High-efficiency super lens based on refractive index matching and design method thereof

Abstract

The invention relates to a high-efficiency super lens based on refractive index matching and a design method thereof. The super lens comprises a super atom structure layer and a bonding substrate layer on any surface, the difference value between the refractive index of any substrate layer and the average effective refractive index of the super-atomic structure layer is smaller than a preset value; when the super lens is designed, the relation among the average effective refractive index, the impedance and the S parameter of the super-atom structure layer is constructed, the structure parameter of the super-atom structure layer is determined based on the requirement parameter of the super lens, the preset S parameter of the super-atom structure layer is obtained based on electromagnetic simulation, and the average effective refractive index of the super-atom structure layer is calculated. And the substrate layer is used as an expected refractive index matching material and is bonded on one surface or two surfaces of the super-atomic structure layer. According to the invention, the high-efficiency super lens is obtained by using the principle of refractive index matching and processing methods such as large-area bonding, the focusing efficiency of the super lens is greatly improved, the application of the super lens is promoted, and the leap-type upgrading of optical devices in the dimensions of light weight and high performance is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of optical elements, systems or instruments, and in particular to a high-efficiency metalens based on refractive index matching and a design method thereof. Background Art

[0002] Metalens is a new type of optical device based on metasurface technology. It is composed of subwavelength nanostructures, such as nanoantennas or metastructure units. Unlike traditional refractive lenses that rely on curved surface shapes to control light waves, metalens precisely control the phase, amplitude and polarization of light by regulating artificial microstructures such as the size and rotation angle of nanostructures to realize the function of a planar lens, significantly reducing the thickness and weight of the optical system and achieving ultra-thin, lightweight, high-performance optical focusing and imaging.

[0003] However, existing metalens technology still has some problems, such as chromatic aberration and efficiency issues, which greatly hinder its practical application. Many solutions have been proposed to address the chromatic aberration problem, such as phase compensation based on chromatic aberration technology, Taylor formula expansion, dispersion-phase space method, and discrete multi-wavelength achromatic aberration method. These achromatic aberration solutions require finding a large number of qualified superatomic structures. However, the transmittance of superatomic structures of different sizes and shapes generally fluctuates, which will significantly reduce the overall focusing efficiency of the metalens. Traditional solutions to improve the efficiency of metalens mainly include optimizing the materials, shape, and arrangement of the metalens unit structure. These methods can only optimize metalens for specific wavelengths and functions, limiting their scope of application. In addition, some scholars have used the Huygens principle to design high-transmittance metalens. When the magnetic dipole and electric dipole meet specific resonance conditions, theoretically, 100% transmission efficiency will be achieved. However, few superatomic structures meet these conditions, and the phase continuity of the metalens is poor, typically only achieving a phase gradient of ≤4, resulting in low focusing efficiency of the resulting metalens. Therefore, it is very necessary to design high-quality metalenses with high focusing efficiency.

[0004] In order to achieve a high-focusing-efficiency metalens, several factors need to be met, including:

[0005] (1) High transmittance; specifically, the transmittance of each super-atom structure in the metalens is high and the transmittance variance is small, which avoids the situation where the metalens generates multiple focal points in the z direction due to the large variance of the transmittance, thereby reducing the focusing efficiency of the metalens;

[0006] (2) The phase of each meta-atom in the metalens needs to satisfy the variation of 0-2π and have a certain phase continuity (phase gradient ≥ 8).

[0007] The focusing efficiency of most traditional metalenses can only reach about 80%. On the one hand, since traditional metalenses generally select a medium with a high refractive index as the material, there is a large refractive index difference between the substrate and the metasurface structure layer, and between the structure layer and free space. According to the Fresnel principle, the dielectric layer is equivalent to an equivalent refractive index thin film. According to the Fresnel formula, the larger the refractive index difference between adjacent materials, the lower the transmittance. On the other hand, since the meta-atom structures of metalenses are all sub-wavelength in size, incident light is prone to cause mode resonance after incidence. When the structure size satisfies the mode resonance condition, the transmittance will show obvious fluctuations, which is very disadvantageous for the design of metalenses. Summary of the Invention

[0008] The present invention solves the problems existing in the prior art and provides a high-efficiency metasurface based on refractive index matching and its design method.

