A multi-layer composite super-lens based on optical admittance theory optimization

Abstract

The application discloses a kind of multilayer composite superlenses based on optical admittance theory optimization, comprising: substrate, transition film layer and nano cell array;Substrate, transition film layer and nano cell array are sequentially arranged to constitute multilayer composite superlens;Nano cell array is composed of several nano cells.The application proposes multilayer film structure antireflection transmission type superlens, nano cell is Al2O3 (medium refractive index), TiO2 (high refractive index), MgF2 (low refractive index) laminated structure, substrate is SiO2, and in double side plating MgF2 and H4 (titanium lanthanum mixture) alternate film layer.The results show that the transmittance is 89.31% at the design wavelength of 600nm, the transmittance is higher than 74% in the wavelength range of 500~700nm, and the average transmittance is 82.01%.

Description

Technical Field

[0001] This invention belongs to the field of micro-nano optical device technology, specifically relating to a multilayer composite metalens optimized based on optical admittance theory. Background Technology

[0002] Metalenses are emerging optical devices that enable ultra-thin, ultra-lightweight, and high-quality imaging. These artificially designed and manufactured two-dimensional planar optical devices use subwavelength metallic or dielectric structures to control parameters such as the amplitude, phase, and polarization of electromagnetic waves. Metalenses achieve electromagnetic wave manipulation by adjusting the radius of nanounits. When light passes through a traditional lens, high-frequency components cannot pass due to the presence of evanescent waves. However, the nanounits in a metalens are essentially optical waveguides, allowing light to propagate within them while retaining high-frequency components, thus achieving super-resolution imaging. The design principle of the nanounits in metalenses follows the Mie resonance theory. Nanoantennas made of low- to medium-refractive-index materials can exhibit this effect when excited at the nanoscale. However, low- to medium-refractive-index materials have weak light confinement capabilities, leading to higher radiation losses and less pronounced Mie resonance. In contrast, high-refractive-index nanoantennas generate stronger Mie resonances, resulting in a strong electromagnetic field enhancement within the nanoantenna, which improves transmittance and effectively suppresses scattering. Therefore, current metalens designs primarily use SiO2 substrates, on which high-refractive-index materials such as SiN (n=2), TiO2 (n=2.4), and Si (n=3.8) are deposited and etched to form nanounits. Some researchers have studied reducing scattering from nanounits by optimizing nanounit materials and geometric parameters using Mie resonance theory and Kerker conditions to reduce scattering from the nanounits themselves. However, they have not considered the reflection and scattering at the interface between the substrate and the nanounit, or between the nanounit and the exit medium.

[0003] Currently, metalenses generally have low transmittance, reaching 80% in the infrared band but only 48% in the visible light band, significantly reducing image quality and practicality. Designing multilayer film structures on the substrate can greatly improve transmittance, such as a distributed Bragg grating (DBR) structure with alternating layers of two dielectric materials, which can increase transmittance at the designed wavelength. However, DBR structures can only achieve high transmittance within a very narrow bandwidth, similar to a filter, and cannot achieve high transmittance in the visible light band. Summary of the Invention

[0004] This invention aims to address the shortcomings of existing technologies and provides the following solutions:

[0005] A multilayer composite metalens optimized based on optical admittance theory includes: a substrate, a transition film layer, and a nano-unit array;

[0006] The substrate, the transition film layer, and the nanounit array are arranged sequentially to form the multilayer composite metalens; the nanounit array is composed of several nanounits.

[0007] Preferably, the substrate is SiO2.

[0008] Preferably, the nanounit has a multilayer structure, consisting of a medium refractive index material layer, a high refractive index material layer, and a low refractive index material layer arranged sequentially.

[0009] The intermediate refractive index material layer is made of Al2O3 with a refractive index of 1.37±0.02. Based on the optical admittance theory, the thickness is designed to be 1 / 2λ0, where λ0 is the design wavelength.

[0010] The high refractive index material layer is made of TiO2 with a refractive index of 2.5±0.05, and its thickness is designed to be 3×1 / 2λ0 based on optical admittance theory.

