Multi-layer composite super-structure lens based on optical admittance theory optimization

Abstract

The invention discloses a multilayer composite super-structure lens based on optical admittance theory optimization. The multilayer composite super-structure lens comprises a substrate, a transition film layer and a nanometer unit array. The substrate, the transition film layer and the nano unit array are sequentially arranged to form a multi-layer composite super-structure lens; the nanometer unit array is composed of a plurality of nanometer units. According to the multi-layer film structure enhanced transmission type super-structure lens, a nanometer unit is of an Al2O3 (medium refractive index), TiO2 (high refractive index) and MgF2 (low refractive index) laminated structure, a substrate is made of SiO2, and the double faces of the substrate are plated with MgF2 and H4 (titanium-lanthanum mixture) alternating film layers. The result shows that the transmissivity at the designed wavelength of 600nm reaches 89.31%, the transmissivity at the waveband of 500-700nm is higher than 74%, and the average transmissivity reaches 82.01%.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of micro-nano optical devices, and particularly relates to a multilayer composite superlens based on optical admittance theory optimization. BACKGROUND

[0002] The superlens is a new optical device with ultra-thinness, ultra-lightness and high-quality imaging. This two-dimensional planar optical device designed and manufactured artificially can regulate the amplitude, phase, polarization and other parameters of electromagnetic waves through subwavelength metal or dielectric structures. The superlens regulates electromagnetic waves by regulating the radius of nanometer units. When light passes through a traditional lens, high-frequency components cannot pass due to the existence of evanescent waves. However, in the superlens, nanometer units are essentially light waveguides, and light propagating in the light waveguides can retain high-frequency components, thereby realizing super-resolution imaging. The design principle of nanometer units of the superlens follows the Mie resonance theory. Nanometer antennas composed of low-refractive-index materials can exhibit this effect when excited at the nanometer scale. However, the low-refractive-index materials have weak light confinement ability, resulting in high radiation loss and insignificant Mie resonance. In contrast, high-refractive-index nanometer antennas produce strong Mie resonance, strong electromagnetic field enhancement inside the nanometer antenna, improved transmittance and effective suppression of scattering. Therefore, the current superlens design structure mainly uses a SiO2 substrate, deposits high-refractive-index materials such as SiN (n=2), TiO2 (n=2.4), Si (n=3.8) on the substrate, and performs etching to form nanometer units. Some scholars have studied the reduction of nanometer unit scattering by optimizing the nanometer unit material and geometric parameters based on the Mie resonance theory and kerker condition. However, the reflection and scattering at the interface between the substrate and the nanometer unit and the interface between the nanometer unit and the exit medium are not considered.

[0003] The current superlens has generally low transmittance. The transmittance in the infrared band reaches 80%, and the transmittance in the visible band is only 48%, which greatly reduces the imaging quality and practicality. The transmittance can be greatly improved by designing a multilayer film structure on the substrate. For example, a distributed Bragg grating (DBR) structure in which two dielectric materials are alternately stacked can improve the transmittance at the design wavelength. However, the DBR structure 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

[0004] The present application aims to solve the problems of the prior art and provides the following solutions.

[0005] A multilayer composite superlens based on optical admittance theory optimization, comprising a substrate, a transition film layer and a nanometer unit array.

[0006] The substrate, the transition film layer and the nanometer unit array are arranged in sequence to form the multilayer composite superlens, and the nanometer unit array is composed of a plurality of nanometer units.

[0007] Preferably, the substrate adopts SiO2.

[0008] Preferably, the nano unit is a multilayer structure, which is composed of a high refractive index material layer, a middle refractive index material layer and a low refractive index material layer arranged in sequence.

[0009] The middle refractive index material layer adopts Al2O3, the refractive index is 1.37±0.02, and the thickness is designed to be 1 / 2λ0 based on the optical admittance theory, and λ0 is the design wavelength.