[0009] The technical solution adopted by the present invention is a high-efficiency metasurface based on refractive index matching. The metasurface includes a meta-atom structure layer, and a substrate layer is bonded to any surface of the meta-atom structure layer; the difference between the refractive index of any substrate layer and the average equivalent refractive index of the meta-atom structure layer is less than a preset value.

[0010] Preferably, the preset value is less than 0.5.

[0011] Preferably, substrate layers are bonded to both the top surface and the bottom surface of the meta-atom structure layer.

[0012] Preferably, an anti-reflection film is coated on the surface of any substrate layer facing away from the meta-atom structure layer. <s

[0013] A design method for the high-efficiency metasurface based on refractive index matching as described above, the design method includes the following steps:

[0014] S1.1 Establish the relationship between the average equivalent refractive index n of the meta-atom structure layer and the S parameters;

[0015] S1.2 Determine the structural parameters of the meta-atom structure layer based on the required parameters of the metasurface;

[0016] S1.3 Obtain the S parameters of the preset meta-atom structure layer based on electromagnetic simulation;

[0017] S1.4 Calculate the average equivalent refractive index n of the meta-atom structure layer based on the structural parameters and S parameters of the meta-atom structure layer;

[0018] S1.5 Use the average equivalent refractive index n as the desired refractive index, match the material as the substrate layer, and bond it to one or both sides of the meta-atom structure layer.

[0019] Preferably, in S1.1, the relationship between the equivalent refractive index n of any dielectric monomer in the superatom structure layer and the S parameter satisfies that

[0020]

[0021] where k is the wave number, d is the thickness of the dielectric monomer, and S21 and S11 are S parameters.

[0022] Preferably, in S1.2, the required parameters of the superlens include the working band of the superlens, the refractive index of the superlens, and the polarization characteristics, and the structural parameters include the shape, period, and thickness of the superatom structure layer; in practical applications, in addition to the thickness, the shape and period will also affect the S parameter, that is, they will affect the equivalent refractive index.

[0023] Preferably, in S1.5, the substrate layer is bonded to both sides of the superatom structure layer.

[0024] Preferably, the difference between the refractive index of the matching material and the average equivalent refractive index n is less than 0.5.

[0025] Preferably, the method further includes: S1.6 coating an antireflection film on the bonded substrate layer.

[0026] The present invention relates to a high-efficiency superlens based on refractive index matching and its design method. The superlens includes a superatom structure layer, and a substrate layer is bonded to any one side of the superatom structure layer; the difference between the refractive index of any substrate layer and the average equivalent refractive index of the superatom structure layer is less than a preset value; when designing the superlens, the relationship between the average equivalent refractive index n, impedance z, and S parameter of the superatom structure layer is constructed, the structural parameters of the superatom structure layer are determined based on the required parameters of the superlens, the S parameter of the preset superatom structure layer is obtained based on electromagnetic simulation, the average equivalent refractive index n of the superatom structure layer is calculated, the average equivalent refractive index n is used as the desired refractive index, the matching material is used as the substrate layer, and bonding is performed on one or both sides of the superatom structure layer.

[0027] The technical principle of the present invention is that, according to Maxwell's equations and boundary conditions, in the case of a periodic interface, the traditional Fresnel theorem is supplemented. When an s-wave is incident, it can be obtained that when the refractive index of the transmission layer is greater than the refractive index of the incident layer, the transmittance has a maximum value. The curve of the equivalent refractive index varying with the radius of the dielectric column is calculated using the S parameter method, and the average equivalent refractive index of the superlens is calculated, so as to determine the range of the equivalent refractive index required for the substrate layer. Considering that the value of the optimal refractive index required for the substrate layer is related to the wavelength, period, incident angle, etc., parameter scanning is performed within this range to determine the optimal refractive index of the substrate layer.

