CN118393621B - Super-lens for achromatism, catadioptric hybrid lens, and method of designing super-lens - Google Patents
Super-lens for achromatism, catadioptric hybrid lens, and method of designing super-lens Download PDFInfo
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Abstract
The invention provides a design method for an achromatic super lens, a folded super hybrid lens and a super lens, wherein the super lens comprises the following components: a substrate having a first surface and a second surface disposed opposite to each other; the modulation functional layer is arranged on the first surface and/or the second surface, and is provided with a plurality of micro-nano units which are rotationally symmetrically arranged along the central axis of the superlens, and the projection of the micro-nano units on the substrate is in a regular polygon shape, so that the projection shape of all the micro-nano units on the substrate is the same as the shape of the regular polygon; the micro-nano unit comprises micro-nano structures arranged in the center of the micro-nano unit, all the micro-nano structures are different in shape and/or size along the radial direction of the superlens, and the superlens meets the minimum optimization target I in the preset wavelength range. The invention solves the problems that the eyeball tracking optical module in the prior art is difficult to achieve miniaturization, small chromatic aberration and good processability.
Description
Technical Field
The invention relates to the technical field of eyeball tracking optical equipment, in particular to a super-lens for achromatism, a folded and super-mixed lens and a design method of the super-lens.
Background
With the leap in information interaction demands, users put higher performance demands on consumer-grade cell phone cameras, AR/MR devices, etc., and high performance has to be achieved by means of more cumbersome and more complex optical systems. Meanwhile, in order to meet wearing comfort and use comfort, extremely "light and thin" is also being pursued for optical systems.
The eyeball tracking technology is also called 'gaze point rendering', by automatically detecting the relative position of the pupils of human eyes or estimating the direction of the sight, the demand of XR scene rendering calculation force can be greatly reduced by utilizing the human visual characteristics, and meanwhile, the resolution ratio is improved and the immersive experience is improved. Meanwhile, the eyeball tracking technology is used as a feature recognition technology, and has application requirements in personal recognition, XR payment and the like as the Face ID. The development requirement of the XR equipment for the whole machine is thinner and thinner, so that the eyeball tracking module is changed from an external one to an internal one, and the module is closer to the human eye, and smaller requirements are put forward on the module size. At the same time, the object distance becomes smaller, resulting in an increase in the demand for the angle of view. In a word, the demand for miniaturization, thinness and thinness of the eyeball tracking module is more remarkable.
The superlens is different from the traditional refractive optical element, realizes random modulation of the light field by means of a large number of micro-nano structural elements arranged according to rules, has the effective thickness of wavelength magnitude only, and has the potential of realizing miniaturization of the eyeball tracking optical module. Superlenses are wavelength sensitive and deviations from the design center wavelength tend to result in reduced image quality and reduced diffraction efficiency. Meanwhile, the color difference characteristic of the superlens is larger than that of a conventional diffraction element and the characteristic of full electromagnetic field simulation calculation is required, and the hybrid system of the superlens and the conventional refraction lens is difficult to simulate and evaluate. The eyeball tracking optical module is difficult to meet the use requirements of small chromatic aberration and high image quality on the basis of miniaturization.
In addition, chiral metamaterials and supersurfaces have wide applications in circular dichroism recognition, selective wavefront shaping, and multidimensional light field manipulation and biosensing. To date, many results have been reported on chiral supersurfaces and metamaterials while they involve wide bandwidth circular dichroism, but there is also a need for circular dichroism with narrow bandwidth and high quality factor, e.g., for chiral sensing with high spectral resolution, spin-selective wavefront shaping and secure optical communication, efficient circular dichroism nonlinear generation, and circularly polarized lasers with low threshold, using quasi-BIC supersurfaces with different topological polarization state characteristics may be a potential solution. However, recent reports on chiral quasi-BIC supersurfaces suggest the use of bilayer structures or the introduction of out-of-plane perturbations to obtain high Q-factor chiral optical responses requiring complex fabrication processes.
That is, the eye tracking optical module in the prior art has the problem that miniaturization, small chromatic aberration and good processability are difficult to be achieved.
Disclosure of Invention
The invention mainly aims to provide an achromatic superlens, a catadioptric superhybrid lens and a design method of the superlens, so as to solve the problem that an eyeball tracking optical module in the prior art is difficult to achieve miniaturization, small chromatic aberration and good processability.
In order to achieve the above object, according to one aspect of the present invention, there is provided a superlens for achromatizing, comprising: a substrate having a first surface and a second surface disposed opposite to each other; the modulation functional layer is arranged on the first surface and/or the second surface, and is provided with a plurality of micro-nano units which are rotationally symmetrically arranged along the central axis of the superlens, and the projection of the micro-nano units on the substrate is in a regular polygon shape, so that the projection shape of all the micro-nano units on the substrate is the same as the shape of the regular polygon; the micro-nano unit comprises micro-nano structures arranged in the center of the micro-nano unit, all the micro-nano structures are different in shape and/or size along the radial direction of the superlens, the superlens meets the minimum optimization target I in the preset wavelength range, and the superlens meets the following formula:
Formula (1);
formula (2);
formula (3);
Wherein wav represents a preset center wavelength within a preset wavelength range; r represents the radial position of the micro-nano structure from the center of the superlens, and the unit is mm; Representing the relative phase response of the ith micro-nano structure at radial position R of the superlens at wav wavelength after 2 pi phase solution envelope unwrap expansion based on the Nth micro-nano structure; indicating a target phase response of the superlens with micro-nano structure at wav wavelength; phase i (wav) represents the phase of the complex amplitude transmittance of the ith micro-nano structure at the wav wavelength; phase N (wav) represents the phase of the complex amplitude transmittance of the nth micro-nanostructure at the wav wavelength; ci represents a binary face coefficient; normR denotes the normalized radius in mm.
