Light field modulation method based on double-layer metasurface unitary jones matrix

Abstract

The application discloses a light field regulation method based on a double-layer super surface unitary Jones matrix, and belongs to the fields of micro-nano optics, diffraction optics and light field regulation applications. The application is realized in the following method: a super surface is composed of double-layer rectangular nano column arrays; a double-layer super surface Jones matrix is represented by the product of two single-layer structure Jones matrices; a unit medium structure is scanned by using a rigorous coupled wave analysis (RCWA) method, and complex amplitude transmission coefficients of rectangular nano column structures with different cross section sizes under different polarized incident lights are obtained; a unitary Jones matrix is accurately decoupled into the product of two unitary symmetric Jones matrices, target complex amplitude transmission coefficients and rotation angles of each single-layer rectangular column nano structure are determined according to eigenvalues and eigenvectors of the unitary symmetric Jones matrix; geometric parameters of each single-layer super surface structure are accurately solved by using geometric phase and propagation phase principles and based on the decomposition method of the unitary Jones matrix, and high-precision light field regulation is realized by using the double-layer super surface of the unitary Jones matrix.

Description

Technical Field

[0001] This invention relates to a method for optical field manipulation based on a unitary Jones matrix of a double-layer metasurface, belonging to the fields of micro-nano optics, diffraction optics, and optical field manipulation applications. Background Technology

[0002] Information transmission via light can be achieved by controlling optical parameters. The manipulation of optical parameters such as angular momentum, frequency, intensity, and phase distribution is of great significance in numerous scientific fields, including photonic information technology, nonlinear optics, quantum / optical imaging, displays, communications, and computing. The core of wavefront manipulation is controlling optical parameters using components according to design objectives. Metasurfaces are high-performance optical field manipulation platforms capable of precisely and flexibly adjusting various parameters at subwavelength scales, possessing rich functionality and enabling multi-channel, high-efficiency, and multi-functional optical field modulation. Single-layer anisotropic metasurfaces inherently have limited degrees of freedom. Bilayer metasurfaces, by breaking spatial symmetry, offer more design channels and features than single-layer metasurfaces. Bilayer metasurfaces have been shown to achieve arbitrary independent modulation of the amplitude and phase of incident light, but previous works have not provided analytical solutions for bilayer structures, or have been limited to specific polarization state transitions, or have used macropixels leading to increased pixel size. Summary of the Invention

[0003] The purpose of this invention is to provide a method for optical field manipulation based on a unitary Jones matrix of a double-layer metasurface. The Jones matrix of the double-layer metasurface is represented by the product of the Jones matrices of two single-layer structures, and this Jones matrix is ​​a unitary matrix. By constructing a unitary Jones matrix decomposition method for the double-layer metasurface, the unitary Jones matrix is ​​decoupled into the product of two unitary symmetric Jones matrices. The target complex amplitude transmission coefficient and rotation angle of each single-layer rectangular column structure are determined based on the eigenvalues ​​and eigenvectors of the unitary symmetric Jones matrix. The unitary Jones matrix decomposition method for the double-layer metasurface requires no algorithm optimization or approximation, which accelerates the solution speed of the metasurface parameters, and provides accurate and easily reproducible calculations. Compared with traditional optical field manipulation methods using other devices, the metasurface has a very small size and greater degrees of freedom for manipulation. The thickness of the metasurface is on the order of micrometers. This invention has advantages such as accurate metasurface parameter solution, simple optical field manipulation process, high manipulation precision, rich functionality, high information density, and small size and weight, and can be applied to fields such as optical field modulation, information encryption, spin-orbit interaction, and novel displays.

[0004] The objective of this invention is achieved through the following technical solution.

