CN115755384A - Polarization-independent super-surface design method based on medium structure and super-surface lens - Google Patents
Polarization-independent super-surface design method based on medium structure and super-surface lens Download PDFInfo
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Abstract
The invention relates to the field of micro-nano optics and optical chip integration, in particular to a polarization-independent super-surface design method based on a medium structure and a super-surface lens comprising the super-surface structure; the super surface design method comprises the following steps: s1, constructing a unit structure database which corresponds to a plurality of wavelengths and can cover 0-2 pi transmission phases to obtain transmission phase data; s2, calculating ideal phase distribution of the super-surface structure according to the superposition principle of the hologram; s3, matching the ideal phase distribution obtained in the step S2 with the transmission phase data obtained in the step S1, optimizing the difference between the phases as a target evaluation function, and forming a super-surface structure by using the finally obtained structural parameters; the super-surface structure can realize array multi-wavelength multiplexing in the same view field, avoids the influence on incident light beam splitting, multi-wavelength chromatic aberration and the like compared with the splicing of a plurality of super lenses, and has great application prospect.
Description
Technical Field
The invention relates to the field of micro-nano optics and optical chip integration, in particular to a polarization-independent super-surface design method based on a medium structure and a super-surface lens comprising the super-surface structure.
Background
The array beam has the advantages of being fast, parallel and simultaneous in processing, and is widely applied to the fields of imaging, optical communication and the like. For the communication field, the vortex light beams of the array can not only improve the information safety, but also improve the information capacity; topological charge carried by orbital angular momentum and annular light intensity distribution can provide torque moment and gradient force for tiny particles, can be applied to the control of microscopic particles, and vortex beams of the array can capture more particles simultaneously, and change the distribution and mode of the captured particles through the loading of functions such as wavelength multiplexing and the like; in the field of imaging, the multiplexed focusing light beams are more convenient for regulating and controlling and comparing light beams with different channels, and the method has great significance for simplifying an imaging system.
At present, a beam splitter, a lens array, a diffractive optical element and the like are mainly used for generating an array light beam to divide an incident light beam into a plurality of beams, and the array light beam is widely applied to the fields of imaging, optical communication and the like. However, the manufacturing process of the optical element is usually very complex, and the corresponding optical system is also bulky, which brings difficulties to the miniaturization of the structure, and limits the application of the optical element in the field of integrated optics, and for some complex application fields, the non-modulation of the optical element also limits the flexibility of the application. In recent years, research based on the super surface field has attracted the attention of a large number of researchers.
The super surface is a periodic or non-periodic array composed of sub-wavelength structures, and corresponding optical response is obtained by controlling the geometric parameters of the unit structure, so that the incident electromagnetic waves are regulated and controlled. Compared with the traditional optical lens, the super surface introduces a sudden change phase, does not depend on phase accumulation in the propagation process, has the advantages of miniaturization, easy control and the like, and has the functions of plane lens, structural beam generator, optical holography, polarization control and the like.
Aiming at the realization of the array beam function, in 2016, m.q. mehmood and the like generate a poly Jiao Guoxuan beam by utilizing spatial multiplexing, in 2019, HAORAN LV and the like propose an optical super-surface super lens of a multi-focus metal sub-wavelength grating, however, the realization of most super-surface array beams still depends on a geometric phase structure based on polarized light, and in order to further improve energy efficiency and simplify an optical system, particularly when the super-surface super lens is used for an unpolarized light source, a polarization-independent holographic super surface needs to be designed. For example, single molecule detection techniques of fluorescent labeling, especially studies on multi-color single molecule fluorescent arrays and biomolecular chirality, have a significant demand for multi-color non-polarized arrays to focus light beams. In addition, optical communication, optical particle manipulation, etc. require high energy density vortex beams, and polarization independent holographic vortex light array beams would have significant advantages.
Disclosure of Invention
In order to solve the problems, the invention provides a polarization-independent multi-wavelength multi-focus super surface design method based on a medium structure.