Further, the plane parallel to the substrate has an x-axis and a y-axis which are perpendicular to each other with the center of the superlens as an origin, and projections of the plurality of micro-nano structures on the substrate are symmetrical along the x-axis and the y-axis.
Further, the projection shape of the micro-nano structure on the substrate comprises one of square, round, cross fork and circular ring.
Further, the heights of all micro-nano structures on the modulation functional layer along the direction vertical to the substrate are the same.
According to another aspect of the present invention, there is provided a catadioptric hybrid lens including the above-described superlens for achromatism and refractive lens group, central axes of the superlens and refractive lens group being collinear as an optical axis of the catadioptric hybrid lens.
Further, the super lens is located at the object side of the refraction lens group, the object side of the super lens is provided with a modulation function layer, and the diaphragm of the refraction and super-mixing lens is arranged at the object side of the super lens.
Further, the difference of the focal lengths of the folded and super-mixed lens is within a range of + -0.02 mm at a plurality of preset center wavelengths within a preset wavelength range of the super-lens.
Further, the optical distortion of the folded and super-mixed lens is less than 5%; and/or the relative illuminance of the folding and super-mixing lens is more than or equal to 40%; and/or MTF of the folding and super-mixing lens is more than or equal to 0.65 at 60 lp/mm.
According to still another aspect of the present invention, there is provided a design method for an achromatic superlens, the design method for an achromatic superlens including: step S10: determining a preset wavelength range of the superlens, and determining a plurality of preset center wavelengths in the preset wavelength range; step S20: establishing a structure library of micro-nano structures of micro-nano units of a modulation function layer of the superlens; step S30: selecting micro-nano structure combination mode of superlens in the structure library so as to make the superlens meet optimization goal in preset wavelength range, and make the optimization goal meet I minimum,
Formula (1);
Wherein wav represents a preset center wavelength within a preset wavelength range; r represents the radial position of the micro-nano structure from the center of the superlens, and the unit is mm; Representing the relative phase response of the ith micro-nano structure at radial position R of the superlens at wav wavelength after 2 pi phase solution envelope unwrap expansion based on the Nth micro-nano structure; indicating the target phase response of the superlens with micro-nano structure at wav wavelength.
Further, step S20 includes: determining an optional shape of a projected shape of the micro-nano structure on the substrate of the superlens; a selectable range of sizes of the micro-nano structure under all selectable shapes is determined.
Further, the optimization objective satisfies the formula (2) and the formula (3),
Formula (2);
formula (3);
Wherein phase i (wav) represents the phase of the complex amplitude transmittance of the ith micro-nano structure at the wav wavelength; phase N (wav) represents the phase of the complex amplitude transmittance of the nth micro-nanostructure at the wav wavelength; ci represents a binary face coefficient; normR denotes the normalized radius in mm.
Further, step S30 further includes: taking the binary face coefficient Ci as a variable to obtain an initial micro-nano structure combination in a structure library; and optimizing the initial micro-nano structure combination by adopting a particle swarm optimization algorithm so as to ensure that an optimization target meets the I minimum.
Further, the optimizing the initial micro-nano structure combination by adopting the particle swarm optimization algorithm to ensure that the optimization target meets the minimum I comprises the following steps: determining the maximum absolute phase difference of the structure library in a preset wavelength range; Determining a maximum target phase response difference for the superlens at each radial position at all preset center wavelengths; Control ofLess than or equal toThe micro-nano structure is selected within the structural library to optimize the initial micro-nano structure combination.
By applying the technical scheme of the invention, the super lens for achromatizing comprises a substrate and a modulation functional layer, wherein the substrate is provided with a first surface and a second surface which are oppositely arranged; the modulation functional layer is arranged on the first surface or the second surface or both the first surface and the second surface, the modulation functional layer is provided with a plurality of micro-nano units which are rotationally symmetrically arranged along the central axis of the superlens, and the projection of the micro-nano units on the substrate is in a regular polygon shape, so that the projection shape of all the micro-nano units on the substrate is the same as the shape of the regular polygon; the micro-nano unit comprises micro-nano structures arranged in the center of the micro-nano unit, the shapes or the sizes or the shapes and the sizes of all the micro-nano structures are different along the radial direction of the superlens, and the superlens meets the minimum optimization target I in the preset wavelength range.