[0005] This invention discloses a method for optical field manipulation based on a unitary Jones matrix of a bilayer metasurface. The metasurface is composed of a bilayer array of rectangular nanopillars, where the first layer has different dimensions and in-plane rotation angles, and the second layer has the same dimensions but different in-plane rotation angles. The Jones matrix of the bilayer metasurface is represented by the product of the Jones matrices of the two single-layer structures, and this Jones matrix is ​​a unitary matrix. Rigorous Coupled Wave Analysis (RCWA) is used to scan the unitary dielectric structure to obtain the complex amplitude transmission coefficients of rectangular nanopillar structures with different cross-sectional dimensions under different polarized incident light. By constructing a unitary Jones matrix decomposition method, the unitary Jones matrix is ​​precisely decoupled into the product of two unitary symmetric Jones matrices. Based on the eigenvalues ​​and eigenvectors of the unitary symmetric Jones matrix, the target complex amplitude transmission coefficient and rotation angle of each single-layer rectangular pillar nanostructure are determined. Utilizing the principles of geometric phase and propagation phase, the geometric parameters of each single-layer metasurface structure are accurately solved based on the decomposition method of the unitary Jones matrix. A bilayer metasurface is formed by vertically stacking two single-layer metasurfaces, and high-precision optical field manipulation is achieved using the bilayer metasurface with a unitary Jones matrix.

[0006] The optical field manipulation method based on the unitary Jones matrix of a bilayer metasurface disclosed in this invention includes the following steps:

[0007] Step 1: The Jones matrix of the double-layer metasurface used is a unitary matrix, formed by stacking two anisotropic metasurfaces. The Jones matrix J of the double-layer metasurface is described by the product of the Jones matrices of the two single-layer metasurfaces, i.e., J = U2·U1. The single-layer anisotropic metasurface is described as a linear birefringent waveplate. The Jones matrix of the single-layer anisotropic metasurface is a unitary symmetric matrix with equal off-diagonal elements. The product of two unitary symmetric matrices is an asymmetric unitary matrix; therefore, the Jones matrix J is an arbitrary unitary matrix. Through analytical decomposition, the unitary Jones matrix J is decoupled into the product of two unitary symmetric Jones matrices U1 and U2.

[0008] Unitary symmetric matrices U1 and U2 can be represented by eigenvalues ​​and eigenvectors through eigendecomposition as follows:

[0009]

[0010] Where m = 1 or 2, representing two unitary symmetric matrices respectively. and For U m Two eigenvalues, It is an orthogonal matrix, and its column vectors are U. m Two eigenvectors.

[0011] The specific decomposition steps for decoupling the unitary Jones matrix J into the product of two unitary symmetric Jones matrices U1 and U2 are as follows:

[0012] For any unitary matrix of complex amplitude form The two column vectors of a unitary matrix are orthogonal, therefore The unitary matrix J is represented as

[0013]

[0014] Among them, the average phase shift According to the unitary matrix condition J·J H = Ι, where the superscript H denotes the conjugate transpose of the matrix, Ι is the identity matrix, and A is derived from formula (2). 2 +B 2 =1 and C = ±B.

[0015] When C = B,

[0016]

[0017] When C = -B,

[0018]

[0019] in, Any 2×2 unitary matrix J can be decomposed into the product of two unitary symmetric matrices U1 and U2, i.e., J = U2·U1. U1 and U2 are represented as U1 = [U2]. -1 ·J,U2=J·[U1] -1 Based on the condition that the off-diagonal elements of matrices U1 and U2 are equal, substituting equations (1), (3), and (4) into the relationship between U1, U2, and J yields:

[0020]

[0021] in, Im denotes taking the imaginary part of a complex number, and Re denotes taking the real part of a complex number. If and only if θ² always has a solution. Let It is derived from formula (5):

[0022]

[0023] From formula (6), we know that θ2 is determined by u and v, and u and v are determined by the original unitary matrix J. Substitute θ2 into formula (1) to calculate U2. U1 is obtained through U1=[U2] -1 ·J is calculated, where U1 is a diagonalizable unitary symmetric matrix. Its eigenvectors and eigenvalues ​​are calculated through eigenvalue decomposition. The unitary matrix property of U1 ensures that the eigenvectors of U1 are orthogonal, and the eigenvalues ​​are complex exponents. U1 is decomposed into the standard form of formula (1), and its eigenvectors and eigenvalues ​​are determined. θ1.

[0024] According to equations (1) to (6), the unitary Jones matrix J is decoupled into the product of two unitary symmetric Jones matrices U1 and U2 through analytical decomposition.

