A design method of a metasurface planar lens

Abstract

The application discloses a design method of a metasurface plane lens and belongs to the technical field of nano optics, and particularly relates to the following steps: first, constructing a micro-element structure unit, taking the conversion efficiency greater than 95% as a target, and designing an optimal micro-element structure unit; based on the optimal micro-element structure unit, simulating and constructing a metasurface plane structure, and calculating the deflection angle of all micro-nano structures; intercepting multiple sub-fan structures with different central angles in the metasurface plane structure, simulating and constructing the sub-lenses corresponding to each sub-fan structure based on the specific size and deflection angle of the optimal micro-element structure unit, and performing far-field focusing; selecting the sub-lens with the maximum half-height value of the electric field intensity at the focal point as the fan-shaped lens; and finally, obtaining the metasurface plane lens by co-center splicing the multiple fan-shaped lenses in the clockwise or counterclockwise direction. The application guarantees the focusing efficiency and imaging effect, takes into account the macro-scale demand of a practical lens, reduces the computer resource consumption in the simulation process, and is more practical.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of nano-optics, and particularly relates to a design method of a metasurface planar lens. BACKGROUND

[0002] Electromagnetic metamaterials based on artificial micro-nano structures have attracted attention of scholars in the fields of electromagnetism, physics and materials due to their electromagnetic / optical characteristics (such as negative refraction) which traditional natural materials do not have, and the unique characteristics of arbitrary control of electromagnetic parameters. By constructing a spatial refractive index gradient through artificial sophisticated metamaterials, the deflection of a wave beam can be achieved.

[0003] Everything has two sides, and metamaterials are no exception. Metamaterials have high sensitivity to ohmic loss, and it is difficult to process three-dimensional metamaterial structures working in the visible light band, which to a large extent limits the further development and application of three-dimensional metamaterials. Therefore, people have thought of a simplified version of the structure - metasurface, which is a two-dimensional metamaterial structure, greatly reducing the difficulty of processing, making it easier to become practical. The advantage of metasurface is to break through the shackles of the traditional three-dimensional metamaterial body structure, and to construct various structures which are easier to prepare using existing technology, showing superiority in controlling phase, amplitude, polarization and impedance, and having broad application prospects.

[0004] Since the birth of metasurface, it has been developing towards the direction of improving the applicability. Due to its novel physical mechanism, rich physical image, flexible structure design and other characteristics, researchers have successively proposed many novel optical devices, including planar lenses, polarizers, absorbers and the like. Among them, the metasurface planar lens is the main object of study in the present application. So far, in the design process of the metasurface planar lens, a periodic structure with a phase gradient composed of a plurality of micro-structure units needs to be constructed. The spatial phase represented by the azimuth angle of the micro-nano structure on each micro-structure unit needs to be calculated one by one with the aid of simulation software, thereby forming a database. The azimuth angle of the micro-nano structure of all micro-structure units distributed on the metasurface planar lens is selected from the database according to the set phase gradient, and the azimuth angle of the micro-nano structure of all micro-structure units distributed on the metasurface planar lens is selected from the database according to the set phase gradient. Obviously, it is not conducive to the popularization of the technology to practicality that astronomical number of micro-structure unit arrangement design data need to be processed when constructing a complete metasurface lens. SUMMARY

[0005] The purpose of the present application is to solve the problems in the prior art, and to provide a design method of a metasurface planar lens, which greatly reduces the consumption of computer resources and running time in the simulation design process while meeting the demand of macro scale (diameter of millimeter level).

[0006] The technical scheme adopted by the present application is as follows:

[0007] The application discloses a design method of a metasurface plane lens.

[0008] Step 1, constructing a micro-element structure unit, including a cuboid base and a micro-nano structure of a cuboid located at the center of the cuboid base; the optimal cuboid base size and micro-nano structure size are designed to obtain an optimal micro-element structure unit with a conversion efficiency greater than 95%.