The invention provides a polarization-independent super-surface design method based on a medium structure, which comprises the following steps:
s1, constructing a unit structure database which corresponds to a plurality of wavelengths and can cover 0-2 pi transmission phases to obtain transmission phase data;
s2, calculating the ideal phase distribution of the super-surface structure according to the superposition principle of the hologram as follows:
Φ(x,y,λ)＝arg(E(x,y,λ))；
phi (x, y, lambda) represents the ideal phase of the holographic super surface with different wavelengths, x and y represent the position coordinates of the unit structure on the super lens, E represents the amplitude distribution after interference, and lambda represents the wavelength;
and S3, matching the ideal phase distribution obtained in the step S2 with the transmission phase data obtained in the step S1, optimizing the difference between the phases as a target evaluation function, and forming the super-surface structure by using the finally obtained structural parameters.
Preferably, in S2, the formula of the complex amplitude distribution of the focused beam array which is superimposed by the superposition principle of the hologram is as follows:
(x m ,y n ) Denotes the abscissa and ordinate of the respective focal spot with respect to the lens center, f denotes the axial distance of the focal plane with respect to the lens, A mn Representing the amplitude distribution of the corresponding focal spot.
Preferably, in S2, the formula of the complex amplitude distribution of the focused vortex beam array superimposed by the superposition principle of the hologram is as follows:
(x m ,y n ) Denotes the abscissa and ordinate of the respective focal spot relative to the center of the lens, f denotes the axial distance of the focal plane relative to the lens, A mn Representing the amplitude distribution of the corresponding focal spot, e representing an index.
Preferably, the difference in wavelength between each of the plurality of wavelengths is not less than 100nm.
Preferably, the constructing of the cell structure database corresponding to a plurality of wavelengths and capable of covering the transmission phase of 0 to 2 pi includes scanning the cell structure with different radius values through linearly polarized light in any direction, and obtaining the transmission phase data of the cell structure.
Preferably, the wavelength range of the linearly polarized light scanning is 80nm to 310nm.
Preferably, the unit structure comprises an upper layer structure and a lower layer structure, the upper layer structure is a dielectric nano-pillar, and the lower layer structure is a dielectric substrate; the medium nano column is of a cylindrical structure; the dielectric substrate is of a cube structure.
Preferably, the matching of the ideal phase distribution obtained in step S2 and the transmission phase data obtained in step S1 is implemented by a genetic algorithm.
Preferably, the calculation formula of the objective evaluation function is as follows:
The invention also provides a super-surface lens which comprises a super-surface structure, wherein the super-surface structure is designed by the super-surface design method.
The invention provides a wavelength multiplexing multi-channel array light beam generator by combining a genetic algorithm and a phase type computer holography method, the array light beam can be reconstructed by adjusting the wavelength of incident light, and the transmission phase of the structure is utilized, so that the structure has the characteristic of polarization insensitivity; the super-surface structure designed by the design method can realize array multi-wavelength multiplexing in the same view field, avoids the influence on incident light beam splitting and multi-wavelength chromatic aberration and the like compared with the splicing of a plurality of super lenses, and has great application prospect.
Drawings
FIG. 1 is a phase distribution diagram of a cell structure at three RGB wavelengths according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a cell structure in a super-surface lens in an embodiment of the present invention;
FIG. 3 is a normalized intensity distribution of a focused beam array representing a B, G, R three wavelength focal plane in one embodiment of the present invention;
FIG. 4 is a top view of a super surface lens structure in an embodiment of the invention;
FIG. 5 is a normalized intensity distribution of a focused vortex beam array representing a B, G, R three wavelength focal planes in another embodiment of the present invention;
FIG. 6 is a top view of a super surface lens structure in another embodiment of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not to be construed as limiting the invention.
In a specific embodiment of the present invention, a polarization independent super-surface design method based on a medium structure is provided, and the super-surface design method includes the steps of:
s1, constructing a unit structure database which corresponds to a plurality of wavelengths and can cover 0-2 pi transmission phases to obtain transmission phase data;
s2, calculating the ideal phase distribution of the super-surface structure according to the superposition principle of the hologram as follows:
Ф(x,y,λ)＝arg(E(x,y,λ))；
phi (x, y, lambda) represents the ideal phase of the holographic super surface with different wavelengths, x and y represent the position coordinates of the unit structure on the super lens, E represents the amplitude distribution after interference, and lambda represents the wavelength;
in a specific embodiment, the principle of hologram superposition mainly refers to that each focal point on the focal plane is regarded as a luminous spherical wave, interference is performed on a superlens, and the phase of the field after interference is extracted, and E is the amplitude distribution after interference.
And S3, matching the ideal phase distribution obtained in the step S2 with the transmission phase data obtained in the step S1, optimizing the difference between the phases as a target evaluation function, and arranging the finally obtained structural parameters into a super-surface structure.