[0025] Step 2: Each unitary symmetric Jones matrix obtained in Step 1 is realized through anisotropic rectangular nanopillars. Using the principle of geometric phase and propagation phase, the geometric dimensions and in-plane rotation angle of the rectangular nanopillar unit are determined according to the complex amplitude distribution of the unitary symmetric Jones matrix to be encoded, thereby generating the processing file of the corresponding metasurface structure. The unitary matrix J is realized by a double layer of superatoms composed of two vertically stacked nanopillars. The light incident on the double layer of superatoms is modulated by the Jones matrices U1 and U2 of the first and second layer nanopillars in turn.

[0026] In formula (1), the unitary symmetric Jones matrices U1 and U2 are decomposed into... and θ represents the phase delay of the anisotropic nanopillar in the x and y directions. m The rotation angle of the nanopillar is represented. The phase delay of the superatom in the x and y directions is altered by changing the period P, the height H, and the cross-sectional dimensions L and W of the nanopillar. With the nanopillar height H and period P fixed, a two-dimensional scan of the major axis length L and minor axis length W of the nanopillar is performed using simulation software based on the rigorous coupled-wave analysis method RCWA, obtaining the transmission coefficient t corresponding to nanopillars of different sizes. xx and t yy During simulation, the wavelength of the incident light, the type of material constituting the nanopillar, the height H of the nanopillar, and the period P should be selected to ensure the phase of the transmission coefficient. and It can cover 0 to 2π.

[0027] The selected structure should be as close as possible to the target's transmission phase. and As described in step one, the decomposition process is as follows: The second layer structure has a fixed phase shift, based on the geometric phase principle of metasurfaces, and is implemented by an array of nanopillars of the same size but different rotation angles. The first layer structure has both a variable phase shift and rotation angle, and is implemented by an array of nanopillars of different sizes and rotation angles, utilizing both propagation phase and geometric phase principles. Based on the selected nanopillar unit's major axis length L, minor axis length W, and rotation angle, a fabrication file for the corresponding dielectric metasurface structure is generated.

[0028] Step 3: Using the fabrication file of the dielectric metasurface structure obtained in Step 2, a transmissive dielectric metasurface is fabricated using micro / nano fabrication methods such as electron beam lithography and vapor deposition. Utilizing the principles of geometric phase and propagation phase, the geometric parameters of each monolayer metasurface structure are precisely solved based on the unitary matrix decomposition method. A bilayer metasurface is formed by vertically stacking two monolayer metasurfaces, and precise optical field manipulation is achieved using the bilayer metasurface with a unitary Jones matrix.

[0029] Beneficial effects:

[0030] 1. The light field modulation method based on the unitary Jones matrix of a double-layer metasurface disclosed in this invention uses a double-layer metaatom to break the symmetry of the single-layer structure and uses a double-layer metasurface to achieve high-precision light field modulation based on an arbitrary unitary Jones matrix. It has the advantages of accurate metasurface parameter solution, simple light field modulation process, high modulation accuracy, rich functions, high information density, and small size and weight. It can be applied to fields such as light field modulation, information encryption, spin-orbit interaction, and new displays.

[0031] 2. This invention discloses a light field manipulation method based on the unitary Jones matrix of a bilayer metasurface. It constructs a decomposition method for the unitary Jones matrix of the bilayer metasurface, decoupling the phase and in-plane rotation angle of the transmission coefficient of each monolayer rectangular nanopillar structure. This decomposition method is simple and direct to implement, computationally fast, and yields an exact solution, which helps simplify the metasurface design process and facilitates reproducibility.

[0032] 3. The light field modulation method based on the unitary Jones matrix of a double-layer metasurface disclosed in this invention uses a double-layer metasurface to realize the light field modulation function. Compared with traditional catadioptric and diffractive optical elements, the metasurface has a very small size and greater design freedom and modulation precision. It is easy to realize multi-channel function multiplexing, has high information density, and is conducive to the integration and miniaturization of optoelectronic systems.

