Method for carrying out effective phase encoding on incident light at any space angle based on metasurface

Abstract

The invention provides a metasurface-based method for performing effective phase encoding on incident light at any space angle, and belongs to the technical field of micro-nano optics and integrated photonics. According to the invention, the metasurface atomic displacement is associated with any predefined angle of the space incident light, and the gradient descent algorithm is adopted to optimize the phase matrix, so that effective phase coding in the whole angle space is realized. As a concept verification, the invention shows an omnidirectional angle multiplexing super-structure holography for any space light incidence, successfully realizes an augmented reality holographic image with as many as 22 channels, and proves that meaningful phase coding is realized by any incident angle degree of freedom, and the holographic image has the advantage of high signal-to-noise ratio. The arbitrary full-angle multiplexing holography shows good application potential in practical application aspects such as data storage, virtual / augmented reality and optical encryption.

Description

Technical Field

[0001] The present invention relates to the technical fields of micro-nano optics and integrated photonics, and specifically relates to a method for realizing arbitrary omnidirectional angle multiplexing holography by effectively phase encoding incident light at any spatial angle (including azimuth angle and elevation angle) based on a metasurface. Background Art

[0002] A metasurface consists of an array of precisely designed meta-atoms, providing unprecedented degrees of freedom for off-chip incident light manipulation and enabling precise control of the phase, amplitude, wavelength, and polarization of light waves. This excellent ability to manipulate the light field enables the metasurface to be widely applied in various fields, including complex beam generation, imaging, and holography. Recently, the invention of the metasurface integrated on an optical waveguide (referred to as an on-chip metasurface) has brought a new type of compact optical device with the advantages of high fidelity and zero-order diffraction-free. This has enabled a series of innovative applications, including mode conversion, metaholography, and augmented reality. So far, researchers have mainly explored and designed various controllable optical parameters to achieve independent degrees of freedom for on-chip or off-chip light multiplexing, including wavelength, polarization, intensity, orbital angular momentum, etc.

[0003] In previous explorations of independent encoding degrees of freedom for on-chip and off-chip metasurfaces, the incident angle of spatial incident light (including azimuth angle and elevation angle) has been regarded as one of the key parameters in the optical degrees of freedom, with great potential to enhance the multiplexing ability and achieve angle multiplexing. However, the degrees of freedom of this key parameter have not been fully explored or widely applied to incident cases at arbitrary angles. Previous studies have mainly focused on realizing optical manipulation of fixed orthogonal angle incidence through on-chip metasurfaces, failing to fully utilize the potential of arbitrary azimuth angles. Similarly, under off-chip incident conditions, free-space incident light is usually limited to a finite elevation angle of a set of fixed azimuth angles, resulting in the underutilization of the elevation angle degree of freedom. The angle multiplexing of arbitrary spatial rays is restricted mainly due to the lack of an effective encoding strategy to integrate multiple meaningful phase distributions at different incident angles. For example, in a metasurface array designed for a specific incident angle, when the illumination direction changes (either azimuth angle or elevation angle), the generated holographic image may still be similar, but accompanied by distortion or efficiency reduction. Therefore, how to fully utilize arbitrary spatial rays, achieve omnidirectional angle multiplexing, and further improve the information storage capacity of the entire angular space remains an important challenge and a highly valuable research direction. Summary of the Invention

[0004] Aiming at the deficiencies of the above prior art, the present invention provides a method for effectively phase encoding incident light at any spatial angle (including azimuth angle and elevation angle) based on a metasurface. Based on the idea of inverse design, the displacement of the unit structure of the metasurface (retrograde phase) is optimized through a gradient descent algorithm to achieve arbitrary omnidirectional angle multiplexing holography.