By arranging all micro-nano structures on the superlens according to the optimized target I, the difference value between the relative phase response and the target phase response at different radial positions R of the superlens is minimum at each preset center wavelength within the preset wavelength range, and the achromatic effect within the preset wavelength range is facilitated to be obtained. By arranging that the shapes or the sizes or the shapes and the sizes of all micro-nano structures along the radial direction of the superlens are different, the micro-nano structures at different shapes, sizes and different radial positions have different phase responses to light rays, the phase difference interval which can be covered is enlarged, so that the selectable micro-nano structures are more under the same target phase response, and the requirement of simultaneously meeting the target phase response of each preset center wavelength is favorably met. The micro-nano units are rotationally symmetrically arranged to form a regular polygon, so that the method is favorable for adapting to light rays with various polarization states, reduces the manufacturing process difficulty of the super lens, and ensures that the super lens has a high quality factor.
Drawings
The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this specification, illustrate embodiments of the application and together with the description serve to explain the application. In the drawings:
FIG. 1 is a top view showing a partial structure of a superlens according to an embodiment of the present invention;
FIG. 2 shows a schematic view of the superlens of FIG. 1 in a catadioptric hybrid lens;
FIG. 3 shows a front view of a portion of the structure of the superlens of FIG. 1;
FIG. 4 shows a schematic dimensional view of the micro-nano structure of FIG. 1;
FIG. 5 shows a schematic diagram of relative phase versus absolute phase difference for the micro-nano structure of FIG. 4 with a circular cross section;
FIG. 6 shows a schematic diagram of relative phase versus absolute phase difference for the micro-nano structure of FIG. 4 with a square cross section;
FIG. 7 shows the maximum absolute phase difference of the superlens of FIG. 1 at three preset center wavelengths Schematic of (2);
FIG. 8 shows a one-dimensional data comparison of target phase response versus actual phase response for the superlens of FIG. 1 at three wavelengths 900nm, 850nm, 800 nm;
FIG. 9 shows a two-dimensional phase distribution of the superlens of FIG. 1 at three wavelengths 900nm, 850nm, 800 nm;
fig. 10 shows a Layout diagram of a folding and superhybrid lens according to a first embodiment of the present invention;
FIG. 11 illustrates a center field of view focal length schematic of the catadioptric hybrid lens of FIG. 10;
FIG. 12 shows MTF, distortion and relative illuminance diagrams of the catadioptric hybrid lens of FIG. 10 at 800nm, 850nm, 900nm wavelength configurations;
FIG. 13 shows a flow chart of a method of designing an achromatic superlens according to an alternative embodiment of the present invention.
Wherein the above figures include the following reference numerals:
10. a substrate; 20. modulating a functional layer; 30. a micro-nano unit; 40. a micro-nano structure; 50. a superlens; 60. a refractive lens group; 61. a meniscus double-aspherical lens; 62. a filter; 63. a glass cover plate; 70. a diaphragm.
Detailed Description
It should be noted that, without conflict, the embodiments of the present application and features of the embodiments may be combined with each other. The application will be described in detail below with reference to the drawings in connection with embodiments.
It is noted that all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs unless otherwise indicated.
In the present invention, unless otherwise indicated, terms of orientation such as "upper, lower, top, bottom" are used generally with respect to the orientation shown in the drawings or with respect to the component itself in the vertical, upright or gravitational direction; also, for ease of understanding and description, "inner and outer" refers to inner and outer relative to the profile of each component itself, but the above-mentioned orientation terms are not intended to limit the present invention.
In order to solve the problems that an eyeball tracking optical module in the prior art is difficult to achieve miniaturization, small chromatic aberration and good processability, the invention provides an achromatic superlens, a catadioptric superhybrid lens and a design method of the superlens.
As shown in fig. 1 to 13, the superlens for achromatism includes a substrate 10 and a modulation function layer 20, the substrate 10 having a first surface and a second surface disposed opposite to each other; the modulation functional layer 20 is arranged on the first surface or the second surface or both the first surface and the second surface, the modulation functional layer 20 is provided with a plurality of micro-nano units 30 which are rotationally symmetrically arranged along the central axis of the superlens, and the projection of the micro-nano units 30 on the substrate 10 is in a regular polygon shape, so that the projection of all the micro-nano units 30 on the substrate 10 is the same as the regular polygon shape; wherein, the micro-nano unit 30 includes micro-nano structures 40 disposed at the center of the micro-nano unit 30, all the micro-nano structures 40 have different shapes or sizes or shapes and sizes along the radial direction of the superlens, the superlens satisfies the minimum optimization objective I within the preset wavelength range, and the superlens 50 satisfies the following formula:
Formula (1);
formula (2);
formula (3);
Wherein wav represents a preset center wavelength within a preset wavelength range; r represents the radial position of the micro-nano structure from the center of the superlens, and the unit is mm; Representing the relative phase response of the ith micro-nano structure at radial position R of the superlens at wav wavelength after 2 pi phase solution envelope unwrap expansion based on the Nth micro-nano structure; indicating a target phase response of the superlens with micro-nano structure at wav wavelength; phase i (wav) represents the phase of the complex amplitude transmittance of the ith micro-nano structure at the wav wavelength; phase N (wav) represents the phase of the complex amplitude transmittance of the nth micro-nanostructure at the wav wavelength; ci represents a binary face coefficient; normR denotes the normalized radius in mm.
