Phase modulation method and optical device

Abstract

This application provides a phase modulation method and an optical device, relating to the field of optical devices. The phase modulation method is applied to a cascaded double-layer diffractive optical device, which includes a top-layer diffractive optical device and a bottom-layer diffractive optical device. The phase modulation method includes: controlling the top-layer diffractive optical device to continuously move from an initial state to a second side by a target displacement; completing the continuous movement to obtain the cascaded phase values ​​of all channels of the double-layer diffractive optical device; and determining the top-layer phase of the top-layer diffractive optical device and the bottom-layer phase of the bottom-layer diffractive optical device based on the target light field phase and the cascaded phase values ​​of all channels. The phase modulation method provided in this application can optimize the phase distribution and increase the number of cascaded channels; during the manufacturing of the diffractive device, the incident light is modulated based on the phase distribution to form a target light field in the far field.

Description

Technical Field

[0001] This application relates to the field of optical devices, and more specifically, to a phase modulation method and an optical device. Background Technology

[0002] The phase of an optical device refers to the spatial delay characteristic of the wavefront as light passes through the optical element. It directly determines the propagation direction and wavefront shape of the light wave. By precisely controlling the phase distribution, diffractive optical devices can achieve complex manipulation of light waves, such as beam deflection, focusing, beam splitting, and holographic imaging. Once a diffractive optical device is fabricated, its phase distribution remains fixed, making it difficult to adapt to dynamically changing application requirements.

[0003] Traditional solutions achieve multi-channel multiplexing by manipulating properties such as the polarization state, wavelength, incident angle, or orbital angular momentum of incident light, thereby improving the functional utilization of individual devices. However, this method, which relies on the manipulation of incident light parameters, has essentially exhausted the multiplexing dimensions of individual devices, making it difficult to further increase the number of channels and still unable to meet complex application requirements. Summary of the Invention

[0004] The purpose of this application is to provide a phase modulation method and an optical device. The phase modulation method adopts a segmented optimization strategy based on the switching between cascaded channels through continuous pixel-level lateral displacement, and uses a genetic algorithm to solve for the global optimal solution in the process. This not only makes the channel switching smoother and easier to align, but also enables the encoding of more cascaded channels, and greatly improves the accuracy and efficiency of the calculation.

[0005] In a first aspect, embodiments of this application provide a phase modulation method applied to a cascaded double-layer diffractive optical device, the double-layer diffractive optical device including a top-layer diffractive optical device and a bottom-layer diffractive optical device; the phase modulation method includes: controlling the top-layer diffractive optical device to continuously move from an initial state to a second side with a target displacement; wherein, the initial state is a state in which the starting pixels of the top-layer diffractive optical device and the bottom-layer diffractive optical device are aligned on a first side; completing the continuous movement to obtain the cascaded phase values ​​of all channels of the double-layer diffractive optical device; and determining the top-layer phase of the top-layer diffractive optical device and the bottom-layer phase of the bottom-layer diffractive optical device based on the target light field phase and the cascaded phase values ​​of all channels.

[0006] In the above implementation process, the phase modulation method proposed in this application realizes multi-channel dynamically adjustable cascaded phase control by controlling the top diffractive optical device to perform continuous pixel-level lateral displacement relative to the bottom diffractive optical device; and generates cascaded phases of different channels by utilizing the relative displacement of the double-layer diffractive devices, and calculates the phase distribution of the top and bottom layers, which significantly improves the number of channels and the flexibility of light field control.

[0007] Optionally, in this embodiment, the total number of pixels of the top-layer diffractive optical device is N, and the total number of pixels of the bottom-layer diffractive optical device is N+M-1, where M is the total number of channels; controlling the top-layer diffractive optical device to move continuously from the initial state to the second side with a target displacement includes: segmenting the top-layer diffractive optical device, and controlling each segment to include (M-1) pixels with determined top-layer phase values ​​and (M-1) pixels with undetermined top-layer phase values; segmenting the bottom-layer diffractive optical device, and controlling each segment to include 2(M-1) pixels with undetermined bottom-layer phase values; controlling each movement to align the (M-1) pixels with undetermined top-layer phase values ​​in the top-layer diffractive optical device with the first (M-1) pixels with undetermined bottom-layer phase values ​​in the bottom-layer diffractive optical device.

