Wavefront regulation and control method based on dielectric metasurface

Abstract

The invention discloses a wavefront regulation and control method based on a dielectric metasurface, which belongs to the technical field of wavefront regulation and control, and comprises the following steps of: resolving a Helmholtz equation, obtaining a self-acceleration Bessel beam, solving a first-order derivative of the self-acceleration Bessel beam, obtaining a generalized Bessel type self-acceleration beam, and carrying out wavefront regulation and control on the basis of complex amplitude distribution of the generalized Bessel type self-acceleration beam. And a pure-phase computer-generated hologram is calculated by using complex amplitude coding. According to the electrolyte metasurface, materials with high modulation efficiency can be found in a wide wave band range, and large-scale mass production is expected to be achieved with low cost due to the common silicon-based materials and the common titanium dioxide-based materials; the metasurface is utilized to realize joint regulation and control of multiple parameters of the light beam, so that functional diversification is realized, and the application range is widened.

Description

Technical Field

[0001] The invention discloses a wavefront control method based on a dielectric metasurface, belonging to the technical field of wavefront control. Background Art

[0002] Traditional wavefront manipulation methods primarily rely on optoelectronic devices such as digital micromirrors, spatial light modulators, and deformable mirrors to manipulate parameters such as amplitude, phase, and polarization. Refraction, imaging, and beam splitting of light beams are achieved through lenses, mirrors, gratings, and diffractive optical elements. However, these optical elements typically require cumulative changes in characteristics such as phase and are limited by the refractive index of the optical material, resulting in drawbacks such as bulk, weight, limited functionality, and complex manufacturing processes. Summary of the Invention

[0003] The purpose of the present invention is to provide a wavefront control method based on dielectric metasurface to solve the problems in the prior art that the optical element device for wavefront control is complex and costly.

[0004] A wavefront control method based on a dielectric metasurface includes solving the Helmholtz equation to obtain a self-accelerating Bessel beam, taking the first-order derivative of the self-accelerating Bessel beam to obtain a generalized Bessel-type self-accelerating beam, and using complex amplitude coding to calculate a phase-only computer-generated hologram based on the complex amplitude distribution of the generalized Bessel-type self-accelerating beam.

[0005] The dielectric metasurface is composed of discrete unit structures, wherein the unit structures use polysilicon as the material of the nanocolumns and silicon dioxide as the substrate material.

[0006] The scalar Helmholtz equation is:

[0007]

[0008] Where U = U(x,z) is the complex amplitude distribution of the light beam, k is the wave number in vacuum, x represents the x-axis coordinate, z represents the z-axis coordinate, and λ is the wavelength. The exact solution of the Helmholtz equation is a Bessel function.

[0009] The self-accelerating Bessel beam in Cartesian coordinates is:

[0010]

[0011] Where, J β represents the Bessel function of the first kind, and β represents the order of the Bessel function.

[0012] When z = 0, the first-order derivative of the self-accelerating Bessel beam is obtained, and the generalized Bessel-type self-accelerating beam is obtained:

[0013] U(x,0)=Jβ ′(kx)exp(-αx);

[0014] Where α is the attenuation coefficient.

[0015] Based on the complex amplitude distribution of the generalized Bessel self-accelerating beam, the amplitude information is introduced into the grating by setting a phase grating. The loaded phase grating G(x,y) is:

[0016]

[0017] Where y represents the y-axis coordinate, γ(x,y) represents the phase variation range of a single grating period, mod[] represents the remainder function, Express request The remainder after dividing by 2π, u0, represents the spatial frequency, Represents the phase distribution.

[0018] The computer generated hologram loaded onto the dielectric metasurface is:

[0019]

[0020] Where, sin c -1 Represents the inverse function of the sinc function.

[0021] The polarization state of the incident light beam is circular polarization. After the incident light beam passes through the dielectric metasurface, the transmission field E cp-out The expression is:

[0022]

[0023] Where T is the amplitude transmittance, e is a natural constant, and i is an imaginary number. represents the transmission phase, δ represents the phase delay of the two components, 1+i represents the left-handed circular polarization state, 1-i represents the right-handed circular polarization state, e i2θ is the geometric phase term, and θ is the rotation angle of the unit structure.

[0024] The nanopillars are cuboids with a height of 590 nm, a length of 80 nm, and a width of 176 nm. The unit period of the substrate material is 300 nm.

[0025] Set δ = π, the wavelength of the incident beam is 633 nm, β = 150, α = 10 5 m -1 , 0≤γ(x,y)≤1.