In a specific embodiment, as shown in fig. 2, which is a schematic diagram of a unit structure in a super-surface lens according to an embodiment of the present invention, it can be seen from the diagram that the designed structure arrangement of the super-surface lens includes an upper layer structure and a lower layer structure, where the upper layer structure is a dielectric nano-pillar 2, and the lower layer structure is a dielectric substrate 1, that is, the dielectric substrate 1 and the dielectric nano-pillar 2 are included from top to bottom. In the specific embodiment, the dielectric substrate 1 is a cubic structure, the material of the dielectric substrate 1 may be silicon dioxide, silicon, sapphire, gallium arsenide and other dielectric materials with low loss in visible light wavelength, and in the specific embodiment, nano SiO is used 2 For example, a side length of P, i.e., the period P of the cell structure, which is the sampling frequency of the phase profile, must satisfy the nyquist sampling condition, i.e., P < λ/2NA, where λ is the wavelength and NA is the numerical aperture of the lens; by setting the p value to be smaller than all the wavelengths in the free space, the waveguide mode resonance can be excited to generate abnormal phase response, and the purpose of inhibiting the higher diffraction order is achieved.
In the specific embodiment, the dielectric nanorod 2 is a cylindrical structure, and the dielectric nanorod 2 may be made of titanium dioxide, gallium nitride, silicon nitride, or other high refractive index and low loss materials, in which case the dielectric nanorod 2 is made of nano-TiO 2 For example, the diameter of the cylinder is D, the height is H, the diameter D of the cylinder is smaller than the period p, and the larger the height H is, the wider the phase coverage is; the polarization insensitivity of the unit structure can be better realized by selecting the nano column with the cylindrical structure, and meanwhile, the unit structure is a rotational symmetric structure, so that the transmissivity is more uniform; in a specific embodiment, when the unit structure period is 320nm, the nano TiO 2 The diameter D of the cylindrical structure has a minimum value of 80nm, a maximum value of 310nm,namely, when the medium nano-columns with different radius values are scanned, the scanning range is 80nm to 310nm; nano TiO 2 2 The height H of the cylindrical structure may then be chosen to be 600nm.
In a specific implementation mode, firstly, the relation between unit structures with different radius values and transmission phases is obtained so as to carry out matching fitting with ideal phases with different wavelengths; specifically, transmission phase data of the unit structure is obtained by scanning the unit structure with different radius values through linearly polarized light in any direction, so that a unit structure database which corresponds to a plurality of wavelengths and can cover 0-2 pi transmission phases is constructed, and the transmission phase data is obtained.
In a specific embodiment, three wavelengths (486nm, 587nm, 656nm) capable of representing the three primary colors of visible light are selected for design, the unit structure period is 320nm, the upper layer structure is a cylinder of titanium dioxide, and the lower layer is a cube of silicon dioxide. With the aid of simulation software fdtd, transmission phase data of a unit structure are obtained by scanning medium nano-columns with different radius values, wherein the scanning range is 80nm to 310nm; and then, the geometric parameters and phase data obtained by software calculation are used for establishing a structure-phase database required by the next work.
Due to the complete symmetry of the cylindrical structure, the optical fiber is insensitive to light waves polarized in different directions; specifically, the light wave polarized in the x direction is used for the subsequent analysis, because the scanning range is large, the phase response coverage obtained through simulation is large, and in the design process, the condition can be met only by the phase coverage of 0-2 pi, and the designed phase meets the basic requirement according to the phase distribution diagram of the unit structure shown in fig. 1 under the three wavelengths of RGB.
In a specific embodiment, a super surface with a caliber of 16um and a focal length of 10um is designed, the whole super surface is discretized into 100 × 100 pixel points, and a processing phase value of each pixel point can be obtained according to an ideal phase formula.
In a specific embodiment, the ideal phase distribution of the super-surface structure is as shown in formula (1):
Φ(x,y,λ)＝arg(E(x,y,λ)) (1)
phi (x, y, lambda) represents the ideal phase of the holographic super surface with different wavelengths, x and y represent the position coordinates of the unit structure on the super lens, E represents the amplitude distribution after interference, and lambda represents the wavelength;
equation (2) for the complex amplitude distribution of the focused beam array superimposed together by the superposition principle of holograms is:
(x m ,y n ) Denotes the abscissa and ordinate of the respective focal spot relative to the center of the lens, f denotes the axial distance of the focal plane relative to the lens, A mn Representing the amplitude distribution of the corresponding focal spot, e representing an index.