[0008] Optionally, in this embodiment, for the i-th segment of the double-layer diffractive optical device: the segmentation of the top-layer diffractive optical device is: α (i-1)(M-1)+1 …α i(m-1) α i(M-1)+1 …α (i+1)(m-1) ; where α (i-1)(M-1)+1 …α i(M-1) Given the determined top-level phase value, and calculated from the (i-1)th segment, α i(M-1)+1 …α (i+1)(M-1) The top-layer phase value is undetermined; the segmentation of the bottom-layer diffractive optical device is: β i(M-1)+1 …β (i+2)(M-1) ; where β i(M-1)+1 …β (i+2)(M-1) The underlying phase value is undetermined.

[0009] In the above implementation process, the phase modulation method provided in this application divides the double-layer diffractive optical device into multiple sub-segments for recursive optimization. Each segment only processes a limited number of pixels (the top layer contains M-1 pixels with fixed phase and M-1 pixels with undetermined phase, and the bottom layer contains 2(M-1) pixels with undetermined phase). By using a segmentation strategy, the high-dimensional optimization problem is reduced in dimensionality. While ensuring the phase continuity between adjacent segments, the computational complexity is significantly reduced and the computational accuracy is improved, enabling the double-layer diffractive device to efficiently generate multi-channel tunable light field distributions.

[0010] Optionally, in this embodiment of the application, determining the top-level phase of the top-level diffractive optical device and the bottom-level phase of the bottom-level diffractive optical device based on the target light field phase and the cascaded phase values ​​of all channels includes: constructing a system of linear equations between the target light field phase and the top-level and bottom-level phases based on the target light field and the cascaded phase values ​​of all channels; and solving the system of linear equations to obtain the top-level and bottom-level phases.

[0011] Optionally, in embodiments of this application, the system of linear equations includes: Where, Φ m A represents the cascaded phase at each pixel position in the m-th channel; m B is an N×N identity matrix; m It is an N×(N+M-1) matrix, and it is an N×N identity matrix starting from the m-th column; Θ is the phase vector with respect to the partial top-level phase and the partial bottom-level phase.

[0012] In the above implementation process, the phase modulation method provided in this application establishes a linear equation system (Φ=C·Θ) between the target optical field phase and the cascaded phase. By solving this equation system, the static phase distribution (α and β) of the top and bottom diffractive optical devices can be determined simultaneously, so that when the top device moves relative to the bottom device, the cascaded phase Φ... m It can accurately reconstruct the target light field.

[0013] Optionally, in this embodiment of the application, solving the linear equations to obtain the top-level phase and the bottom-level phase includes: defining an objective function to minimize the absolute mean square error between the target light field and the calculated light field; and using an objective optimization algorithm based on the objective function to obtain the phase approximation values ​​of the top-level diffractive optical device and the bottom-level diffractive optical device when M>2, thereby obtaining the top-level phase and the bottom-level phase.

[0014] Optionally, in this embodiment of the application, the objective function is: in, For the target light field, e iCΘ To calculate the light field, Φ tar Let Cθ be the target phase for all channels, CΘ be the cascaded phase for all channels, and C be the coefficient matrix.

[0015] In the above implementation process, the phase modulation method provided in this application embodiment adopts a segmented optimization strategy based on the switching between cascaded channels by continuous pixel-level lateral displacement, and uses a genetic algorithm to solve the global optimal solution in this process; therefore, the phase modulation method provided in this application embodiment can not only make channel switching smoother and easier to align, but also encode more cascaded channels, and the accuracy and efficiency of the calculation are greatly improved.

[0016] Optionally, in an embodiment of this application, the target displacement is an integer multiple of the size of a single pixel of the dual-layer diffractive optical device.

[0017] In the above implementation process, the phase modulation method provided in this application embodiment can achieve a multi-channel dynamically adjustable phase superposition effect by controlling the double-layer diffractive optical device to perform precise lateral displacement in integer multiples of the single pixel size p. After each displacement, the phase distribution of the top and bottom layer devices produces a specific cascaded combination, thereby generating different holographic images in the far field. This ensures both the accuracy and repeatability of phase superposition and achieves dynamic switching of complex optical fields through simple mechanical displacement.