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

[0011] The low refractive index material layer adopts MgF2, the refractive index is 1.38±0.02, and the thickness is designed to be 1 / 4λ0 based on the optical admittance theory.

[0012] Preferably, the transition film layer is arranged between the substrate and the nano unit array, and adopts the structure of MgF2 and H4 titanium lanthanum mixture alternately stacked based on the optical admittance theory, and the thickness of each layer is 1 / 4λ0.

[0013] Compared with the prior art, the present application has the following beneficial effects:

[0014] The present application proposes a multilayer film structure antireflection transmission super lens, the nano unit is an Al2O3 (middle refractive index), TiO2 (high refractive index) and MgF2 (low refractive index) laminated structure, the substrate is SiO2, and MgF2 and H4 (titanium lanthanum mixture) alternating film layers are plated on both sides. The results show that the transmittance at the design wavelength of 600 nm reaches 89.31%, the transmittance in the wavelength range of 500-700 nm is higher than 74%, and the average transmittance reaches 82.01%. BRIEF DESCRIPTION OF DRAWINGS

[0015] In order to more clearly illustrate the technical solutions of the present application, the following briefly introduces the drawings needed in the embodiments. Obviously, the drawings described in the following only some embodiments of the present application, and for those skilled in the art, without creative labor, can also obtain other drawings according to these drawings.

[0016] Figure 1 It is a structure schematic diagram of the super lens of the embodiment of the present application.

[0017] Figure 2 It is a working principle diagram of the nano unit of the embodiment of the present application.

[0018] Figure 3 It is a schematic diagram of the optical admittance calculation principle of the embodiment of the present application.

[0019] Figure 4 A schematic diagram of effective refractive index and radius of the nanometer unit of the embodiment of the present application;

[0020] Figure 5 A schematic diagram of transmittance and reflectance of the nanometer unit of the embodiment of the present application, wherein (a) is a schematic diagram of a single-layer structure nanometer unit, (b) is a schematic diagram of a double-layer structure nanometer unit, and (c) is a schematic diagram of a three-layer structure nanometer unit;

[0021] Figure 6 A schematic diagram of phase of the nanometer unit of the embodiment of the present application, wherein (a) is a schematic diagram of a single-layer structure nanometer unit, (b) is a schematic diagram of a double-layer structure nanometer unit, and (c) is a schematic diagram of a three-layer structure nanometer unit;

[0022] Figure 7 A schematic diagram of transmittance and phase distribution simulation results of the nanometer unit of the embodiment of the present application, wherein (a) is a schematic diagram of transmittance of a single-layer structure nanometer unit, (b) is a schematic diagram of transmittance of a double-layer structure nanometer unit, (c) is a schematic diagram of transmittance of a three-layer structure nanometer unit, (d) is a schematic diagram of phase distribution of a single-layer structure nanometer unit, (e) is a schematic diagram of phase distribution of a double-layer structure nanometer unit, and (f) is a schematic diagram of phase distribution of a three-layer structure nanometer unit;

[0023] Figure 8 A schematic diagram of transmittance of the super-structured lens of the embodiment of the present application. DETAILED DESCRIPTION

[0024] The technical solutions in the embodiments of the present application will be apparently and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative labor fall within the protection scope of the present application.

[0025] In order to make the above-mentioned purposes, features and advantages of the present application more apparent and easy to understand, the present application will be further described in detail below with reference to the drawings and specific embodiments.

[0026] Embodiment one

[0027] In the present embodiment, as shown in the drawing, Figure 1 a multi-layer composite super-structured lens based on optical admittance theory optimization, comprising: a substrate, a transition film layer and a nanometer unit array; the substrate, the transition film layer and the nanometer unit array are arranged in sequence to constitute the multi-layer composite super-structured lens; the nanometer unit array is composed of a plurality of nanometer units.