[0011] The low-refractive-index material layer is made of MgF2 with a refractive index of 1.38±0.02, and its thickness is designed to be 1 / 4λ0 based on optical admittance theory.

[0012] Preferably, the transition film layer is disposed between the substrate and the nanounit array, and adopts a structure of alternating stacks of MgF2 and H4 titanium lanthanum mixture based on optical admittance theory, with each layer having a thickness of 1 / 4λ0.

[0013] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0014] This invention proposes a multilayer transmissive metalens with nanounits consisting of Al2O3 (medium refractive index), TiO2 (high refractive index), and MgF2 (low refractive index) stacked layers. The substrate is SiO2, and alternating layers of MgF2 and H4 (a mixture of titanium and lanthanum) are deposited on both sides. Results show that the transmittance reaches 89.31% at the designed wavelength of 600 nm, and the transmittance in the 500–700 nm band is above 74%, with an average transmittance of 82.01%. Attached Figure Description

[0015] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 This is a schematic diagram of the metalens structure according to an embodiment of the present invention;

[0017] Figure 2 This is a schematic diagram illustrating the working principle of the nanounit in an embodiment of the present invention.

[0018] Figure 3 This is a schematic diagram illustrating the optical admittance calculation principle of an embodiment of the present invention;

[0019] Figure 4 This is a schematic diagram showing the relationship between the effective refractive index and radius of the nanounits in an embodiment of the present invention.

[0020] Figure 5 The diagram shows the transmittance and reflectance of the nanounits in an embodiment of the present invention, wherein (a) is a schematic diagram of a single-layer nanounit, (b) is a schematic diagram of a double-layer nanounit, and (c) is a schematic diagram of a triple-layer nanounit.

[0021] Figure 6 The diagram shows the phase of a nanounit according to an embodiment of the present invention, wherein (a) is a schematic diagram of a single-layer nanounit, (b) is a schematic diagram of a double-layer nanounit, and (c) is a schematic diagram of a triple-layer nanounit.

[0022] Figure 7 The following are schematic diagrams of the simulation results of the transmittance and phase distribution of the nano-units in the embodiments of the present invention. Among them, (a) is a schematic diagram of the transmittance of the single-layer nano-unit, (b) is a schematic diagram of the transmittance of the double-layer nano-unit, (c) is a schematic diagram of the transmittance of the triple-layer nano-unit, (d) is a schematic diagram of the phase distribution of the single-layer nano-unit, (e) is a schematic diagram of the phase distribution of the double-layer nano-unit, and (f) is a schematic diagram of the phase distribution of the triple-layer nano-unit.

[0023] Figure 8 This is a schematic diagram of the transmittance of the metalens in an embodiment of the present invention. Detailed Implementation

[0024] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0025] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0026] Example 1

[0027] In this embodiment, as Figure 1 As shown, a multilayer composite metalens optimized based on optical admittance theory includes: a substrate, a transition film layer, and a nano-unit array; the substrate, the transition film layer, and the nano-unit array are arranged sequentially to form a multilayer composite metalens; the nano-unit array is composed of several nano-units.

[0028] The substrate is SiO2. The nanounits are multilayered, consisting of a medium-refractive-index material layer, a high-refractive-index material layer, and a low-refractive-index material layer arranged sequentially. The medium-refractive-index material layer is Al2O3 with a refractive index of 1.37±0.02, and its thickness is designed to be 1 / 2λ0 based on optical admittance theory, where λ0 is the design wavelength. The high-refractive-index material layer is TiO2 with a refractive index of 2.5±0.05, and its thickness is designed to be 3×1 / 2λ0 based on optical admittance theory. The low-refractive-index material layer is MgF2 with a refractive index of 1.38±0.02, and its thickness is designed to be 1 / 4λ0 based on optical admittance theory. A transition film layer is disposed between the substrate and the nanounit array, and it adopts an alternating stacked structure of MgF2 and H4 titanium-lanthanum mixture based on optical admittance theory, with each layer having a thickness of 1 / 4λ0.