[0018] Optionally, in this embodiment of the application, the dual-layer diffractive optical device includes a device with channel spacing of multiple pixels; the method further includes: dividing the device with channel spacing of multiple pixels into multiple sub-devices with channel spacing of single pixels; calculating the top phase of the top layer diffractive optical device and the bottom phase of the bottom layer diffractive optical device of each sub-device respectively; using the top phase of the multiple sub-devices as the top phase of the top layer diffractive optical device of the device with channel spacing of multiple pixels; and using the bottom phase of the multiple sub-devices as the bottom phase of the bottom layer diffractive optical device of the device with channel spacing of multiple pixels.

[0019] In the above implementation process, the design of a cascaded diffractive optical device with a channel spacing of multiple pixels can be regarded as a combination of several cascaded diffractive optical devices with a channel spacing of single pixels.

[0020] In a second aspect, embodiments of this application also provide an optical device, the optical device comprising a stacked and cascaded top-layer diffractive optical device and a bottom-layer diffractive optical device; the top-layer phase of the top-layer diffractive optical device and the bottom-layer phase of the bottom-layer diffractive optical device are determined according to the phase modulation method in the first aspect of this application.

[0021] Thirdly, embodiments of this application also provide a computer-readable storage medium storing computer program instructions, which, when read and executed by a processor, perform the steps in any of the above implementations. Attached Figure Description

[0022] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments of this application will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0023] Figure 1 A flowchart of the phase modulation method provided in the embodiments of this application;

[0024] Figure 2 A schematic diagram illustrating the generation of cascaded phases in a one-dimensional case, as provided in an embodiment of this application;

[0025] Figure 3 A flowchart of segmented movement provided for embodiments of this application;

[0026] Figure 4 A schematic diagram illustrating the segmented calculation strategy provided in an embodiment of this application;

[0027] Figure 5 A flowchart of phase calculation provided for embodiments of this application;

[0028] Figure 6 A flowchart illustrating the approximate solution solving process provided in this application embodiment;

[0029] Figure 7 These are example holographic images corresponding to different target displacements provided in the embodiments of this application;

[0030] Figure 8 A schematic diagram of the simulation and experimental results of the 12-channel cascaded multiplexed hologram provided in the embodiments of this application. Detailed Implementation

[0031] The technical solutions of the embodiments of this application will now be described with reference to the accompanying drawings. For example, the flowcharts and block diagrams in the drawings illustrate the architecture, functions, and operations of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagram may represent a module, program segment, or part of code, which contains one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than those marked in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagram and / or flowchart, and combinations of blocks in the block diagram and / or flowchart, can be implemented using a dedicated hardware-based system that performs the specified function or action, or can be implemented using a combination of dedicated hardware and computer instructions. In addition, the functional modules in the various embodiments of the present invention may be integrated together to form an independent part, or each module may exist separately, or two or more modules may be integrated to form an independent part.

[0032] Once fabricated, diffractive optical devices have a fixed phase distribution, making them unsuitable for dynamically changing application requirements. Traditional solutions involve manipulating properties such as the polarization state, wavelength, incident angle, or orbital angular momentum of the incident light to achieve multi-channel multiplexing, thereby improving the functional utilization of individual devices. However, this method, which relies on the manipulation of incident light parameters, has essentially exhausted the multiplexing dimensions of individual devices, and further increases in the number of channels face fundamental limitations.

[0033] Currently, schemes have been proposed to achieve multi-channel operation by stacking and spatially cascading two-layer diffractive optical devices, and to achieve channel switching by using external mechanical force to cause in-plane lateral displacement or rotation of these two layers of diffractive optical devices.

[0034] The inventors discovered that, in the case of stacked cascades, the selection of the objective function of the pixel-level phase modulation optimization algorithm and the switching method of the cascaded channels are unreasonable, resulting in a limitation on the number of stacked cascaded channels. In the case of spatial cascades, micron-level spatial alignment errors can lead to a significant decrease in diffraction efficiency, affecting the quality of the reconstructed image; furthermore, a certain spacing needs to be maintained between the two layers of diffractive optics, making the system large and non-compact.

[0035] Based on this, this application proposes a phase modulation method and an optical device. The phase modulation method utilizes continuous lateral single-pixel displacement between layers of diffractive optical devices to realize cascaded multiplexing channels for high-capacity holographic storage, making channel switching smoother and easier to align; for optical devices with a large number of total pixels, a segmented calculation strategy can be adopted, thereby enabling the encoding of more cascaded channels.