Then, the previously calculated transmission phase database is called again, in order to find the most suitable structural arrangement, the transmission phase which is matched with the ideal phase of different wavelengths is also searched for generating the super-surface structure, and the process of searching the transmission phase can quickly find the structure which meets the requirements through solving the minimum value by a genetic algorithm.
In a specific embodiment, matching between ideal phase distribution and transmission phase data is realized through a genetic algorithm, and when the ideal phase distribution and the transmission phase data are specifically matched, a difference between phases can be optimized as an objective evaluation function, specifically, the objective evaluation function is shown as formula (3):
wherein the content of the first and second substances,
representing the actual phase randomly chosen from the database,
represents an ideal phase calculated by formula (1) or formula (2),
then represents the sum of the fitted differences for each wavelength phase; continuously couple through genetic algorithm
Iterative optimization is carried out, and finally matching of the actual phase in the phase database and the ideal phase among different wavelengths is achieved to a certain degree.
The invention also provides a super-surface lens, which comprises a super-surface structure, wherein the super-surface structure is designed by the super-surface design method; the simulation result of the super-surface lens is shown in fig. 3, the first three diagrams from left to right in the diagram represent the normalized light intensity distribution of the focused light beam array of B, G, R with three wavelength focal planes, fig. 4 is a top view of the super-surface lens structure in the specific embodiment, as can be seen from fig. 3 and fig. 4, the position arrangement of the focal spots conforms to the theoretical design, the focal spots are 4 micrometers away from the origin and are hexagonally divided, the maximum position error is only about 0.31 λ, the side lobes are small, the energy is concentrated, the energy efficiency ratios of different light spots in the same wavelength are substantially equal, and the corresponding numerical values are shown in table 1.
TABLE 1 focal position, efficiency, full Width half Max values of Supersurface lenses
The data in table 1 illustrate that the super-surface lens provided by the present invention can realize the function of generating different array beams when incident with different wavelengths.
For better understanding of the present invention, the following is a more detailed description of the specific implementation of the design method of the present invention by means of specific examples.
In other specific embodiments, since the generated focused beams or vortex beams have inconsistent interference amplitudes during the superposition, in order to prove the universality of the polarization-independent super-surface design method based on the medium structure provided by the invention, a wavelength multiplexing vortex beam array generator based on the super-surface structure is additionally designed, in the embodiment, the formula (3) of the complex amplitude distribution of the focused vortex beam array which is superposed together by the superposition principle of the hologram is as follows:
(x m ,y n ) Denotes the abscissa and ordinate of the respective focal spot relative to the center of the lens, f denotes the axial distance of the focal plane relative to the lens, A mn Representing an amplitude distribution of the respective focal spot; similar to the previous embodiment, the corresponding simulation result is obtained as shown in fig. 5, the first three graphs from left to right in the figure show the normalized light intensity distribution of the focused vortex light beam array of B, G, R with three wavelength focal planes, fig. 6 is a top view of the super-surface lens structure in this embodiment, as can be seen from fig. 5 and 6, under the irradiation of light waves with different wavelengths, different vortex arrays are emitted from the super-surface, and the topological charges of the vortex arrays are variable in space, which proves the universality of the polarization-independent super-surface design method based on the medium structure provided by the present invention.
The invention provides a wavelength multiplexing multi-channel array light beam generator by combining a genetic algorithm and a phase type computer holography method, the array light beam can be reconstructed by adjusting the wavelength of incident light, and the transmission phase of the structure is utilized, so that the structure has the characteristic of polarization insensitivity; the super-surface structure designed by the design method can realize array multi-wavelength multiplexing in the same view field, avoids the influence on incident light beam splitting and multi-wavelength chromatic aberration and the like compared with the splicing of a plurality of super lenses, and has great application prospect.
While embodiments of the present invention have been shown and described above, it should be understood that the above embodiments are exemplary and should not be taken as limiting the invention. Variations, modifications, substitutions and alterations of the above-described embodiments may be made by those of ordinary skill in the art without departing from the scope of the present invention.