[0029] In this embodiment, the working principle of the nanounit of the metalens is as follows: Figure 2 As shown, the phase of light is modulated by nanounits. The design typically involves light incident from the substrate onto the nanounits and then exiting into the air. When light is incident from the substrate onto the nanounits, strong reflection and scattering occur when light is incident from an optically less dense medium onto an optically denser medium.

[0030] The reflectivity of nanounit interfaces A and B can be calculated using Fresnel's formula:

[0031] (1)

[0032] Where R represents reflectivity, r represents reflection coefficient, n0 represents the refractive index of the incident medium, and n1 represents the refractive index of the exit medium.

[0033] When the substrate is SiO2 (n=1.45), the nanounit is TiO2 (n=2.4), and the output medium is air (n=1), the reflectivity of interface A is 6.09% and the reflectivity of interface B is 16.96% according to equation (1). However, the transmittance is even lower in actual nanometer single-parameter scanning. When the height of the nanounit is designed to be half-wave plate to form an FP resonant cavity, the transmittance can be improved and the reflection at the interface can be reduced. When the height of the nanounit of the single-layer structure material is half-wave plate, the reflection and scattering are reduced within the nanounit by using different materials and composite multi-layer nanounit structures. The reflection and transmittance of the multi-layer medium are calculated by optical admittance theory, such as Figure 3 The diagram illustrates the principle of optical admittance calculation. For a plane wave normally incident from the substrate onto the nanounit, η... s Let Y be the refractive index of the incident medium. Assuming there are k layers, the admittance Y can be calculated using the following formula:

[0034] (2)

[0035] Where k0 represents the incident light wave vector, E0 represents the incident electric field amplitude, j represents the j-th layer of medium, i represents the imaginary unit, and δj N represents the optical path length of the j-th layer of the medium. j Let d represent the refractive index of the j-th layer. j η represents the thickness of the j-th layer. s E represents the corrected substrate refractive index. k Let λ represent the electric field of the k-th layer, B and C be simplified symbols in the admittance representation, Y represent the admittance, and cosθ = 1 for normal incidence. Then n j =N j cosθ=N j .

[0036] The reflectance at interface A between the substrate and the nanounit is 6.09%, while the reflectance at interface B between the nanounit and air is 16.96%. The transmittance is even lower in actual parameter scanning. The transmittance and reflectance of the nanounit are:

[0037] (3)

[0038] (4)

[0039] Where η0 represents the corrected air refractive index. When calculating the transmittance of the nanounit using equations (2) and (4), the effective refractive index n of the nanounit should be calculated. eff The effective refractive indices of MgF2, TiO2, and Al2O3 nanounits with different radii under the fundamental mode were calculated using the finite-difference time-domain (fdtd) method. Figure 4 As shown.

[0040] The scanning radius of the nanounit parameters ranges from 0.05 μm to 0.25 μm. When the nanounit radius is taken as 0.15 μm, n... eff Substitute into equations (2) and (4) to calculate the admittance and transmittance of the nanounit. The design wavelength λ0 is 600 nm. The design of the metalens increases the transmittance when the height of each layer of the nanounit is an integer multiple of "one-quarter of the design wavelength" (1 / 4λ0). As shown in Figure 5, (a), (b), and (c) are the transmittance of single-layer nanounits, double-layer nanounits (high-low refractive index structure, 2HL), and triple-layer nanounits (medium-high-low refractive index structure, 2M2HL) in the 500-700 nm wavelength range. In "2M2HL", 2 represents that the thickness of the layer is 2 times 1 / 4λ0. H, M, and L are high-, medium-, and low-refractive-index materials, respectively. The substrate of all three structures is SiO2.