[0009] Step 2, a metasurface plane structure with a radius R is simulated and constructed by closely arranging a plurality of optimal micro-element structure units in an XOY two-dimensional plane, and the deflection angle of the micro-nano structure in each optimal micro-element structure unit is calculated according to the center coordinates of the micro-nano structure.

[0010] Step 3, in the metasurface plane structure with known deflection angles of all micro-nano structures, a plurality of sub-fan structures with a radius R and different central angles are intercepted, and a sub-lens corresponding to each sub-fan structure is simulated and constructed based on the specific size and deflection angle of the optimal micro-element structure unit, and the sub-lens is subjected to far-field focusing, and a sub-lens with a maximum half-value of electric field intensity at a focal point is selected as a fan lens, and the central angle corresponding to the fan lens is wherein the central angle of each sub-fan structure is required to be an integral multiple of 360°, and the central angle is not more than 12°.

[0011] Step 4, the fan lenses are circularly spliced in a clockwise or counterclockwise direction to finally obtain a metasurface plane lens.

[0012] Further, the material of the cuboid base is SiO2, and the material of the micro-nano structure is TiO2.

[0013] Further, the size of R is not limited, and can even be greater than 600 μm, and finally a macro-scale (diameter is millimeter level) metasurface plane lens is obtained.

[0014] Further, the center of the metasurface plane structure in step 2 is the origin O of the XOY two-dimensional plane, and the deflection angle θ(x, y) of the bottom long side of each micro-nano structure relative to the X-axis in the metasurface plane structure is calculated assuming that the center coordinates of the micro-nano structure are (x, y).

[0015]

[0016] wherein λ is the wavelength of incident light, and f is the focal length of incident light.

[0017] Further, the focal length f of incident light is nR / NA; wherein n is a spatial refractive index, and NA is a preset numerical aperture of the metasurface plane lens.

[0018] Further, the base length of the bottom surface of the cuboid base of the optimal microelement structure unit is λ / 2~λ, and the thickness is λ~3λ / 2.

[0019] The present application has the following beneficial effects:

[0020] The present application provides a design method of a metasurface plane lens, which comprises the following steps: first, designing a fan-shaped lens with the maximum half-height numerical value (i.e., the optimal focusing efficiency of the lens), and then splicing the fan-shaped lenses one by one to form a metasurface plane lens with a macro scale (with a diameter of millimeter level). The design method provided by the present application takes into account the demand for large-area distribution and macro scale of practical lenses on the basis of ensuring the focusing efficiency and imaging effect of the metasurface plane lens, and more importantly, greatly reduces the consumption of computer memory and running time in the simulation design process, and is more practical. BRIEF DESCRIPTION OF DRAWINGS

[0021] Figure 1 Fig. 1 is a three-dimensional structure diagram of a microelement structure unit in embodiment 1 of the present application;

[0022] Figure 2 Fig. 2 is a conversion efficiency diagram of an optimal microelement structure unit in embodiment 1 of the present application;

[0023] Figure 3 Fig. 3 is a discretization phase distribution diagram of a central part of a metasurface plane structure in embodiment 1 of the present application;

[0024] Figure 4 Fig. 4 is a size schematic diagram of a fan-shaped lens in embodiment 1 of the present application;

[0025] Figure 5 Fig. 5 is an electric field intensity distribution result of a focal point of a sub-lens with a central angle of 6° in embodiment 1 of the present application in the X-axis direction;

[0026] Figure 6 Fig. 6 is an electric field intensity distribution result of a focal point of a sub-lens with a central angle of 6° in embodiment 1 of the present application in the Y-axis direction;

[0027] Figure 7 Fig. 7 is an electric field intensity distribution result of a focal point of a sub-lens with a central angle of 6° in embodiment 1 of the present application in the Z-axis direction;

[0028] Figure 8 Fig. 8 is a top view of a metasurface plane lens in embodiment 1 of the present application;

[0029] Figure 9 Fig. 9 is an enlarged view of an edge part of a metasurface plane lens in embodiment 1 of the present application;

[0030] Figure 10 Fig. 10 is a raw image for simulation imaging in embodiment 1 of the present application;

[0031] Figure 11The effect diagram of simulating imaging by using the metasurface planar lens in embodiment 1 of the present application. DETAILED DESCRIPTION

[0032] In order to make the objects, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application.