By arranging all micro-nano structures 40 on the superlens according to the optimized target I, the difference between the relative phase response at different radial positions R of the superlens and the target phase response is minimized at each preset center wavelength within the preset wavelength range, which is helpful for obtaining the achromatic effect within the preset wavelength range. By arranging that the shapes or the sizes or the shapes and the sizes of all the micro-nano structures 40 along the radial direction of the superlens are different, the micro-nano structures 40 at different shapes, sizes and different radial positions have different phase responses to light rays, the phase difference interval which can be covered is enlarged, so that the selectable micro-nano structures 40 are more under the same target phase response, and the requirement of simultaneously meeting the target phase response of each preset center wavelength is favorably met. The micro-nano units 30 are rotationally symmetrically arranged to form a regular polygon, so that the method is beneficial to adapting to light rays with various polarization states, reduces the manufacturing process difficulty of the super lens, and enables the super lens to have a high quality factor.
Specifically, the target phase response of the micro-nano structure provided by the superlens to the preset center wavelength wav is represented by a coefficient of a binary surface:
formula (3);
wherein Ci represents a binary face coefficient; normR denotes the normalized radius in mm; r represents the radial position of the micro-nano structure from the center of the superlens, and the unit is mm; wav denotes a preset center wavelength within a preset wavelength range.
Specifically, for a group of micro-nano structures, the relative phase is determined by the reference phase. But the corresponding phase differences in the 800nm-900nm wavelength range are absolute.
Formula (2);
Representing the relative phase response of the ith micro-nano structure at radial position R of the superlens at wav wavelength after 2 pi phase solution envelope unwrap expansion based on the Nth micro-nano structure; indicating a target phase response of the superlens with micro-nano structure at wav wavelength; phase i (wav) represents the phase of the complex amplitude transmittance of the ith micro-nano structure at the wav wavelength; phase N (wav) represents the phase of the complex amplitude transmittance of the nth micro-nanostructure at the wav wavelength.
For example, phase i (800 nm) represents the phase of the complex amplitude transmittance of the micro-nano structure with i at a preset center wavelength of 800nm, and phase N (800 nm) represents the phase of the complex amplitude transmittance of the micro-nano structure with NThe micro-nano structure of the representative number i is used as a reference to carry out the relative phase after the 2 pi phase solution envelope unwrap is unfolded.
For a group of micro-nano structures, the relative phase is determined by the reference phase, but the corresponding phase difference is in the wavelength range of 800nm-900nmIs absolute.
It should be noted that, in the prior art, the same micro-nano structure 40 has phase response at different wavelengthsIn contrast, the overall phase response of the superlens constructed according to conventional methods satisfies=When the group of micro-nano structures is used, the phase requirement of the other wavelength is difficult to be met at the same time, i.e.≠，≠This is the chromatic aberration of the superlens. By arranging all micro-nano structures 40 on the superlens according to the optimized target I, the difference between the relative phase response and the target phase response at different radial positions R of the superlens is minimized at each preset center wavelength within the preset wavelength range, thereby being beneficial to obtaining the achromatic effect within the preset wavelength range.
Specifically, the plane parallel to the substrate 10 has an x-axis and a y-axis perpendicular to each other with the center of the superlens 50 as an origin, and the projections of the plurality of micro-nano structures 40 on the substrate 10 are symmetrical along both the x-axis and the y-axis. This arrangement allows the superlens to be polarization insensitive and to be used with any polarization state.
Preferably, the regular polygon is square or regular hexagon in shape. The unit pattern of the supersurface is generally free to design and the different spectral responses of the free-form pattern are due to complex scattering and coupling of propagating bloch modes in the subsurface. The number of propagating bloch modes and the dispersion relation vary with the meta-atomic shape, resulting in different transmission spectra, i.e. spectral modulation characteristics. For the pattern, in a chiral symmetric surface, the c4v symmetry structure, i.e. symmetric about the x, y axis and rotationally symmetric about the z axis by 90 °, can make the polarization state of the superlens of the present application and the optical system with the superlens insensitive and thus can be used to achieve arbitrary polarization states.
Specifically, the projection shape of the micro-nano structure 40 on the substrate 10 includes one of square, round, cross-fork, and circular. Because the phase difference intervals which can be covered by the micro-nano structures 40 with different shapes are different, the phase difference intervals which can be covered by the micro-nano structures 40 with various shapes can be enlarged, the optimization of the target I is facilitated, and the requirement of target phase response of each preset center wavelength is met at the same time, so that better imaging performance is realized.
Specifically, the heights of all the micro-nano structures 40 on the modulation functional layer 20 are the same along the direction perpendicular to the substrate 10. Is beneficial to reducing the processing difficulty of the superlens and realizing higher quality factor. Preferably, the height of the micro-nano structure 40 is in the range of 1 μm.
As shown in fig. 10, the present invention further provides a catadioptric hybrid lens, which includes the above-mentioned superlens and refractive lens group for achromatism, wherein central axes of the superlens and refractive lens group are collinear to serve as an optical axis of the catadioptric hybrid lens. The super lens and the refraction lens group are coaxially arranged to form the catadioptric hybrid lens, which is beneficial to realizing the achromatism of the catadioptric hybrid lens, improving the MTF value and realizing higher imaging quality,
Specifically, the super lens is located at the object side of the refractive lens group, the object side of the super lens is provided with a modulation function layer 20, and the diaphragm of the refractive super hybrid lens is arranged at the object side of the super lens. The modulation functional layer 20 is arranged close to the diaphragm, which is beneficial to reducing the aperture of the effective area of the superlens and the aperture of the refractive lens group, improving the processability and reducing the manufacturing cost.
