Dynamic optical differentiator based on Malus metasurface and design method thereof

Abstract

The invention discloses a Malus metasurface-based dynamic optical differentiator and a design method thereof, the dynamic optical differentiator comprises a metasurface array and a grating structure, and the metasurface array is formed by a plurality of nano brick structure units on the same plane; each nano brick structure unit comprises a silicon substrate, a silicon dioxide layer and a silicon nano brick which are sequentially arranged from bottom to top; a layer of grating structure composed of vanadium dioxide is tightly attached to the bottom of the substrate, and the state of the vanadium dioxide is changed by controlling the temperature, so that dynamic switching between first-order differential and second-order differential is completed, that is, the vanadium dioxide is in a medium state before phase change, the first-order differential is completed, and the vanadium dioxide is in a metal state after phase change, and the second-order differential is completed. The functions of a first-order differentiator and a second-order differentiator can be achieved without additional optical elements, and the vanadium dioxide material is introduced to achieve dynamic regulation and control of functions.

Description

Technical Field

[0001] The present invention belongs to the technical field of micro-nano photonics, and particularly relates to a dynamic optical differentiator based on a Malus metasurface and a design method thereof. Background Art

[0002] Image edge processing has extensive applications in the scientific and industrial fields. At present, most of the implementations of image edge processing adopt electronic methods, but there are still certain difficulties in achieving real-time and low-power image edge processing. In contrast, optical analog computing has the advantages of low power consumption, fast transmission speed, and strong parallel processing ability. A metasurface is an artificial planar material composed of nanostructures at the sub-wavelength scale, which can precisely control the amplitude, phase, frequency, and polarization state of incident light waves with sub-wavelength resolution and has the advantage of a super-compact structure. Currently, first-order and second-order differentials based on metasurfaces have been realized, but most are limited to realizing a single differential function, unable to simultaneously realize multi-order differentials and cannot be dynamically regulated.

[0003] In summary, there is an urgent need to design a dynamic optical differentiator of a metasurface that can realize multi-order differentials and can be dynamically regulated. Summary of the Invention

[0004] To solve the above technical problems existing in the prior art, the present invention provides a dynamic optical differentiator based on a Malus metasurface and a design method thereof. The present invention completes the function of an equivalent differentiator by arranging the steering angles of multiple nano-brick structural units of the same size and combining a grating structure composed of vanadium dioxide distributed on the lower layer of the substrate. When vanadium dioxide is in the dielectric state, the first-order differential function can be completed; when vanadium dioxide is in the metallic state, the second-order differential function can be completed. Considering that vanadium dioxide is a phase change material and exhibits different states before and after 68 °C, a dynamic regulation function can be completed. This method can promote the development of optical computing devices towards miniaturization, high integration, multi-function, and low cost.

[0005] The technical solution adopted by the present invention is as follows:

[0006] In a first aspect of the present invention, a dynamic optical differentiator based on a Malus metasurface is designed, which is characterized in that it includes a metasurface array and a grating structure (4), the metasurface array is arranged above the grating structure (4), the metasurface array is composed of multiple nano-brick structural units on the same plane, and each nano-brick structural unit includes a silicon substrate (1), a silicon dioxide layer (2), and a silicon nano-brick (3) arranged in sequence from bottom to top;

[0007] Two mutually perpendicular sides of the silicon substrate (1) are respectively the x-axis and the y-axis, thereby establishing an xoy coordinate system, and the long axis of the silicon nano-brick (3) forms an angle θ with the x-axis, which is the orientation angle θ of the silicon nano-brick (3);

[0008] The bottom of the silicon substrate (1) is closely attached to a grating structure (4) composed of vanadium dioxide. In the 4f system, during the dynamic transformation process, without the aid of additional optical devices, by only controlling the temperature to change the state of vanadium dioxide without changing the arrangement of the nanobricks, the overall structure has different modulation functions, thereby completing the dynamic switching of first-order and second-order differentials. That is, when vanadium dioxide is in the dielectric state before phase change, first-order differential is completed, and when vanadium dioxide is in the metallic state after phase change, second-order differential is completed.

[0009] Furthermore, the length L, width W, and height H of the silicon nanobricks (3) are optimized by electromagnetic simulation according to the selected incident light wavelength. After optimization, when the incident light wave passes through the silicon nanobricks at the working wavelength, linearly polarized light with the polarization direction along the long axis or short axis of the silicon nanobricks is reflected or transmitted.

