Design of cross-structure double-layer medium broadband achromatic superlens

Abstract

The invention provides a broadband achromatic super lens based on a cross structure double-layer medium. The lens is composed of three layers of structures which are a dielectric layer, a cross-structure alpha-Si array layer and a cross-structure TiO2 array layer from bottom to top in sequence. The double-layer medium shows an approximately linear smooth phase gradient, completely covers a 2pi phase interval, and effectively reduces the aspect ratio to 4: 1. The phase modulation capability of the cross-structured double-layer dielectric arrays with different sizes is obtained through scanning, and the optimal matching of actual phase and theoretical phase contours is carried out, so that the super lens can realize an achromatic function in a target wave band. In addition, the antenna also has the advantages of polarization insensitivity, broadband operation, easy integration and the like. Therefore, a new device design thought is provided for a wide-spectrum imaging and virtual reality / augmented reality optical display system.

Description

Technical Field

[0001] The present invention relates to a broadband achromatic superlens based on a cross-structured double-layer medium, and belongs to the technical field of novel artificial electromagnetic materials and electromagnetic wave control. Background Art

[0002] Metasurfaces are planar structures composed of arrays of subwavelength artificial units. Due to their unique electromagnetic response, they have attracted widespread attention in the fields of optics and optoelectronics in recent years. By spatially adjusting the subwavelength geometric parameter units of the metasurface, the phase and amplitude of electromagnetic waves (EWs) can be precisely manipulated. Compared with traditional optical devices, metasurfaces exhibit basic properties such as abrupt phase transitions and dispersion. However, the sensitivity of the nanostructure units of metalens to wavelength leads to significant dispersion effects. This is because light waves of different wavelengths produce phase delay deviations during propagation, which severely limits its application in broadband imaging. Therefore, how to develop metalens with both wide-band achromatic capabilities and high optical efficiency has become a key challenge to promote its practical application.

[0003] The use of a double-layer structure has many excellent properties. By vertically integrating high-refractive-index amorphous silicon (α-Si) and high-transmittance titanium dioxide (TiO2), a low-aspect-ratio double-layer dielectric metasurface is constructed. Compared with the traditional single-layer structure, the double-layer medium regulates the energy distribution of the light field between high- and low-refractive-index materials, while ensuring 2π phase coverage, and reduces the aspect ratio of the unit structure to 1:4, which is more than 30% less than the single-layer solution in the same band. This design not only optimizes the optical performance, but also enhances the application potential of the material.

[0004] In 2021, ZanYao et al. reduced the unit structure aspect ratio of a dielectric metal lens to 3 (300nm height, 120nm diameter) using a double-layer polysilicon-titanium dioxide nanopillar structure, achieving near-diffraction-limited focusing in the 600–700nm wavelength range, with a focusing efficiency exceeding 22%. In 2022, Basilio-Ortiz et al. proposed a six-layer α-Si / GaN alternating quarter-wavelength stack structure, compressing the unit structure aspect ratio to 3.03 (303nm height, 122nm diameter), improving the focusing efficiency to 36%, and achieving chromatic aberration comparable to a single-layer structure. Therefore, the design of a double-layer dielectric structure metalens has important academic significance and application value. Summary of the Invention

[0005] The invention relates to a broadband achromatic superlens based on a cross-structured double-layer medium, which has a simple structure and is easy to manufacture.

[0006] The present invention is achieved through the following technical solutions:

[0007] Broadband achromatic superlens based on cross-structured double-layer dielectric, such as Figure 1 As shown, the superlens is composed of a dielectric layer composed of SiO2 and a cross-structured amorphous silicon-titanium dioxide double-layer dielectric array layer from bottom to top; the cross-structured amorphous silicon-titanium dioxide double-layer dielectric array layer is composed of 57x57 cross-structured amorphous silicon-titanium dioxide double-layer dielectric unit structures with consistent orientation angles and sizes that change with the unit position.

[0008] The side view and top view of the unit structure are as follows: Figure 1 As shown in (b) and (c), the dimensions are selected from a database, which is established by scanning the longitudinal axis L of the cross structure from 100 nm to 300 nm and the transverse axis W from 100 nm to 300 nm.

[0009] When the structure width increases from 100nm to 300nm, the double-layer medium presents a nearly linear smooth phase gradient, completely covering the 2π phase range, effectively reducing the aspect ratio to 4:1, which is not achievable with a single-layer TiO2 nanopillar at the same aspect ratio. Although a single-layer α-Si nanopillar also achieves 2π phase coverage, its curve has significant nonlinear oscillations, resulting in phase discontinuity, such as Figure 2 shown.

[0010] The metalens designed by the present invention realizes the achromatic function in the wavelength range of 640-740nm. Figure 3 .

[0011] Compared with the non-achromatic metalens, the metalens designed by the present invention has a stable focal length. Figure 4 (a); half-height of length and width is close to the diffraction limit, see Figure 4 (b).

[0012] The metalens designed in this invention has polarization insensitivity within the working band. Figure 5 ;

[0013] The average focusing efficiency of the metalens designed by the present invention can reach 27%, and it has excellent focusing performance. Figure 6 .

[0014] All simulation boundary conditions are set to perfectly matched layer (PML), and the light sources used are of wavelengths of 640 nm, 660 nm, 680 nm, and 700 nm, respectively, and the incident mode is transmission.

[0015] Compared with the prior art, the present invention has the following advantages:

[0016] The double-layer dielectric design combines the high refractive index of α-Si and the high transmittance of TiO2, presenting a nearly linear and smooth phase gradient, completely covering the 2π phase range and effectively reducing the aspect ratio to 4:1.