[0033] 4. The light field modulation method based on the unitary Jones matrix of a double-layer metasurface disclosed in this invention can be applied to the visible light, near-infrared and microwave bands by making reasonable selections of nanopillar materials and optimizing the design of nanopillar structure dimensions to meet different functional and operational requirements. Attached Figure Description

[0034] Figure 1 This is a flowchart of a method for controlling the optical field based on a unitary Jones matrix of a double-layer metasurface according to the present invention;

[0035] Figure 2 This is a schematic diagram of the single-layer and double-layer unit structure of the transmissive double-layer metasurface in an embodiment of the present invention;

[0036] Wherein: (a) — 3D schematic diagram of a single-layer rectangular nanopillar structure, (b) — Top view of a single-layer rectangular nanopillar structure with a rotation angle of θ, (c) — Schematic diagram of wavefront modulation of a double-layer superatomic structure, U1 and U2 represent the Jones matrix of the two nanopillars, respectively, E in and E out These represent the incident and exit electric field distributions, respectively.

[0037] Figure 3 This is a schematic diagram illustrating the principle of spin-orbit angular momentum mapping based on the unitary Jones matrix control of a double-layer metasurface in an embodiment of the present invention.

[0038] Where: (a) — a functional schematic diagram of spin-orbit mapping achieved by the double metasurface; (b) — polarization conversion of the spin-orbit mapping process on the Poincaré sphere; |R>, |L>, |x>, |y> and the arrows in the figure represent polarization states; |0>, |+1>, |-1> represent topological charge numbers; Φ represents azimuth angle.

[0039] Figure 4 This is the optical path diagram used in the experiment in this embodiment of the invention;

[0040] Where: P1, P2 and P3—linear polarizers, S1 and S2—monolayer metasurface samples;

[0041] Figure 5 This is a SEM image of a TiO2 metasurface sample that achieves spin-orbit mapping, prepared in an embodiment of the present invention.

[0042] Wherein: (a) — top view of the first layer sample, (b) — top view of the second layer sample, (c) side view of the second layer sample, (d) a 10×20μm alignment mark at the corner of the metasurface;

[0043] Figure 6 The simulation and experimental results of OAM output light obtained by the double-layer metasurface under right-handed and left-handed circularly polarized light incident in the embodiments of the present invention;

[0044] Wherein: the two arrows on the left of the image represent the polarization directions of the incident circularly polarized light (rotating arrow) and the outgoing linearly polarized light (straight arrow); (a) - Simulation results of the intensity distribution of the OAM beam under right-hand circularly polarized light incident and vertically linearly polarized light outgoing; (b) - Experimental results of the intensity distribution of the OAM beam under right-hand circularly polarized light incident and vertically linearly polarized light outgoing; (c) - Experimental forked interference pattern of the outgoing light and Gaussian beam under right-hand circularly polarized light incident and vertically linearly polarized light outgoing; (d) - Simulation results of the intensity distribution of the OAM beam under left-hand circularly polarized light incident and horizontally linearly polarized light outgoing; (e) - Experimental results of the intensity distribution of the OAM beam under left-hand circularly polarized light incident and horizontally linearly polarized light outgoing; (f) - Experimental forked interference pattern of the outgoing light and Gaussian beam under left-hand circularly polarized light incident and horizontally linearly polarized light outgoing. Detailed Implementation

[0045] The present invention will now be described in detail with reference to the accompanying drawings and embodiments. The technical problems solved by the present invention and its beneficial effects are also described. It should be noted that the described embodiments are only intended to facilitate understanding of the present invention and do not constitute any limitation thereof.

[0046] Angular momentum is one of the fundamental properties of photons, consisting of spin angular momentum (SAM) and orbital angular momentum (OAM). During light propagation, scattering, and interference, the interaction and transformation between the SAM and OAM of light leads to a redistribution of the optical field spin in space. However, studies of spin-orbit interactions typically do not simply follow the conservation of angular momentum between incident and output light, because the transmission medium also imparts an additional angular momentum to the light. Spin-orbit mapping is a special type of spin-orbit interaction where the SAM carried by the incident beam is completely converted into the OAM of the output beam, preserving the conservation of angular momentum between the incident and output beams. Previous studies on spin-orbit interactions of monolayer anisotropic metasurfaces with unitary symmetric Jones matrices have not followed the conservation of angular momentum between incident and output light.