[0026] Compared with the existing technology, the present invention has the following beneficial effects: the electrolyte metasurface can find materials with high modulation efficiency in a wider band range, and the commonly used silicon-based and titanium dioxide-based ones are expected to achieve large-scale mass production at a lower cost; the metasurface is used to realize the joint regulation of multiple parameters of the light beam, realize functional diversification, and broaden the scope of application. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 is the amplitude distribution diagram of the one-dimensional generalized Bessel self-accelerating beam;

[0028] Figure 2 is the phase distribution diagram of the light beam;

[0029] Figure 3 This is a diagram of the propagation process of a generalized Bessel-type self-accelerating beam along the axial direction under one-dimensional conditions;

[0030] Figure 4 The propagation trajectory of the light beam when the order of the Bessel function is 80;

[0031] Figure 5 The propagation trajectory of the light beam when the order of the Bessel function is 120;

[0032] Figure 6 This is the computer-generated hologram of a generalized Bessel-type self-accelerating beam. DETAILED DESCRIPTION

[0033] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention are described clearly and completely below. Obviously, the embodiments described are only some of the embodiments of the present invention, not all of them. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0034] A wavefront control method based on a dielectric metasurface includes solving the Helmholtz equation to obtain a self-accelerating Bessel beam, taking the first-order derivative of the self-accelerating Bessel beam to obtain a generalized Bessel-type self-accelerating beam, and using complex amplitude coding to calculate a phase-only computer-generated hologram based on the complex amplitude distribution of the generalized Bessel-type self-accelerating beam.

[0035] The dielectric metasurface is composed of discrete unit structures, wherein the unit structures use polysilicon as the material of the nanocolumns and silicon dioxide as the substrate material.

[0036] The scalar Helmholtz equation is:

[0037]

[0038] Where U = U(x,z) is the complex amplitude distribution of the light beam, k is the wave number in vacuum, x represents the x-axis coordinate, z represents the z-axis coordinate, and λ is the wavelength. The exact solution of the Helmholtz equation is a Bessel function.

[0039] The self-accelerating Bessel beam in Cartesian coordinates is:

[0040]

[0041] Where, J β represents the Bessel function of the first kind, and β represents the order of the Bessel function.

[0042] When z = 0, the first-order derivative of the self-accelerating Bessel beam is obtained, and the generalized Bessel-type self-accelerating beam is obtained:

[0043] U(x,0)=J β ′(kx)exp(-αx);

[0044] Where α is the attenuation coefficient.

[0045] Based on the complex amplitude distribution of the generalized Bessel self-accelerating beam, the amplitude information is introduced into the grating by setting a phase grating. The loaded phase grating G(x,y) is:

[0046]

[0047] Where y represents the y-axis coordinate, γ(x,y) represents the phase variation range of a single grating period, mod[] represents the remainder function, Express request The remainder after dividing by 2π, u0, represents the spatial frequency, Represents the phase distribution.

[0048] The computer generated hologram loaded onto the dielectric metasurface is:

[0049]

[0050]

[0051] In the formula, sinc -1 Represents the inverse function of the sinc function.

[0052] The polarization state of the incident light beam is circular polarization. After the incident light beam passes through the dielectric metasurface, the transmission field E cp-out The expression is:

[0053]

[0054] Where T is the amplitude transmittance, e is a natural constant, and i is an imaginary number. represents the transmission phase, δ represents the phase delay of the two components, 1+i represents the left-handed circular polarization state, 1-i represents the right-handed circular polarization state, e i2θ is the geometric phase term, and θ is the rotation angle of the unit structure.

[0055] The nanopillars are cuboids with a height of 590 nm, a length of 80 nm, and a width of 176 nm. The unit period of the substrate material is 300 nm.

[0056] Set δ = π, the wavelength of the incident beam is 633 nm, β = 150, α = 10 5 m -1 , 0≤γ(x,y)≤1.

[0057] With the development of modern optics, systems and devices are gradually moving towards miniaturization and integration. The emergence of metasurfaces offers an effective solution to the shortcomings of traditional optical components, such as large size, high loss, and complex processing. Metasurfaces, composed of artificial micro-nanostructures with in-plane feature dimensions on the subwavelength scale, can significantly reduce the complexity of device fabrication and enhance design flexibility. Metasurfaces possess the following characteristics: subwavelength scale, with thickness approaching or less than the wavelength, significantly reducing the loss caused by light beam transmission through the medium and achieving high energy efficiency; high precision, metasurfaces can control light parameters such as amplitude, phase, and polarization with subwavelength precision, eliminating crosstalk caused by diffraction; integration, metasurfaces can be fabricated on various substrates and combined with semiconductor and optoelectronic devices to facilitate the construction of multifunctional integrated optical systems; and reduced manufacturing difficulty and cost, with metasurface unit structures composed of metals or dielectrics, which can be processed using methods compatible with semiconductor chip processing, such as electron beam lithography, focused ion beam etching, and nanoimprinting, significantly reducing manufacturing difficulty and cost.