[0005] To achieve the above purpose, the specific technical solutions of the present invention are as follows:

[0006] In a first aspect, the present invention provides a method for effectively phase encoding incident light at any spatial angle based on a metasurface, comprising the following steps:

[0007] S1: Arrange a nanobrick structure array on top of the optical waveguide layer to form an on-chip metasurface;

[0008] S2: Set the two sides of the optical waveguide layer in parallel with the working surface of the optical waveguide layer. x axis, y Axis, arranged in a direction perpendicular to the working surface of the optical waveguide layer z Axis, build xyz Coordinate system;

[0009] θ represents the azimuth, defined as the angle at which the incident light xy Projection on a plane +x The angle of the axis; represents the pitch angle, defined as the angle between the incident light and +z The angle between the axes; in particular, when = 90 o When , the incident light propagates along the waveguide plane, thus achieving interaction with the nanobricks;

[0010] S3: The position arrangement of the nanobricks is calculated by the circuitous phase principle, and the phase distribution of the incident light when incident along any spatial angle is calculated by the following formula;

[0011] (1);

[0012] (2);

[0013] (3);

[0014] in, From any angle arrive xy The projected component of incident light on a plane; j represents an imaginary unit; represents the wave vector;

[0015] λ represents the wavelength of incident light; n eff represents the effective refractive index;

[0016] Indicates that the incident light is at any angle Phase distribution at the time of incidence; express x The circuitous phase of direction; express y The circuitous phase of direction;

[0017] S4: The target wavelength is λ The incident light is incident along different spatial directions, and the inverse design method is used to optimize the phase using the gradient descent algorithm;

[0018] S5: looping steps S3 and S4, obtaining the positional arrangement of all nanostructures and encoding them to obtain the final on-chip metasurface two-dimensional array.

[0019] Furthermore, in step S3, the relationship between the detour phase and the nanobrick displacement is as follows:

[0020] (4);

[0021] (5);

[0022] in, , Respectively x, y The circuitous phase of direction; P x 、P y Respectively represent the nano brick x, y Cycle of direction; 、 They represent the nanobricks along the period x, y Therefore, the detour phase is determined only by the displacement of the nanobricks. 、 Adjust from 0 to P x 、P y , can achieve from 0 to 2 π Phase modulation.

[0023] Further, step S4 is as follows: for an incident wave driven at any angle, an inverse design method is used to obtain a randomly generated phase matrix using a gradient descent algorithm. and Start the optimization. During the optimization process, the quality of the hologram is evaluated by calculating the root mean square error (RMSE) between the generated hologram and the ideal target, and the RMSE is used as the loss function. and It is continuously updated during the iterative process and eventually converges to the minimum value of the loss function, outputting the optimized phase mask. Finally, based on the optimized phase matrix, the fast Fourier transform (FFT) is used to generate the holographic images of all channels.

[0024] Furthermore, the on-chip metasurface includes a substrate, an optical waveguide layer located on the substrate, and a nanobrick structure array arranged on the optical waveguide layer.

[0025] Furthermore, the substrate is silicon dioxide, the nanobricks are amorphous silicon nanobricks, and the optical waveguide layer is silicon nitride.

[0026] Furthermore, the length and width of the nanobricks are equal and are both sub-wavelength in size, and are completely consistent in size.

[0027] In the second aspect, the present invention provides a method for realizing arbitrary omnidirectional angle multiplexing holography based on a metasurface, selecting a target image, and optimizing the phase matrix using the method, and based on the optimized phase matrix, performing a fast Fourier transform on the phase matrix to generate holographic images of all channels.

[0028] In a third aspect, the present invention provides the application of the method for realizing arbitrary omnidirectional angle multiplexing holography based on metasurface in the fields of data storage, virtual / augmented reality or optical encryption.

[0029] Compared with the prior art, the present invention is beneficial in that:

[0030] 1. The present invention mathematically associates different predefined random incident angles with the circuitous phase response and uses a degree descent algorithm to deeply optimize the phase, thereby successfully expanding the degree of freedom of the incident direction to any spatial ray angle.