[0047] like Figure 1 As shown in this embodiment, the optical field manipulation method of the unitary Jones matrix of the double-layer metasurface realizes spin-orbit angular momentum mapping. The specific implementation method is as follows:

[0048] Step 1: The bilayer metasurface consists of two metasurfaces stacked perpendicularly. Each monolayer metasurface is composed of an array of dielectric nanopillars with different geometric dimensions and rotation angles, each having a rectangular cross-section. A single rectangular nanopillar is shown in the figure. Figure 2As shown in (a), its Jones matrix is ​​a unitary symmetric matrix. Based on the analytical decomposition of the unitary matrix, the unitary symmetric matrices corresponding to the two single-layer rectangular nanostructures at each pixel are obtained. The geometric dimensions include the major axis length L, minor axis length W, and height H of the nanopillar, as well as the period length P of the metasurface unit.

[0049] Each designed monolayer dielectric metasurface is composed of titanium dioxide nanopillars of different sizes and orientations. The working wavelength is 532 nm. With the nanopillar height H and period P fixed, the geometric dimensions of the nanopillars are scanned in two dimensions (L: 100 nm to 350 nm, W: 100 nm to 350 nm) using rigorous coupled-wave analysis (RCWA) to obtain the transmission coefficient t corresponding to nanopillars of different sizes under different linearly polarized incident states. xx and t yy In the simulation, the refractive indices of the titanium dioxide nanopillars and the fused silica substrate were set to n, respectively. TiO2 =2.32 and n sub =1.46. The transmission coefficient t was calculated from the simulated electric field data after linearly polarized light in the x-direction passed through nanopillars of different sizes. xx The amplitude abs(t) xx ) and phase φ xx Similarly, by changing the polarization direction of the incident light to the y-direction, the corresponding transmission coefficient t can be obtained. yy The amplitude abs(t) yy ) and phase φ yy During simulation, the wavelength of the incident light, the type of material constituting the nanopillar, and the height H of the nanopillar should be reasonably selected to ensure the phase φ of the transmission coefficient is within a certain range. xx and φ yy It can cover 0 to 2π. Simultaneously, the amplitude of the transmission coefficient abs(t) xx ) and abs(t yy The value should be close to 1 to improve the working efficiency of the double-layer super-gloss surface.

[0050] The final determination of the nanopillar height H was 600 nm, the period P was 450 nm, and the major axis length L and minor axis length W were both in the range of 100 nm to 350 nm.

[0051] Step 2: Based on the analytical decomposition of the unitary Jones matrix, the unitary symmetric matrices corresponding to the two single-layer rectangular nanostructures at each pixel are obtained. Using the principles of propagation phase and geometric phase, the geometric dimensions and rotation angles of the nanopillar units are selected and determined based on the eigenvalues ​​and eigenvectors of the unitary symmetric matrix, thereby generating the processing file of the corresponding single-layer dielectric metasurface structure.

[0052] Figure 2 (b) is a single-layer rectangular nanopillar structure with a rotation angle of θ, and its corresponding transmission coefficient and propagation phase are φ.xx and φ yy The rectangular nanostructure with the best propagation phase match is found based on the unitary symmetric matrix. The values ​​of its major axis length L and minor axis length W are determined, and the corresponding rotation angle θ is calculated. Based on this, the fabrication file for the corresponding medium metasurface structure is generated.

[0053] The control unit of the bilayer metasurface is a bilayer superatom composed of two layers of rectangular pillars stacked vertically. Figure 2 (c) is a schematic diagram of wavefront modulation of a bilayer superatom. The light incident on the bilayer superatom is modulated by the Jones matrices U1 and U2 of the two nanopillars in sequence.

[0054] Step 3: Implement spin-orbit angular momentum mapping using a two-layer metasurface analysis method. Spin-orbit mapping refers to completely converting the SAM carried by the incident beam into the OAM of the output beam while maintaining the conservation of angular momentum between the incident and output beams. The SAM carried by each photon in right-handed and left-handed circularly polarized light (RCP and LCP) are respectively... and To reduce Planck's constant, the SAM of linearly polarized light is 0; a vortex beam is a structured beam carrying OAM, whose OAM is determined by the helical phase e of the light. ilΦ The vortex beam is generated, where Φ represents the azimuth angle, and the phase is determined by the topological charge l. Each photon in the vortex beam carries... The function of the bilayer metasurface that realizes spin-orbit angular momentum mapping is to convert right- or left-hand circularly polarized light into linearly polarized OAM beams with a topological charge of ±1, represented by the Jones matrix as follows.

