CN109799611B - Design method of achromatic super-structure lens and achromatic super-structure lens - Google Patents
Design method of achromatic super-structure lens and achromatic super-structure lens Download PDFInfo
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Abstract
The invention relates to the technical field of optical lenses, in particular to a design method of an achromatic super-structure lens and the achromatic super-structure lens thereof. The invention can make the achromatic super-structure lens act on a plurality of target wavelengths by carrying out parameter design, laminating combination and arrangement on the nanometer units forming the achromatic super-structure lens, thereby eliminating the chromatic aberration influence brought by the traditional lens, and the area of the achromatic super-structure lens can be increased to the centimeter level or above.
Description
Technical Field
The invention relates to the technical field of optical lenses, in particular to a design method of an achromatic super-structure lens and the achromatic super-structure lens.
Background
The metamaterial surface is an artificial material with a thickness of a sub-wavelength level, and electromagnetic waves are modulated mainly through photon resonance. Their properties are based on the ability to control the phase and polarization of light using sub-wavelength order media or metal nanoresonators. Accordingly, the super-structured surface can change various properties of phase, polarization, intensity and the like of a transmitted or reflected light beam, and realize various extraordinary optical phenomena such as deflection, reverse reflection, polarization conversion, focusing, beam shaping and the like. Compared with a binary amplitude and phase Fresnel zone plate, the sub-wavelength nano structure of the focusing deformation surface, which is generally called a super-structure lens, can provide more accurate and efficient phase control, and can be used for mobile phone camera lenses or ultrathin microscope objective lenses and the like.
In the conventional lens, it is often difficult to use the lens in an imaging system due to the influence of chromatic aberration, and therefore, the achromatic lens plays a significant role in an imaging optical path. Most of the existing super-structure lenses are usually only acted on specific wavelengths, and the action effect of the super-structure lenses outside the specific wavelengths is not satisfactory; if achromatic focusing of a wide spectral band on a single-layer super-structured lens is required, the area of the single-layer super-structured lens is limited by a formula R _ max NA [ delta ] omega [ ltoreq.2 c [ delta ] phi, and the area is greatly reduced (wherein R _ max is the radius of the lens, NA is the numerical aperture, [ delta ] omega is the spectral width, c is the light speed in vacuum, and [ delta ] phi ] is the phase dispersion interval). In addition, most of the super-structured lenses are polarization dependent, which has strict requirements for incident light and is easily affected by stray light of different polarization states. The above limitations result in a super-structured lens that is not ideal for practical use.
Disclosure of Invention
The present invention is directed to overcoming at least one of the above-mentioned drawbacks of the prior art and providing a method for designing an achromatic meta-lens, which enables the achromatic meta-lens to act on a plurality of target wavelengths by performing parametric design, stacking combination and arrangement on nano-elements forming the achromatic meta-lens, thereby eliminating chromatic aberration influence of the conventional lens, and enabling the area of the achromatic meta-lens to be increased to a centimeter level or more.
The invention also discloses an achromatic super-structure lens.
The technical scheme adopted by the invention is as follows:
provided is a method for designing an achromatic super structure lens, wherein the achromatic super structure lens comprises a plurality of layers of nano units, and the method is characterized by comprising the following steps:
s1, determining the total freedom of single nanometer unit, setting the needed incident light wave band, setting the range and interval of each freedom degree geometric parameter, and simulating and scanning each freedom degree geometric parameter of nanometer unit by using a numerical simulation method to obtain the phase shift and transmittance of the single nanometer unit under different geometric parameter combination to the incident light wave band;
s2, changing the wave band of the incident light, repeating the scanning method of the step S1 to obtain the phase shift and the transmittance of the single nanometer unit under different geometric parameter combinations to different wave bands of the incident light;
s3, adding the phase shifts generated by the single nanometer units with different geometric parameter combinations under the same incident light wave band obtained in the steps S1 and S2, and multiplying the corresponding transmittance by the value to obtain the total phase shift and the total transmittance after the nanometer units with different geometric parameter combinations are stacked under the same incident light wave band;
s4 repeating step S3 to obtain data of total phase shift and total transmittance after stacking among all the nano units with different geometric parameter combinations under the set incident light wave band, and putting all the data into a database;
s5, selecting proper nanometer units from the database of the step S4 according to each target wavelength to carry out lamination combination, and enabling the total phase shift of the laminated nanometer units at different plane coordinates to follow the Fresnel hyperbolic curve arrangement rule:
the arrangement is performed wherein x, y are coordinates of each nano-unit,
and (3) phase shift of a nanometer unit, wherein lambda is target wavelength, n is refractive index of a material background, f is a design focal length, and C (lambda) is an initial phase constant, so that the achromatic super-structure lens is obtained.
