CN114895458A - Broadband lens and design method based on quasi-continuous nanoribbon metasurface - Google Patents

Abstract

The invention discloses a quasi-continuous nanobelt super-surface-based broadband lens and a design method thereof, wherein an initial point, a phase requirement and a sample region in which a quasi-continuous nanobelt needs to be formed are determined; then calculating the orientation angle of the quasi-continuous nanobelt; moving the step length along the orientation angle direction to obtain a new nanobelt coordinate point; connecting the calculated nanobelt coordinate points one by one to obtain a quasi-continuous nanowire, and setting the width to obtain a quasi-continuous nanobelt; finally, the cycle is repeated until all quasi-continuous nanoribbons are completed in the sample area, thereby forming a super-surface composed of quasi-continuous nanoribbons. The method adopts a quasi-continuous structure to encode the super lens, and improves the operating waveband range and the energy efficiency of the super lens. The phase relation of the super-diffraction lens is used, the quasi-continuous super-diffraction lens can be designed, the electromagnetic performance of the lens can be improved, and the method improves the electromagnetic performance of the super-lens and enables the super-lens to have broadband high-efficiency characteristics.

Description

Broadband lens and design method based on quasi-continuous nanoribbon metasurface

technical field

The invention relates to the technical field of superdiffractive lenses, in particular to a broadband lens based on a quasi-continuous nanobelt metasurface and a design method.

Background technique

Lenses are an important basic optical element in optical systems. Conventional optical lenses generally modulate the wavefront of the light wave through the difference in thickness at different spatial locations. Limited by the refractive index of natural materials, the thickness of traditional optical lenses is generally much larger than the wavelength, which is not conducive to the miniaturization and integration of optical systems. Metasurfaces have the ability to modulate light waves in the subwavelength scale, and can construct subwavelength optical devices, which is of great significance to the miniaturization and integration of optical systems. The use of metasurfaces to achieve ultrathin and compact lens systems has gained a lot of research progress in recent years.

However, most of the current meta-lenses (meta-lenses) use discrete meta-surfaces for encoding, which affects the optical properties of the meta-lenses. On the one hand, the discretized encoding causes a deviation of the electromagnetic wavefront relative to the theoretical lens, which inevitably degrades the focusing quality and imaging performance of the lens. Of course, a sufficiently small discretized pixel could theoretically ameliorate this detrimental effect, but the fabrication of small-sized metasurface structures is often difficult. On the other hand, limited by the inherent electromagnetic resonance characteristics of discrete structures, discrete metalens often only maintain high energy efficiency around a certain preset wavelength. Deviation from the preset wavelength reduces the energy efficiency, which limits the working wavelength range of the metalens and is not conducive to the practical development of the metalens.

SUMMARY OF THE INVENTION

In view of this, the purpose of the present invention is to provide a broadband lens based on a quasi-continuous nanobelt metasurface and a design method, the method improves the electromagnetic performance of the metalens, and is a metalens that can realize broadband and high efficiency.

To achieve the above object, the present invention provides the following technical solutions:

The broadband lens design method based on the quasi-continuous nanobelt metasurface provided by the present invention comprises the following steps:

S1: Determine the calculation initial point, phase requirements, and sample area that needs to form quasi-continuous nanobelts;

S2: Calculate the quasi-continuous nanoribbon orientation angle according to the initial point and phase requirements;

S3: Calculate the next nanoribbon coordinate point along the quasi-continuous nanoribbon orientation angle direction according to the preset moving step;

S4: connect the calculated nanobelt coordinate points one by one to obtain quasi-continuous nanowires, and set the width to obtain quasi-continuous nanobelts;

S5: The cycle is repeated until all quasi-continuous nanoribbons are completed in the sample area, thereby forming a metasurface composed of quasi-continuous nanoribbons.