[0033] Embodiment 1

[0034] The present embodiment provides a design method of a metasurface planar lens working at a wavelength of 532 nm, which specifically comprises the following steps:

[0035] Step 1, constructing a micro-unit structure as shown in Figure 1 The micro-unit structure includes a cuboid substrate with SiO2 as the material and a micro-nano structure in the center of the cuboid substrate above, and the material of the micro-nano structure is TiO2; the optimal cuboid substrate size and micro-nano structure size are designed to achieve a conversion efficiency of the micro-unit structure greater than 95%, and the optimal micro-unit structure is obtained.

[0036] In the present embodiment, the cuboid substrate is designed as a subwavelength structure, which requires that the bottom side length S of the cuboid substrate is λ / 2~λ, and the thickness W is λ~3λ / 2, and the optimal cuboid substrate size is S=300nm and W=800nm; on this basis, the micro-nano structure size meeting the conversion efficiency greater than 95% is designed, and according to multiple simulation experiments, when the length, width and height of the micro-nano structure are 160nm, 60nm and 500nm respectively, the conversion efficiency is 97.9%; when the length, width and height of the micro-nano structure are 145nm, 70nm and 500nm respectively, the conversion efficiency is 98.3%; when the length, width and height of the micro-nano structure are 180nm, 75nm and 500nm respectively, the conversion efficiency is 98.1%; by adjusting the length, width and height, multiple micro-nano structures with different sizes are also designed, and the conversion efficiency of the micro-unit structure is calculated; finally, the length, width and height of the selected micro-nano structure are 150nm, 45nm and 500nm respectively, and the conversion efficiency is as high as 98.7%, as shown in Figure 2 .

[0037] Step 2, simulating and constructing a metasurface planar structure with a radius R by closely arranging multiple optimal micro-unit structures in an XOY two-dimensional plane, the center of the metasurface planar structure is the origin of the XOY two-dimensional plane, and the center coordinates of the micro-nano structure in each optimal micro-unit structure in the metasurface planar structure are (x, y), and since the phase distribution φ(x, y) of each micro-nano structure in the focusing lens satisfies:

[0038]

[0039] Further, the phase distribution of all micro-nano structures on the metasurface plane structure can be calculated by simulation, as shown in Figure 3 According to the PB (Pancharatnam-Berry) phase theory, the deflection angle θ(x, y) of the long side of the bottom surface of each micro-nano structure in the metasurface plane structure relative to the X-axis direction can be calculated as follows:

[0040]

[0041] wherein λ is the wavelength of the incident light; f is the focal length of the incident light, f = nR / NA; wherein n is the spatial refractive index; and NA is the numerical aperture of the preset metasurface plane lens, and in the present embodiment, NA = 0.8, so f = 750 μm;

[0042] In the present embodiment, R = 600 μm.

[0043] Step 3. In the metasurface plane structure in which the deflection angles of all micro-nano structures are known, a plurality of sub-fan structures with a radius of R and different central angles are intercepted, and based on the specific size and deflection angle of the optimal micro-element structure unit, a sub-lens corresponding to each sub-fan structure is simulated and constructed, and the sub-lens is subjected to far-field focusing, and the sub-lens with the maximum numerical value of the half-height value of the electric field intensity at the focal point is selected as the fan lens, and the central angle corresponding to the fan lens is wherein it is required that the central angle of each sub-fan structure can be divided by 360°;