[0010] Furthermore, the length L, width W, and height H of the silicon nanobricks (3) are all sub-wavelength levels.

[0011] Furthermore, the value range of the orientation angle θ is [0, π].

[0012] The second aspect of the present invention designs a design method for a dynamic optical differentiator based on a Malus metasurface, which is characterized in that the design method of the dynamic optical differentiator includes the following steps:

[0013] S1. Optimization simulation

[0014] According to the incident light wavelength, the unit structure of the nanobricks is optimized and simulated by the electromagnetic simulation software CST to obtain the optimized size parameters of the silicon nanobricks, that is, the length L, width W, and height H of the nanobricks, and the above size parameters are all at the sub-wavelength level; the optimized unit structure of the nanobricks can be regarded as an ideal polarizer in the transmission mode;

[0015] S2. Constructing the metasurface

[0016] A plurality of optimized nanobrick structural units are formed into a metasurface on the same plane;

[0017] The metasurface is placed above the grating structure composed of vanadium dioxide;

[0018] S3. Dynamic regulation

[0019] The above metasurface is placed on the Fourier plane in the 4f system. When the incident light passes through the metasurface at the working wavelength, the y-polarized light is incident on the metasurface. By regulating the temperature to change the state of vanadium dioxide, that is, the dielectric state before phase change and the metallic state after phase change, first-order and second-order differentials are respectively realized and the dynamic regulation effect is achieved. The transmitted light then completes the tasks of edge detection or edge enhancement through inverse Fourier transform.

[0020] Further, in step S3, the modulation function of the metasurface is consistent with the transfer function of the differentiator, that is, the modulation function H(θ)=θ before the phase change of vanadium dioxide and the modulation function H(θ)=θ after the phase change of vanadium dioxide 2 is consistent with the transfer function H(k x )∝(ik x ) n of the differentiator. The metasurface will modulate the frequency domain components of the input information, and the differential results of different orders can be obtained from the output light;

[0021] where H(k x ) is the transfer function, k x is the frequency component, and n represents the order.

[0022] Further, in step S3, when vanadium dioxide is in the dielectric state before the phase change, the modulation effect of the grating can be almost ignored. At this time, the complex amplitude E of the transmitted light when the y-polarized light is incident on the metasurface and passes through the grating structure can be expressed as:

[0023]

[0024] where A and B are the complex transmission coefficients of the major axis and minor axis of the silicon nanobrick, respectively; θ is the orientation angle of the silicon nanobrick; when the silicon nanobrick is a polarizer, that is, A = 1 and B = 0, the complex amplitude of the transmitted light can be expressed as:

[0025] E = sin(θ) (2).

[0026] Further, in step S3, when vanadium dioxide is in the metallic state after the phase change, the grating design is equivalent to an analyzer. At this time, the complex amplitude E of the transmitted light when the y-polarized light is incident on the metasurface and passes through the grating structure can be expressed as:

[0027]

[0028] where A and B are the complex transmission coefficients of the major axis and minor axis of the silicon nanobrick, respectively; θ is the orientation angle of the silicon nanobrick; at this time, the complex amplitude of the transmitted light can be expressed as:

[0029] E = sin 2 (θ) (4).

[0030] Further, when the orientation angle θ of the silicon nanobrick is small enough, the complex amplitude E of the transmitted light satisfies:

[0031] E = sinθ ~ θ (5).

[0032] Further, when the orientation angle θ of the silicon nanobrick is small enough, the complex amplitude E of the transmitted light satisfies:

[0033] E = sin 2 θ ~ θ2 (6).

[0034] Compared with the prior art, the beneficial effects of the present invention are embodied in:

[0035] 1) The present invention only needs to arrange the steering angles of the single-size nanobrick structural units and does not need to combine multiple nanobrick structures, thus greatly reducing the difficulty of its processing and design;

[0036] 2) The metasurface designed by the present invention can achieve the functions of first-order and second-order differentiators without the aid of additional optical elements, and introduces vanadium dioxide material to realize the dynamic regulation of functions;

[0037] 3) The overall structure of the present invention is small in volume, light in weight and highly integrable, which is very suitable for the development of future miniaturized, micro-sized and portable optical technologies;

[0038] 4) The metasurface produced by the present invention is a all-dielectric structure, which is more economical compared with the metasurface structure using metal to achieve reflection type. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 is a schematic diagram of the unit structure of the metasurface of the present invention;

[0040] Figure 2 is a scanning diagram of the transmittance of the unit structure of the present invention;

[0041] Figure 3 is a schematic diagram of the metasurface array of the present invention;

[0042] Figure 4 is a simulation diagram of the first-order differential transfer function of the present invention;

[0043] Figure 5 is a simulation diagram of the second-order differential transfer function of the present invention;

[0044] Figure 6a and Figure 6b are the original image and the first-order differential effect image of the present invention;

[0045] Figure 7a and Figure 7b are the original image and the second-order differential effect image of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0046] The following will describe in detail the specific embodiments of the embodiments of the present invention with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are only used to illustrate and explain the embodiments of the present invention, and are not used to limit the embodiments of the present invention.