[0028] The substrate is SiO2. The nano-unit is a multilayer structure, which is composed of a layer of medium-refractive-index material, a layer of high-refractive-index material and a layer of low-refractive-index material arranged in sequence; the layer of medium-refractive-index material is Al2O3, the refractive index of which is 1.37±0.02, and the thickness thereof is 1 / 2λ0 designed based on the optical admittance theory, wherein λ0 is the design wavelength; the layer of high-refractive-index material is TiO2, the refractive index of which is 2.5±0.05, and the thickness thereof is 3×1 / 2λ0 designed based on the optical admittance theory; the layer of low-refractive-index material is MgF2, the refractive index of which is 1.38±0.02, and the thickness thereof is 1 / 4λ0 designed based on the optical admittance theory. The transition film layer is arranged between the substrate and the nano-unit array, and is composed of MgF2 and H4 titanium lanthanum mixture alternately stacked, and the thickness of each layer is 1 / 4λ0.

[0029] In the embodiment, the working principle of the nano-unit of the super-structured lens is shown in Figure 2 The phase of light is modulated by the nano-unit, and the design is generally from the substrate to the nano-unit and then to air. When light is incident on the nano-unit from the substrate, strong reflection and scattering occur when the light-avoiding medium is incident on the light-dense medium.

[0030] According to the Fresnel formula, the reflectivity of the interfaces A and B of the nano-unit can be calculated as follows:

[0031] (1)

[0032] Wherein, R represents the reflectivity, r represents the 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 nano-unit is TiO2 (n=2.4), and the exit medium is air (n=1), the reflectivity of the interface A is 6.09% and the reflectivity of the interface B is 16.96% according to formula (1), and the actual nano-unit parameter scanning is lower. The transmission rate is improved and the reflection at the interface is reduced when the nano-unit height is designed as a half-wave plate. When the nano-unit height of the single-layer structure material is a half-wave plate, the transmission rate is improved and the reflection and scattering in the nano-unit are reduced by using different materials and composite multilayer nano-unit structure. The reflectivity and transmission rate of the multilayer medium are calculated by the optical admittance theory as shown in Figure 3 The calculation principle of the optical admittance is shown in s Wherein, η0 is the refractive index of the incident medium, and k layers of structure are provided, and the admittance Y can be calculated by the following formula:

[0034] (2)

[0035] Wherein, k0 represents the incident light wave vector, E0 represents the incident light electric field amplitude, j represents the jth layer of medium, i represents the imaginary unit, and δj represents the jth layer medium optical path, N j represents the jth layer refractive index, d j represents the jth layer thickness, η s represents the corrected substrate refractive index, E k represents the kth layer electric field, λ represents wavelength, B, C are simplified symbols in admittance representation, Y represents admittance, cosθ = 1 at normal incidence, n j = N j cosθ = N j .

[0036] The interface A between the substrate and the nano-unit has a reflectivity of 6.09%, and the interface B between the nano-unit and air has a reflectivity of 16.96%. The actual parameter scanning has a lower transmittance, and the transmittance and reflectance of the nano-unit are:

[0037] (3)

[0038] (4)

[0039] wherein η0represents the corrected air refractive index. When calculating the nano-unit transmittance through equation (2) and equation (4), the effective refractive index n eff of the nano-unit should be calculated. The effective refractive index of MgF2, TiO2, and Al2O3 in different radius nano-units under the fundamental mode is calculated by the finite-difference time-domain (fdtd) method, as shown in Figure 4 .