Further, the phase requirement in the step S1 is obtained according to the following steps:

Wherein, k ₀ =2π/λ ₀ ;

λ ₀ is the calculated wavelength;

f ₀ is the focal length of the lens;

(x, y) are the coordinates of the lens plane;

m is an integer;

Find the phase requirement at O ₁ (x ₀ , y ₀ ) by using (x ₀ , y ₀ ) coordinates instead of (x, y) coordinates in equation (a)

Further, the next nanobelt coordinate point in the step S3 is calculated according to the following formula:

得到点O₁(x₀,y₀)处的准连续纳米带取向角；所述取向角为准连续纳米带在该处的切线方向角；Using the PB phase relationship

Obtain the orientation angle of the quasi-continuous nanobelt at the point O ₁ (x ₀ , y ₀ ); the orientation angle of the tangential direction of the quasi-continuous nanobelt there;

Another point A ₁ (x ₁ , y ₁ ) is obtained by moving the step S along the direction of the orientation angle α ₁ , and its coordinates are expressed as:

x ₁ =x ₀ +S*cos(α ₁ );

y ₁ =y ₀ +S*sin(α ₁ );

Among them, S represents the moving step size.

Further, the next nanoribbon coordinate point in the step S3 is formed by moving along the negative direction _of the orientation angle α1, and is specifically calculated according to the following formula:

Moving S along the negative direction of the orientation angle, another point B ₁ (x1', y1') can be obtained, and its coordinate relationship is:

x' ₁ =x ₀ -S*cos(α ₁ );

y'1=y ₀ -S*sin(α ₁ ).

Further, the calculation points on the nanobelt are set within the sample area, and the interval between the calculation points on adjacent nanobelts matches the initially preset minimum spacing distance of the grating.

Further, the interval between the calculation points formed by the moving step matches the minimum interval distance of the grating.

Further, the phase requirement in the step S1 obtains the phase requirement of the superdiffractive lens according to the following steps:

为使用线性规划法得到所需要的二元制相位；where k ₀ =2π/λ ₀ , and λ ₀ is the calculated wavelength. f ₀ is the focal length of the superdiffractive lens, (x, y) is the coordinate of the superdiffractive lens plane, and m is an integer;

To obtain the required binary phase using the linear programming method;

According to the phase requirement of the superdiffractive lens, a broadband superdiffractive lens based on the quasi-continuous nanoribbon metasurface is obtained.

The lens provided by the present invention includes a substrate and a quasi-continuous nanobelt structure on the substrate, and the quasi-continuous nanobelt structure is obtained by using the above design method.

Further, the substrate is made of silicon dioxide.

Further, the quasi-continuous nanobelt structure is made of titanium dioxide material.

The beneficial effects of the present invention are:

The broadband lens and design method based on the quasi-continuous nanobelt metasurface provided by the invention firstly determine the initial point for calculation, the phase requirements and the sample area that needs to form the quasi-continuous nanobelt; and then calculate the quasi-continuous nanobelt according to the initial point and the corresponding demand. orientation angle; calculate the next coordinate point of the nanobelt according to the preset movement step along the orientation angle of the quasi-continuous nanobelt; connect the calculated coordinate points of the nanobelt one by one to obtain a quasi-continuous nanowire, and set the width to obtain a quasi-continuous nanobelt; The final cycle is repeated until all quasi-continuous nanoribbons are completed in the sample area, thereby forming a metasurface composed of quasi-continuous nanoribbons. The method uses a quasi-continuous structure to encode the metalens, which improves the operating band range and energy efficiency of the metalens. Using the phase relationship of superdiffractive lenses, quasi-continuous superdiffractive superlenses can be designed, which can improve the electromagnetic performance of such lenses. At the same time, if this method is used to fabricate common metalens, and the phase relationship of common metalens can be used, a quasi-continuous common metalens can be designed, which can improve the electromagnetic performance of common metalens. This method improves the electromagnetic properties of the metalens, making the metalens have broadband and high-efficiency properties.

Other advantages, objects, and features of the present invention will be set forth in the description that follows, and will be apparent to those skilled in the art based on a study of the following, to the extent that is taught in the practice of the present invention. The objectives and other advantages of the present invention may be realized and attained by the following description.