[0058] In the field of modern optics and optoelectronics, light field control plays a key role in defense, communications, energy, and medical fields. Exploring miniaturized, lightweight, and integrated optical devices has significant application value. Metasurfaces simplify the three-dimensional structure of metamaterials into a two-dimensional planar structure, which can significantly reduce the complexity and difficulty of preparation and improve the flexibility of design. The present invention proposes a wavefront control method based on metasurfaces, which achieves wide-band and high-processing precision based on the geometric phase of the metasurface. A new type of generalized Bessel-type self-accelerating beam is designed, and its amplitude and phase structure is assigned to the metasurface through complex amplitude coding technology, so as to transform the straight-line transmission trajectory of the incident light beam into a large-angle deflection and semicircular transmission trajectory, providing a new technical solution for optical devices to achieve beam deflection.

[0059] The dielectric metasurface is composed of discrete unit structures. Polycrystalline silicon, with high refractive index and low loss, is chosen as the material for the nanopillars, which are shaped into rectangular parallelepipeds. Silicon dioxide, with its high transmittance and low absorption loss, is chosen as the substrate. The high refractive index of dielectric materials effectively localizes the mode field within the unit structure, and coupling between adjacent structures is negligible. Studying the unit structure of the dielectric metasurface can explain its ability to manipulate light beams. The modulation effect of the metasurface unit structure is equivalent to a birefringent element, which can exert different amplitude and phase modulation effects on the linear polarization components of the long and short axes of the waveguide.

[0060] The wavefront control method of the present invention is based on the geometric phase modulation of the metasurface. The geometric phase requires that the polarization state of the incident light beam is circularly polarized. The expression of the transmitted field contains two orthogonal circular polarization components, a polarization component with the same polarization as the incident light beam, and an orthogonal polarization component. The transmission phases of the two transmitted components are consistent, while the light intensities are complementary and controlled by the phase delay δ. In order to obtain the required geometric phase term e i2θ , set the phase delay δ = π to eliminate the same polarization component.

[0061] Phase control using dielectric metasurfaces can be categorized into two main types: transmission phase and geometric phase. This method, based on geometric phase, determines the phase value by the rotation angle θ of the unit structure. Using periodically arranged rectangular nanopillars as nanounits, eight unit structures are selected to achieve a phase range of 0 to 2π. By rotating the unit structure by an angle of 0 to π, a phase shift of 0 to 2π can be achieved.

[0062] Figure 1 Figure 2 shows the amplitude distribution of a one-dimensional generalized Bessel self-accelerating beam. The beam amplitude exhibits a striped distribution, with the main lobe intensity reaching a peak. Due to the attenuation coefficient, the sidelobe intensity gradually decreases and approaches zero. Figure 2 The phase distribution of the beam is represented by . The phase of the beam is a binary phase of 0 and π, and changes alternately. Furthermore, the Rayleigh-Sommerfeld vector diffraction theory is used to numerically simulate the axial transmission process of the generalized Bessel type self-accelerating beam under one-dimensional conditions, as shown in the following example: Figure 3 As shown, this beam exhibits self-bending properties similar to those of an Airy beam. Starting from the origin, the beam propagates along the z-axis, gradually deflecting its trajectory until the entire trajectory takes on a shape similar to a quarter of a circle. Due to the strong diffraction effect, the beam's deflection angle does not reach 90°, diverging outward as it approaches the z-axis. This control method achieves large-angle bending and deflection of the beam in the non-paraxial region, with potential applications in particle transport and optical trapping. Furthermore, the Bessel order can adjust the radius of the beam's propagation trajectory. Figure 4 and Figure 5The transmission trajectories of the beam when the order is 80 and 120 respectively. As the order decreases, the beam transmission distance shortens and the radius of the circular trajectory also decreases. Based on the complex amplitude distribution of the generalized Bessel type self-accelerating beam, a pure phase computer hologram is calculated using the complex amplitude encoding technology. This method requires setting a phase grating and introducing amplitude information into the grating. The grating coefficient is selected as 10 6 For a generalized Bessel-type self-accelerating beam, the pure phase diagram containing amplitude and phase information is as follows: Figure 6 As shown. This invention utilizes geometric phase control of an electrolyte metasurface, achieving high-precision modulation by rotating the angle of the unit structure. Utilizing inverse sinc complex amplitude encoding, the beam's amplitude and phase information are assigned to a phase-only computer-generated hologram. By solving the Helmholtz equation, a new class of generalized Bessel-type self-accelerating beams with large-angle deflection is obtained in the non-paraxial region.