[0047] It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other.

[0048] The present invention will be described in detail below with reference to the accompanying drawings and in conjunction with exemplary embodiments.

[0049] Embodiment 1

[0050] A dynamic optical differentiator based on a Malus metasurface of the present invention includes a metasurface array and a grating structure (4). The metasurface array is disposed above the grating structure (4). The metasurface array is composed of a plurality of nano-brick structural units on the same plane. Each nano-brick structural unit includes a silicon substrate (1), a silicon dioxide layer (2), and a silicon nano-brick (3) sequentially arranged from bottom to top.

[0051] Two mutually perpendicular sides of the silicon substrate (1) are respectively the x-axis and the y-axis, and thus an xoy coordinate system is established. The major axis of the silicon nano-brick (3) forms an orientation angle θ with the x-axis.

[0052] The bottom of the silicon substrate (1) is closely attached to a grating structure (4) composed of vanadium dioxide. By controlling the temperature to change the state of vanadium dioxide, dynamic switching between first-order and second-order differentiation is completed. That is, when vanadium dioxide is in the dielectric state before phase change, first-order differentiation is completed, and when vanadium dioxide is in the metallic state after phase change, second-order differentiation is completed.

[0053] In this embodiment, the length L, width W, and height H of the silicon nano-brick (3) are optimized by electromagnetic simulation according to the selected incident light wavelength. After optimization, when the incident light wave passes through the silicon nano-brick at the working wavelength, linearly polarized light with a polarization direction along the major axis or minor axis of the silicon nano-brick is reflected or transmitted.

[0054] In this embodiment, the length L, width W, and height H of the silicon nano-brick (3) are all sub-wavelength levels.

[0055] In this embodiment, the value range of the orientation angle θ is [0, π].

[0056] Embodiment 2

[0057] A design method of a dynamic optical differentiator based on a Malus metasurface of the present invention is characterized in that the design method of the dynamic optical differentiator includes the following steps:

[0058] S1. Optimization simulation

[0059] According to the incident light wavelength, the nano-brick unit structure is optimized and simulated by electromagnetic simulation software CST to obtain the optimized size parameters of the silicon nano-brick, that is, the length L, width W, and height H of the nano-brick. The above size parameters are all sub-wavelength levels. The optimized nano-brick unit structure can be regarded as an ideal polarizer in the transmission mode.

[0060] Specifically, the wavelength of the incident light is selected as λ = 633 nm. For this wavelength, the nano-brick unit structure is optimized and simulated through the electromagnetic simulation software CST. As Figure 1 shown, the size parameters of the optimized silicon nano-brick are: the length is L = 180 nm, the width is W = 60 nm, the height is H = 220 nm, and the side length of the unit structure substrate is P = 300 nm. The transmission efficiencies of the silicon nano-brick for linearly polarized light incident along the long axis and short axis of the nano-brick are as Figure 2 shown, where Tl and Ts respectively represent the transmission efficiencies of the transmitted light along the long axis and short axis of the nano-brick. Specifically, at the incident light wavelength (working wavelength) of 633 nm, the transmittance Tl in the long axis direction of the silicon nano-brick reaches 0.8, while the transmittance Ts along the short axis direction of the nano-brick is suppressed to about 0. Therefore, at the wavelength of 633 nm, the optimized nano-brick can be regarded as an ideal polarizer in the transmission mode.

[0061] S2. Constructing a metasurface

[0062] Multiple optimized nano-brick structural units are formed into a metasurface on the same plane;

[0063] The metasurface is placed above a grating structure composed of vanadium dioxide;

[0064] Specifically, as Figure 3 shown. The metasurface is placed on the Fourier plane of the 4f system. When y-polarized light with a working wavelength of 633 nm is incident on the metasurface, by controlling the temperature to change the state of vanadium dioxide, first-order and second-order differentials are respectively achieved and a dynamic regulation effect is obtained. The transmitted light then undergoes an inverse Fourier transform to complete the tasks of edge detection or edge enhancement.

