing channels of a non-interlaced multi-dimensional channel multiplexing metasurface, which can obtain phase distribution information required to be generated by a target metasurface through a GS algorithm optimized based on a first-class Rayleigh-Sommerpheny formula, and can obtain the number of multiplexing channels of the target metasurface by using a dispersive Jones matrix and a gradient descent method. According to the method, multiple pieces of phase distribution information can be optimized into required superatom information, then the superatom information is compared with a superatom phase database, and finally a target metasurface is formed. According to the non-staggered metasurface produced by the method, the available dimensions can be expanded to three, namely a wavelength, a polarization state and a diffraction distance, and three polarization channels, three wavelength channels and two reconstruction distances can be utilized at the same time, so that the number of multiplexing channels is increased to 18.

Description

Technical Field

[0001] The present invention relates to metasurface technology, and specifically refers to a method for increasing the number of multiplexed channels of a non-interlaced multi-dimensional channel multiplexing metasurface based on a dispersion Jones matrix, a first-kind Rayleigh-Sommerfeld diffraction formula, a GS algorithm, and a gradient descent method. The method can be used to design a non-interlaced metasurface for multi-dimensional channel multiplexing, and increase the number of multi-dimensional multiplexing channels that can be realized by the metasurface. Background Art

[0002] Metasurface is a two-dimensional device composed of sub-wavelength nano-units arranged in a certain pattern. It has extremely high precision in manipulating the phase, amplitude and polarization state of electromagnetic waves. Compared with traditional optical devices with large volume and weight, metasurface has the advantages of small size, light weight, low cost, multi-function and easy integration. Metasurface is used to realize multi-dimensional channel multiplexing, and holographic imaging is realized through metasurface holography. The core of this method is to use meta-atoms to manipulate the physical parameters of light in multiple dimensions such as polarization, wavelength, orbital angular momentum, imaging distance, etc., so that a single metasurface can realize the reproduction of multiple holographic images, thereby improving the optical information storage density of the device. This is of great significance and value to meet the actual needs of future optical color imaging, optical encryption, information storage and transmission, etc.

[0003] The currently proven metasurface design methods mainly increase the number of reusable channels by designing staggered metasurfaces and non-staggered metasurfaces. Staggered metasurfaces obtain more degrees of freedom by combining multiple meta-atoms into a unit. Each meta-atom in a single unit can independently manipulate light waves of different wavelengths or polarization states according to its own physical properties. When the light wave passes through a unit, it will be independently manipulated by different meta-atoms and finally synthesized into the output light wave required by the design, which exists as a pixel on the metasurface holographic imaging. This design method is simple and intuitive, but too large a unit will reduce the periodicity and the quality of the reconstructed image. Non-staggered metasurfaces combine the limited degrees of freedom of the meta-atom itself with the physical dimensions such as the wavelength, polarization state and reconstruction distance of the light wave to realize the reuse of multi-dimensional channels. However, the existing design methods are not perfect for the design of two or more dimensions. For example, the wavelength, polarization state, topological charge and reconstruction distance of the holographic image either only use one or two of them, or use three dimensions but only have two polarization state channels. There is room to further increase the number of reusable channels. The present invention provides a novel method for inversely designing a non-staggered metasurface. Summary of the invention

[0004] The purpose of the present invention is to provide a method for increasing the number of multiplexed channels of a non-interleaved multidimensional channel multiplexing metasurface, mainly to solve the technical problem of the small number of multiplexed channels in the existing method. It uses the dispersion Jones matrix to regulate the perfectly isolated polarization channels at different wavelengths, optimizes the known GS algorithm and gradient descent method through the first-class Rayleigh-Sommerfeld formula to reversely design the metasurface, and explores the application potential of the reconstruction distance variable. Finally, it can realize multidimensional channel multiplexing of three polarization channels, three wavelength channels and two reconstruction distances, and expand the number of multiplexed channels to 18.

[0005] To achieve the above object, the technical solution of the present invention is as follows:

[0006] A method for increasing the number of multiplexing channels of a non-interleaved multi-dimensional channel multiplexing metasurface, characterized in that it comprises:

[0007] The first kind of Rayleigh-Sommerfeld diffraction formula is used to optimize the traditional GS algorithm. This optimization method regards the diffraction process as a response process and extracts the response function from the first kind of Rayleigh-Sommerfeld diffraction formula, and then performs iterative calculations.