Specifically, the difference of the focal lengths of the folded and super-mixed lens is within a range of +/-0.02 mm under a plurality of preset center wavelengths within a preset wavelength range of the super-lens. The focus difference values under a plurality of preset center wavelengths are controlled within the range of +/-0.02 mm, and the catadioptric hybrid lens can achieve achromatism performance in the preset wavelength range.
Specifically, the optical distortion of the super-refractive hybrid lens can be set to be less than 5%, or the relative illuminance of the super-refractive hybrid lens is greater than or equal to 40%, or the MTF of the super-refractive hybrid lens is greater than or equal to 0.65 at 60lp/mm, or any combination of the two or three, so that the super-refractive hybrid lens can achieve high imaging quality in a preset wavelength range, and meanwhile, the super-refractive hybrid lens has the advantage of miniaturization.
As shown in fig. 13, the present invention also provides a design method for an achromatic superlens, the design method for an achromatic superlens comprising: step S10: determining a preset wavelength range of the superlens, and determining a plurality of preset center wavelengths in the preset wavelength range; step S20: establishing a structure library of micro-nano structures 40 of micro-nano units 30 of a modulation function layer 20 of the superlens; step S30: selecting micro-nano structure combination mode of superlens in the structure library so as to make the superlens meet optimization goal in preset wavelength range, and make the optimization goal meet I minimum,
Formula (1);
Wherein wav represents a preset center wavelength within a preset wavelength range; r represents the radial position of the micro-nano structure from the center of the superlens, and the unit is mm; Representing the relative phase response of the ith micro-nano structure at radial position R of the superlens at wav wavelength after 2 pi phase solution envelope unwrap expansion based on the Nth micro-nano structure; indicating the target phase response of the superlens with micro-nano structure at wav wavelength.
The preset wavelength range and the plurality of preset center wavelengths are determined in step S10, so that the fixed band range of the superlens application is determined. The structure library of the micro-nano structure 40 is constructed through the step S20, richer choices are provided for the micro-nano structure 40 to cover a larger range of phase difference intervals, and the step S30 meets the optimization target within the preset wavelength range, so that the relative phase response of the super-lens at different radial positions R is controlled to be close to the target phase response, and the achromatic function is realized.
Specifically, step S20 includes: determining an optional shape of the projected shape of the micro-nano structure 40 on the substrate 10 of the superlens; the selectable range of sizes of the micro-nano structure 40 under all selectable shapes is determined. By determining different selectable shapes and different selectable ranges of sizes, the selectable arrangement of the superlens surface micro-nano structure 40 is richer, covering a larger range of phase difference intervals.
Specifically, the optimization objective satisfies the formulas (2) and (3),
Formula (2);
formula (3);
Wherein phase i (wav) represents the phase of the complex amplitude transmittance of the ith micro-nano structure at the wav wavelength; phase N (wav) represents the phase of the complex amplitude transmittance of the nth micro-nanostructure at the wav wavelength; ci represents a binary face coefficient; normR denotes the normalized radius in mm.
By setting the optimization target I to be minimum, the difference between the relative phase response at different radial positions R of the superlens and the target phase response is minimized at each preset center wavelength within the preset wavelength range, which is conducive to obtaining an achromatic effect within the preset wavelength range.
Specifically, step S30 includes: taking the binary face coefficient Ci as a variable to obtain an initial micro-nano structure combination in a structure library; and optimizing the initial micro-nano structure combination by adopting a particle swarm optimization algorithm so as to ensure that an optimization target meets the I minimum. And (3) obtaining an initial micro-nano structure combination in design software by taking Ci as a variable, optimizing, and searching for the minimum meeting optimization target I by utilizing a particle swarm optimization algorithm, namely, the difference value between the relative phase response and the target phase response at different radial positions R of the superlens is minimum at each preset central wavelength in a preset wavelength range, thereby realizing achromatism in the preset wavelength range.
Specifically, the process of optimizing the initial micro-nano structure combination by adopting the particle swarm optimization algorithm to ensure that the optimization target meets the minimum I comprises the following steps: determining the maximum absolute phase difference of the structure library in a preset wavelength range; Determining a maximum target phase response difference for the superlens at each radial position at all preset center wavelengths; Control ofLess than or equal toThe micro-nano structure is selected within the structural library to optimize the initial micro-nano structure combination. By determining the maximum absolute phase difference of micro-nano structures 40 within the library of structuresWhen selecting the micro-nano structure combination mode of the super lens, the maximum target phase response difference at each preset center wavelength and each radial positionAre all atIn the range of (2), the dispersion span of the superlens is not larger than the dispersion span which can be met by the structural library, and the phase response requirements of the micro-nano structure under different center wavelengths are met.