[0065] S3. Dynamic regulation

[0066] The above metasurface is placed on the Fourier plane in the 4f system. When the incident light passes through the metasurface at the working wavelength, y-polarized light is incident on the metasurface. By controlling the temperature to change the state of vanadium dioxide, that is, the dielectric state before phase change and the metallic state after phase change, first-order and second-order differentials are respectively achieved and a dynamic regulation effect is obtained. The transmitted light then undergoes an inverse Fourier transform to complete the tasks of edge detection or edge enhancement.

[0067] In this embodiment, in step S3, the modulation function of the metasurface is consistent with the transfer function of the differentiator, that is, the modulation function H(θ) = θ before the phase change of vanadium dioxide and the modulation function H(θ) = θ after the phase change of vanadium dioxide 2 is the same as the transfer function H(k x ) ∝ (ik x ) nIn a consistent form, the metasurface modulates the frequency-domain components of the input information, and the differential results of different orders can be obtained from the output light;

[0068] where H(k x ) is the transfer function, k x is the frequency component, and n represents the order.

[0069] In this embodiment, in step S3, when vanadium dioxide is in the dielectric state before phase change, the modulation effect of the grating can be almost ignored. At this time, the complex amplitude E of the transmitted light when the y-polarized light is incident on the metasurface and passes through the grating structure can be expressed as:

[0070]

[0071] where A and B are the complex transmission coefficients of the major axis and minor axis of the silicon nanobrick, respectively; θ is the orientation angle of the silicon nanobrick; when the silicon nanobrick is a polarizer, that is, A = 1 and B = 0, the complex amplitude of the transmitted light can be expressed as:

[0072] E = sin(θ) (2).

[0073] In this embodiment, in step S3, when vanadium dioxide is in the metallic state after phase change, the grating design is equivalent to an analyzer. At this time, the complex amplitude E of the transmitted light when the y-polarized light is incident on the metasurface and passes through the grating structure can be expressed as:

[0074]

[0075] where A and B are the complex transmission coefficients of the major axis and minor axis of the silicon nanobrick, respectively; θ is the orientation angle of the silicon nanobrick; at this time, the complex amplitude of the transmitted light can be expressed as:

[0076] E = sin 2 (θ) (4).

[0077] In this embodiment, when the orientation angle θ of the silicon nanobrick is small enough, the complex amplitude E of the transmitted light satisfies:

[0078] E = sinθ ~ θ (5).

[0079] In this embodiment, when the orientation angle θ of the silicon nanobrick is small enough, the complex amplitude E of the transmitted light satisfies:

[0080] E = sin 2 θ ~ θ 2 (6).

[0081] The present invention can construct a metasurface material based on a single type of single-sized nanostructure. When the metasurface is placed on the Fourier plane in a 4f system, at this time, the modulation function of the metasurface is consistent with the transfer function of the differentiator, and the metasurface will modulate the frequency-domain components of the input information. This process can be approximately considered that the metasurface can equivalently implement the function of the differentiator, and then edge detection or edge enhancement is completed through inverse Fourier transform.

[0082] The present invention can achieve the functions of first-order and second-order differentiators without the aid of additional optical elements, and introduce vanadium dioxide material to realize dynamic regulation of the function. The overall structure is small in volume, light in weight, and highly integrated. Therefore, the present invention is also very suitable for the development of future miniaturized, micro-sized, and portable optical technologies.

[0083] Although the embodiments of the present invention have been shown and described above, it can be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those of ordinary skill in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention.

Claims

1. A dynamic optical differentiator based on Malus metasurface, characterized in that: The invention comprises a super surface array and a grating structure (4), wherein the super surface array is arranged above the grating structure (4), and the super surface array is composed of a plurality of nano brick structural units on the same plane, and each of the nano brick structural units comprises a silicon substrate (1), a silicon dioxide layer (2) and a silicon nano brick (3) arranged in sequence from bottom to top; The two mutually perpendicular sides of the silicon substrate (1) are respectively the x-axis and the y-axis, thereby establishing an xoy coordinate system, and the angle between the long axis of the silicon nanobrick (3) and the x-axis is the orientation angle θ of the silicon nanobrick (3); A grating structure (4) composed of vanadium dioxide is closely attached to the bottom of the silicon substrate (1). The state of the vanadium dioxide is changed by controlling the temperature so that the overall structure has different modulation functions, thereby completing the dynamic switching of the first-order and second-order differentials, that is, when the vanadium dioxide is in a dielectric state before the phase change, the first-order differential is completed, and when the vanadium dioxide is in a metallic state after the phase change, the second-order differential is completed.