[0008] The ability of meta-atoms on the metasurface to control the light field can be expressed using the Jones matrix To describe, when the superatom rotates, the Jones matrix becomes

[0009]

[0010] After processing the target image with the optimized GS algorithm, the phase distribution information required for designing the metasurface can be obtained. Then, the phase distribution information is processed by the Jones matrix and gradient descent method to obtain the phase Ψ related to the specific metaatom. x , y and the information distribution of the rotation angle θ, and the superatom Ψ x , y The phase database is compared to obtain the required meta-atoms and finally the target meta-surface.

[0011] The method for increasing the number of multiplexing channels of a non-interleaved multi-dimensional channel multiplexing metasurface is characterized by:

[0012] The response function extracted from the first kind of Rayleigh-Sommerfeld diffraction formula is The Rayleigh-Sommerfeld formula of the first kind becomes U = F -1 {F{U0}F{h}}, to ensure the iteration is valid, the inverse diffraction needs to be changed to

[0013]

[0014] The method for increasing the number of multiplexing channels of a non-interleaved multi-dimensional channel multiplexing metasurface is characterized by:

[0015] Jones Matrix The elements of the Jones matrix represent polarization channels. To ensure that the energy of each channel is uniform, that is, the amplitude of all channels is the same, the Jones matrix is ​​restricted to Ψ1, Ψ2 and Ψ3 are about Ψ x , y and a function of the rotation angle θ.

[0016] The method for increasing the number of multiplexing channels of a non-interleaved multi-dimensional channel multiplexing metasurface is characterized by:

[0017] The loss function of the gradient descent method is: Δ i is the difference between the target value and the calculated value.

[0018] The method of the present invention has the following advantages:

[0019] 1. The method of the present invention adopts the first kind of Rayleigh-Sommerfeld formula as the diffraction formula and optimizes the traditional GS algorithm, resulting in better imaging effect;

[0020] 2. The method of the present invention utilizes the gradient descent method to optimize parameters, and the optimization and convergence speeds are fast.

[0021] 3. Using the method of the present invention, a non-interlaced metasurface with a large number of reusable multi-dimensional channels can be produced, which effectively increases the number of channels of the non-interlaced metasurface device.

[0022] 4. The method of the present invention is simple and direct. The subsequent simulation examples prove the effectiveness and reliability of the method and have practical engineering significance. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 is a schematic diagram of a supercell and a supersurface provided by an embodiment of the present invention;

[0024] Figure 2 is a phase database of an embodiment of the present invention;

[0025] Figure 3 is a flow chart of an embodiment of the present invention;

[0026] Figure 4 It is an iterative cycle diagram of the GS algorithm optimized by the present invention;

[0027] Figure 5 is a Loss curve diagram of the gradient descent algorithm provided by an embodiment of the present invention;

[0028] Figure 6It is a schematic diagram of the results of a holographic imaging experiment with three polarization channels, three wavelength channels, and double diffraction distances in a non-interlaced metasurface inverse design method provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0029] The present invention discloses a method for increasing the number of multiplexed channels of a non-interlaced multi-dimensional channel multiplexing metasurface, which specifically comprises the following steps:

[0030] Step 1: Use the first kind of Rayleigh-Sommerfeld formula to optimize the traditional GS algorithm. The first kind of Rayleigh-Sommerfeld formula is as follows:

[0031]

[0032] Where r is the distance between the reconstructed light field and the metasurface. If the process of reconstructing the light field is regarded as a response process, then the response function is The Rayleigh-Sommerfeld formula of the first kind becomes U = F -1 {F{U0}F{h}} can be brought into the GS algorithm for iterative calculation. In order to ensure that the iteration is valid, it is necessary to The optimized GS algorithm is obtained. Since the first-type Rayleigh-Sommerfeld formula contains parameters such as light wavelength and diffraction distance, in this step, different wavelengths and diffraction distances can be set to assign the target image to different wavelength channels and diffraction distances, thereby realizing multiplexing in two dimensions: wavelength and diffraction distance. Finally, the intensity map of the target image and the intensity of the incident light are brought into the optimized GS algorithm to obtain the phase distribution information required for designing the metasurface.