[0031] 2. If the decoded spatial angle parameters cannot be accurately obtained, it is impossible to extract the correct holographic image, which enhances the storage capacity and encryption security of the metadevice; as a proof of concept, the present invention successfully constructed omnidirectional angle multiplexing holography and captured different holographic images at up to 22 predefined arbitrary spatial angles within the same output field of view, proving the meaningful phase encoding of the newly introduced arbitrary incident angle degree of freedom; due to the robustness of the detour phase, the obtained holographic image has the advantage of high signal-to-noise ratio.

[0032] 3. The arbitrary full-angle multiplexed holography demonstrated by the present invention exhibits good information density and quality, and shows good potential in practical applications such as data storage, virtual / augmented reality, and optical encryption. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1A schematic diagram of a method for effectively phase encoding incident light at any spatial angle based on a metasurface provided by the present invention;

[0034] Figure 2 A top-down view of the on-chip metasurface and a schematic diagram of light waves incident on the metasurface from space; in the figure, the height of the nanobricks H The thickness of the silicon nitride optical waveguide layer is 220 nm, and the thickness of the silicon dioxide substrate is 500 μm. L are the length and width of the nanobrick, P is the period of the unit structure, 、 They represent the nanobricks along the period x, y Directional displacement;

[0035] Figure 3 are the phase distributions of three arbitrary incident angles and incident light at different angles in the spherical coordinate system;

[0036] Figure 4 A flow chart of an on-chip metasurface optimization algorithm designed in an embodiment of the present invention;

[0037] Figure 5 The simulation results of multi-channel holographic images at different incident angles in the embodiment of the present invention;

[0038] Figure 6 A schematic diagram of an optical measurement device for multiplexing holographic images at any angle in an embodiment of the present invention and a scanning electron microscope (SEM) image;

[0039] Figure 7 The following are experimental measurement results in the embodiments of the present invention. DETAILED DESCRIPTION

[0040] The technical solution of the present invention will be described clearly and completely below. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0041] The present invention provides a method for effectively phase encoding incident light at any spatial angle based on a metasurface, comprising the following steps:

[0042] S1: Using silicon dioxide as a substrate, a silicon nitride optical waveguide layer is set on the substrate, and an amorphous silicon nanobrick structure array is set on the silicon nitride optical waveguide layer to form an on-chip metasurface.

[0043] S2: Set the two sides of the optical waveguide layer in parallel with the working surface of the optical waveguide layer. xaxis, y Axis, arranged in a direction perpendicular to the working surface of the optical waveguide layer z Axis, build xyz Coordinate system;

[0044] θ represents the azimuth, defined as the angle at which the incident light xy The angle between the projection on the plane and the +x axis; represents the pitch angle, defined as the angle between the incident light and +z The angle between the axes; in particular, when = 90 o When , the incident light propagates along the waveguide plane, thereby interacting with the nanobricks.

[0045] S3: The relationship between the detour phase and the nanobrick displacement is as follows:

[0046] (4);

[0047] (5);

[0048] in, , Respectively x, y The circuitous phase of direction; P x 、P y Respectively represent the nano brick x, y Cycle of direction; 、 They represent the nanobricks along the period x, y Directional displacement;

[0049] The phase distribution of incident light at any spatial angle is calculated using the following formula:

[0050] (1);

[0051] (2);

[0052] (3);

[0053] in, From any angle arrive xy The projected component of incident light on a plane; j represents an imaginary unit; represents the wave vector;

[0054] λ represents the wavelength of incident light; n effrepresents the effective refractive index;

[0055] Indicates that the incident light is at any angle Phase distribution at the time of incidence; express x The circuitous phase of direction; express y The detour phase of direction.

[0056] S4: The incident light with the target wavelength λ is incident along different incident directions in space, and the inverse design method is used to use the gradient descent algorithm to obtain the randomly generated phase matrix and Start the optimization. During the optimization process, the quality of the hologram is evaluated by calculating the root mean square error (RMSE) between the generated hologram and the ideal target, and the RMSE is used as the loss function. and It is continuously updated during the iterative process and eventually converges to the minimum value of the loss function, outputting the optimized phase mask. Finally, based on the optimized phase matrix, the fast Fourier transform (FFT) is used to generate the holographic images of all channels.

