CN114895458A - Quasi-continuous nanoribbon super-surface-based broadband lens and design method - Google Patents
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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
Technical Field
The invention relates to the technical field of super-diffraction lenses, in particular to a quasi-continuous nanoribbon super-surface-based broadband lens and a design method thereof.
Background
A lens is an important basic optical element in an optical system. Conventional optical lenses typically modulate the wavefront of an optical wave by differences in thickness at different spatial locations thereof. Due to the limitation of the refractive index of natural materials, the thickness of the conventional optical lens is generally far greater than the wavelength, which is not favorable for the miniaturization and integration of the optical system. The super-surface has the capability of modulating light waves in a sub-wavelength scale range, can construct a sub-wavelength optical device, and has great significance for miniaturization and integration of an optical system. The realization of ultra-thin compact lens systems using super-surfaces has achieved a lot of research progress in recent years.
However, most of the current super-surface lenses (superlenses) adopt discrete super-surfaces for encoding, which affects the optical performance of the superlenses. On the one hand, discretized encoding can cause deviations of the electromagnetic wavefront from the theoretical lens, which inevitably reduces the focusing quality and imaging performance of the lens. Of course, a discretized pixel that is theoretically small enough can ameliorate this adverse effect, but the fabrication of small-sized super-surface structures is often difficult. On the other hand, discrete superlenses often only maintain high energy efficiency around a certain preset wavelength, limited by the inherent electromagnetic resonance characteristics of the discrete structure. Deviation from the preset wavelength reduces the energy efficiency, which limits the working wavelength range of the superlens and is not beneficial to the practical development of the superlens.
Disclosure of Invention
In view of this, the present invention provides a broadband lens based on a quasi-continuous nanoribbon super surface and a design method thereof, which improves the electromagnetic performance of the super lens and is a super lens capable of realizing broadband high efficiency.
In order to achieve the purpose, the invention provides the following technical scheme:
the invention provides a design method of a broadband lens based on a quasi-continuous nanoribbon super surface, which comprises the following steps:
s1: determining and calculating an initial point, a phase requirement and a sample region required to form a quasi-continuous nanobelt;
s2: calculating the orientation angle of the quasi-continuous nanobelt according to the initial point and the phase requirement;
s3: calculating the next nanobelt coordinate point according to a preset moving step length along the orientation angle direction of the quasi-continuous nanobelt;
s4: 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;
s5: the cycle repeats until all quasi-continuous nanoribbons are completed in the sample area, thereby forming a super-surface composed of quasi-continuous nanoribbons.
Further, the phase requirement in step S1 is obtained according to the following steps:
wherein k is 0 ＝2π/λ 0 ；
λ 0 Is the calculated wavelength;
f 0 is the lens focal length;
(x, y) are coordinates of the lens plane;
m is an integer;
by using (x) 0 ,y 0 ) The coordinates are substituted for the (x, y) coordinates in equation (a) to determine O 1 (x 0 ,y 0 ) Phase requirement of
Further, the next nanobelt coordinate point in the step S3 is calculated according to the following formula:
using PB phase relationship
Point O is obtained 1 (x 0 ,y 0 ) The quasi-continuous nanoribbon orientation angle of (a); the orientation angle is the tangential direction angle of the quasi-continuous nanoribbon at the position;
along the orientation angle alpha 1 Is moved by a step S to obtain another point a 1 (x 1 ,y 1 ) The expression of the coordinates is:
x 1 ＝x 0 +S*cos(α 1 )；
y 1 ＝y 0 +S*sin(α 1 )；
where S denotes a moving step.
Further, the next nanoribbon coordinate point in the step S3 is along the orientation angle α 1 The negative direction movement of (a) is formed, specifically calculated according to the following formula:
by moving S in the negative direction of the orientation angle, another point B can be obtained 1 (x1 ', y 1') having the coordinate relationship:
x′ 1 ＝x 0 -S*cos(α 1 )；
y′1＝y 0 -S*sin(α 1 )。
further, the calculation points on the nanobelts are arranged in the range of the sample area, and the interval between the calculation points on the adjacent nanobelts is matched with the initial preset minimum interval distance of the grating.