[0033] Step 2: Use Jones matrix to realize polarization state channel allocation. The super atom used is a cubic structure. When the super atom does not rotate, the outgoing light generated by the incident light passing through the super atom can be expressed by the following Jones matrix:

[0034]

[0035] Among them Ψ x and y They are the phase shifts caused by x-polarized light and y-polarized light passing through a superatom with a rotation angle of 0. When the superatom has a rotation angle θ, the Jones matrix becomes Where R(θ) is the rotation matrix. Since the present invention includes more than two polarization channels, it is necessary to ensure that the energy of each channel is uniform, that is, the amplitude of all channels is the same, so the above Jones matrix needs to be limited to Ψ1, Ψ2 and Ψ3 are related to Ψ x ,Ψ y and the function of the rotation angle θ, the relationship between the incident light and the outgoing light can be described as E o =J θ ·Ein The phase Ψ1 corresponds to the polarization state channel of x polarization -> x polarization, the phase shift Ψ2 controls the cross polarization state channel of x polarization -> y polarization / y polarization -> x polarization, and the phase shift Ψ3 is the polarization state channel of y polarization -> y polarization. By matching the phase distribution information obtained in step 1 with Ψ1, Ψ2, and Ψ3, the target image can be assigned to a specific polarization state channel.

[0036] Step 3: Use the gradient descent method and Ψ1, Ψ2, Ψ3 about Ψ x , y , the function of the rotation angle θ, and the phase Ψ associated with the specific superatom is obtained x , y The phase distribution information is used as Ψ1, Ψ2 and Ψ3 in the function, and Ψ x , y and the rotation angle θ are set as optimization variables, and the loss function Loss is used i :

[0037]

[0038] Among them, Δ i is the difference between the target value and the calculated value. Since the elements in the Jones matrix represent the light field, the target light field p can be obtained. i and the calculated light field When calculating the loss function, the two light fields need to be split into their real parts Re(p i ), and the imaginary part Im(p i ), Difference Δ i Also divided into and There are two types, and the corresponding loss function is Loss i-1 and Loss i-2 , the overall loss function is In order to ensure the efficiency of calculating the differentials of multiple variables, the present invention uses PyTorch to implement the gradient descent method, and finally obtains Ψ x , y and the phase distribution of the rotation angle θ.

[0039] Step 4: Use FDTD commercial software to scan the designed superatom to obtain the Ψ that superatoms of different sizes can generate x , y , and the obtained metasurface Ψ x , y The phase distribution is compared and selected to obtain the required meta-atom, and finally the required metasurface is designed based on the phase distribution of the rotation angle θ.

[0040] Example

[0041] In order to better understand the process, purpose and advantages of the present invention, the method of the present invention will be described in detail below with reference to the accompanying drawings.

[0042] Step 1: First, we need to scan and obtain the Ψ that can be produced by superatoms of different sizes. x , y In this case, the working wavelengths of the light waves are 3.5μm, 4μm, and 4.5μm, the materials of the super-atom and the substrate are Si, and the geometric shape of the super-atom is a cube, such as Figure 1 As shown, the period P = 1.8μm, the height H = 7μm, and the length and width range from 200nm to 1200nm. The length and width of the superatom are equally spaced at 50 points, and a total of 2500 superatoms of different geometric sizes are selected. The three target wavelengths of light waves are irradiated with linearly polarized light of x polarization and y polarization, respectively, and the superatom's ability to manipulate light waves with wavelengths of 3.5μm, 4μm, and 4.5μm is obtained. Figure 2 The three pictures above are superatomic Ψ x Database, the three pictures below are y Database. In each database, x , y All achieve full coverage from -π to +π and a phase shift of Ψ at the same wavelength x , y Furthermore, light waves of different wavelengths have different phase shifts for the same superatom, which shows that a single superatom can manipulate light waves of different wavelengths at the same time, achieving dispersion holography.

[0043] Step 2: Apply the optimized GS algorithm for iterative calculation to obtain the phase distribution information of each target pattern. The metasurface of this implementation case is designed as a non-interlaced metasurface with a pixel size of 250×250 (450μm×450μm). First, the target patterns need to be distributed according to the wavelength and diffraction distance. The digital images "1" to "9" are planned to be reproduced on the focal plane at 250μm from the metasurface, and the uppercase letter images "A" to "I" are planned to be reproduced on the focal plane at 650μm. Images "1", "2", "3", "A", "B", and "C" are reconstructed using light waves with a wavelength of 3.5μm, "4", "5", "6", "D", "E", and "F" are reconstructed using light waves with a wavelength of 4μm, and "7", "8", "9", "G", "H", and "I" are reconstructed using light waves with a wavelength of 4.5μm. Then the distance parameters and wavelength parameters corresponding to each target image are substituted into the first-class Rayleigh-Sommerfeld formula to obtain the corresponding response function. Finally, according to the following Figure 4The optimized GS algorithm shown is used for iterative calculation to obtain the required phase distribution information.