The above embodiments of the present invention should not be construed as limiting the scope of the present invention. Any other corresponding changes and modifications made according to the technical idea of the present invention should be included in the protection scope of the claims of the present invention.
Claims (10)
1. A polarization-independent super-surface design method based on a medium structure is characterized by comprising the following steps:
s1, constructing a unit structure database which corresponds to a plurality of wavelengths and can cover 0-2 pi transmission phases to obtain transmission phase data;
s2, calculating the ideal phase distribution of the super-surface structure according to the superposition principle of the hologram as follows:
Ф(x,y,λ)＝arg(E(x,y,λ))；
phi (x, y, lambda) represents the ideal phase of the holographic super surface with different wavelengths, x and y represent the position coordinates of the unit structure on the super lens, E represents the amplitude distribution after interference, and lambda represents the wavelength;
and S3, matching the ideal phase distribution obtained in the step S2 with the transmission phase data obtained in the step S1, optimizing the difference between the phases as a target evaluation function, and arranging the finally obtained structural parameters into a super-surface structure.
2. The method of claim 1, wherein in S2, the formula of the complex amplitude distribution of the focused beam array superimposed by the superposition principle of the hologram is:
(x m ,y n ) Denotes the abscissa and ordinate of the respective focal spot relative to the center of the lens, f denotes the axial distance of the focal plane relative to the lens, A mn Representing the amplitude distribution of the corresponding focal spot, e representing an index.
3. The method according to claim 1, wherein in S2, the formula of the complex amplitude distribution of the focused vortex beam array superimposed by the superposition principle of the hologram is:
(x m ,y n ) Denotes the abscissa and ordinate of the respective focal spot relative to the center of the lens, f denotes the axial distance of the focal plane relative to the lens, A mn Representing the amplitude distribution of the corresponding focal spot.
4. A method for super-surface design according to claim 1, wherein the difference in wavelength between each of the plurality of wavelengths is not less than 100nm.
5. The method according to claim 1, wherein the constructing of the cell structure database corresponding to a plurality of wavelengths and capable of covering the transmission phase of 0-2 pi includes scanning the cell structure with different radius values by linearly polarized light in any direction, and obtaining the transmission phase data of the cell structure.
6. A method of designing a meta-surface as claimed in claim 5 wherein the wavelength of the linearly polarised light scan is in the range 80nm to 310nm.
7. The method of claim 5, wherein the unit structure comprises an upper layer structure and a lower layer structure, the upper layer structure is a dielectric nano-pillar, and the lower layer structure is a dielectric substrate; the medium nano column is of a cylindrical structure; the dielectric substrate is of a cubic structure.
8. A method for designing a meta-surface according to claim 1 wherein the matching of the ideal phase distribution obtained in step S2 with the transmitted phase data obtained in step S1 is performed by genetic algorithms.
9. A method for designing a meta surface according to claim 8, wherein the objective merit function is calculated as follows:
10. A super-surface lens, characterized in that the super-surface lens comprises a super-surface structure, and the super-surface structure is designed by the super-surface design method of any one of claims 1 to 9.
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| CN116680766A (en) * | 2023-08-01 | 2023-09-01 | 杭州纳境科技有限公司 | Method and device for determining achromatic superlens, electronic equipment and storage medium |
| CN116720420A (en) * | 2023-08-07 | 2023-09-08 | 杭州纳境科技有限公司 | Super-surface light beam regulation and control method and device |
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| CN116430678A (en) * | 2023-03-23 | 2023-07-14 | 华中科技大学 | Femtosecond laser direct writing system based on multifocal superlens |
| CN116430678B (en) * | 2023-03-23 | 2024-02-06 | 华中科技大学 | Femtosecond laser direct writing system based on multifocal superlens |
| CN116449490A (en) * | 2023-06-19 | 2023-07-18 | 南昌大学 | Preparation method of three-dimensional light quantum chip module and three-dimensional light quantum chip module |
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| CN116680766A (en) * | 2023-08-01 | 2023-09-01 | 杭州纳境科技有限公司 | Method and device for determining achromatic superlens, electronic equipment and storage medium |
| CN116680766B (en) * | 2023-08-01 | 2023-11-10 | 杭州纳境科技有限公司 | Method and device for determining achromatic superlens, electronic equipment and storage medium |
| CN116720420A (en) * | 2023-08-07 | 2023-09-08 | 杭州纳境科技有限公司 | Super-surface light beam regulation and control method and device |
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