Further, the interval between the calculation points formed by the moving step is matched with the minimum interval distance of the grating.
Further, the phase requirement in step S1 is obtained according to the following steps:
wherein k is 0 ＝2π/λ 0 ，λ 0 Is the calculated wavelength. f. of 0 Is the focal length of the super-diffraction lens, (x, y) are the coordinates of the plane of the super-diffraction lens, and m is an integer;
obtaining a required binary system phase by using a linear programming method;
and obtaining the broadband super-diffraction lens based on the quasi-continuous nanoribbon super surface according to the phase requirement of the super-diffraction lens.
The lens provided by the invention comprises a substrate and a quasi-continuous nanobelt structure on the substrate, wherein the quasi-continuous nanobelt structure is obtained by adopting the design method.
Further, the substrate is made of silicon dioxide.
Furthermore, the quasi-continuous nano-belt structure is made of a titanium dioxide material.
The invention has the beneficial effects that:
the invention provides a quasi-continuous nanobelt super-surface-based broadband lens and a design method thereof.A calculation 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 according to the initial point and the corresponding requirement; calculating the next nanobelt coordinate point according to a preset moving step length along the orientation angle direction of the quasi-continuous nanobelt; 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. By using the phase relation of the super-diffraction lens, the quasi-continuous super-diffraction lens can be designed, and the electromagnetic performance of the lens can be improved. Meanwhile, if the method is used for manufacturing the common super lens, the quasi-continuous common super lens can be designed by using the phase relation of the common super lens, and the electromagnetic performance of the common super lens can be improved. The method improves the electromagnetic performance of the super lens, so that the super lens has the property of high broadband efficiency.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention may be realized and attained by the means of the instrumentalities and combinations particularly pointed out hereinafter.
Drawings
In order to make the object, technical scheme and beneficial effect of the invention more clear, the invention provides the following drawings for explanation:
FIG. 1 is a schematic diagram of a design process of a broadband lens based on a quasi-continuous nanoribbon super-surface.
FIG. 2 is a schematic diagram of the distribution of quasi-continuous nanoribbon superlens structures.
Detailed Description
The present invention is further described with reference to the following drawings and specific examples so that those skilled in the art can better understand the present invention and can practice the present invention, but the examples are not intended to limit the present invention.
Example 1
As shown in fig. 1, in the design method of the quasi-continuous nanoribbon super-surface-based broadband lens provided in this embodiment, the manner of adjusting the electromagnetic wave phase by the quasi-continuous nanoribbon super-surface is based on the principle of geometric phase (also called Pancharatnam-Berry phase, abbreviated as PB phase). In general, the geometric phase is related to the spatial orientation of the planar structure and often corresponds to cross-polarization components in the transmitted or reflected light. Compared with the holographic imaging using the quasi-continuous structure, the invention uses the quasi-continuous structure to realize the lens function, and the design and the effect are different. On the one hand, the phase requirements of the lens 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 requirement of holographic imaging is often disordered and irregular, and the phase requirement of positions with close intervals may have large difference or even abrupt change, so that a quasi-continuous structure generates more discontinuous points. In contrast, the continuity of the lens phase requirement is better, and the lens phase requirement can be better fused with a quasi-continuous structure.
If the corresponding phase is 0 when the structure orientation angle is 0, theta is calculated (x,y) Representing the spatial orientation angle of a structure at the coordinate (x, y) position, the geometric phase carried by the point-cross-polarized electromagnetic wave is
σ ± 1 corresponds to the illumination light being left-handed or right-handed circularly polarized light, respectively.
Conventional discrete PB phase superlenses often employ some anisotropic nanostructures (e.g., elliptical holes, elliptical cylinders, rectangular holes, rectangular cylinders, etc.) for phase encoding. During the encoding process, the phase requirements of the lens must be discretized and sampled with a sampling period corresponding to the period size of the super-surface unit structure. Theoretically, the phase requirement of the lens is continuously variable with the spatial position. The use of discrete phase encoding can cause phase deviation from the ideal lens, and ultimately affect the optical performance of the superlens.