Optionally, after determining the preset wavelength range, the selectable range of dimensions of the micro-nano structure 40 is determined to be within the half-wave scale of the preset wavelength range. For example, eye tracking is typically performed using infrared light, requiring micro-nano structures 40 having a size in the half-wave range of infrared light, thereby determining that micro-nano structures 40 are selected in the range of 100-450nm, and then calculating the phase and amplitude of micro-nano structures 40 in the range of 100-450nm using the electromagnetic field simulation method of FDTD or RCWA. After scanning the micro-nano structures 40 of various shapes and sizes, the scanning can be performed according to the materials, but the wavelength range is generally determined, and the materials are also determined. Thus, a structure library can be established, and the maximum absolute phase difference of the structure library in a preset wavelength range can be obtained。
In particular, toIs realized by optimizing and combining self-compiling macros under each preset center wavelength.
Example 1
As shown in fig. 1 to 11, there is shown a catadioptric hybrid lens, which includes a superlens 50 and a refractive lens group 60 from an object side to an image side as shown in fig. 10, the refractive lens group 60 including a piece of meniscus double-aspherical lens 61, a piece of IR filter 62, and a glass cover plate 63 located in front of the chip. As shown in fig. 2 and 3, the object side of the super lens 50 has a modulation function layer 20, and a diaphragm 70 of the folded super hybrid lens is closely attached to the object side of the super lens 50.
The preset wavelength range of the catadioptric hybrid lens of the embodiment is 850+/-50 nm, namely the catadioptric hybrid lens is applicable to near infrared bands. In particular, the whole focal length of the catadioptric hybrid lens is consistent at preset center wavelengths of 800 nm, 850 nm and 900 nm, and the difference is within the range of +/-0.02 mm, so that achromatism is realized.
As shown in fig. 1, the micro-nano units 30 are rotationally symmetrically arranged, and the micro-nano structures 40 at different positions from the center to the maximum radius are different along the radial direction of the superlens 50. The differences may be different in size or shape. The micro-nano structures 40 disposed on the same surface of the substrate 10 have the same height, and the cross section of the micro-nano structures 40 is parallel to the surface of the substrate 10. The micro-nano structure 40 at different radial positions has a different phase response to wavelength.
Taking 800nm as an example of the preset center wavelength, the micro-nano structure 40 in the modulation functional layer 20 can cover a phase difference interval of 900nm-800nm center wavelength under the 800nm center wavelength, and can realize the combination of various micro-nano structures 40, so that the phase difference space which can be covered can be enlarged, more selectable micro-nano structures 40 can be realized under the same target phase, and the requirements of simultaneously meeting three target phase responses of the preset center wavelength can be met, so that better imaging performance can be realized.
Optionally, the substrate 10 is made of glass. The bulk material of the micro-nano structure 40 is amorphous silicon, and the refractive index is about 3.6 within the range of 850+ -50 nm. The meniscus double aspherical lens is of material EP7000 and is a double aspherical convex lens which helps to focus the beamlets from the first superlens 50, thus achieving a small TTL.
In this embodiment, the micro-nano structure 40 in the modulation functional layer 20 has different phase responses in the wavelength range of 800 nm-900 nm. Specifically, by providing three configurations, the center wavelength of each configuration, i.e., the predetermined center wavelength, is 800 nm, 850 nm, and 900 nm, respectively. Optimizing the phase of the micro-nano structure 40 at different radial positions, i.e. optimizing the coefficient of Binary2, while controlling the maximum absolute phase difference at three preset center wavelengths at each radial position RNot exceeding the maximum absolute phase difference span of the structural library. The control of the maximum absolute phase difference of the three preset center wavelengths is realized by combining multi-configuration optimization with self-compiling macros. The dispersion span required by the folded and super-mixed lens can be ensured not to be larger than the dispersion span which can be satisfied by the structural library, and the phase response requirement of the micro-nano structure 40 under different preset center wavelengths can be satisfied.
As shown in fig. 4 to 7, in order to meet the requirement of achromatism of 850±50nm, the projection shape of the micro-nano structure 40 on the substrate 10, that is, the cross section of the micro-nano structure 40 includes four types of square, circular, cross fork shape and circular ring shape, and the height of the micro-nano structure 40 is unified to be 1um. Wherein the side length A of the square cross section micro-nano structure 40 is in a range of 70nm-310nm; the diameter D of the circular cross-section micro-nano structure 40 varies from 70nm to 310nm; the length axis L, W of the cross-fork-shaped cross-section micro-nano structure 40 has a size variation range of 60nm-320nm; the outer ring diameter Dout of the circular cross section micro-nano structure 40 has a size variation range of 100nm-330nm, and the inner ring diameter Din has a size variation range of 40nm-170nm. The present embodiment scans 25250 micro-nano structures 40 with circular, square, cross fork and circular cross sections of different sizes, and constructs a structure library. The relative phase of the micro-nano structure 40 of the structure library and the maximum absolute phase difference within the preset wavelength range can be obtained. The maximum absolute phase difference of this structural library is about 5rad. The relative phase and absolute phase difference of the micro-nano structure 40 are shown in fig. 4 to 7.
The initial micro-nano structure combination is obtained in the structure library by taking the Binary face coefficient Ci (i is 1-15) as a variable, and the target phases (namely the Binary2 coefficients) of the superlens 50 under three groups of wavelengths are shown in the table 1.
TABLE 1
The initial micro-nano structure combination is optimized by means of a particle swarm optimization algorithm, and the optimal micro-nano structure combination is selected from 25250 micro-nano structures 40, so that the difference value between the relative phase response and the target phase response at different radial positions R of the superlens 50 is minimum at each preset center wavelength in a preset wavelength range, namely the optimization target I is minimum. As shown in fig. 8, the resulting superlens 50 has a relative phase response at three wavelengths, 800nm, 850nm and 900nm, that substantially coincides with the target phase response.