[0017] Compared with achromatic metalenses operating at a single wavelength, this design has a remarkably wide-bandwidth operating range. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 (a) is a diagram showing the working principle of the superlens; Figure 1 (b) is a side view of the unit structure; Figure 1 (c) is a top view of the unit structure.

[0019] Figure 2 This is a comparison of the phase control performance of three structural units with the same height. The total height is 400nm and the vertical axis L is 100nm.

[0020] Figure 3 is the normalized field intensity distribution in the xz plane (upper sub-figure) and xy plane (lower sub-figure) near the focus;

[0021] Figure 4 (a) Comparison of focal length changes of achromatic metalens and chromatic metalens; Figure 4 (b) is the FWHM of the focused spot.

[0022] Figure 5 is the variation of focal length and FWHM with wavelength under x-polarized and y-polarized light incidence;

[0023] Figure 6 is the focusing efficiency of the metalens. DETAILED DESCRIPTION

[0024] In order to better understand the present invention, the present invention is further explained below in conjunction with embodiments and drawings. The following embodiments are only for illustration of the present invention and are not intended to limit the present invention.

[0025] like Figure 1 As shown in (a), the super lens consists of a dielectric layer composed of SiO2 and a cross-structured amorphous silicon-titanium dioxide double-layer dielectric array layer from bottom to top.

[0026] The cross structures on the x-axis and y-axis of the double-layer dielectric layer are arranged with a period of 350nm. Figure 1 In (b), L is the length of the longitudinal axis of the cross structure, and W is the length of the transverse axis of the cross structure.

[0027] After introducing the particle swarm optimization algorithm to compensate for the dispersion of the material, the phase at any position on the metasurface can be obtained by the following formula:

[0028] Photolithography or lithography can be used to obtain the cross-structure array of the double-layer dielectric layer.Linearly polarized light is incident on the double-layer dielectric metasurface from the SiO2 dielectric layer and propagates along the z-axis.

[0029] The size parameters of the double-layer dielectric layer unit structure are scanned and optimized by the finite difference time domain method (FDTD). The specific method is: using a single-layer cross-structured hydrogenated amorphous silicon (α-Si), a single-layer cross-structured titanium dioxide (TiO2) material and a double-layer dielectric cross structure, the incident light wavelength is 640nm linear polarized light, and the length of the vertical axis L is fixed to 100nm. The horizontal axis length parameter W of the cross structure is scanned, and the optimal solution is selected after analyzing the phase modulation capabilities of unit structures of different sizes. The unit structure finally selected presents an approximately linear smooth phase gradient in the target band, completely covering the 2π phase range, and effectively reducing the aspect ratio to 4:1, such as Figure 2 shown.

[0030] exist Figure 3 In FIG, the intensity distribution of the transmitted field in the xz plane shows that the focusing of the transmitted light can be clearly observed at a position of about z = 27 μm.

[0031] exist Figure 4 In (a), the focal length stability of this design is significantly improved compared to the traditional metalens, with the maximum deviation controlled within ±4.5%.

[0032] Figure 4 In (b), the full width at half maximum (FWHM) of the focused spot of the present invention is very close to the theoretical diffraction limit width (λ / 2NA), which indicates that the focal diameter of the metalens is also effectively controlled.

[0033] Figure 5 In the figure, the focal length and FWHM under the two polarization states are almost consistent within the working band curve. This polarization independence is due to the high symmetry of the cross-shaped structural unit, which eliminates the sensitivity of traditional metasurfaces to polarization states and can significantly improve the stability of the optical system under non-polarized light sources or complex polarization environments.

[0034] exist Figure 6 In the paper, the focusing efficiency of the metalens in the 640-740 Å band was collected. It can be seen that the average focusing efficiency in the working band can reach 27%, showing excellent focusing performance.

[0035] It should be noted that although the embodiments of the present invention described above are illustrative, they are not intended to limit the present invention. Therefore, the present invention is not limited to the above-mentioned specific embodiments. Without departing from the principles of the present invention, any other embodiments obtained by those skilled in the art under the guidance of the present invention are deemed to be within the protection of the present invention.

Claims

1. A broadband achromatic metalens based on a cross-structured double-layer medium, as shown in Figure 1. It is characterized by: From bottom to top, the superlens consists of a dielectric layer composed of SiO2, a cross-structured α-si array layer, and a cross-structured TiO2 array layer; the cross-structured α-si and TiO2 array layers are composed of cross-structured α-si and TiO2 unit structures with consistent orientation angles and sizes that change with the unit position.

2. The broadband achromatic metalens based on a cross-structured double-layer medium according to claim 1, characterized in that: The cross-structured double-layer dielectric unit structure is shown in Figure 1(b), where the titanium dioxide height H1 = 320nm, the amorphous silicon height H2 = 80nm, and the period P = 350nm.

3. The broadband achromatic metalens based on a cross-structured double-layer medium according to claim 1, characterized in that: The sizes of the nanopillars within the metasurface layer were selected from a database created by scanning the longitudinal axis L of the cross structure from 100nm to 300nm and the transverse axis W from 100nm to 300nm.

4. The broadband achromatic metalens based on a cross-structured double-layer medium according to claim 1, characterized in that: The particle swarm algorithm was introduced to optimize the phase profile, which effectively compensated for the material dispersion and reduced the matching error by more than 65%.

5. The broadband achromatic metalens based on a cross-structured double-layer medium according to claim 1, characterized in that: The superlens consists of 57x57 cross-structured double-layer dielectric unit structures. The diameter of the superlens is 21um and the numerical aperture NA=0.3667.

6. The broadband achromatic metalens based on a cross-structured double-layer medium according to claim 1, characterized in that: The metalens can effectively control dispersion in a broadband range of 640-740nm. It has almost the same focusing performance under x-polarized and y-polarized light incidence, with an average focusing efficiency of up to 27%.

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