Description of drawings

In order to make the purpose, technical solutions and beneficial effects of the present invention clearer, the present invention provides the following drawings for description:

Figure 1 is a schematic diagram of the design process of a broadband lens based on a quasi-continuous nanoribbon metasurface.

FIG. 2 is a schematic diagram of the structure distribution of the quasi-continuous nanoribbon metalens.

Detailed ways

The present invention is further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand the present invention and implement it, but the embodiments are not intended to limit the present invention.

Example 1

As shown in FIG. 1 , the broadband lens design method based on the quasi-continuous nanoribbon metasurface provided in this embodiment, the quasi-continuous nanoribbon metasurface modulates the phase of the electromagnetic wave based on the geometric phase (also known as the Pancharatnam-Berry phase, referred to as the Pancharatnam-Berry phase for short). PB phase). In general, the geometric phase is related to the spatial orientation of the planar structure and often corresponds to cross-polarized components in transmitted or reflected light. Compared with the holographic imaging using the quasi-continuous structure, the present invention uses the quasi-continuous structure to realize the lens function, and its design and effect are different. On the one hand, the phase requirements of lenses are often different from those of holographic imaging, and the methods for obtaining the phase requirements are also different. On the other hand, the phase requirements of holographic imaging are often chaotic and irregular, and the phase requirements of closely spaced positions may have large differences or even sudden changes, resulting in more discontinuous points in the quasi-continuous structure. In contrast, the continuity of the lens phase requirements is better, and it can be better integrated with the quasi-continuous structure.

σ＝±1分别对应于照明光为左旋或右旋圆偏振光。If the structure orientation angle is 0 and the corresponding phase is 0, and the spatial orientation angle of a structure at the coordinate (x, y) position is represented by θ _{(x, y)} , then the geometry carried by the cross-polarized electromagnetic wave at this point Phase is

σ=±1 corresponds to the illumination light being left-handed or right-handed circularly polarized light, respectively.

Traditional discrete PB phase metalens often use some anisotropic nanostructures (such as elliptical apertures, elliptical cylinders, rectangular apertures, rectangular cylinders, etc.) for phase encoding. During the encoding process, the phase requirement of the lens must be sampled discretely, and the sampling period corresponds to the period size of the metasurface element structure. Theoretically, the phase requirement of a lens varies continuously with spatial position. The use of discrete phase encoding will cause phase deviation from the ideal lens, which will ultimately affect the optical performance of the metalens.

The broadband lens design method based on the quasi-continuous nanoribbon metasurface provided in this embodiment takes into account the requirements for continuous phase control and convenient processing of the metalens. band composition. The phase of electromagnetic waves is modulated by the orientation difference of the curvilinear trajectory of quasi-continuous nanoribbons at different spatial positions. On the one hand, the use of the quasi-continuous structure can realize the quasi-continuous change of the spatial phase. Compared with the discrete structure used by the traditional metalens, it can improve the phase control deviation caused by the spatial sampling. On the other hand, benefiting from the excellent electromagnetic properties of the quasi-continuous structure, the encoded metalens can maintain high energy efficiency in a wide wavelength range, that is, the characteristics of broadband and high efficiency.

This embodiment takes the design of a quasi-continuous ordinary superlens as an example, and the specific steps are:

From the perspective of space limit, quasi-continuous nanoribbons can be equivalent to nano-gratings. The grating material is titanium dioxide and the substrate is silicon dioxide. Determine the optimal grating width W=100nm, minimum interval P=160nm, height parameter H=600nm from the target wavelength range 450nm～1000nm, as an example to illustrate the design process of the quasi-continuous broadband high-efficiency lens. It should be noted that for different structural layer materials or different operating band ranges, the grating parameters need to be flexibly changed. The schematic diagram of the design process is shown in Figure 1. The specific steps are:

(1) First, a series of calculation initial points need to be selected. Take 833×833 points equally spaced along the x-axis and y-axis (with an interval of 0.36 μm) as the initial points (the spatial range is −149.76 μm to 149.76 μm).