[0028] The beneficial effects of the present invention are as follows: By using the principle of refractive index matching, the optimal refractive index of the substrate layer is calculated and optimized, and the superlens dielectric columns arranged according to a certain arrangement rule are combined with the substrate layer by processing methods such as large-area bonding to obtain a high-efficiency superlens; the focusing efficiency of the superlens is greatly improved, promoting its applications in fields such as AR / VR, high-resolution imaging, and laser processing, and realizing a leapfrog upgrade of optical devices in terms of lightweight and high performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 It is a schematic diagram of the superlens structure of the present invention;

[0030] Figure 2 It is a flowchart of the design method of the present invention;

[0031] Figure 3 It is a curve of the equivalent refractive index of a single dielectric unit in the superatom structure layer changing with the radius of the superatom structure layer in the experimental example of the present invention;

[0032] Figure 4 It is a diagram of the change of the transmission field phase with the radius of the unit structure when the refractive index of the substrate layer changes in the experimental example of the present invention;

[0033] Figure 5 It is the transmission efficiency curve of the superlens under different substrate layer conditions in the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0034] The following further describes the present invention in detail with reference to embodiments, but the protection scope of the present invention is not limited thereto.

[0035] The present invention relates to a design method of a high-efficiency superlens based on refractive index matching. The technical principle derivation of this method is as follows:

[0036] The equivalent electromagnetic parameters, also known as constitutive parameters (equivalent permittivity and equivalent permeability), are an important technical index for studying the electromagnetic characteristics of metamaterials. The S-parameter inversion method is an efficient and concise method for extracting equivalent electromagnetic parameters. Essentially, it extracts the permittivity and permeability from the data of the reflection coefficient S11 and the transmission coefficient S21; for a uniform dielectric plate with a thickness of d placed in free space, its S parameters satisfy S11 = S22, S21 = S12, and its transmission matrix T can be defined as , where , E and H respectively represent the electric field and the magnetic field, and the transmission matrix T is:

[0037] (1)

[0038] Among them, is the effective refractive index, is the impedance, and the relationship between ( ) and ( ) is , is the wave number, is the wavelength; thus, the S-parameters of the metamaterial (metaatom structure layer 1) can be obtained as:

[0039] (2)

[0040] (3)

[0041] Based on this, the relationship between the equivalent refractive index n, impedance z, and S-parameters can be obtained as:

[0042] (4)

[0043] (5)

[0044] Therefore, the S-parameters of the superlens can be obtained by using electromagnetic simulation methods such as FDTD or RCWA. Furthermore, according to the Fresnel formula, when the s / p wave is incident, the reflection / transmission coefficients are respectively:

[0045] (6)

[0046] (7)

[0047] (8)

[0048] (9)

[0049] Among them, and respectively represent the refractive indices of the incident layer and the transmission layer, and respectively represent the incident angle and the exit angle; according to formulas (6)-(9), when the difference between and is small enough (less than ०.5), the transmission coefficients Ts and Tp tend to 1; that is, when the equivalent refractive index of the superlens is obtained, a material with a refractive index close to it can be used to replace the substrate layer 2 of the superlens by bonding to improve the overall efficiency of the superlens.

[0050] In this context, the design method of the present invention includes the following steps:

[0051] S1.1 Establish the relationship between the average equivalent refractive index n, impedance z, and S-parameters of the metaatom structure layer 1;

[0052] In S1.1, the relationship between the equivalent refractive index n of any dielectric monomer in the superatom structure layer 1 and the S parameters satisfies that

[0053]

[0054] where k is the wave number, d is the thickness of the dielectric monomer, and S21 and S11 are the S parameters.

[0055] In practical applications, the average equivalent refractive index of the superatom structure layer 1 is calculated based on the equivalent refractive indices of the dielectric monomers at different positions, which is easy for those skilled in the art to understand, and those skilled in the art can calculate it according to their needs.