Formula (1);
wherein wav represents a preset center wavelength within a preset wavelength range; r represents the radial position of the micro-nano structure from the center of the superlens 50 in mm; Representing the relative phase response of the ith micro-nano structure at radial position R of superlens 50 at the wav wavelength, as developed by 2pi phase solution envelope unwrap with respect to the nth micro-nano structure; indicating the target phase response of the superlens 50 provided with micro-nano structures at the wav wavelength.
Table 2 shows the basic structural parameters of the catadioptric hybrid lens, wherein the units of radius of curvature, thickness, and net caliber are all millimeter mm.
TABLE 2
The surface shape of the aspherical lens can be defined by, but not limited to, the following aspherical formula:
formula (4);
Wherein x is the distance vector height from the vertex of the aspheric surface when the aspheric surface is at the position with the height h along the optical axis direction; c is the paraxial curvature of the aspherical surface, c=1/R, i.e. paraxial curvature c is the reciprocal of the radius of curvature R in table 1 above; k is a conic coefficient; ai is the correction coefficient of the aspherical i-th order. The following table 3 gives the higher order coefficients A0 to a14 that can be used for each aspherical mirror in the present embodiment.
TABLE 3 Table 3
The focal length distribution of the catadioptric hybrid lens is shown in table 4. The super lens 50 and the refractive lens group 60 form a super-refractive hybrid lens, and the super lens 50 achieves the best phase response after being combined with the refractive lens group at the wavelengths of 800 nm, 850 nm and 900 nm respectively. Helps to obtain achromatic effect in the range of 850+/-50 nm and improves MTF value. The relative shift of focal length of the catadioptric hybrid lens at three wavelengths is not more than 1% (as shown in fig. 11), and an achromatic effect is obtained.
TABLE 4 Table 4
As shown in fig. 12, fig. 12 (a-1), (b-1), and (c-1) show MTF, distortion, and relative illuminance diagrams of the catadioptric hybrid lens of fig. 10 in an 800nm wavelength configuration, respectively; FIG. 12 (a-2), (b-2), and (c-2) are schematic views showing MTF, distortion, and relative illuminance of the catadioptric hybrid lens of FIG. 10 in a 850nm wavelength configuration, respectively; the MTF, distortion and relative illuminance of the catadioptric hybrid lens of FIG. 10 at a 900nm wavelength configuration are shown in FIGS. 12 (a-3), (b-3) and (c-3), respectively. The folding and super-mixing lens has the characteristics of large view field (90.6 degrees), small total length (TTL=1.63 mm), small distortion (optical distortion < 5%), relative illuminance not less than 40% and better resolution (0-0.8F, MTF >0.65@60 lp/mm).
From the above description, it can be seen that the above embodiments of the present invention achieve the following technical effects:
1. by arranging all micro-nano structures 40 on the superlens according to the optimized target I, the difference between the relative phase response at different radial positions R of the superlens and the target phase response is minimized at each preset center wavelength within the preset wavelength range, which is helpful for obtaining the achromatic effect within the preset wavelength range.
2. By arranging that the shapes or the sizes or the shapes and the sizes of all the micro-nano structures 40 along the radial direction of the superlens are different, the micro-nano structures 40 at different shapes, sizes and different radial positions have different phase responses to light rays, the phase difference interval which can be covered is enlarged, so that the selectable micro-nano structures 40 are more under the same target phase response, and the requirement of simultaneously meeting the target phase response of each preset center wavelength is favorably met.
3. The micro-nano units 30 are rotationally symmetrically arranged to form a regular polygon, and the micro-nano structure 40 is symmetrical with C4 v. The super lens has polarization insensitivity, can be used for any polarization state, reduces the manufacturing process difficulty of the super lens, and has high quality factor.
It will be apparent that the embodiments described above are merely some, but not all, embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present invention without making any inventive effort, shall fall within the scope of the present invention.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the present application. As used herein, the singular is also intended to include the plural unless the context clearly indicates otherwise, and furthermore, it is to be understood that the terms "comprises" and/or "comprising" when used in this specification are taken to specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof.
It should be noted that the terms "first," "second," and the like in the description and the claims of the present application and the above figures are used for distinguishing between similar objects and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used may be interchanged where appropriate such that embodiments of the application described herein may be implemented in sequences other than those illustrated or otherwise described herein.