[0036] Please refer to Figure 1 and Figure 2 , Figure 1 A flowchart of the phase modulation method provided in the embodiments of this application; Figure 2 This diagram illustrates the generation of cascaded phase in a one-dimensional scenario, as provided in an embodiment of this application. This application provides a phase modulation method and an optical device. The phase modulation method is applied to a cascaded double-layer diffractive optical device, which includes a top-layer diffractive optical device and a bottom-layer diffractive optical device. It should be noted that, in this embodiment, the top-layer and bottom-layer diffractive optical devices are cascaded in a stacked manner to form the double-layer diffractive optical device. This stacking and cascading involves tightly fitting or micro-spacing multiple diffractive optical devices along the optical axis. Light passes through each layer sequentially, and each layer modulates the light field step-by-step, ultimately creating a multi-channel effect through the cascaded arrangement.

[0037] The phase modulation method provided in this application includes the following steps:

[0038] Step S100: Control the top diffractive optics to move continuously from the initial state to the second side with the target displacement.

[0039] In step S100 above, the top-layer diffractive optical device is controlled to move continuously from the initial state to the second side with a target displacement. Please refer to [link / reference needed]. Figure 2 In this embodiment, the initial state is that the starting pixels of the top-layer diffractive optical device and the bottom-layer diffractive optical device are aligned on the first side. Figure 2 In the middle, the first side is the left side and the second side is the right side. That is, the top diffraction optical device α1 and the bottom diffraction optical device β1 on the left are aligned. The top diffraction device is controlled to move continuously to the right each time the target displacement is moved. The continuous pixel-level lateral displacement can realize the switching between channels.

[0040] Step S200: Complete continuous movement to obtain the cascaded phase values ​​of all channels of the double-layer diffractive optical device.

[0041] In step S200 above, multiple consecutive movements are performed until the continuous movement calculation is completed and the cascaded phase of all channels of the double-layer diffraction optical device is obtained. Please refer to [link / reference needed]. Figure 2 Top-layer diffractive optical devices ( Figure 2The red portion (in the middle) moves from left to right by one pixel with side length p, interacting with the underlying diffraction optics. Figure 2 The blue portion in the middle combines to create a cascaded channel (initially, the upper and lower liquid crystal layers are aligned on the left). When the top diffractive optical device moves m-1 pixels, the cascaded channel number is m. At this time, the nth pixel of the top layer coincides with the (n+m-1)th pixel of the bottom layer in the horizontal position (e.g., ...). Figure 2 As shown), the cascaded phase, i.e. the total phase delay, can be expressed as: Where α represents the top phase of the top diffractive optical device and β represents the bottom phase of the bottom diffractive optical device, M represents the total number of channels, and N represents the top liquid crystal, i.e., the total number of pixels of the top diffractive optical device.

[0042] It should be noted that a two-dimensional cascaded diffractive optical device can be considered as a combination of several independent one-dimensional structures.

[0043] Step S300: Determine the top phase of the top diffractive optical device and the bottom phase of the bottom diffractive optical device based on the target light field phase and the cascaded phase values ​​of all channels.

[0044] In step S300 above, the top phase α of the top diffractive optical device and the bottom phase β of the bottom diffractive optical device are calculated based on the target light field phase and the cascaded phase value obtained in step S200. After obtaining the top phase α and the bottom phase β, they are used to control the incident light so that it forms the target light field (such as a hologram or energy distribution) in the far field.

[0045] pass Figure 1 and Figure 2 As can be seen, the phase modulation method proposed in this application realizes multi-channel dynamically adjustable cascaded phase modulation by controlling the top diffractive optical device to perform continuous pixel-level lateral displacement relative to the bottom diffractive optical device; and generates cascaded phases of different channels by utilizing the relative displacement of the double-layer diffractive devices, and calculates the phase distribution of the top and bottom layers, which significantly improves the number of channels and the flexibility of light field modulation.