[0041] The single-layer nanounit material is TiO2 with a thickness of 1 / 2λ0, as shown in Figure 5(a). At the designed wavelength λ0, the transmittance is close to 1, but the overall transmittance is not high from 500-700 nm, with a minimum transmittance of 89.5% and an average transmittance of 94.6% at 500 nm. The double-layer (2HL) material is TiO2 and MgF2 with thicknesses of 1 / 2λ0 and 1 / 4λ0 respectively. The minimum transmittance at 500 nm is 92.8%, and the average transmittance is 97.1%. The triple-layer... The structure (2M2HL) is composed of Al2O3, TiO2, and MgF2, with thicknesses of 1 / 2λ0, 1 / 2λ0, and 1 / 4λ0, respectively. The lowest transmittance at 500 nm is 94.4%, and the average transmittance is 97.8%. High-transmittance materials typically use the "M2HL" structure. However, at the nanoscale, the effective refractive index of Al2O3 (n=1.37) is lower than that of the substrate SiO2 (n=1.45), hence the thickness of the intermediate refractive index material layer is 1 / 2λ0 instead of 1 / 4λ0. The phase modulation method for the nanounits is related to the material's refractive index and the height of the nanounits, following the formula:

[0042] (5)

[0043] in, Let h represent the output phase of the nanounit, and h represent the height of the nanounit; as shown in equation (5), the larger the height h of the nanounit, the stronger the phase modulation capability; n eff Given the effective refractive index of the nanounit, when the height h of the nanounit remains constant, the change in radius causes n to... eff The change modulates the phase. When the nanounit is considered as a waveguide, the wave equation in the z-direction is:

[0044] (6)

[0045] Where k represents the beam propagation wave vector, β represents the propagation constant, and β = k0n eff E t Indicates the electric field in the z-direction. Let z represent the Laplace operator in the z-direction. Equation (5) is the phase change of the traveling wave solution of equation (6), i.e. When designing multilayer nanounit structures and forming FP resonant cavities, equation (5) is no longer applicable because the traveling wave solution only considers the incident light and does not consider the interference between the reflected light and the incident light to form a standing wave. The transmission coefficient t is calculated by equation (2), and the phase of the outgoing light is the phase angle of t:

[0046] (7)

[0047] in, n represents the phase angle. sThe refractive index of the substrate is represented. The meanings of the variables in equation (7) are consistent with those in equation (2). Figures (a), (b), and (c) in Figure 6 show the phases of single-layer nanounits, double-layer nanounits, and triple-layer nanounits calculated by equation (7). When the TiO2 layer height is 2H and 4H, the parameter scan cannot cover 0~2π. Therefore, when performing the parameter scan, the single-layer nanounit is replaced by 6H instead of 2H, and the triple-layer nanounit 2M2HL is replaced by 2M6HL.

[0048] Figure 7 shows the transmittance and phase distribution of single-layer (6H), double-layer (6HL), and triple-layer (2M6HL) nanounits at different wavelengths and radii. The height of the single-layer structure is the same as that of the 2M6HL nanounit, which is 823 nm. Figures 7(a), (b), and (c) show the transmittance of the single-layer, 6HL, and 2M6HL nanounits, with average transmittances of 78.89%, 81.92%, and 85.11%, respectively. The average transmittance of the 2M6HL nanounit is 10.27% higher than that of the single-layer structure. As shown in Figure 7(d), (e), and (f), the phase parameter scans of the single-layer structure, 6HL structure, and 2M6HL structure nanounits are presented. The single-layer structure and 2M6HL structure can achieve 0~2π phase modulation; however, the 6HL structure exhibits a phase jump in the 610nm~650nm band, as shown in Figure 7(e). When the height of the nanounit is a half-wave plate, the phase modulation by geometric phase modulation exhibits a jump phenomenon, thus failing to cover 0~2π. A similar situation occurs with the propagation phase, and the phase basically does not change with the change of the nanounit radius, failing to cover 0~2π phase modulation.

[0049] In this embodiment, the substrate is fused silica glass (SiO2), which has a refractive index of 1.45 in the 500-700nm band. The size can be set according to requirements, and the low refractive index characteristic can be adapted to the impedance matching design of the subsequent transition film. The core structure of the nanounit adopts a 2M6HL multilayer structure (Al2O3 / TiO2 / MgF2) with a "medium-high-low" refractive index gradient and a total height of 823nm. The medium refractive index layer (Al2O3) has a refractive index of 1.37 at 600 nm and a thickness of 226 nm. The high refractive index layer (TiO2) is an amorphous structure with a refractive index of 2.4 at 600 nm and a thickness of 450 nm, with the thickness error controlled within ±5 nm. The low refractive index layer (MgF2) has a refractive index of 1.38 at 600 nm and a thickness of 147 nm. To further reduce interface reflection, a mixture of MgF2 (n=1.38) and H4 titanium lanthanum (n=2.1) is added between the substrate and the nanounit. In terms of macroscopic lens design, the lens radius is 20 μm, the focal length is 140 μm, the numerical aperture (NA) is 0.14, and it is suitable for the 500-700 nm visible light band. The phase distribution uses a quadratic formula to correct the edge field aberration, and the dispersion is further optimized in a wide band using particle swarm optimization (PSO).