[0044] Step 3: Assign the target image to different polarization channels according to Ψ1, Ψ2, and Ψ3. x ,Ψ y , a function of the rotation angle θ, and applying the gradient descent method, we get the Ψ required to select the unit x ,Ψ y , the rotation angle θ distribution information. Assign images "1", "4", "7", "A", "D", and "G" to the x polarization-x polarization state channel, and images "2", "5", "8", "B", "E", and "H" to the x polarization-y polarization / y polarization-x polarization cross channel, and "3", "6", "9", "C", "F", and "I" to the y polarization-y polarization channel. Substitute the data of each channel into the corresponding Ψ1, Ψ2, and Ψ3 functions, and convert Ψ x ,Ψ y and the rotation angle θ are set as optimization variables, and the gradient descent method is used for optimization. The descent curve of the loss function is as follows: Figure 5 As shown, the desired Ψ can be obtained in the end x ,Ψ y and the rotation angle θ distribution information.

[0045] Step 4: According to the obtained Ψ x ,Ψ y And the rotation angle θ distribution information selects super atoms and forms a super surface. x ,Ψ y The phase distribution information is respectively related to the phase shift Ψ of the corresponding wavelength x ,Ψ y The database is compared, that is, for a certain pixel point, the corresponding phase shift Ψ x ,Ψ y It is transformed into a complex function form and subtracted from the data in the database to obtain the modulus. Since there are multiple Ψ x ,Ψ y , we need to add their results and take the minimum value to find the most satisfactory superatom. After obtaining the required superatom, combined with the rotation angle θ distribution information, we can design the required metasurface. The holographic imaging results of three polarization channels, three wavelength channels, and dual diffraction distances realized by the non-interlaced metasurface designed in this implementation case are shown in the figure. Figure 6 As shown, on the focal plane of f=250 μm, nine digital patterns from “1” to “9” are reproduced, and on the focal plane of f=650 μm, nine capital letter patterns from “A” to “I” are reproduced.

[0046] In summary, the method of the present invention perfectly realizes 18 multi-dimensional multiplexed channels, and the 18 channels have been proven by holographic imaging simulation tests. The present invention has very important practical significance for the research on increasing the number of multi-dimensional multiplexed channels of non-interlaced metasurfaces.

Claims

1. A method for increasing the number of multiplexed channels of a non-interleaved multi-dimensional channel multiplexing metasurface, characterized in that: It includes The first kind of Rayleigh-Sommerfeld diffraction formula is used to optimize the traditional GS algorithm. This optimization method regards the diffraction process as a response process and extracts the response function from the first kind of Rayleigh-Sommerfeld diffraction formula, and then performs iterative calculations. The ability of meta-atoms on the metasurface to control the light field can be expressed using the Jones matrix To describe, when the superatom rotates, the Jones matrix becomes After processing the target image with the optimized GS algorithm, the phase distribution information required for designing the metasurface can be obtained. Then, the phase distribution information is processed by the Jones matrix and gradient descent method to obtain the phase Ψ related to the specific metaatom. x ,Ψ y and the information distribution of the rotation angle θ, and the superatom Ψ x ,Ψ y The phase database is compared to obtain the required meta-atoms and finally the target meta-surface.

2. The method for increasing the number of multiplexed channels of a non-interlaced multi-dimensional channel multiplexing metasurface according to claim 1, characterized in that: The response function extracted from the first kind of Rayleigh-Sommerfeld diffraction formula is The Rayleigh-Sommerfeld formula of the first kind becomes U = F -1 {F{U0}F{h}}, to ensure the iteration is valid, the inverse diffraction needs to be changed to 3. The method for increasing the number of multiplexing channels of a non-interleaved multi-dimensional channel multiplexing metasurface according to claim 1, characterized in that: Jones Matrix The elements of the Jones matrix represent polarization channels. To ensure that the energy of each channel is uniform, that is, the amplitude of all channels is the same, the Jones matrix is ​​restricted to Ψ1, Ψ2 and Ψ3 are about Ψ x ,Ψ y and a function of the rotation angle θ.

4. The method for increasing the number of multiplexing channels of a non-interleaved multi-dimensional channel multiplexing metasurface according to claim 1, characterized in that: The loss function of the gradient descent method is: Δ i is the difference between the target value and the calculated value.

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