[0063] The present invention provides a wavefront control method based on a metasurface, which has the following advantages:

[0064] (1) Miniaturization. The present invention is based on a metasurface with a sub-wavelength feature size in the plane and uses polysilicon as a unit structure to achieve miniaturization of the wavefront control device with high integration.

[0065] (2) Low cost. The fabrication process of the metasurface is compatible with complementary metal oxide semiconductor (CMOS) technology and can be manufactured on a large scale, thereby reducing production costs.

[0066] (3) Multi-degree-of-freedom control of wavefront, designing the geometric parameters and arrangement of the structure, and flexibly controlling the amplitude, phase, polarization state and other parameters of the light beam on the micro-nano scale by the metasurface.

[0067] (4) Large-angle deflection of the light beam. After passing through the metasurface, the Gaussian beam is regulated into a generalized Bessel-type self-accelerating beam with self-bending characteristics and a large-angle deflection of an approximately circular trajectory.

[0068] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents, and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A wavefront control method based on dielectric metasurface, characterized in that: It includes solving the Helmholtz equation, obtaining the self-accelerating Bessel beam, taking the first-order derivative of the self-accelerating Bessel beam, obtaining the generalized Bessel-type self-accelerating beam, and based on the complex amplitude distribution of the generalized Bessel-type self-accelerating beam, using complex amplitude coding to calculate a pure phase computer-generated hologram.

2. The wavefront control method based on dielectric metasurface according to claim 1, characterized in that: The dielectric metasurface is composed of discrete unit structures, wherein the unit structures use polysilicon as the material of the nanocolumns and silicon dioxide as the substrate material.

3. The wavefront control method based on dielectric metasurface according to claim 2, characterized in that: In the non-paraxial region, the scalar Helmholtz equation is: Where U = U(x,z) is the complex amplitude distribution of the light beam, k is the wave number in vacuum, x represents the x-axis coordinate, z represents the z-axis coordinate, and λ is the wavelength. The exact solution of the Helmholtz equation is a Bessel function.

4. The wavefront control method based on dielectric metasurface according to claim 3, characterized in that: The self-accelerating Bessel beam in Cartesian coordinates is: Where, J β represents the Bessel function of the first kind, and β represents the order of the Bessel function.

5. The wavefront control method based on dielectric metasurface according to claim 4, characterized in that: When z = 0, the first-order derivative of the self-accelerating Bessel beam is obtained, and the generalized Bessel-type self-accelerating beam is obtained: U(x,0)=J β ′(kx)exp(-αx); Where α is the attenuation coefficient.

6. The wavefront control method based on dielectric metasurface according to claim 5, characterized in that: Based on the complex amplitude distribution of the generalized Bessel self-accelerating beam, the amplitude information is introduced into the grating by setting a phase grating. The loaded phase grating G(x,y) is: Where y represents the y-axis coordinate, γ(x,y) represents the phase variation range of a single grating period, mod[] represents the remainder function, Express request The remainder after dividing by 2π, u0, represents the spatial frequency, Represents the phase distribution.

7. The wavefront control method based on dielectric metasurface according to claim 6, characterized in that: The computer generated hologram loaded onto the dielectric metasurface is: In the formula, sinc -1 Represents the inverse function of the sinc function.

8. The wavefront control method based on dielectric metasurface according to claim 7, characterized in that: The polarization state of the incident light beam is circular polarization. After the incident light beam passes through the dielectric metasurface, the transmission field E cp-out The expression is: Where T is the amplitude transmittance, e is a natural constant, and i is an imaginary number. represents the transmission phase, δ represents the phase delay of the two components, 1+i represents the left-handed circular polarization state, 1-i represents the right-handed circular polarization state, e i2θ is the geometric phase term, and θ is the rotation angle of the unit structure.

9. The wavefront control method based on dielectric metasurface according to claim 8, characterized in that: The nanopillars are cuboids with a height of 590 nm, a length of 80 nm, and a width of 176 nm. The unit period of the substrate material is 300 nm.

10. The wavefront control method based on dielectric metasurface according to claim 9, characterized in that: Set δ = π, the wavelength of the incident beam is 633 nm, β = 150, α = 10 5 m -1 , 0≤γ(x,y)≤1.

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