[0056] S1.2 Determine the structural parameters of the superatom structure layer 1 based on the required parameters of the superlens;

[0057] In S1.2, the required parameters of the superlens include the working wavelength band of the superlens, the refractive index of the superlens, and the polarization characteristics, and the structural parameters include the shape, period, and thickness of the superatom structure layer 1.

[0058] S1.3 Obtain the S parameters of the preset superatom structure layer 1 based on electromagnetic simulation;

[0059] S1.4 Calculate the average equivalent refractive index n of the superatom structure layer 1 based on the structural parameters and S parameters of the superatom structure layer 1;

[0060] S1.5 Use the average equivalent refractive index n as the desired refractive index, match the material as the substrate layer 2, and bond it on one or both sides of the superatom structure layer 1.

[0061] In S1.5, the substrate layer 2 is bonded to both sides of the superatom structure layer 1.

[0062] In the present invention, generally, a layer of refractive index matching material is bonded to the upper and lower surfaces of the superatom structure layer 1 as the substrate layer 2 to improve the efficiency of the superlens.

[0063] The difference between the refractive index of the matching material and the average equivalent refractive index n is less than 0.5.

[0064] Further, the method further includes: S1.6 Coat an antireflection film 3 on the bonded substrate layer 2.

[0065] In the present invention, the antireflection film 3 is used to reduce the interface reflection between the air and the substrate, and further improve the efficiency of the superlens.

[0066] Accordingly, the present invention relates to a high-efficiency superlens based on refractive index matching. The superlens includes a superatom structure layer 1, and a substrate layer 2 is bonded to any surface of the superatom structure layer 1; the difference between the refractive index of any substrate layer 2 and the average equivalent refractive index of the superatom structure layer 1 is less than a preset value.

[0067] In the present invention, the superatom structure layer 1 includes arrayed superatom unit bodies. Considering that a cylindrical superlens has a polarization-insensitive effect, a cylindrical structure is generally adopted; in practical applications, the radius setting of each superatom unit body will affect the S parameters, so it is necessary to use electromagnetic simulation algorithms such as FDTD or RCWA to calculate the relationship between the two and obtain the optimal value.

[0068] The preset value by which the difference between the refractive index of any substrate layer 2 and the average equivalent refractive index of the superatom structure layer 1 is less than is less than 0.5. Obviously, it is greater than 0.

[0069] Substrate layers 2 are bonded to both the top surface and the bottom surface of the superatom structure layer 1.

[0070] An antireflection film 3 is coated on the surface of any substrate layer 2 facing away from the superatom structure layer 1.

[0071] In the present invention, in order to verify the feasibility of the solution, the following experimental examples are proposed.

[0072] Experimental Example 1

[0073] Taking a polarization-insensitive diamond superlens in the 1030 nm band as an example, the efficiency of the traditional method and the superlens of the present invention is compared; since the superlens needs to be polarization-insensitive, the superatom unit body is set to be cylindrical, the lattice size is 500 nm, and the height of the dielectric column is 1200 nm;

[0074] According to the S parameters, the curve of the equivalent refractive index changing with the radius of the superatom unit body is as Figure 3 shown. As the radius (abscissa) increases, its equivalent refractive index (ordinate) also increases, which conforms to the actual law;

[0075] Calculate the curve of the phase of the transmission field changing with the radius, as Figure 4 shown, showing the change diagram of the transmission field phase with the superatom unit body when the refractive index of the substrate layer 2 changes from 1 to 2.4; it can be seen from the figure that the refractive index of the substrate layer 2 does not affect the change range of the transmission field phase (both satisfy the change range of 0 - 2π), that is to say, the refractive index of the substrate layer 2 has little effect on the overall phase distribution of the lens (has no effect on the focal length f of the superlens), and only affects its efficiency;

[0076] Under the premise that the dielectric pillars of the metalens satisfy 0 - 2π, considering factors such as the aspect ratio of the metalens, the range of the dielectric pillar radius is selected as 50nm - 200nm as the variation range of the dielectric pillars of the metalens.