The degree of freedom refers to the number of geometric parameters required to fully describe the geometric features of a nano-unit, at least. The method comprises the steps of utilizing a numerical simulation method, such as a time domain finite difference method, a finite element difference method, a coupled wave analysis method and the like, to carry out simulation scanning on a single nanometer unit, and then carrying out numerical simulation on the simulation scanning result to directly obtain the phase shift and transmittance of the single nanometer unit to a corresponding incident light wave band, specifically obtaining electromagnetic field data of the light wave through numerical simulation, wherein the electromagnetic field data specifically comprises intensity, component, polarization, phase, transmittance and the like. The purpose of analog scanning of individual nano-elements is: the phase shift and transmittance of the nano-units under different geometric parameter combinations can be determined, so that proper parameter data can be found when the nano-units are stacked and arranged, and the operation memory and time can be greatly reduced by only carrying out analog scanning on a single nano-unit. In addition, the phase shift between the nano-units under different parameter combinations is added numerically, and the corresponding transmittance is multiplied numerically, so as to: (1) the total phase shift and the total transmittance of the stacked multilayer nano units can be directly calculated, and compared with a single-layer nano unit, the total phase shift and the total transmittance are more in combination, so that a database is greatly enriched; (2) only a single nanometer unit is needed to be scanned, so that the scanning times and the design time can be greatly reduced, and the method plays an important role in the design of the chromatic aberration canceling hyperstructural lens; (3) the processing complexity of each layer of achromatic super-structure lens is reduced, the production and the manufacture are convenient, and the achromatic super-structure lens with the centimeter-level area is easy to manufacture.
If achromatic focusing of a wide spectral band is required to be achieved on a single-layer super-structural lens, the area of the single-layer super-structural lens is limited by a formula R _ max NA delta omega which is less than or equal to 2c delta phi, and the area is greatly reduced (wherein R _ max is the radius of the lens, NA is the numerical aperture, delta omega is the spectral width, c is the light speed in vacuum, and delta phi is the phase dispersion interval).
In the scheme, the method firstly carries out analog scanning on each degree of freedom geometric parameter of a single nano unit, then carries out numerical addition on the phase shift generated by the nano units with different geometric parameter combinations, and carries out numerical multiplication on the transmittance so as to obtain the total phase shift and the total transmittance after the multilayer nano units are superposed, thus obtaining more abundant phase shift and transmittance data and being beneficial to searching for the nano units with proper parameters for laminating combination. And then arranging the superposed nano units according to a Fresnel hyperbolic rule corresponding to each target wavelength, thereby obtaining the achromatic super-structure lens, wherein the achromatic super-structure lens can act on various wavelengths, and the focuses of the achromatic super-structure lens on each wavelength are at the same position, thereby eliminating the chromatic aberration influence of the traditional lens, and the design is more reasonable.
Preferably, in step S5, when the selected nano-cells from the database of step S4 have multiple geometric parameter combinations satisfying the fresnel hyperbolic layout rule, the nano-cells with the geometric parameter combination having a high transmittance are selected for stacking combination to obtain an efficient achromatic super-structural lens.
Preferably, in step S5, before the stack combination, the nanocells having transmittances close to each other for each target wavelength and each phase are selected from the database of step S4 to further improve the achromatic performance of the super-structured lens.