[0044] In the present embodiment, the sub-fan structures with central angles of 3°, 6°, 12°, 20° and 45° are intercepted, and since the time for simulating and constructing the corresponding sub-lenses based on the specific size and deflection angle of the optimal micro-element structure unit is too long for the sub-fan structures with central angles of 20° and 45°, they are not selected. The sub-lenses of the sub-fan structures with central angles of 3°, 6° and 12° are subjected to far-field focusing, and the half-height values of the electric field intensity at the focal points are obtained, and it is found that the half-height value of the electric field intensity at the focal point of the sub-lens with a central angle of 6° is larger than that of the sub-lens with a central angle of 3° or 12°, wherein for the sub-lens with a central angle of 6°, the electric field intensity distribution results of the focal point in the X-axis direction, Y-axis direction and Z-axis direction are as shown in Figures 5 to 7 Therefore, in the present embodiment, the sub-lens with a central angle of 6° is selected as the fan lens, as shown in Figure 4

[0045] Step 4. The fan lenses are circularly spliced in the clockwise or counterclockwise direction, and finally a macro-scale (with a diameter of millimeter level) metasurface plane lens as shown in Figure 8 is obtained, and the enlarged view of the edge portion of the metasurface plane lens is as shown in Figure 9 It can be seen that the macro-scale metasurface plane lens is composed of a plurality of micro-element structure units with different deflection angles of micro-nano structures. ​

[0046] The focusing efficiency p of the designed metasurface planar lens at a single wavelength of 532 nm is 39.7%, and under this efficiency, a simulation optical system is established for imaging performance evaluation of the metasurface planar lens. Through simulation test, a simulation imaging result graph of the original image is obtained, as shown in Figure 10 Figure 11

[0047] The above embodiments only illustrate the principles and advantages of the present application, and are not used to limit the present application. In order to help understand the principles of the present application, the protection scope of the present application is not limited to the above configurations and embodiments. Those skilled in the art can make other various specific modifications and combinations without departing from the essence of the present application according to the disclosed technology, and still within the protection scope of the present application.​​

Claims

1. A method of designing a metasurface planar lens, characterized in that, The method comprises the following steps: Step 1, constructing a micro-element structure unit, comprising a cuboid base and a micro-nano structure of a cuboid located at the center above the cuboid base; With the conversion efficiency of the micro-element structure unit being greater than 95% as the target, the optimal cuboid base size and micro-nano structure size are designed to obtain an optimal micro-element structure unit; Step 2, by closely arranging a plurality of optimal micro-element structure units in an XOY two-dimensional plane, a metasurface plane structure with a radius R is simulated and constructed, and according to the center coordinates of the micro-nano structures in each optimal micro-element structure unit, the deflection angles of the corresponding micro-nano structures are calculated; Step 3, in the metasurface plane structure in which the deflection angles of all micro-nano structures are known, a plurality of sub-fan structures with a radius R and different central angles are intercepted, based on the specific size and deflection angle of the optimal micro-element structure unit, a sub-lens corresponding to each sub-fan structure is simulated and constructed, and the sub-lens is subjected to far-field focusing, and the sub-lens with the maximum half-value of electric field intensity at the focal point is selected as the fan-shaped lens, and the corresponding central angle is wherein it is required that the central angle of each sub-fan structure can be divided by 360°, and the central angle is not more than 12°. Step 4, the Fan-shaped lenses are co-centered in the clockwise or counterclockwise direction, and finally a metasurface planar lens is obtained.

2. The method of designing a metasurface planar lens according to claim 1, wherein, The material of the cuboid base is SiO2, and the material of the micro-nano structure is TiO2.

3. The method of designing a metasurface planar lens according to claim 1, wherein, The center of the metasurface plane structure in step 2 is the origin O of the XOY two-dimensional plane, and assuming that the center coordinates of the micro-nano structure are (x, y), the deflection angle θ(x, y) of the long side of the bottom surface of each micro-nano structure relative to the X-axis in the metasurface plane structure is calculated: Wherein, λ is the wavelength of the incident light; f is the focal length of the incident light.

4. The method of designing a metasurface planar lens according to claim 1, wherein, The bottom side length of the cuboid base in the optimal micro-element structure unit is λ / 2~λ, and the thickness is λ~3λ / 2.

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