[0046] Please refer to Figure 3 and Figure 4 , Figure 3 A flowchart of segmented movement provided for embodiments of this application; Figure 4 This is a schematic diagram of the segmented calculation strategy provided in this application embodiment; wherein, the total number of pixels of the top diffractive optical device is N, the total number of pixels of the bottom diffractive optical device is N+M-1, and M is the total number of channels. When N is large enough, for example, N is greater than 50, the segmented calculation strategy can be used; the control of the top diffractive optical device in the above step S100 to move continuously from the initial state to the second side with a target displacement can be achieved through the following steps:

[0047] Step S110: Segment the top-layer diffractive optical device, and control that the top-layer diffractive optical device in each segment includes (M-1) pixels with determined top-layer phase values ​​and (M-1) pixels with undetermined top-layer phase values.

[0048] Step S120: Segment the bottom diffractive optical device and control that each segment includes 2 (M-1) pixels with undetermined bottom phase values.

[0049] Step S130: Control the alignment of (M-1) pixels with undetermined top-level phase values ​​in the top-level diffractive optical device with the first (M-1) pixels with undetermined bottom-level phase values ​​in the bottom-level diffractive optical device in each segment during each movement.

[0050] In steps S110 to S130 above, the top-layer diffraction optical device and the bottom-layer diffraction optical device are segmented respectively. Excluding the initial segmentation, each top-layer diffraction optical device is guaranteed to include (M-1) pixels with determined top-layer phase values ​​and (M-1) pixels with undetermined top-layer phase values, and each bottom-layer diffraction optical device is guaranteed to include 2(M-1) pixels with undetermined bottom-layer phase values. Furthermore, as... Figure 4 As shown, the (M-1) pixels with undetermined top-level phase values ​​in the top-level diffractive optical device are aligned with the first (M-1) pixels with undetermined bottom-level phase values ​​in the bottom-level diffractive optical device.

[0051] In this process, the overall phase error obtained by the calculation of the upper (M-1) unknown phase pixels is relatively low. At the same time, it can also reduce the total number of unknown phase pixels in each segment. The smaller number of unknown phase pixels can reduce the calculation time and improve the calculation accuracy.

[0052] For example, Figure 4 The second segment, α1 to α m-1 For pixels in the top layer whose top-level phase values ​​have been determined, α m To α 2(M-1) For pixels in the top layer whose top-level phase value is not determined, β M To β 3(M-1) For pixels in the underlying layer whose underlying phase values ​​are not yet determined; in this segment, α M To α 2(M-1) With β M To β 2(M-1) Alignment.

[0053] In the above implementation process, Figure 4 The pixels highlighted by the red dashed line participated in the optimization of the preceding and following segments, ensuring efficient connection between adjacent segments.

[0054] In one possible embodiment, assuming the double-layer diffractive optical device is divided into i segments, the segmentation of the i-th segment is as follows: The segmentation of the top layer diffractive optical device is: α (i-1)(M-1)+1 …α i(M-1) α i(M-1)+1 …α (i+1)(M-1) ; where α (i-1)(M-1)+1 …α i(M-1) Given the determined top-level phase value, and calculated from the (i-1)th segment, α i(M-1)+1 …α (i+1)(M-1) The top-level phase value is undetermined.

[0055] The segmentation of the underlying diffractive optical device is: β i(M-1)+1 …β (i+2)(M-1) ; where β i(M-1)+1 …β (i+2)(M-1) The underlying phase value is undetermined.

[0056] pass Figure 3 and Figure 4 As can be seen, the phase modulation method provided in this application divides the double-layer diffractive optical device into multiple sub-segments for recursive optimization. Each segment only processes a limited number of pixels (the top layer contains M-1 pixels with known phase and M-1 pixels with undetermined phase, and the bottom layer contains 2(M-1) pixels with undetermined phase). By using a segmentation strategy, the high-dimensional optimization problem is reduced in dimensionality. While ensuring the phase continuity between adjacent segments, the computational complexity is significantly reduced and the computational accuracy is improved, enabling the double-layer diffractive device to efficiently generate multi-channel tunable light field distributions.

[0057] Please refer to Figure 5 , Figure 5 The flowchart for phase calculation provided in this application embodiment; in an optional embodiment of this application embodiment, the determination of the top-level phase of the top-level diffractive optical device and the bottom-level phase of the bottom-level diffractive optical device based on the target light field phase and the cascaded phase values ​​of all channels in step S300 can be achieved through the following steps:

[0058] Step S310: Based on the target light field and the cascaded phase values ​​of all channels, construct a system of linear equations between the target light field phase and the top and bottom layer phases.