[0077] Experimental Example 2

[0078] Based on Experimental Example 1, the efficiency curves of metalenses in different situations are proposed, such as Figure 5 shown Figure 5 In it, (a) is the design scheme of the traditional metalens, that is, directly etching the metalens structure on the diamond substrate. This method has the simplest process flow. However, as can be seen from the results in the figure, in the radius variation range of 50nm - 200nm, even with the AR film (anti-reflection film 3) coated, its average efficiency is poor, and the variance of the transmittance is large, which will greatly affect the focusing efficiency of the metalens; (b) and (c) are the transmittance distributions after optimizing the diamond metasurface structure using the refractive index matching scheme, which are the single-layer refractive index matching and double-layer refractive index matching schemes respectively. As can be seen from the results, after designing the metasurface using the refractive index matching scheme, its transmittance in the 50nm - 200nm range is significantly improved, and the variance is also greatly reduced, and the double-layer scheme is better than the single-layer scheme. However, in practice, it is impossible to find a processing material with a refractive index of 1.25;

[0079] It should be noted that since the metasurface unit structure is a sub-wavelength structure, the mode resonance phenomenon generated thereby cannot be avoided, which is also an important reason for the different refractive index values required for the double-layer scheme and the single-layer scheme. In practical applications, it is necessary to determine whether to use the single-layer scheme or the double-layer scheme according to the refractive index of the actual material.

[0080] Although the preferred embodiments of the present invention have been described, those skilled in the art can make additional changes and modifications to these embodiments once they know the basic creative concept. Therefore, the appended claims are intended to be interpreted to include the preferred embodiments and all changes and modifications falling within the scope of the present invention.

[0081] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention is also intended to include these modifications and variations.

Claims

1. A high-efficiency metalens based on refractive index matching, characterized in that: The superlens includes a superatom structure layer, and a substrate layer is bonded to any surface of the superatom structure layer; the difference between the refractive index of any one of the substrate layers and the average equivalent refractive index of the superatom structure layer is less than a preset value.

2. The high-efficiency superlens based on refractive index matching according to claim 1, wherein: The preset value is less than 0.

5.

3. The high-efficiency superlens based on refractive index matching according to claim 1, wherein: Substrate layers are bonded to both the top surface and the bottom surface of the superatom structure layer.

4. The high-efficiency superlens based on refractive index matching according to claim 1, wherein: An anti-reflection film is coated on the surface of any one of the substrate layers facing away from the superatom structure layer.

5. A design method of a high-efficiency superlens based on refractive index matching according to any one of claims 1 to 4, characterized in that: The design method includes the following steps: S1.1 Establish the relationship between the average equivalent refractive index n, impedance z, and S parameters of the superatom structure layer; S1.2 Determine the structural parameters of the superatom structure layer based on the required parameters of the superlens; S1.3 Obtain the S parameters of the preset superatom structure layer based on electromagnetic simulation; S1.4 Calculate the average equivalent refractive index n of the superatom structure layer based on the structural parameters and S parameters of the superatom structure layer; S1.5 Use the average equivalent refractive index n as the desired refractive index, match the material as the substrate layer, and bond it to one or both sides of the superatom structure layer.

6. The design method according to claim 5, characterized in that: In S1.1, the relationship between the equivalent refractive index n and the S parameters of any one of the dielectric monomers in the superatom structure layer satisfies ， where k is the wave number, d is the thickness of the dielectric monomer, and S21 and S11 are the S parameters.

7. The design method according to claim 5, characterized in that: In S1.2, the required parameters of the superlens include the working band of the superlens, the refractive index of the superlens, and the polarization characteristics, and the structural parameters include the shape, period, and thickness of the superatom structure layer.

8. The design method according to claim 5, characterized in that: In S1.5, the substrate layer is bonded to both sides of the superatom structure layer.

9. The design method according to claim 5, characterized in that: The difference between the refractive index of the matching material and the average equivalent refractive index n is less than 0.

5.

10. The design method according to claim 5, wherein: The method further includes: S1.6 Coat an anti-reflection film on the bonded substrate layer.

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