(2) Take a certain initial point O ₁ (x ₀ , y ₀ ) (optionally x ₀ =-149.76, y ₀ =-149.76) as the starting point for design.

(3) Calculate the phase requirement of the initial point O ₁ (x ₀ , y ₀ ).

When designing a common lens, the calculation formula for the phase requirement is:

Wherein, k ₀ =2π/λ ₀ ;

λ ₀ =632.8nm is the calculation wavelength;

f ₀ =1mm is the focal length of the lens; (x, y) is the coordinate of the lens plane;

处于–π～π的范围内。m is an integer such that the phase

in the range of –π to π.

The phase requirement at O ₁ (x ₀ , y ₀ ) can be found by using the (x ₀ , y ₀ ) coordinates in place of the (x, y) coordinates in equation (a)

得到点O₁(x₀,y₀)处的准连续纳米带取向角。这里的取向角实际就是准连续纳米带在该处的切线方向角。(4) Using the PB phase relationship

The quasi-continuous nanoribbon orientation angle at point O ₁ (x ₀ , y ₀ ) is obtained. The orientation angle here is actually the tangential direction angle of the quasi-continuous nanoribbon there.

(5) Another point A ₁ (x ₁ , y ₁ ) can be obtained by moving the step S=20 nm along the positive direction of the orientation angle α ₁ , and the expression of its coordinates is:

x ₁ =x ₀ +S*cos(α ₁ );

y ₁ =y ₀ +S*sin(α ₁ );

Theoretically, the smaller the S, the better the continuity of the nanoribbons. But a smaller S means that a nanoribbon of the same length contains more coordinate points, which corresponds to longer computing time and greater computing resource requirements. Considering comprehensively, S=20nm is set here, which should be determined according to actual hardware resource conditions and computing time requirements.

(6) The required phase at point A ₁ (x ₁ , y ₁ ) can be calculated using (x ₁ , y ₁ ) coordinates instead of (x, y) coordinates in formula (a), using step (4) can Calculate the tangent orientation angle α ₂ at this point, and use step (5) to obtain another point A ₂ (x ₂ , y ₂ ) whose coordinates are expressed as:

x ₂ =x ₁ +S*cos(α ₂ )=x ₀ +S*cos(α ₁ )+S*cos(α ₂ );

y ₂ =y ₁ +S*sin(α ₂ )=y ₀ +S*sin(α ₁ )+S*sin(α ₂ );

(7) Using similar loop iteration steps, a series of points A _n (x _n , y _n ) on the nanobelt along the positive tangent direction can be obtained, and the coordinate relationship is:

x _n =x ₀ +S*cos(α ₁ )+...+S*cos(α _n );

y _n =y ₀ +S*sin(α ₁ )+...+S*sin(α _n );

(8) Move S along the negative tangent direction at O ₁ (x ₀ , y ₀ ), and another point B ₁ (x′ ₁ , y′ ₁ ) can also be obtained, and its coordinate relationship is:

x' ₁ =x ₀ -S*cos(α ₁ );

y' ₁ =y ₀ -S*sin(α ₁ );

(9) Using the coordinates of the point B ₁ (x1', y1') to replace the coordinates of (x, y) in the formula (a), the phase requirement at this point can also be calculated, and the position at this point can be obtained by using step (4). The orientation angle β ₂ (x1', y1'). By moving S in the negative direction of this orientation angle, another point B ₂ (x2', y2') can be obtained. Its coordinate relationship is:

x' ₂ =x ₀ -S*cos(α ₁ )-S*cos(β ₂ );

y' ₂ =y ₀ -S*sin(α ₁ )-S*sin(β ₂ );

处的取向角。Among them, β ₂ is the abbreviation of β ₂ (x1′, y1′), which means

Orientation angle at .