[0059] In step S310 above, based on the target optical field Φ and the cascaded phase value Φ of all channels... m Construct a system of linear equations relating the target light field Φ to the top layer phase α and the bottom layer phase β.

[0060] Cascaded phase value Φ m The cascaded phase at each pixel position when the channel number is m is represented as:

[0061]

[0062] in,

[0063] In addition, Φ m A represents the cascaded phase at each pixel position in the m-th channel; m B is an N×N identity matrix; m It is an N×(N+M-1) matrix, and it is an N×N identity matrix starting from the m-th column; Θ is the phase vector with respect to the top-level phase and the bottom-level phase.

[0064] Furthermore, by integrating the cascaded phase calculations across all channels, a system of linear equations is obtained between the target optical field Φ and the top-layer phase α and the bottom-layer phase β:

[0065]

[0066] Where C is a coefficient matrix of dimension (M·N)×(2N+M-1).

[0067] Step S320: Solve the system of linear equations to obtain the top-level phase and the bottom-level phase.

[0068] In step S320 above, the linear equation system of equation (3) above is solved to obtain the top layer phase α and the bottom layer phase β.

[0069] When M≤2, the rank of matrix C and the rank of augmented matrix [C|Φ] are both equal to the number of rows M·N. They are less than the number of variables 2N+M-1. Therefore, the system of equations (3) has infinitely many solutions.

[0070] When M > 2, the rank of matrix C is 2N + M - 2, while the rank of the augmented matrix [C|Φ] is 2N + M - 1. Therefore, the system of equations has no exact solution. Thus, when M > 2, only an approximate solution for the phase can be obtained.

[0071] pass Figure 5 As can be seen, the phase modulation method provided in this application establishes a linear equation system (Φ=C·Θ) between the target optical field phase and the cascaded phase. By solving this equation system, the static phase distribution (α and β) of the top and bottom diffractive optical devices can be determined simultaneously, so that when the top device moves relative to the bottom device, the cascaded phase Φ... m It can accurately reconstruct the target light field.

[0072] Please refer to Figure 6 , Figure 6 The flowchart for solving the approximate solution provided in the embodiments of this application is shown. In an optional embodiment of this application, when solving the approximate solution of the linear equation system between the target light field phase and the top layer phase and the bottom layer phase, a genetic algorithm with global optimization capability can be used to design the phase distribution of the diffractive optical device.

[0073] The above step S320, solving the linear equation system to obtain the top-level and bottom-level phases, can be achieved in the following way:

[0074] Step S321: Define the objective function to minimize the absolute mean square error between the target light field and the calculated light field.

[0075] In step S321 above, an objective function is defined to minimize the absolute mean square error between the target light field and the calculated light field. Considering the 2π periodicity of the phase, the objective function is defined as follows:

[0076]

[0077] in, For the target light field, e iCΘ To calculate the light field, Φ tar Let Cθ be the target phase for all channels, CΘ be the cascaded phase for all channels, and C be the coefficient matrix.

[0078] Step S322: Based on the objective function, use the objective optimization algorithm to find the phase approximation values ​​of the top-layer diffractive optical device and the bottom-layer diffractive optical device when M>2, and obtain the top-layer phase and the bottom-layer phase.

[0079] In step S322 above, the target optimization algorithm is a genetic algorithm or similar algorithm with global optimization capabilities. This application uses a genetic algorithm as an example for detailed description. In practical applications, other optimization algorithms, such as particle swarm optimization and ant colony optimization, can also be used.

[0080] It should be noted that genetic algorithms simulate processes such as natural selection, crossover, and mutation in biological evolution, seeking the global optimal solution to a problem through iterative generational approaches. However, the computational accuracy and convergence speed of genetic algorithms decrease sharply with the increase in the number of variables, posing a challenge to optimizing large-size cascaded diffraction optical devices. Therefore, when N is large, the segmented calculation strategy described in steps S110 to S130 above needs to be used; the overall calculation is improved by dividing the whole into several smaller parts and performing calculations on each part separately.