[0055]

[0056] Where J is the Jones matrix of the metasurface. The metasurface converts incident RCP light |R> into vertically linearly polarized light |y> with a topological charge of 1, and incident LCP light |L> into horizontally linearly polarized light |x> with a topological charge of -1, and Φ represents the azimuth angle.

[0057] Figure 3 This is a schematic diagram illustrating the principle of the spin-orbit angular momentum mapping method based on the unitary Jones matrix control of a double-layer metasurface in this embodiment of the invention.

[0058] Figure 3 (a) is a functional schematic diagram of spin-orbit mapping achieved by a bilayer metasurface. The metasurface converts incident RCP light |R> into vertically linearly polarized light |y> with a topological charge of 1, and converts incident LCP light |L> into horizontally linearly polarized light |x> with a topological charge of -1.

[0059] This bilayer metasurface completely converts the SAM carried by the incident beam into the OAM of the output beam, maintaining the conservation of angular momentum between the incident and output beams, achieving a polarization state conversion from circularly polarized to linearly polarized light. Simultaneously, it adds a spiral phase with topological charges of 1 and -1 to the output beam. This polarization conversion on a Poincaré sphere is as follows: Figure 3 As shown in (b).

[0060] Under linear polarization basis The Jones matrix is ​​derived as follows:

[0061]

[0062] Where J is an asymmetric unitary matrix, and J is decomposed into the form of the product of two unitary symmetric matrices, i.e., J = U2·U1.

[0063] Step one involves decomposing the unitary matrix, and step two uses the fabrication file obtained from step two to realize the spin-orbit angular momentum mapping of the dielectric metasurface structure. Two transmissive dielectric metasurfaces are then fabricated using micro / nano fabrication methods such as electron beam lithography and vapor deposition. In the experimental optical path, a displacement platform is used to align the two metasurfaces, enabling the modulation function of the double-layer metasurface. This converts incident light with different circularly polarized states into linearly polarized vortex light with a topological charge of ±1, thus achieving spin-orbit angular momentum mapping.

[0064] The two metasurface layers were fabricated independently. To reduce the difficulty of experimental alignment, 16×16 superatoms with a period of 450nm were combined into a single control pixel unit, such as... Figure 5 As shown in (a) and (b). To improve the accuracy of the experimental alignment, three 10×20μm alignment marks were designed at the corners of the metasurface, as shown in (a) and (b). Figure 5 As shown in (d), each metasurface has an overall size of 496.8 × 496.8 μm and includes 1104 × 1104 superatoms with a period of 450 nm. Each metasurface also has 69 × 69 control pixel units. The modulation function of the unitary Jones matrix is ​​achieved by sequentially controlling the incident light through the bilayer dielectric nanostructure.

[0065] Figure 4This is the optical path diagram used in the experiment of this invention embodiment. A laser emits a 532nm wavelength laser beam, which is split into two arms by a beam-splitting prism. Arm 1 is incident on the double-layer metasurface, and arm 2 is a Gaussian reference beam. Only arm 1 is used when measuring the intensity of the transmitted light, while arm 2 is blocked. The light in arm 1 is converted into circularly polarized light by polarizer P1 and a quarter-wave plate. Rotating the quarter-wave plate changes the left- or right-hand polarization state of the circularly polarized light. Polarizer P2 is used to filter out the desired x or y polarization components from the transmitted light. The imaging optical system consists of a microscope objective and a convex lens. A CMOS camera is placed on the Fourier surface of the imaging optical system to capture images. The two metasurfaces are aligned by mounting them on displacement stages. One displacement stage is manually adjusted with a precision of 1μm to accurately control the lateral displacement, and a pitch stage is added to control the relative rotation of the two metasurfaces. When probing the phase of the transmitted light, the light from arm 1 and arm 2 is made to interfere. The light from arm 2 is modulated by P3 to the same polarization state as P2. The two beams are combined by a prism and are tilted to each other, producing a forked interference pattern on the camera.