[0057] S5: looping steps S3 and S4, obtaining the positional arrangement of all nanostructures and encoding them to obtain the final on-chip metasurface two-dimensional array.

[0058] This embodiment selects carefully arranged nanobricks to form an on-chip metasurface to achieve arbitrary omnidirectional angle multiplexing holography. Figure 1 The schematic diagram of the method for effectively phase encoding incident light at any spatial angle based on a metasurface illustrates the use of the proposed on-chip metasurface configuration to achieve multiplexing of any spatial omnidirectional angle. Specifically, by associating the detour phase driven by the incident wave with the incident angle and then using algorithmic deep optimization, the method achieves the multiplexing of any azimuth angle. θ and pitch angle φ Independent coding of direction. Figure 2 Schematic diagram of the top view of the on-chip metasurface and the schematic diagram of the light wave incident on the metasurface from space; Figure 2 b is the corresponding unit structure schematic diagram, x, y The cycles of the directions are P x = P y = 600 nm, the nanostructures that make up the on-chip metasurface are amorphous silicon nanobricks, and the height of the nanobricks is H is 360 nm, and the length and width are W = 90nm; optical waveguide layer is Si 3 N 4(thickness is 220 nm), the waveguide refractive index is 2.05; the substrate is silicon dioxide (thickness is 500 μm). The displacement of the nanobrick is calculated by formulas (4) and (5) through the circuitous phase principle, and the phase distribution of the incident light at any spatial angle is calculated by formulas (1)-(3). Figure 3 The corresponding simulation results are shown in Figure 2. The phase modulation is different under different incident angles, but no meaningful phase distribution is generated before the holographic phase optimization. In order to give a meaningful phase distribution to each angle multiplexing scheme of arbitrary spatial light, this embodiment adopts the inverse design method and optimizes the phase using the gradient descent algorithm, such as Figure 4 For an incident wave driven along an arbitrary angle, the optimization process starts from two randomly generated phase matrices and Start, where and Respectively indicate along x Direction and y Each arbitrary incident angle is uniquely encoded by a separate holographic image.

[0059] During the optimization process, the quality of the hologram is evaluated by calculating the root mean square error (RMSE) between the generated hologram and the ideal target, and RMSE is used as the loss function. and It is continuously updated during the iteration process and finally converges to the minimum value of the loss function, outputting the optimized phase mask. Finally, based on the optimized phase matrix, the fast Fourier transform (FFT) is used to generate the holographic images of all channels. The simulated holographic images are as follows: Figure 5 shown.

[0060] In order to demonstrate the omnidirectional angle multiplexing meta-holographic strategy, this embodiment produced a metasurface hologram sample and measured 22 channels of holographic images. The manufacturing process is as follows:

[0061] First, a silicon nitride waveguide structure was created on a fused silica substrate (500 μm thick) using plasma enhanced chemical vapor deposition (PECVD) to form a 220 nm thick optical waveguide layer. 3 N 4The waveguide was coated with a 360nm amorphous silicon (α-Si) coating. To create the metasurface pattern, polymethyl methacrylate (PMMA) was spin-coated onto the α-Si layer and then baked at 150 °C for 3 min. The pattern was achieved by electron beam lithography (Raith eLine Plus, 20 kV) followed by an 80 s development process. A 20 nm chromium film was deposited as an anti-etching mask by thermal evaporation technology before the PMMA was removed by acetone-based lift-off. The chromium pattern was transferred to the α-Si layer by reactive ion etching (RIE) and then lift-off using a chromium-specific etchant solution. A 22-channel hologram was fabricated, each consisting of 800 x 800 pixels, composed of 600 x 600 meta-atoms (nanobricks), with an overall sample size of 480 x 480 μm². The incident light wavelength was 500 nm and illuminated the fabricated metasurface at different incident angles. By changing the incident angle, different holographic images can be captured in the far field at the same exit viewing angle.