The method for designing the quasi-continuous nanoribbon super-surface-based broadband lens provided by the embodiment gives consideration to the phase continuous regulation and control requirement and the convenient processing requirement of the superlens, and the quasi-continuous lens is different from a discrete superlens structure and consists of a large number of nanoribbons with fixed widths. The electromagnetic wave phase is modulated by the orientation difference of the curve tracks of the quasi-continuous nanobelts at different spatial positions. On the one hand, the quasi-continuous structure can realize the quasi-continuous change of the space phase, and compared with a discrete structure used by the traditional super lens, the quasi-continuous structure can improve the phase regulation deviation problem caused by space sampling. On the other hand, the coded super lens can keep higher energy efficiency in a wider waveband range, namely the characteristic of broadband high efficiency due to the excellent electromagnetic performance of the quasi-continuous structure.
In this embodiment, a quasi-continuous common superlens is designed as an example, and the specific steps are as follows:
from the perspective of spatial limitation, the quasi-continuous nanobelt can be equivalent to a nanograting. The grating is made of titanium dioxide and the substrate is silicon dioxide. The design process of the quasi-continuous broadband high-efficiency lens is described by determining the width W of the optimized grating to be 100nm, the minimum interval P to be 160nm and the height parameter H to be 600nm according to the target wavelength range of 450nm to 1000 nm. It should be noted that, for different structural layer materials or different operating band ranges, the grating parameters need to be changed flexibly, the schematic design process is shown in fig. 1, and the specific steps are as follows:
(1) first a series of calculation initiation points needs to be selected. The initial point was 833 x 833 points equally spaced (0.36 microns apart) along the x and y axes (spatial range-149.76 μm to 149.76 μm).
(2) At a certain initial point O 1 (x 0 ,y 0 ) (alternative x) 0 ＝-149.76，y 0 -149.76) as a starting point for design.
(3) Calculating the initial point O 1 (x 0 ,y 0 ) The phase requirement of (1).
When designing a normal lens, the phase requirement is calculated by the formula:
wherein k is 0 ＝2π/λ 0 ；
λ 0 632.8nm is the calculated wavelength;
f 0 1mm is the focal length of the lens; (x, y) are coordinates of the lens plane;
m is an integer such that the phase
Is in the range of-pi to pi.
By using (x) 0 ,y 0 ) The coordinates can be obtained by substituting the (x, y) coordinates in the formula (a) for the coordinates 1 (x 0 ,y 0 ) Phase requirement of
(4) Using PB phase relationship
Point O is obtained 1 (x 0 ,y 0 ) Quasi-continuous nanoribbon orientation angle of (d). The orientation angle here is actually the tangential direction angle of the quasi-continuous nanoribbon there.
(5) Along the orientation angle alpha 1 Another point a can be obtained by moving the step length S of 20nm in the positive direction 1 (x 1 ,y 1 ) The expression of the 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 nanobelt. But a smaller S means that nanobelts of the same length contain more coordinate points, corresponding to longer computation time and greater computational resource requirements. Considering comprehensively, S is set to 20nm here, and should be determined according to actual hardware resource conditions and calculation time requirements.
(6) Point A 1 (x 1 ,y 1 ) The phase required can be used (x) 1 ,y 1 ) Coordinates are calculated instead of the (x, y) coordinates in formula (a), and the tangential orientation angle α at that point can be calculated using step (4) 2 Another point A can be obtained using step (5) 2 (x 2 ,y 2 ) The expression of the coordinates is:
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 iterative steps of the loop, a series of points A along the positive tangential direction on the nanoribbon can be obtained n (x n ,y n ) The coordinate relationship is as follows:
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) at O 1 (x 0 ,y 0 ) Another point B can be obtained by moving S along the negative direction of the tangent 1 (x′ 1 ,y′ 1 ) The coordinate relationship is as follows:
x′ 1 ＝x 0 -S*cos(α 1 )；
y′ 1 ＝y 0 -S*sin(α 1 )；
(9) using B 1 (x1 ', y 1') point coordinates instead of the (x, y) coordinates in the formula (a), can also be calculatedPhase requirement at the point, the orientation angle β at the point can be obtained using step (4) 2 (x1 ', y 1'). By moving S in the negative direction of the orientation angle, another point B can be obtained 2 (x2 ', y 2'). The coordinate relation is as follows:
x′ 2 ＝x 0 -S*cos(α 1 )-S*cos(β 2 )；
y′ 2 ＝y 0 -S*sin(α 1 )-S*sin(β 2 )；
wherein, beta 2 Is beta 2 Abbreviations of (x1 ', y 1') denote
The orientation angle of (d).
