High-low column structure achromatic super lens and design method

Abstract

The invention relates to an achromatic super lens with a high-low column structure and a design method, the achromatic super lens is formed by periodically arranging a plurality of primitives, and the primitives are micro-nano cylinders with different heights and radiuses. During design, a primitive library is firstly constructed, each primitive in the primitive library is a micro-nano cylinder, the height and radius of the micro-nano cylinder are changed through simulation software, and the phase and transmittance of each primitive in the primitive library under different incident wavelengths are obtained; then, optimizing by adopting a particle swarm algorithm by taking the minimum total phase difference of the achromatic superlens as a target to obtain an element structure of each position; and finally, selecting proper primitives from the primitive library according to the obtained primitive structure, and performing periodic arrangement to obtain the achromatic super lens. The aperture and the numerical aperture can be increased, and meanwhile bandwidth achromatism is achieved.

Description

Technical Field

[0001] The present invention relates to the field of micro-nano photonics, and in particular to an achromatic super lens with a high-low column structure and a design method thereof. Background Art

[0002] Traditional metalenses can achieve the focusing function at a single wavelength, but when it is necessary to achieve broadband multi-wavelength achromatic focusing function on a metalens, it is difficult to achieve the traditional metalenses of equal height primitives, because the phase coverage range of each wavelength of the primitive library of equal height primitives is small. In the prior art, there are methods of using multiple primitive shapes of equal height, such as fork, cross, diamond, etc., in order to increase the phase coverage range of each wavelength and increase the diversity of the primitive library. However, when the goal is to design achromatic metalenses with a wider bandwidth, and to increase the aperture and maintain a larger numerical aperture, the method of simply increasing the primitive shape is often difficult to meet the phase coverage requirements of achromaticity in each band. Summary of the invention

[0003] The technical problem to be solved by the present invention is to provide a high-low column structure achromatic super lens and a design method, which can increase the aperture and numerical aperture and achieve bandwidth achromatism at the same time.

[0004] The technical solution adopted by the present invention to solve its technical problem is: to provide a high-low column structure achromatic super lens, which is composed of a plurality of periodically arranged primitives, and the primitives are micro-nano cylinders with different heights and radii.

[0005] The phase of the primitive is: Wherein, φ(r,ω) is the phase of the element, r is the distance from the center of the achromatic superlens to the center of the element, ω is the angular frequency of the incident wavelength, c is the speed of light, and f is the focal length of the achromatic superlens.

[0006] The technical solution adopted by the present invention to solve the technical problem is: to provide a design method of a high-low column structure achromatic metalens, comprising the following steps:

[0007] Constructing a primitive library, wherein each primitive in the primitive library is a micro-nano cylinder, and changing the height and radius of the micro-nano cylinder by simulation software to obtain the phase and transmittance of each primitive in the primitive library under different incident wavelengths;

[0008] The particle swarm algorithm is used to optimize the achromatic metalens with the goal of minimizing the total phase difference, and the primitive structure at each position is obtained;

[0009] According to the obtained elementary structure, suitable elementary elements are selected from the elementary library for periodic arrangement to obtain an achromatic superlens.

[0010] The fitness function of the particle swarm algorithm is: in, is the total phase difference of the achromatic superlens; i represents the position number on the achromatic superlens, and n represents the number of all incident wavelengths in the working band. is the phase of the ideal achromatic correction of the primitive at the ith position on the achromatic metalens for the nth incident wavelength, is the actual phase of the element at the ith position on the achromatic metalens for the nth incident wavelength.

[0011] The phase of the ideal achromatic correction of the primitive at the i-th position on the achromatic metalens for the n-th incident wavelength is Among them, r i is the distance from the center of the primitive at the ith position to the center of the achromatic metalens, ω n is the angular frequency of the nth incident wavelength, c is the speed of light, and f is the focal length of the achromatic metalens.

[0012] Beneficial Effects

[0013] Due to the adoption of the above technical solution, the present invention has the following advantages and positive effects compared with the prior art: the present invention forms a superlens by periodically arranging nanocolumns of varying heights, which can effectively increase the phase coverage range of the elementary library. Compared with conventional superlenses, the device of the present invention has a numerical aperture NA that is significantly larger than other superlenses of the same aperture while achieving achromatic aberration at a larger aperture. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 1 is a schematic diagram of an achromatic metalens with a high-low column structure according to an embodiment of the present invention;

[0015] Figure 2 is a phase diagram of a primitive library in an embodiment of the present invention;

[0016] Figure 3 is a transmittance graph of a primitive library in an embodiment of the present invention;

[0017] Figure 4 is a convergence curve diagram of the particle swarm algorithm in an embodiment of the present invention;

[0018] Figure 5 is a geometrical schematic diagram of a high-low column structure achromatic metalens constructed in an embodiment of the present invention;

[0019] Figure 6 It is the simulation result of the high-low column structure achromatic superlens constructed in the implementation mode of the present invention. DETAILED DESCRIPTION

[0020] The present invention will be further described below in conjunction with specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention. In addition, it should be understood that after reading the content taught by the present invention, those skilled in the art can make various changes or modifications to the present invention, and these equivalent forms fall within the scope limited by the appended claims of the application equally.

[0021] An embodiment of the present invention relates to an achromatic superlens with a high-low column structure, which is composed of a plurality of periodically arranged primitives, wherein the primitives are micro-nano cylinders with different heights and radii.