[0040] The nano-unit parameter scanning radius range is 0.05 μm~0.25 μm, and when the nano-unit radius is 0.15 μm, n eff is substituted into equation (2), (4) to calculate the nano-unit admittance and transmittance. The design wavelength λ0is taken as 600 nm. The design superlens improves the transmittance when the height of each layer of the nano-unit is an integer multiple of “one-fourth design wavelength” (1 / 4 λ0), as shown in (a), (b), and (c) in FIG. 5, which are the transmittance of the single-layer structure nano-unit, the double-layer structure nano-unit (high-low refractive index structure, 2HL), and the three-layer structure nano-unit (medium-high-low refractive index structure, 2M2HL) nano-unit in the 500-700 nm wavelength band. In the “2M2HL”, 2 represents that the thickness of the layer is 2 times 1 / 4 λ0, H, M, and L are high, medium, and low refractive index materials, and the substrates of the three structures are 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 base refractive index is represented. The meaning of each variable in formula (7) is consistent with formula (2). Figures (a), (b), (c) in Figure 6 show the phase of the single-layer nano unit, double-layer nano unit, and three-layer structure nano unit calculated by formula (7). The height of the TiO2 layer is 2H and 4H. The parameter scanning cannot cover 0-2π, so the height of the single-layer structure nano unit is replaced by 6H, and the height of the three-layer structure nano unit 2M2HL is replaced by 2M6HL when the parameter scanning is performed.

[0048] The transmittance and phase distribution of the single-layer structure (6H), double-layer structure (6HL), and three-layer structure (2M6HL) nano unit at different wavelengths and radii are shown in Figure 7. The height of the single-layer structure is consistent with the height of the 2M6HL structure nano unit, which is 823 nm. Figures (a), (b), and (c) in Figure 7 show the transmittance of the single-layer structure, 6HL structure, and 2M6HL structure nano unit. The average transmittance is 78.89%, 81.92%, and 85.11%, respectively. The average transmittance of the 2M6HL structure nano unit is 10.27% higher than that of the single-layer structure. Figures (d), (e), and (f) in Figure 7 show the phase parameter scanning of the single-layer structure, 6HL structure, and 2M6HL structure nano unit. The single-layer structure and 2M6HL structure can achieve 0-2π phase modulation. However, the 6HL structure exhibits phase jump in the wavelength range of 610-650 nm. As shown in Figure 7 (e), when the height of the nano unit is half a wave plate, the phase jump phenomenon occurs through geometric phase modulation, which cannot cover 0-2π. The propagation phase also exhibits similar behavior, and the phase does not change with the radius of the nano unit, which cannot cover 0-2π phase modulation.

[0049] In this embodiment, the substrate is fused quartz glass (Si02), which has a refractive index of 1.45 in the 500-700 nm wavelength band, and the size can be set according to the requirements. The low refractive index characteristics can be adapted to the impedance matching design of the subsequent transition film layer; the core structure of the nano unit adopts a 2M6HL multilayer structure (Al203 / Ti02 / MgF2) with a "medium-high-low" refractive index gradient, with a total height of 823 nm. Among them, the medium refractive index layer (Al203) has a refractive index of 1.37 at 600 nm, a thickness of 226 nm, the high refractive index layer (Ti02) is an amorphous structure, a refractive index of 2.4 at 600 nm, and a thickness of 450 nm, with a thickness error controlled within ±5 nm, and the low refractive index layer (MgF2) has a refractive index of 1.38 at 600 nm, a thickness of 147 nm; In order to further reduce the interface reflection, MgF2 (n=1.38) and H4 titanium lanthanum mixture (n=2.1) are added between the substrate and the nano unit; In terms of macro 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 500-700 nm visible light band. The phase distribution adopts a quadratic formula to correct the edge field aberration, and the dispersion is further optimized in a wide wavelength band by particle swarm optimization (PSO).

[0050] The Al203 / Ti02 / MgF2 "sandwich" structure antireflection transmission type superlens structure is shown in Figure 1 , wherein the optical thickness of Al203 is 1 / 2 x λ0, and the physical thickness is 1 / 2 / n eff1 x λ0, wherein λ0 is the design wavelength, n eff1 is the effective refractive index of the material (Al203); the optical thickness of Ti02 is 3 / 2 x λ0, and the physical thickness is 3 / 2 / n eff2 x λ0, wherein n eff2 is the effective refractive index of the material (Ti02); the optical thickness of MgF2 is 1 / 4 x λ0, and the physical thickness is 1 / 4 / n eff3 x λ0, n eff3 is the effective refractive index of the material (MgF2). MgF2 and H4 (titanium lanthanum mixture) are alternately stacked between the substrate and the nano unit. In addition, a quadratic phase distribution is designed to correct the edge field aberration, and the aberration is further optimized in the 500-700 nm wavelength band by particle swarm optimization (PSO), and finally an overall superlens is formed: radius 20 μm, focal length 140 μm, numerical aperture 0.14, total height of nano unit 823 nm (Al203 226 nm + Ti02 450 nm + MgF2 147 nm).