The utility model provides an achromatic super structure lens, includes the substrate and locates substrate one side and carry out the multilayer nanometer unit of range upon range of combination, the nanometer unit is sub-wavelength size, and the multilayer nanometer unit after range upon range of combination is according to fei nieer hyperbola type law:
arranged, wherein x, y are coordinates of each nano-unit,
for the phase shift of the nano-unit, λ is the target wavelength, n is the index of refraction of the material background, f is the design focal length, and C (λ) is the initial phase constant.
For the achromatic super-structure lens, the target wavelength lambda has a plurality of values, so the superposed nano units need to simultaneously meet the Fresnel hyperbolic law of each target wavelength so as to meet the achromatic effect on incident light with different target wavelengths. The nanometer units form an achromatic metamorphic lens through parameter design, stacking and arrangement, the condition of achromatism can be met for a plurality of target wavelengths, the achromatic function of the centimeter-level metamorphic lens can be realized, and more practical applications can be realized, such as a mobile phone camera, a high-resolution microscope, virtual reality and the like.
Preferably, an adhesive layer is also arranged between the nano units of the adjacent layers which are subjected to the stacking combination.
Preferably, the nano-units are symmetrical structures. Namely, the nanometer units act on incident lights in different linear polarization states in a consistent manner, so that the achromatic super-structure lens also meets the polarization-independent condition at the same time, has no strict requirement on the polarization state of the incident lights and has wider action range.
Preferably, the nano-unit is prepared by adopting one optical medium material of optical crystal, optical glass, optical film, optical plastic, optical metal or optical metamaterial. The optical crystal includes optical single crystal, optical polycrystal, optical amorphous, etc.; the nano-unit can be prepared from different optical medium materials such as optical crystals, optical glass, optical films, optical plastics, optical metals or optical metamaterials and the like.
Preferably, the nano units are provided with micro-nano structures arranged in a graphical manner. The required micro-nano structure can be etched on the nano unit through dry etching or wet etching.
Further preferably, the patterned arrangement method of the micro-nano structures is one or more of electron beam etching, ultraviolet lithography and laser direct writing. The super-structure lens can be used for arranging the graphical micro-nano structure by methods such as but not limited to electron beam etching, ultraviolet lithography, laser direct writing and the like.
Compared with the prior art, the invention has the beneficial effects that:
firstly, the phase shifts generated by the nanometer units with different geometric parameter combinations are added in numerical value, the transmittance is multiplied in numerical value, the scanning of the multilayer nanometer unit with extremely large scanning parameter quantity can be avoided, and the following effects are achieved: (1) compared with a single-layer nanometer unit, the phase shift and transmittance data are more, and a database is greatly enriched; (2) the stacked combination design of the nanometer units can greatly reduce the scanning times and the design time, and plays an important role in the design of the achromatic super-structure lens; (3) the processing complexity of each layer of the super-structure lens is reduced, the production and the manufacture are convenient, and the achromatic super-structure lens with the centimeter-level area is easy to manufacture.
The superposition method of the invention is equivalent to the division of a target focusing light wave band into a plurality of independent target wave bands, and the achromatic focusing is realized by the super-structure lenses of different layers, thereby reducing the spectral dispersion of each layer of structure, effectively increasing the area of the achromatic super-structure lens to be at the centimeter level or above, and having important application in the aspect of imaging.
In addition, the super-structured lens meets the polarization non-relevant condition, has no harsh requirement on the polarization state of incident light, and is more reasonable in design.
And fourthly, numerical value superposition combination is carried out on the phase shift and the transmittance generated by the nano units combined by different geometric parameters, as long as proper nano unit parameters are found, the obtained super-structure surface can meet the achromatic effect on incident light with any wavelength, and meanwhile, the obtained super-structure lens can be applied to more practical applications, such as high-resolution and low-consumption confocal microscopes, mobile phone cameras, virtual reality and the like.
Drawings
Fig. 1(a) is a front view of a cylindrical nano-element of the achromatic meta-lens.