The above description is only of the preferred embodiments of the present invention and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (10)
1. A superlens for achromatism, comprising:
a substrate (10), the substrate (10) having oppositely disposed first and second surfaces;
A modulation functional layer (20), wherein the modulation functional layer (20) is arranged on the first surface and/or the second surface, the modulation functional layer (20) is provided with a plurality of micro-nano units (30) which are rotationally symmetrically arranged along the central axis of the super lens (50), and the projection of the micro-nano units (30) on the substrate (10) is in a regular polygon shape, so that the projection of all the micro-nano units (30) on the substrate (10) is the same as the regular polygon shape;
the micro-nano unit (30) comprises micro-nano structures (40) arranged in the center of the micro-nano unit (30), shapes and/or sizes of all the micro-nano structures (40) are different along the radial direction of the super lens (50), the super lens (50) meets the minimum optimization target I in a preset wavelength range, and the super lens (50) meets the following formula:
Formula (1);
Formula (2);
Formula (3);
Wherein wav represents a preset center wavelength within the preset wavelength range; r represents the radial position of the micro-nano structure from the center of the super lens, and the unit is mm; representing the relative phase response of an ith micro-nano structure at radial position R of the superlens at wav wavelength after 2 pi phase solution envelope unwrap expansion based on an Nth micro-nano structure (40); indicating a target phase response of the superlens provided with the micro-nano structure at the wav wavelength; phase i (wav) represents the phase of the complex amplitude transmittance of the ith micro-nano structure at the wav wavelength; phase N (wav) represents the phase of the complex amplitude transmittance of the nth micro-nanostructure at the wav wavelength; ci represents a binary face coefficient; normR denotes the normalized radius in mm.
2. The superlens for achromatism according to claim 1, characterized in that on a plane parallel to the substrate (10) there are mutually perpendicular x-and y-axes with the center of the superlens (50) as origin, along which x-and y-axes the projections of the plurality of micro-nano structures (40) on the substrate (10) are symmetrical.
3. The superlens for achromatism according to claim 2, wherein the projected shape of the micro-nano structure (40) on the substrate (10) comprises one of square, circular, cross-forked, circular ring shape.
4. The superlens for achromatism according to claim 1, wherein all the micro-nano structures (40) on the modulation functional layer (20) are of the same height in a direction perpendicular to the substrate (10).
5. A catadioptric hybrid lens comprising the superlens for achromatism of any one of claims 1 to 4 and a refractive lens group (60), the central axes of the superlens (50) and the refractive lens group (60) being collinear as the optical axis of the catadioptric hybrid lens.
6. The catadioptric hybrid lens of claim 5, wherein the superlens (50) is located on the object side of the refractive lens group (60), the object side of the superlens (50) has a modulating functional layer (20), and the diaphragm (70) of the catadioptric hybrid lens is disposed on the object side of the superlens (50).
7. The catadioptric hybrid lens of claim 5, wherein the difference in focal length of the catadioptric hybrid lens is within ± 0.02 mm at a plurality of preset center wavelengths within a preset wavelength range of the superlens (50).
8. The catadioptric hybrid lens of claim 5,
The optical distortion of the folded and super-mixed lens is less than 5%; and/or
The relative illuminance of the folding and supermixing lens is more than or equal to 40%; and/or
The MTF of the folded and super mixed lens is more than or equal to 0.65 at 60 lp/mm.
9. A design method for achromatic superlens, characterized in that, the design method for the achromatic superlens comprises the following steps:
step S10: determining a preset wavelength range of the superlens (50), and determining a plurality of preset center wavelengths in the preset wavelength range;
step S20: establishing a structure library of micro-nano structures (40) of micro-nano units (30) of a modulation functional layer (20) of the superlens (50);
Step S30: selecting a micro-nano structure (40) combination mode of the super lens (50) in the structure library so that the super lens (50) meets an optimization target in the preset wavelength range, the optimization target meets the requirement of the I minimum,
Formula (1);
Wherein wav represents a preset center wavelength within the preset wavelength range; r represents the radial position of the micro-nano structure from the center of the super lens, and the unit is mm; representing the relative phase response of an ith micro-nano structure at radial position R of the superlens at wav wavelength after 2 pi phase solution envelope unwrap expansion based on an Nth micro-nano structure (40); Indicating a target phase response of the superlens provided with the micro-nano structure at the wav wavelength;
the optimization objective satisfies the formula (2) and the formula (3),
Formula (2);
Formula (3);
Wherein phasei (wav) represents the phase of the complex amplitude transmittance of the ith micro-nano structure at the wav wavelength; phaseN (wav) represents the phase of the complex amplitude transmittance of the nth micro-nanostructure at the wav wavelength; ci represents a binary face coefficient; normR denotes the normalized radius in mm;
the step S30 includes: taking the binary face coefficient Ci as a variable to obtain an initial micro-nano structure combination in the structure library; optimizing the initial micro-nano structure combination by adopting a particle swarm optimization algorithm so as to ensure that the optimization target meets the requirement of I minimum;
The process of optimizing the initial micro-nano structure combination by adopting a particle swarm optimization algorithm so that the optimization target meets the minimum I comprises the following steps:
Determining the maximum absolute phase difference of the structure library in the preset wavelength range ；
Determining a maximum target phase response difference for said superlens (50) at each radial position at all said preset center wavelengths；
Controlling the saidLess than or equal to theThe micro-nano structure (40) is selected within the library of structures to optimize the initial micro-nano structure combination.
10. The method for designing an achromatic superlens according to claim 9, wherein said step S20 includes:
determining an alternative shape of the projected shape of the micro-nano structure (40) on the substrate (10) of the superlens (50);
-determining a selectable range of dimensions of said micro-nano structure (40) under all said selectable shapes.
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| CN116859590A (en) * | 2023-07-18 | 2023-10-10 | 郑州航空工业管理学院 | Broadband achromatic polarization insensitive super-structured lens and design method thereof |
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