[0051] The overall transmittance of the superlens is shown in FIG. 8, and the average transmittance in the 500-700 nm wavelength band is 82.02%, and the transmittance at the design wavelength 600 nm is the highest, reaching 89.31%.

[0052] Embodiment two

[0053] In this embodiment, the feasibility of the design verification and auxiliary tool guarantee scheme is ensured by pre-calculating the effective refractive index n of the nanometer unit in the range of 0.05 μm to 0.25 μm radius by using the finite difference time domain (FDTD) software (such as Lumerical FDTD Solutions), and simulating the transmittance and reflectance and phase distribution of the multi-layer structure to ensure that the transmittance at the design wavelength of 600 nm is greater than or equal to 89% and the phase covers 0 to 2π, and the test equipment is selected according to the design target to ensure that the accuracy of the spectrometer (transmittance test accuracy ± 0.1%), atomic force microscope (AFM, topography resolution ≤ 0.1 nm), and laser confocal microscope (spot size test accuracy ± 0.05 μm) meets the verification requirements. eff (Select n of 0.15 μm radius eff for subsequent calculation), while simulating the transmittance and reflectance and phase distribution of the multi-layer structure to ensure that the transmittance at the design wavelength of 600 nm is greater than or equal to 89% and the phase covers 0 to 2π, and the test equipment is selected according to the design target to ensure that the accuracy of the spectrometer (transmittance test accuracy ± 0.1%), atomic force microscope (AFM, topography resolution ≤ 0.1 nm), and laser confocal microscope (spot size test accuracy ± 0.05 μm) meets the verification requirements.

[0054] The above-described embodiments are only descriptions of the preferred modes of the present application and do not limit the scope of the present application. Without departing from the design spirit of the present application, various modifications and improvements to the technical solutions of the present application made by those of ordinary skill in the art shall fall within the scope of protection determined by the claims of the present application.

Claims

1. A multilayer composite superlens based on optimization of optical admittance theory, characterized in that, The application relates to a multilayer composite superlens, which comprises a substrate, a transition film layer and a nano unit array. The substrate, the transition film layer and the nano unit array are sequentially arranged to form the multilayer composite superlens; the nano unit array is composed of a plurality of nano units. The substrate is made of SiO2. 2.The multi-layer composite meta-lens based on optical admittance theory optimization according to claim 1, wherein, The nano unit is a multilayer structure, which is sequentially arranged by a medium refractive index material layer, a high refractive index material layer and a low refractive index material layer. 3.The multi-layer composite meta-lens based on optical admittance theory optimization according to claim 1, wherein, The medium refractive index material layer is made of Al2O3, the refractive index is 1.37+ / -0.02, the thickness is 1 / 2 lambda0 based on optical admittance theory, and lambda0 is a design wavelength. The high refractive index material layer is made of TiO2, the refractive index is 2.5+ / -0.05, the thickness is 3*1 / 2 lambda0 based on optical admittance theory. The low refractive index material layer is made of MgF2, the refractive index is 1.38+ / -0.02, and the thickness is 1 / 4 lambda0 based on optical admittance theory. The transition film layer is arranged between the substrate and the nano unit array, and is made of MgF2 and H4 titanium lanthanum mixture which are alternately stacked based on optical admittance theory, and the thickness of each layer is 1 / 4 lambda0.

4. The multi-layer composite meta-lens based on optical admittance theory optimization according to claim 3, characterized in that, ​

Images