Fig. 1(b) is a left side view of the cylindrical nano-elements of the achromatic meta-lens.
Fig. 1(c) is a top view of a cylindrical nano-element of the achromatic super lens.
Fig. 2 is a schematic structural diagram of an achromatic super-structured lens with three superimposed layers.
Fig. 3 is a schematic diagram of the degree of coincidence between the actual phase shift of the three superimposed achromatic meta-lenses at different radial coordinates for different wavelengths and the desired phase shift required by the fresnel hyperbola.
FIG. 4 is a partial view of the surface of the arrangement of nano-elements of the achromatic meta-lens.
FIG. 5 is a side view of a partial arrangement of the nano-elements of the achromatic meta-lens.
The reference numbers illustrate: 1, a substrate; 2 a first nano-unit; 3 a first adhesive layer; 4 a second nano-unit; 5 a second adhesive layer; 6 third nano-unit.
Detailed Description
The drawings are only for purposes of illustration and are not to be construed as limiting the invention. For a better understanding of the following embodiments, certain features of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product; it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
Example 1
A method for designing an achromatic super structure lens, as shown in fig. 1-2, taking an achromatic super structure lens formed by stacking three layers of a first nano unit 2, a second nano unit 4 and a third nano unit 6 as an example, the first nano unit 2, the second nano unit 4 and the third nano unit 6 have three degrees of freedom respectively, and the total degree of freedom of stacking three layers is nine, and the method includes the following steps:
s1, determining the total degree of freedom of each of the single nanometer units 2, 4 and 6, setting a required incident light waveband, setting the range and interval of geometric parameters of each degree of freedom, and performing simulation scanning on the geometric parameters of each degree of freedom of the nanometer units 2, 4 and 6 by using a numerical simulation method to obtain the phase shift and transmittance of each incident light waveband of each of the single nanometer units 2, 4 and 6 under different geometric parameter combinations;
s2, changing the incident light wave band, repeating the scanning method of step S1 to obtain the phase shift and transmittance of the single nanometer unit 2, 4, 6 under different geometric parameter combination to different incident light wave bands;
s3, adding the phase shifts generated by the single nanometer units 2, 4 and 6 with different geometric parameter combinations under the same incident light wave band obtained in the steps S1 and S2, and multiplying the corresponding transmittance by the value to obtain the total phase shift and the total transmittance after the nanometer units 2, 4 and 6 with different geometric parameter combinations are stacked under the same incident light wave band;
s4 repeating step S3 to obtain data of total phase shift and total transmittance after stacking of all the nano units 2, 4 and 6 with different geometric parameter combinations under the set incident light wave band, and putting all the data into a database;
s5, selecting appropriate nano- units 2, 4, and 6 from the database of step S4 according to the respective target wavelengths, and stacking and combining the nano- units 2, 4, and 6, so that the total phase shift of the stacked nano- units 2, 4, and 6 at different plane coordinates follows the fresnel hyperbolic curve arrangement rule:
the arrangement is performed wherein x, y are coordinates of each nano-unit,
and (3) phase shift of a nanometer unit, wherein lambda is target wavelength, n is refractive index of a material background, f is a design focal length, and C (lambda) is an initial phase constant, so that the achromatic super-structure lens is obtained.
The invention utilizes a numerical simulation method, such as a time domain finite difference method, a finite element difference method, a coupled wave analysis method and the like to carry out simulation scanning on the single nanometer units 2, 4 and 6, and then the results of the simulation scanning are subjected to numerical simulation to directly obtain the phase shift and the transmittance of the single nanometer units 2, 4 and 6 to the corresponding incident light wave bands, specifically, the electromagnetic field data of the light waves can be obtained through the numerical simulation, and the electromagnetic field data specifically comprise intensity, component, polarization, phase, transmittance and the like. The superposition method of the invention is equivalent to the division of a target focusing light wave band into a plurality of independent target wave bands, and the achromatic focusing is realized by the super-structure lenses of different layers, thereby reducing the spectral dispersion of each layer of structure, effectively increasing the area of the achromatic super-structure lens to be at the centimeter level or above and promoting the application of the achromatic super-structure lens in the aspect of imaging.