(10) Using a similar loop iteration process, a series of points B _n (xn',yn') along the negative direction of the tangent can be obtained, and the coordinate relationship is:

x' _n =x ₀ -S*cos(α ₁ )-S*cos(β ₂ )-...-S*cos(β _n );

y' _n =y ₀ -S*sin(α ₁ )-S*sin(β ₂ )-...-S*sin(β _n );

(11) Connect the points obtained above one by one to obtain a quasi-continuous line. Let the width of the line be 100 nm, a quasi-continuous nanobelt with a width of the preset grating width W=100 nm is obtained.

(12) Starting from another initial point O ₂ (optional O ₂ (-149.76, -149.40)), repeat steps (3)-(11) until all the initial points preset in step (1) participate in calculate. A series of quasi-continuous nanoribbons can be obtained, and these quasi-continuous nanoribbons constitute a quasi-continuous nanoribbon superlens, as shown in Fig. 2 .

In the design process of this embodiment, the calculation point on the nanobelt cannot exceed the preset sample area, and here a circular area with a radius of R=150 μm is taken as an example. The calculation points on the nanobelt are set within the sample area, and the interval between the calculation points on adjacent nanobelts matches the initially preset minimum spacing distance of the grating. The interval between the calculated points formed by the moving step matches the minimum interval distance of the grating. The meaning of matching here is as follows: the interval between calculation points on adjacent nanoribbons cannot be smaller than the initially preset minimum interval P of the grating (the minimum interval in this embodiment takes P=160 nm as an example). In addition, in the calculation process of each initial point, the interval between the calculation points that move more than a preset number of steps (take 20 steps in this embodiment as an example) cannot be less than the minimum grating interval P=160nm.

本实施例中，设置目标光场中心焦斑全宽是对应艾里斑中心焦斑全宽的0.7倍，最大的旁瓣强度是中心焦斑最大强度的0.15倍。使用线性规划法获得二元制相位

其只存在0、π两种值，对应于π的相位突变，只在有限的几个位置产生额外的π相位突变。然后使用相位关系：In this embodiment, a common lens can be designed by using the above steps, and a superdiffractive lens can be designed by a similar method. Taking the design of a superoscillating lens as an example, the required binary phase can be obtained by using the linear programming method

In this embodiment, the full width of the central focal spot of the target light field is set to be 0.7 times the full width of the central focal spot corresponding to the Airy disk, and the maximum side lobe intensity is 0.15 times the maximum intensity of the central focal spot. Obtain Binary Phase Using Linear Programming

There are only two values of 0 and π, which correspond to the phase mutation of π, and only generate additional π phase mutation in a limited number of positions. Then use the phase relationship:

处于–π～π的范围内)Among them, k ₀ =2π/λ ₀ and λ ₀ =632.8nm are the calculation wavelengths. f ₀ =1mm is the focal length of the superdiffractive lens, (x,y) is the coordinate of the superdiffractive lens plane, and m is an integer such that the phase

in the range of –π～π)

Alternative formula:

By performing the phase requirement calculation in steps (3) (6) (9), a broadband high-efficiency superdiffractive lens based on a quasi-continuous nanoribbon metasurface can be designed.

Example 2

In this embodiment, the quasi-continuous nanoribbon-based metasurface broadband lens obtained by the above design method includes a silicon dioxide substrate and a large number of quasi-continuous nanoribbon structures made of titanium dioxide on the substrate. These quasi-continuous nanoribbons with varying spatial orientations along the spatial position can realize the phase modulation function of ordinary metalens or superdiffractive metalens. Compared with the common discrete metasurface lens, this quasi-continuous nanoribbon metasurface lens can better realize the function of broadband and high efficiency.

The above-mentioned embodiments are only preferred embodiments for fully illustrating the present invention, and the protection scope of the present invention is not limited thereto. Equivalent substitutions or transformations made by those skilled in the art on the basis of the present invention are all within the protection scope of the present invention. The protection scope of the present invention is subject to the claims.