[0081] pass Figure 6 As can be seen, the phase modulation method provided in this application embodiment adopts a segmented optimization strategy based on the switching between cascaded channels by continuous pixel-level lateral displacement, and uses a genetic algorithm to solve the global optimal solution in this process; therefore, the phase modulation method provided in this application embodiment not only makes channel switching smoother and easier to align, but also encodes more cascaded channels, and the accuracy and efficiency of the calculation are greatly improved.

[0082] Please refer to Figure 7 , Figure 7Example holographic images corresponding to different target displacements provided in the embodiments of this application; in an optional embodiment, the target displacement is an integer multiple of the size of a single pixel of the double-layer diffractive optics.

[0083] For each lateral displacement, the total output phase is obtained by superimposing the phases of the two diffractive optical layers. For example... Figure 7 As shown, p is the size of a single pixel. Figure 7 In this process, two diffractive optical devices are aligned under different lateral displacements (p, 2p…(m-1)p…), and their superimposed phases produce different holographic images in the far field.

[0084] Therefore, the phase modulation method provided in this application can achieve a multi-channel dynamically adjustable phase superposition effect by controlling the double-layer diffractive optical device to perform precise lateral displacement in integer multiples of the single pixel size p. After each displacement, the phase distributions of the top and bottom layers of the device produce a specific cascaded combination, thereby generating different holographic images in the far field. This ensures both the accuracy and repeatability of phase superposition and achieves dynamic switching of complex optical fields through simple mechanical displacement.

[0085] In an optional embodiment, the dual-layer diffractive optical device includes a device with channel spacing of multiple pixels; the phase modulation method provided in this application embodiment further includes:

[0086] The device with a channel spacing of multiple pixels is divided into multiple sub-devices with a channel spacing of single pixels; the top phase of the top diffractive optical device and the bottom phase of the bottom diffractive optical device of each sub-device are calculated respectively; the top phase of the multiple sub-devices is used as the top phase of the top diffractive optical device of the device with a channel spacing of multiple pixels; and the bottom phase of the multiple sub-devices is used as the bottom phase of the bottom diffractive optical device of the device with a channel spacing of multiple pixels.

[0087] Therefore, the design of a cascaded diffractive optical device with a channel spacing of multiple pixels can be regarded as a combination of several cascaded diffractive optical devices with a channel spacing of single pixels.

[0088] Please refer to Figure 8 , Figure 8 This diagram illustrates the simulation and experimental results of a 12-channel cascaded multiplexed hologram provided in this embodiment of the application; the two layers of diffractive optics achieve holographic channel switching through the lateral displacement of two pixels. Here, p is the size of a single pixel.

[0089] Liquid crystals were used as diffractive optical devices to demonstrate the phase-tunable function of cascaded diffractive optical devices. The top liquid crystal contained 500×500 pixels, while the bottom liquid crystal had M-1 more columns than the top to ensure that the effective number of pixels in the cascaded hologram was equal in each channel, and the size of a single pixel was set to 8.64μm.

[0090] Using the twelve constellations as target images, reconstruction was performed with different lateral relative displacements under 532nm light illumination. Figure 8 Cascaded holography for each channel was demonstrated through simulation and experiments, with a lateral displacement interval of two individual pixels. Simulation results show no crosstalk between channels, and the reconstructed image information is clearly visible. Compared with the simulation results, the experimental results show slightly more background noise, mainly due to limitations in liquid crystal manufacturing precision and alignment errors during the experiment.

[0091] This application also provides an optical device comprising a stacked and cascaded top-layer diffractive optical device and a bottom-layer diffractive optical device, wherein the top-layer phase of the top-layer diffractive optical device and the bottom-layer phase of the bottom-layer diffractive optical device are determined according to the phase modulation method described above.

[0092] Based on the same inventive concept, embodiments of this application also provide a computer-readable storage medium storing computer program instructions, which, when read and executed by a processor, perform steps in any implementation of the phase modulation method described above.

[0093] The computer-readable storage medium can be any medium capable of storing program code, such as Random Access Memory (RAM), Read Only Memory (ROM), Programmable Read-Only Memory (PROM), Erasable Programmable Read-Only Memory (EPROM), Electrically Erasable Programmable Read-Only Memory (EEPROM).

[0094] In this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, without necessarily requiring or implying 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, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising..." does not exclude the presence of additional identical elements in the process, method, article, or apparatus that includes said element.