The method firstly carries out analog scanning on the geometric parameters of each degree of freedom of the single nanometer units 2, 4 and 6, then carries out numerical addition on the phase shifts generated by the nanometer units 2, 4 and 6 with different geometric parameter combinations, and carries out numerical multiplication on the transmittance so as to obtain the total phase shift and the total transmittance after the multilayer nanometer units 2, 4 and 6 are superposed, thus obtaining richer phase shift and transmittance data and being beneficial to searching for the nanometer units 2, 4 and 6 with proper parameters to carry out lamination combination. And then arranging the superposed nano units 2, 4 and 6 according to a Fresnel hyperbolic rule meeting the correspondence of each target wavelength to obtain the achromatic super-structure lens, wherein the achromatic super-structure lens can act on various wavelengths, and the focuses of the achromatic super-structure lens on each wavelength are at the same position, so that the chromatic aberration influence of the traditional lens is eliminated, and the design is more reasonable.
In step S5, when the multiple combinations of the geometric parameters of the nano- cells 2, 4, and 6 selected from the database in step S4 all satisfy the fresnel hyperbolic curve arrangement rule, the nano- cells 2, 4, and 6 with the geometric parameter combination having a high transmittance are preferably selected for stacking and combining. Furthermore, it is ensured that the selection of nanocells 2, 4, 6 with close transmission for each target wavelength and each phase is possible before the stack combination to obtain an efficient achromatic meta-lens.
Example 2
As shown in fig. 2, 4, and 5, the achromatic super structure lens design method according to embodiment 1 includes a substrate 1 and a plurality of stacked nano- elements 2, 4, and 6 disposed on one side of the substrate 1, wherein the nano- elements 2, 4, and 6 are of sub-wavelength size, and the stacked and combined plurality of nano- elements 2, 4, and 6 follow fresnel hyperbolic law:
arranged, wherein x, y are coordinates of each nano-unit,
for the phase shift of the nano-unit, λ is the target wavelength, n is the index of refraction of the material background, f is the design focal length, and C (λ) is the initial phase constant.
As shown in fig. 2, 4 and 5, taking an achromatic super lens in which three layers are stacked as an example, the first nanocell 2 and the second nanocell 4 are cylindrical nanocells of single crystal silicon, and the third nanocell 6 is a cylindrical nanocell of silicon nitride. An adhesive layer is further disposed between adjacent nano units 2, 4, and 6 for stacking and combining, as shown in fig. 2, a first adhesive layer 3 is disposed between the first nano unit 2 and the second nano unit 4, and a second adhesive layer 5 is disposed between the second nano unit 4 and the third nano unit 6. Because the lens is an achromatic super-structure lens, a plurality of target wave bands lambda exist, and therefore the total phase shift of the designed nano units 2, 4 and 6 after being laminated can simultaneously meet the Fresnel hyperbolic rule corresponding to each target wave band. As shown in fig. 3, the three superimposed layers of the achromatic meta-lens correspond to the ideal phase required by the fresnel hyperbola in different positions for different wavelengths of actual phase.
In particular, the nano- units 2, 4, 6 are preferably of a symmetrical structure to satisfy the polarization-independent condition, so that the polarization state of the incident light is not critical and the design is more reasonable.
The nano units 2, 4 and 6 are prepared from one optical medium material of optical crystal, optical glass, optical film, optical plastic, optical metal or optical metamaterial.
By adopting the design method and arrangement mode described in embodiment 1, the achromatic super-structure lens can perform patterned micro-nano structure arrangement on the nano units 2, 4 and 6 by methods such as but not limited to electron beam etching, ultraviolet lithography, laser direct writing and the like, and etch the required micro-nano structure on the wafers of the nano units 2, 4 and 6 by dry etching or wet etching.
Of course, the number of stacked achromatic meta-lenses of the present invention is not limited to three-layer structures, and can be flexibly designed according to the requirements of various target wavelengths.