[0066] Figure 5 These are SEM images of the prepared TiO2 metasurface samples. Figure 5 (a) and (b) are top views of the first and second layer samples, respectively. The yellow dashed lines in the figures distinguish different control pixel units, and the structures within the regions are completely identical. Figure 5 (c) shows a side view of the second layer sample. Figure 5 (d) shows a 10×20μm alignment mark at the corner of the metasurface, used for experimental alignment.

[0067] Figure 6 The simulation and experimental results of OAM output light obtained by the double-layer metasurface under right-handed and left-handed circularly polarized light incident in the embodiments of the present invention are as follows.

[0068] Under the condition of right-handed circularly polarized light incident and vertically linearly polarized light exiting, we obtained Figure 6 (a) and Figure 6 (b) Simulation and experimental results of the intensity distribution of the OAM beam show that the OAM beam exhibits a "donut" shape. The interference between the emitted OAM beam and the Gaussian beam yields... Figure 6 (c) shows the experimental forked interferogram. The number of fringe branches indicates that the absolute value of the topological charge is 1, and the upward opening of the fringe indicates that the topological charge of the OAM beam is +1.

[0069] By changing the polarization state of the incident circularly polarized light, with left-handed circularly polarized light incident and horizontally linearly polarized light exiting, we obtained... Figure 6 (d) and Figure 6 Simulation and experimental results of the intensity distribution of the OAM beam in (e). Figure 6In the experimental forked interferogram (f), the fringes open downwards, indicating that the topological charge of the OAM beam is -1.

[0070] This embodiment discloses a light field manipulation method based on the unitary Jones matrix of a bilayer metasurface. It analytically provides a mathematical method for decomposing the unitary Jones matrix of the bilayer metasurface, directly determining the rotation angle and phase modulation parameters along the major and minor axes of each monolayer structure from the target unitary Jones matrix. This method is simple and direct to implement, computationally fast, and yields an exact solution. It decouples the design parameters of the bilayer metasurface, increasing the design freedom and resulting in richer functionality and higher information density. This provides a pathway for exploring more complex and diverse metasurface functions in the future, and can be applied to fields such as quantum optics, light field modulation, information encryption, information transmission, and special structure light conversion.

[0071] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for controlling the optical field based on the unitary Jones matrix of a double-layer metasurface, characterized in that: Includes the following steps, Step 1: The Jones matrix of the double-layer metasurface used is a unitary matrix, formed by stacking two anisotropic metasurfaces. The Jones matrix J of the double-layer metasurface is described by the product of the Jones matrices of the two single-layer metasurfaces, i.e., J = U2·U1. The single-layer anisotropic metasurface is described as a linear birefringent waveplate. The Jones matrix of the single-layer anisotropic metasurface is a unitary symmetric matrix with equal off-diagonal elements. The product of two unitary symmetric matrices is an asymmetric unitary matrix. Therefore, the Jones matrix J is an arbitrary unitary matrix. The unitary Jones matrix J is decoupled into the product of two unitary symmetric Jones matrices U1 and U2 through analytical decomposition. Step 2: Each unitary symmetric Jones matrix obtained in Step 1 is realized through anisotropic rectangular nanopillars. Using the principle of geometric phase and propagation phase, the geometric dimensions and in-plane rotation angle of the rectangular nanopillar unit are determined according to the complex amplitude distribution of the unitary symmetric Jones matrix to be encoded, thereby generating the processing file of the corresponding metasurface structure; the unitary matrix J is realized by a double layer of superatoms composed of two vertically stacked nanopillars. The light incident on the double layer of superatoms is modulated by the Jones matrices U1 and U2 of the first and second layer nanopillars in turn; Step 3: Using the fabrication file of the medium metasurface structure obtained in Step 2, prepare a transmissive medium metasurface; using the principles of geometric phase and propagation phase, accurately solve the geometric parameters of each monolayer metasurface structure based on the unitary matrix decomposition method, and form a double-layer metasurface by vertically stacking two monolayer metasurfaces, and use the double-layer metasurface with the unitary Jones matrix to achieve precise light field control.