[0095] The above description is merely an embodiment of this application and is not intended to limit the scope of protection of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A phase modulation method, characterized in that, The phase modulation method is applied to a cascaded double-layer diffractive optical device, which includes a top-layer diffractive optical device and a bottom-layer diffractive optical device; the phase modulation method includes: The top-layer diffractive optics is controlled to move continuously from an initial state to a second side with a target displacement; wherein, the initial state is the state in which the starting pixels of the top-layer diffractive optics and the bottom-layer diffractive optics are aligned on a first side; The continuous movement is completed to obtain the cascaded phase values ​​of all channels of the double-layer diffractive optical device; Based on the target light field phase and the cascaded phase values ​​of all channels, determine the top-level phase of the top-level diffractive optical device and the bottom-level phase of the bottom-level diffractive optical device; The step of determining the top-level phase of the top-level diffractive optical device and the bottom-level phase of the bottom-level diffractive optical device based on the target light field phase and the cascaded phase values ​​of all channels includes: Based on the target optical field and the cascaded phase values ​​of all channels, a system of linear equations is constructed between the target optical field phase and the top-level and bottom-level phases; Solve the system of linear equations to obtain the top-level phase and the bottom-level phase; The linear equation system includes: ， Where M is the total number of channels. The cascaded phase at each pixel position in the m-th channel; It is an N×N identity matrix; B m for N ×( N + M A matrix of size -1), and whose m-th column is an N×N identity matrix; This is the phase vector with respect to the top-level phase and the bottom-level phase.

2. The method of claim 1, wherein, in, The total number of pixels in the top-layer diffractive optical device is N, and the total number of pixels in the bottom-layer diffractive optical device is N+M-1; controlling the top-layer diffractive optical device to continuously move from the initial state to the second side with a target displacement includes: The top-level diffractive optical device is segmented, and each segment is controlled to include (M-1) pixels with determined top-level phase values ​​and (M-1) pixels with undetermined top-level phase values. The underlying diffractive optical device is segmented, and each segment is controlled to include 2 (M-1) pixels with undetermined underlying phase values. Each time the movement is performed, the (M-1) pixels in the top diffractive optical device with undetermined top phase values ​​are aligned with the first (M-1) pixels in the bottom diffractive optical device with undetermined bottom phase values.

3. The method of claim 2, wherein, in, For the i-th segment of the double-layer diffractive optical device: The top-layer diffractive optical device is segmented as follows: , ;in, The top-level phase value is already determined and is calculated from the (i-1)th segment. The top-level phase value is undetermined; The segments of the underlying diffractive optical device are as follows: ;in, The underlying phase value is undetermined.

4. The method of claim 1, wherein, Solving the linear equation system to obtain the top-level phase and the bottom-level phase includes: The objective function is defined to minimize the absolute mean square error between the target light field and the calculated light field. Based on the objective function, an objective optimization algorithm is used to obtain the phase approximation values ​​of the top-layer diffractive optical device and the bottom-layer diffractive optical device when M>2, thereby obtaining the top-layer phase and the bottom-layer phase.

5. The method of claim 4, wherein, The objective function is: in, For the target light field, e iCΘ To calculate the light field, Φ tar Let Cθ be the target phase for all channels, CΘ be the cascaded phase for all channels, and C be the coefficient matrix.

6. The method according to claim 1, characterized in that, in, The target displacement is an integer multiple of the size of a single pixel in the dual-layer diffractive optical device.

7. The method according to claim 1, characterized in that, The dual-layer diffractive optical device includes a device with channel spacing of multiple pixels; the method further includes: The device with channel spacing of multiple pixels is divided into multiple sub-devices with channel spacing of single pixels; Calculate the top phase of the top diffractive optical device and the bottom phase of the bottom diffractive optical device for each sub-device. The top-level phase of the multiple sub-devices is used as the top-level phase of the top-level diffractive optical device of the device with channel spacing of multiple pixels; and The bottom phase of the multiple sub-devices is used as the bottom phase of the bottom diffractive optical device of the device with a channel spacing of multiple pixels.

8. An optical device, characterized by The optical device includes a top-level diffractive optical device and a bottom-level diffractive optical device stacked and cascaded; the top-level phase of the top-level diffractive optical device and the bottom-level phase of the bottom-level diffractive optical device are determined according to the phase modulation method of any one of claims 1-7.

Images