It should be understood that the above-mentioned embodiments of the present invention are only examples for clearly illustrating the technical solutions of the present invention, and are not intended to limit the specific embodiments of the present invention. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention claims should be included in the protection scope of the present invention claims.
Claims (9)
1. A method of designing an achromatic metamorphic lens comprising a plurality of layers of nano-elements, comprising the steps of:
s1, determining the total freedom of single nanometer unit, setting the needed incident light wave band, setting the range and interval of each freedom degree geometric parameter, and simulating and scanning each freedom degree geometric parameter of nanometer unit by using a numerical simulation method to obtain the phase shift and transmittance of the single nanometer unit under different geometric parameter combination to the incident light wave band;
s2, changing the wave band of the incident light, repeating the scanning method of the step S1 to obtain the phase shift and the transmittance of the single nanometer unit under different geometric parameter combinations to different wave bands of the incident light;
s3, adding the phase shifts generated by the single nanometer units with different geometric parameter combinations under the same incident light wave band obtained in the steps S1 and S2, and multiplying the corresponding transmittance by the value to obtain the total phase shift and the total transmittance after the nanometer units with different geometric parameter combinations are stacked under the same incident light wave band;
s4 repeating step S3 to obtain data of total phase shift and total transmittance after stacking among all the nano units with different geometric parameter combinations under the set incident light wave band, and putting all the data into a database;
s5, selecting proper nanometer units from the database of the step S4 according to each target waveband, stacking and combining, and enabling the total phase shift of the stacked nanometer units at different plane coordinates to follow the Fresnel hyperbolic curve arrangement rule:
the arrangement is performed wherein x, y are coordinates of each nano-unit,
and (3) phase shift of a nanometer unit, wherein lambda is target wavelength, n is refractive index of a material background, f is a design focal length, and C (lambda) is an initial phase constant, so that the achromatic super-structure lens is obtained.
2. The method of claim 1, wherein in step S5, when the selected nano-cells from the database of step S4 have a plurality of geometrical parameter combinations satisfying the Fresnel hyperbolic curve layout rule, the nano-cells with the geometrical parameter combination having a high transmittance are selected for stacking and combining.
3. The method of designing an achromatic meta-lens according to claim 1, wherein in step S5, before the stack combination, the nano-elements having transmittances close to each target wavelength band and each phase are selected from the database in step S4.
4. An achromatic super-structure lens designed by the design method of any one of claims 1 to 3, comprising a substrate and a plurality of layers of nano-units which are arranged on one side of the substrate and are stacked and combined, wherein the nano-units have a sub-wavelength band size, and the stacked and combined plurality of layers of nano-units follow the Fresnel hyperbolic law:
arranged, wherein x, y are coordinates of each nano-unit,
for the phase shift of the nano-unit, λ is the target wavelength, n is the index of refraction of the material background, f is the design focal length, and C (λ) is the initial phase constant.
5. An achromatic super-structured lens according to claim 4, characterised in that an adhesive layer is also provided between the nano-elements of adjacent layers of the superimposed assembly.
6. An achromatic super lens according to claim 4, characterised in that the nano-elements are symmetrical structures.
7. An achromatic metamorphic lens as in claim 4, wherein said nano-elements are fabricated from an optical medium material selected from the group consisting of optical crystals, optical glasses, optical films, optical plastics, optical metals and optical metamaterials.
8. An achromatic super structure lens according to claim 4, wherein patterned micro-nano structures are provided on said nano-elements.
9. The achromatic super structure lens according to claim 8, wherein the patterned arrangement method of the micro-nano structures is one or more of electron beam etching, ultraviolet lithography and laser direct writing.
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| KR102587958B1 (en) * | 2017-02-03 | 2023-10-11 | 삼성전자주식회사 | Meta optical device and method of fabricating the same |
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| CN109164574B (en) * | 2018-09-19 | 2020-08-28 | 北京理工大学 | Method for realizing wavefront modulation based on medium conformal metasurface |
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