2. A dynamic optical differentiator based on Malus metasurface as claimed in claim 1, characterized in that: The length L, width W and height H of the silicon nanobrick (3) are obtained by optimizing the selected wavelength of incident light through electromagnetic simulation. After optimization, when the incident light wave passes through the silicon nanobrick at the working wavelength, linearly polarized light with a polarization direction along the long axis or short axis of the silicon nanobrick is reflected or transmitted.

3. A dynamic optical differentiator based on Malus metasurface as claimed in claim 1, characterized in that: The length L, width W and height H of the silicon nanobrick (3) are all at sub-wavelength level.

4. A dynamic optical differentiator based on Malus metasurface as claimed in claim 1, characterized in that: The value range of the orientation angle θ is [0, π].

5. A design method for a dynamic optical differentiator based on Malus metasurface, characterized in that: The design method of the dynamic optical differentiator comprises the following steps: S1. Optimization simulation According to the wavelength of the incident light, the nanobrick unit structure is optimized and simulated by electromagnetic simulation software CST to obtain the optimized size parameters of the silicon nanobrick, namely the length L, width W and height H of the nanobrick, all of which are sub-wavelength level; the optimized nanobrick unit structure can be regarded as an ideal polarizer in the transmission mode; S2. Constructing a super surface Multiple optimized nanobrick structural units are placed on the same plane to form a super surface; The metasurface is placed over a grating structure composed of vanadium dioxide; S3. Dynamic Control The above-mentioned metasurface is placed on the Fourier plane in the 4f system. When the incident light passes through the metasurface at the working wavelength, the y-polarized light is incident on the metasurface. The state of vanadium dioxide is changed by adjusting the temperature, that is, the dielectric state before the phase change and the metallic state after the phase change, to realize the first-order and second-order differentials respectively and achieve a dynamic control effect. The transmitted light is then transformed through inverse Fourier transform to complete the task of edge detection or edge enhancement.

6. The design method of a dynamic optical differentiator based on Malus metasurface according to claim 5, characterized in that: In step S3, the modulation function of the metasurface is consistent with the transfer function of the differentiator, that is, the modulation function H(θ)=θ before the vanadium dioxide phase change and the modulation function H(θ)=θ after the vanadium dioxide phase change. 2 The transfer function H(k x )∝(ik x ) n In the same form, the metasurface modulates the frequency domain components of the input information, where the differential results of different orders can be obtained from the output light; Among them, H(k x ) is the transfer function, k x is the frequency component, and n represents the order.

7. The design method of a dynamic optical differentiator based on Malus metasurface according to claim 5, characterized in that: In step S3, when the vanadium dioxide is in a dielectric state before the phase transition, the modulation effect of the grating can be almost ignored. At this time, the complex amplitude E of the transmitted light after the y-polarized light is incident on the metasurface and passes through the grating structure can be expressed as: Where A and B are the complex transmission coefficients of the long axis and short axis of the silicon nanobrick, respectively; θ is the orientation angle of the silicon nanobrick; when the silicon nanobrick is a polarizer, that is, A = 1, B = 0, the complex amplitude of the transmitted light can be expressed as: E = sin(θ) (2).

8. The method for designing a dynamic optical differentiator based on a Malus metasurface as claimed in claim 5, characterized in that: In step S3, when vanadium dioxide changes to a metallic state after phase transition, the grating design is equivalent to a polarizer. At this time, the complex amplitude E of the transmitted light after the y-polarized light is incident on the metasurface and passes through the grating structure can be expressed as: Among them, A and B are the complex transmission coefficients of the long axis and short axis of the silicon nanobrick respectively; θ is the orientation angle of the silicon nanobrick; at this time, the complex amplitude of the transmitted light can be expressed as:

9. The method for designing a dynamic optical differentiator based on a Malus metasurface according to claim 7, characterized in that: When the orientation angle θ of the silicon nanobrick is small enough, the complex amplitude E of the transmitted light satisfies: E = sinθ~θ(5).

10. The design method of a dynamic optical differentiator based on Malus metasurface according to claim 8, characterized in that: When the orientation angle θ of the silicon nanobrick is small enough, the complex amplitude E of the transmitted light satisfies: E=sin 2 θ~θ 2 (6)。

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