[0050] Al2O3 / TiO2 / MgF2 “sandwich” structure transmissive metalens structure, such as Figure 1 As shown, the optical thickness of Al2O3 is 1 / 2×λ0, and the physical thickness is 1 / 2 / n. eff1 ×λ0, where λ0 is the design wavelength, n eff1 The effective refractive index of the material (Al2O3); the optical thickness of TiO2 is 3 / 2×λ0, and the physical thickness is 3 / 2 / n. eff2 ×λ0, where n eff2 The effective refractive index of the material (TiO2); the optical thickness of MgF2 is 1 / 4×λ0, and the physical thickness is 1 / 4 / n. eff3 ×λ0,n eff3 The effective refractive index of the material (MgF2) is given. Alternating stacked layers of MgF2 and H4 (a mixture of titanium and lanthanum) are added between the substrate and the nanounits. In addition, a quadratic phase distribution is designed to correct edge field aberrations, and particle swarm optimization (PSO) is used to further optimize aberrations in the 500-700nm band, ultimately forming an integral metalens with a radius of 20μm, a focal length of 140μm, a numerical aperture of 0.14, and a total height of 823nm for the nanounits (Al2O3 226nm + TiO2 450nm + MgF2 147nm).

[0051] The overall transmittance of the meta-lens is shown in Figure 8. The average transmittance in the 500~700nm band is 82.02%, and the highest transmittance of 89.31% is achieved at the designed wavelength of 600nm.

[0052] Example 2

[0053] In this embodiment, the feasibility of the scheme is ensured through design verification and auxiliary tools. Specifically, the effective refractive index n of the nanounits in the radius range of 0.05μm to 0.25μm is pre-calculated using finite-difference time-domain (FDTD) software (such as Lumerical FDTD Solutions). eff (Select n with a radius of 0.15μm) eff (For subsequent calculations), while simulating the transmittance and reflectance and phase distribution of the multilayer structure to ensure that the transmittance at the design wavelength of 600nm is ≥89% and the phase covers 0~2π. It is also necessary to select test equipment according to the design objectives to ensure that the accuracy of the spectrometer (transmittance test accuracy ±0.1%), atomic force microscope (AFM, morphology resolution ≤0.1nm), and laser confocal microscope (spot size test accuracy ±0.05μm) meets the verification requirements.

[0054] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A multilayer composite metalens optimized based on optical admittance theory, characterized in that, include: Substrate, transition film layer and nanounit array; The substrate, the transition film layer, and the nanounit array are arranged sequentially to form the multilayer composite metalens; the nanounit array is composed of several nanounits. The substrate is made of SiO2; The nanounit has a multilayer structure, consisting of a medium refractive index material layer, a high refractive index material layer, and a low refractive index material layer arranged sequentially. The intermediate refractive index material layer is made of Al2O3 with a refractive index of 1.37±0.02, and its thickness is designed to be 1 / 2 based on optical admittance theory. λ 0, λ 0 represents the design wavelength; The high-refractive-index material layer is made of TiO2 with a refractive index of 2.5 ± 0.05, and its thickness is designed to be 3 × 1 / 2 based on optical admittance theory. λ 0; The low-refractive-index material layer is made of MgF2 with a refractive index of 1.38 ± 0.02, and its thickness is designed to be 1 / 4 based on optical admittance theory. λ 0; The transition film layer is disposed between the substrate and the nanounit array, and adopts a structure of alternating stacks of MgF2 and H4 titanium lanthanum mixture based on optical admittance theory, with each layer having a thickness of 1 / 4λ0.

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