[0022] like Figure 1 As shown, under normal incidence, in order to achieve the diffraction limit and focus the incident light field at the focal point, this embodiment uses a hyperbolic phase distribution to design a metalens, and the phase of the element is:

[0023]

[0024] Wherein, φ(r,ω) is the phase of the element, r is the distance from the center of the achromatic superlens to the center of the element, ω is the angular frequency of the incident wavelength, c is the speed of light, and f is the focal length of the achromatic superlens.

[0025] For an achromatic metalens, it is necessary to work at different frequencies of light waves to satisfy the above formula in order to achieve broadband achromatic function.

[0026] The design process of the high-low column structure achromatic metalens of this embodiment is given below.

[0027] First, a primitive library is constructed, in which each primitive is a micro-nano cylinder. The height and radius of the micro-nano cylinder are changed by simulation software to obtain the phase and transmittance of each primitive in the primitive library under different incident wavelengths.

[0028] In order to increase the phase coverage of the primitive library, this embodiment uses polarization-insensitive micro-nano cylinders with different heights and radii as primitives. The polarization insensitivity of the cylindrical shape further improves the transmittance of visible light, and the primitives in the primitive library vary in radius and height, so that the primitive library can achieve 0-2π phase coverage in all wavelengths of visible light, thereby meeting the design requirements of achromatic metalenses. Figure 2 and Figure 3 The phase and transmittance of the primitive library are given respectively.

[0029] Then, the particle swarm algorithm is used to optimize the achromatic metalens with the goal of minimizing the total phase difference, and the primitive structure at each position is obtained.

[0030] The optimization goal of the particle swarm algorithm in this embodiment is to minimize the total phase difference of the achromatic metalens, that is, the sum of the phase differences of each element on the achromatic metalens for each incident wavelength in the working wavelength range, which can be expressed as:

[0031]

[0032] Where i represents the position number on the achromatic metalens, n represents the number of all incident wavelengths in the working band, is the phase of the ideal achromatic correction of the primitive at the ith position on the achromatic metalens for the nth incident wavelength, is the actual phase of the element at the ith position on the achromatic metalens for the nth incident wavelength.

[0033] Among them, for the nth incident wavelength, the phase of the ideal achromatic correction of the primitive at the i-th position on the achromatic metalens can be calculated by the following formula:

[0034]

[0035] The actual phase of the element at the ith position on the achromatic metalens for the nth incident wavelength can be obtained through simulation.

[0036] According to the Rayleigh criterion, when the maximum wave aberration of an optical system is less than λ / 4, the system is perfect, and it is pointed out that if the defective wavelength accounts for a small enough proportion of the entire wave surface, even if the defective wave aberration is greater than λ / 4, it can be ignored. Figure 4 As shown, after hundreds of iterations, the minimum value can be obtained, and the optimal solution can be obtained, that is, the optimal primitive structure at each position is obtained.

[0037] Finally, according to the obtained primitive structure, appropriate primitives are selected from the primitive library for periodic arrangement to obtain the following Figure 5 The achromatic metalens shown. Figure 6 The simulation results of the achromatic superlens are shown in Figure 1. It can be seen that it can achieve achromaticity of larger aperture for different wavelengths, and the numerical aperture NA is significantly larger than other superlenses with the same aperture, showing the good phase coverage of the high and low column primitive library.

Claims

1. A high-low column structure achromatic metalens, characterized in that: It is composed of a plurality of periodically arranged primitives, wherein the primitives are micro-nano cylinders with different heights and radii.

2. The high-low column structure achromatic superlens according to claim 1, characterized in that: The phase of the primitive is: Wherein, φ(r,ω) is the phase of the element, r is the distance from the center of the achromatic superlens to the center of the element, ω is the angular frequency of the incident wavelength, c is the speed of light, and f is the focal length of the achromatic superlens.

3. A design method for a high-low column structure achromatic metalens, characterized in that: The following steps are involved: Constructing a primitive library, wherein each primitive in the primitive library is a micro-nano cylinder, and changing the height and radius of the micro-nano cylinder by simulation software to obtain the phase and transmittance of each primitive in the primitive library under different incident wavelengths; The particle swarm algorithm is used to optimize the achromatic metalens with the goal of minimizing the total phase difference, and the primitive structure at each position is obtained; According to the obtained elementary structure, suitable elementary elements are selected from the elementary library for periodic arrangement to obtain an achromatic superlens.

4. The design method of the high-low column structure achromatic metalens according to claim 3, characterized in that: The fitness function of the particle swarm algorithm is: in, is the total phase difference of the achromatic superlens; i represents the position number on the achromatic superlens, and n represents the number of all incident wavelengths in the working band. is the phase of the ideal achromatic correction of the primitive at the ith position on the achromatic metalens for the nth incident wavelength, is the actual phase of the element at the ith position on the achromatic metalens for the nth incident wavelength.

5. The design method of the high-low column structure achromatic metalens according to claim 3, characterized in that: The phase of the ideal achromatic correction of the primitive at the i-th position on the achromatic metalens for the n-th incident wavelength is Among them, r i is the distance from the center of the primitive at the ith position to the center of the achromatic metalens, ω n is the angular frequency of the nth incident wavelength, c is the speed of light, and f is the focal length of the achromatic metalens.

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