(10) Using a similar iterative process of the loop, a series of points B along the negative direction of the tangent can be obtained n (xn ', yn') with the coordinate relationship:
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) the points obtained above are connected one by one to obtain a quasi-continuous line. Let the width of the line be 100nm, and obtain a quasi-continuous nanoribbon with a preset grating width W of 100 nm.
(12) From another initial point O 2 (optional O) 2 (-149.76, -149.40)) and repeating the steps (3) - (11) until all initial points preset in the step (1) participate in the calculation. A series of quasi-continuous nanoribbons can be obtained, which constitute a quasi-continuous nanoribbon superlens, as schematically shown in fig. 2.
In the design process of the embodiment, the calculated point on the nanobelt cannot exceed the preset sample area, and here, a circular area with the radius R being 150 μm is taken as an example. The calculation points on the nanobelts are arranged in the range of the sample area, and the interval between the calculation points on the adjacent nanobelts is matched with the initial preset minimum interval distance of the grating. The spacing between the calculated points formed by the moving step is matched with the minimum spacing distance of the grating. Here, the matching means are as follows: the spacing between the calculated points on adjacent nanoribbons cannot be smaller than the originally preset minimum grating spacing P (the minimum spacing in this embodiment is P ═ 160nm for 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 (20 steps in the present embodiment as an example) cannot be less than the grating minimum interval P of 160 nm.
In the present embodiment, a normal lens can be designed by using the above steps, and a super-diffractive lens can be designed by a similar method. Taking the design of the super-oscillating lens as an example, the linear programming method can be used to obtain the required binary system phase
In this embodiment, the full width of the central focal spot of the target light field is set to be 0.7 times of the full width of the central focal spot of the corresponding airy disk, and the maximum side lobe intensity is set to be 0.15 times of the maximum intensity of the central focal spot. Obtaining binary system phase using linear programming
It has only two values of 0 and pi, corresponding to pi phase mutation, and generates additional pi phase mutation at limited positions. Then using the phase relationship:
wherein k is 0 ＝2π/λ 0 ，λ 0 632.8nm is the calculated wavelength. f. of 0 1mm is the super-diffractive lens focal length, (x, y) are the coordinates of the super-diffractive lens plane, m is an integer such that the phase is
In the range of-pi to pi)
Instead of the formula:
and (4) performing phase requirement calculation in the steps (3), (6) and (9), and designing and obtaining the broadband high-efficiency super-diffraction lens based on the quasi-continuous nanobelt super surface.
Example 2
In this embodiment, the quasi-continuous nanoribbon-based super-surface broadband lens obtained by the above design method includes a silica substrate and a plurality of quasi-continuous nanoribbon structures made of titania on the silica substrate. These quasi-continuous nanoribbons of varying spatial orientation along the spatial position enable the phase modulation function of a common superlens or a superdiffractive superlens. Compared with a common discrete super-surface lens, the quasi-continuous nanoribbon super-surface lens can better realize the function of high efficiency of broadband.
The above-mentioned embodiments are merely preferred embodiments for fully illustrating the present invention, and the scope of the present invention is not limited thereto. The equivalent substitution or change made by the technical personnel in the technical field on the basis of the invention is all within the protection scope of the invention. The protection scope of the invention is subject to the claims.