Claims (10)

1. based on the broadband lens design method of quasi-continuous nanobelt metasurface, it is characterized in that: comprise the following steps: S1: Determine the calculation initial point, phase requirements, and sample area that needs to form quasi-continuous nanobelts; S2: Calculate the quasi-continuous nanoribbon orientation angle according to the initial point and phase requirements; S3: Calculate the next nanoribbon coordinate point along the quasi-continuous nanoribbon orientation angle direction according to the preset moving step; S4: connect the calculated nanobelt coordinate points one by one to obtain quasi-continuous nanowires, and set the width to obtain quasi-continuous nanobelts; S5: The cycle is repeated until all quasi-continuous nanoribbons are completed in the sample area, thereby forming a metasurface composed of quasi-continuous nanoribbons. 2. the broadband lens design method based on quasi-continuous nanobelt metasurface as claimed in claim 1, is characterized in that: the phase requirement in described step S1 is obtained according to the following steps:

Wherein, k ₀ =2π/λ ₀ ; λ ₀ is the calculated wavelength; f ₀ is the focal length of the lens; (x, y) are the coordinates of the lens plane; m is an integer; Find the phase requirement at O ₁ (x ₀ , y ₀ ) by using (x ₀ , y ₀ ) coordinates instead of (x, y) coordinates in equation (a)

3. the broadband lens design method based on quasi-continuous nanobelt metasurface as claimed in claim 1, is characterized in that: the next nanobelt coordinate point in described step S3 is calculated according to following formula: Using the PB phase relationship

Obtain the orientation angle of the quasi-continuous nanobelt at the point O ₁ (x ₀ , y ₀ ); the orientation angle of the tangential direction of the quasi-continuous nanobelt there; Another point A ₁ (x ₁ , y ₁ ) is obtained by moving the step S along the direction of the orientation angle α ₁ , and its coordinates are expressed as: x ₁ =x ₀ +S*cos(α ₁ ); y ₁ =y ₀ +S*sin(α ₁ ); Among them, S represents the moving step size. 4. the broadband lens design method based on quasi-continuous nanoribbon metasurface as claimed in claim 1, is characterized in that: the next nanoribbon coordinate point in described step S3 is to move along the negative direction of orientation angle α ₁ to form , which is calculated according to the following formula: Move S in the negative direction of this orientation angle to get another point

Its coordinate relationship is: x' ₁ =x ₀ -S*cos(α ₁ ); y' ₁ =y ₀ -S*sin(α ₁ ). 5. The broadband lens design method based on quasi-continuous nanobelt metasurface as claimed in claim 1, wherein the calculation point on the nanobelt is set within the sample area, and the calculation point on the adjacent nanobelt The spacing matches the initially preset minimum raster spacing distance. 6 . The broadband lens design method based on the quasi-continuous nanoribbon metasurface according to claim 1 , wherein the interval between the calculation points formed by the moving step matches the minimum interval distance of the grating. 7 . 7. the broadband lens design method based on quasi-continuous nanobelt metasurface as claimed in claim 1, is characterized in that: the phase requirement in described step S1 obtains the phase requirement of superdiffraction lens according to the following steps:

where k ₀ =2π/λ ₀ , and λ ₀ is the calculated wavelength. f ₀ is the focal length of the superdiffractive lens, (x, y) is the coordinate of the superdiffractive lens plane, and m is an integer;

To obtain the required binary phase using the linear programming method; According to the phase requirement of the superdiffractive lens, a broadband superdiffractive lens based on the quasi-continuous nanoribbon metasurface is obtained. 8. A lens, characterized in that: the lens comprises a substrate and a quasi-continuous nanoribbon structure on the substrate, and the quasi-continuous nanoribbon structure is obtained by using the design method of any one of claims 1-6. 9. The lens of claim 8, wherein the substrate is made of silicon dioxide. 10 . The lens of claim 8 , wherein the quasi-continuous nanobelt structure is made of titanium dioxide. 11 .

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