2. The optical field manipulation method based on the unitary Jones matrix of a double-layer metasurface as described in claim 1, characterized in that: The implementation method for step one is as follows: Unitary symmetric matrices U1 and U2 can be represented by eigenvalues ​​and eigenvectors through eigendecomposition as follows: Where m = 1 or 2, representing two unitary symmetric matrices respectively. and For U m Two eigenvalues, It is an orthogonal matrix, and its column vectors are U. m Two eigenvectors; The specific decomposition steps for decoupling the unitary Jones matrix J into the product of two unitary symmetric Jones matrices U1 and U2 are as follows: For any unitary matrix of complex amplitude form The two column vectors of a unitary matrix are orthogonal, therefore The unitary matrix J is represented as Among them, the average phase shift According to the unitary matrix condition J·J H = Ι, where the superscript H denotes the conjugate transpose of the matrix, Ι is the identity matrix, and A is derived from formula (2). 2 +B 2 =1 and C = ±B; When C = B, When C = -B, in, Any 2×2 unitary matrix J can be decomposed into the product of two unitary symmetric matrices U1 and U2, i.e., J = U2·U1; U1 and U2 are represented as U1 = [U2] -1 ·J,U2=J·[U1] -1 Based on the condition that the off-diagonal elements of matrices U1 and U2 are equal, substituting equations (1), (3), and (4) into the relationship between U1, U2, and J yields: in, Im represents taking the imaginary part of the complex number, and Re represents taking the real part of the complex number; if and only if θ2 always has a solution; let It is derived from formula (5): From formula (6), we know that θ2 is determined by u and v, and u and v are determined by the original unitary matrix J; Substitute θ2 into formula (1) to calculate U2; U1 is obtained through U1=[U2] -1 ·J is calculated, where U1 is a diagonalizable unitary symmetric matrix. Its eigenvectors and eigenvalues ​​are calculated through eigenvalue decomposition. The unitary matrix property of U1 ensures that the eigenvectors of U1 are orthogonal, and the eigenvalues ​​are complex exponents. U1 is decomposed into the standard form of formula (1), and its eigenvectors and eigenvalues ​​are determined. θ1; According to equations (1) to (6), the unitary Jones matrix J is decoupled into the product of two unitary symmetric Jones matrices U1 and U2 through analytical decomposition.

3. The optical field manipulation method based on the unitary Jones matrix of a double-layer metasurface as described in claim 2, characterized in that: The second step is implemented as follows: In formula (1), the unitary symmetric Jones matrices U1 and U2 are decomposed into... and θ represents the phase delay of the anisotropic nanopillar in the x and y directions. m The rotation angle of the nanopillar is represented by [reference needed]. The phase delay of the superatom in the x and y directions is altered by changing the period P, the height H, and the cross-sectional dimensions L and W of the nanopillar. With the height H and period P fixed, a two-dimensional scan of the major axis length L and minor axis length W of the nanopillar is performed using simulation software based on the rigorous coupled-wave analysis method RCWA, yielding the transmission coefficient t for nanopillars of different sizes. xx and t yy During simulation, the wavelength of the incident light, the type of material constituting the nanopillar, the height H of the nanopillar, and the period P should be selected to ensure the phase of the transmission coefficient. and Capable of covering 0 to 2π; The selected structure should be as close as possible to the target's transmission phase. and Pick The phase shift of the second layer is fixed, based on the geometric phase principle of metasurfaces, and is achieved by an array of nanopillars of the same size but different rotation angles; the phase shift and rotation angle of the first layer are both variable, and are achieved by an array of nanopillars of different sizes and rotation angles, utilizing both propagation phase and geometric phase principles; based on the major axis length L, minor axis length W, and rotation angle of the selected nanopillar units, the corresponding processing file for the medium metasurface structure is generated.

4. The optical field manipulation method based on the unitary Jones matrix of a double-layer metasurface as described in claim 3, characterized in that: Transmissive dielectric metasurfaces were fabricated using micro-nano fabrication methods such as electron beam lithography and vapor phase deposition.

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