Claims (10)
1. The design method of the broadband lens based on the quasi-continuous nanoribbon super surface is characterized in that: the method comprises the following steps:
s1: determining and calculating an initial point, a phase requirement and a sample region required to form a quasi-continuous nanobelt;
s2: calculating the orientation angle of the quasi-continuous nanobelt according to the initial point and the phase requirement;
s3: calculating the next nanobelt coordinate point according to a preset moving step length along the orientation angle direction of the quasi-continuous nanobelt;
s4: 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;
s5: the cycle repeats until all quasi-continuous nanoribbons are completed in the sample area, thereby forming a super-surface composed of quasi-continuous nanoribbons.
2. The method for designing a broadband lens based on the super surface of the quasi-continuous nanobelt according to claim 1, wherein: the phase requirement in step S1 is obtained according to the following steps:
wherein k is 0 ＝2π/λ 0 ；
λ 0 Is the calculated wavelength;
f 0 is the lens focal length;
(x, y) are coordinates of the lens plane;
m is an integer;
by using (x) 0 ,y 0 ) The coordinates are substituted for the (x, y) coordinates in equation (a) to determine O 1 (x 0 ,y 0 ) Phase requirement of
3. The method for designing a broadband lens based on the super surface of the quasi-continuous nanobelt according to claim 1, wherein: the next nanoribbon coordinate point in step S3 is calculated according to the following formula:
using PB phase relationship
Point O is obtained 1 (x 0 ,y 0 ) The quasi-continuous nanoribbon orientation angle of (a); the orientation angle is the tangential direction angle of the quasi-continuous nanoribbon at the position;
along the orientation angle alpha 1 Is moved by a step S to obtain another point a 1 (x 1 ,y 1 ) The expression of the coordinates is:
x 1 ＝x 0 +S*cos(α 1 )；
y 1 ＝y 0 +S*sin(α 1 )；
where S denotes a moving step.
4. The method for designing a broadband lens based on the super surface of the quasi-continuous nanobelt according to claim 1, wherein: the next nanoribbon coordinate point in step S3 is along the orientation angle α 1 The negative direction movement of (a) is formed, specifically calculated according to the following formula:
by moving S in the negative direction of the orientation angle, another point can be obtained
The coordinate relation is as follows:
x′ 1 ＝x 0 -S*cos(α 1 )；
y′ 1 ＝y 0 -S*sin(α 1 )。
5. the method for designing a broadband lens based on the super surface of the quasi-continuous nanobelt according to claim 1, wherein: the calculation points on the nanobelts are arranged in the range of the sample area, and the interval between the calculation points on the adjacent nanobelts is matched with the initial preset minimum interval distance of the grating.
6. The method for designing a broadband lens based on the super surface of the quasi-continuous nanobelt according to claim 1, wherein: the spacing between the calculated points formed by the moving step is matched with the minimum spacing distance of the grating.
7. The method for designing a broadband lens based on the super surface of the quasi-continuous nanobelt according to claim 1, wherein: the phase requirement in step S1 is obtained according to the following steps:
wherein k is 0 ＝2π/λ 0 ，λ 0 Is the calculated wavelength. f. of 0 Is the focal length of the super-diffraction lens, (x, y) are the coordinates of the plane of the super-diffraction lens, and m is an integer;
obtaining a required binary system phase by using a linear programming method;
and obtaining the broadband super-diffraction lens based on the quasi-continuous nanoribbon super surface according to the phase requirement of the super-diffraction lens.
8. A lens, characterized by: the lens comprises a substrate and a quasi-continuous nanoribbon structure on the substrate, wherein the quasi-continuous nanoribbon structure is obtained by the design method of any one of claims 1 to 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 nano-belt structure is made of titanium dioxide.
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| CN114675519A (en) * | 2022-03-31 | 2022-06-28 | 重庆大学 | Color hologram design method and device based on PB phase type quasi-continuous super surface |
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| CN113625375A (en) * | 2021-08-02 | 2021-11-09 | 福州大学 | Quasi-periodic superlens based on genetic algorithm optimization |
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| CN109709784A (en) * | 2019-02-01 | 2019-05-03 | 暨南大学 | Super surface color vector complex amplitude holographic element |
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