[0062] Scanning electron microscope (SEM) images of the samples and the experimental setup are shown in Figure 2. Figure 6 To simplify the experimental measurement, the sample is rotated to achieve the desired incident angle. Finally, the 22-channel holographic images obtained in the experiment are highly consistent with the simulation results, as shown in Figure 7 The results show that the holographic images at different incident angles are clearly visible with low noise.

[0063] The above specific embodiments describe the implementation of the present invention in detail, but the present invention is not limited to the specific details in the above embodiments. Within the scope of the claims and technical concept of the present invention, the technical solution of the present invention can be modified and changed in many simple ways, and these simple modifications all belong to the protection scope of the present invention.

Claims

1. A method for effectively phase encoding incident light at any spatial angle based on a metasurface, characterized in that: The steps include: S1: Arrange a nanobrick structure array above the optical waveguide layer to form an on-chip metasurface; S2: Set the two sides of the optical waveguide layer in parallel with the working surface of the optical waveguide layer. x axis, y Axis, arranged in a direction perpendicular to the working surface of the optical waveguide layer z Axis, build xyz Coordinate system; θ represents the azimuth, defined as the angle at which the incident light xy Projection on a plane +x The angle of the axis; represents the pitch angle, defined as the angle between the incident light and +z The angle of the axis; S3: The position arrangement of the nanobricks is calculated by the circuitous phase principle, and the phase distribution of the incident light at any spatial angle is calculated by the following formula: ； ； ； in, From any angle arrive xy The projected component of incident light on a plane; j represents an imaginary unit; represents the wave vector; λ represents the wavelength of incident light; n eff represents the effective refractive index; Indicates that the incident light is at any angle Phase distribution at the time of incidence; express x The circuitous phase of direction; express y The circuitous phase of direction; S4: The target wavelength is λ The incident light is incident along different spatial directions, and the phase is optimized using the gradient descent algorithm; S5: loop S3 and S4 to obtain the positional arrangement of all nanostructures and encode them to obtain the final on-chip metasurface two-dimensional array.

2. According to claim 1, a method for effectively phase encoding incident light at any spatial angle based on a metasurface is characterized in that: Step S4 is as follows: for an incident wave driven at any angle, a gradient descent algorithm is used to obtain a randomly generated phase matrix and Start the optimization. During the optimization process, the quality of the hologram is evaluated by calculating the root mean square error between the generated hologram and the ideal target, and the root mean square error is used as the loss function; and It is continuously updated during the iterative process and eventually converges to the minimum value of the loss function, outputting the optimized phase mask. Finally, based on the optimized phase matrix, the fast Fourier transform is used to generate the holographic images of all channels.

3. The method for effectively phase encoding incident light at any spatial angle based on a metasurface according to claim 1, characterized in that: The relationship between the detour phase and the nanobrick displacement is as follows: ； ； in, , Respectively x , y The circuitous phase of direction; P x , P y Respectively represent the nano brick x , y Cycle of direction; , They represent the nanobricks along the period x , y Direction displacement.

4. The method for effectively phase encoding incident light at any spatial angle based on a metasurface according to claim 1, characterized in that: The on-chip metasurface comprises a substrate, an optical waveguide layer located on the substrate, and a nanobrick structure array arranged on the optical waveguide layer.

5. The method for effectively phase encoding incident light at any spatial angle based on a metasurface according to claim 4, characterized in that: The substrate is silicon dioxide, the nanobricks are amorphous silicon nanobricks, and the optical waveguide layer is silicon nitride.

6. The method for effectively phase encoding incident light at any spatial angle based on a metasurface according to claim 4, characterized in that: The length and width of the nanobricks are equal and are both sub-wavelength in size, and are completely consistent in size.

7. A method for realizing arbitrary omnidirectional angle multiplexing holography based on a metasurface, characterized in that: The following steps are involved: A target image is selected, and the phase matrix is ​​optimized using the method described in any one of claims 1 to 6. Based on the optimized phase matrix, the phase matrix is ​​subjected to a fast Fourier transform to generate holographic images of all channels.

8. Application of the method of claim 7 in the fields of data storage, virtual / augmented reality or optical encryption.

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