CN113296167B - Design method of full-space focus adjustable super-structure lens - Google Patents
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Abstract
The invention discloses a full-space focal point adjustable super-structure lens and a design method thereof, wherein the method comprises the following steps: the phase of an outgoing wave corresponding to each nano antenna on the first super-structure surface meets the formula: p 1 ＝‑a((x 1 +d) 2 +y 1 2 ) The phase of the outgoing wave corresponding to each nano antenna on the second superstructure surface satisfies the formula: p 2 ＝a((x 2 +d) 2 +y 2 2 )(a(x 2 2 +y 2 2 ))φ 1 The phase of the outgoing wave corresponding to each nano antenna on the third superstructure surface satisfies the formula: p 3 ＝‑(a(x 3 2 +y 3 2 ))φ 2 Wherein a and d are constants, x 1 And y 1 A first planar coordinate, x, corresponding to each nano-antenna of the first nanostructured surface 2 And y 2 Second planar coordinates, x, corresponding to respective nano-antennas of a second nanostructured surface 3 And y 3 A third planar coordinate, phi, corresponding to each nano-antenna of the third meta-surface 1 And phi 2 Is an angle phi in a cylindrical coordinate system 1 ＝tan ‑1 (y 2 /x 2 )，φ 2 ＝tan ‑1 (y 3 /x 3 ). The planar structure of the super-structure lens avoids the generation of spherical aberration and chromatic aberration, increases the numerical aperture, has small volume, is beneficial to integration, and can realize free adjustment of a full-space focus.
Description
Technical Field
The invention relates to the technical field of optics, in particular to a full-space focus adjustable super-structured lens and a design method thereof.
Background
The adjustable-focus optical lens can realize multi-focus adjustment and is widely applied to the aspects of multi-focus plane microscopy, bifocal objective lenses and the like, but the existing adjustable-focus optical lens is realized based on a micro lens, on one hand, the diffraction limit of the micro lens cannot be further reduced, and on the other hand, the larger the adjustable range of the focus is, the larger the space occupied by the mechanical movement of the micro lens is, so that the existing adjustable-focus optical lens is large in size. In addition, microlenses made based on diffractive optical elements are confined to a narrow band, resulting in a smaller numerical aperture of existing focus-tunable optical lenses.
Therefore, the prior art is to be further improved.
Disclosure of Invention
In view of the above-mentioned deficiencies of the prior art, an object of the present invention is to provide a full-space focus adjustable super-structured lens and a design method thereof, so as to solve the problems of large volume and small numerical aperture of the existing focus adjustable optical lens.
The technical scheme of the invention is as follows:
a full-space adjustable-focus super-structured lens, comprising: the first, second and third super-structure surfaces are composed of a substrate layer and a plurality of nano-antennas arranged on the substrate layer, and the phase of an emergent wave corresponding to each nano-antenna on the first super-structure surface satisfies a formula: p 1 ＝-a((x 1 +d) 2 +y 1 2 ) The phase of the outgoing wave corresponding to each nano antenna on the second superstructure surface satisfies the formula: p 2 ＝a((x 2 +d) 2 +y 2 2 )(a(x 2 2 +y 2 2 ))φ 1 The phase of the outgoing wave corresponding to each nano antenna on the third superstructure surface satisfies the formula: p 3 ＝-(a(x 3 2 +y 3 2 ))φ 2 Wherein a and d are constants, x 1 And y 1 A first planar coordinate, x, corresponding to each nano-antenna of the first nanostructured surface 2 And y 2 Second planar coordinates, x, corresponding to respective nano-antennas of a second nanostructured surface 3 And y 3 A third plane coordinate, phi, corresponding to each nano-antenna of the third metamaterial surface 1 And phi 2 As an angle in a cylindrical coordinate system，φ 1 ＝tan -1 (y 2 /x 2 )，φ 2 ＝tan -1 (y 3 /x 3 )。
The full-space focus adjustable metamaterial lens is characterized in that the plurality of nano-antennas on the first metamaterial surface are arranged periodically, and the plurality of nano-antennas on the first metamaterial surface are different in size.
The full-space focus adjustable super-structure lens is characterized in that the plurality of nano-antennas on the second super-structure surface are arranged periodically, and the plurality of nano-antennas on the second super-structure surface are different in size.
The full-space focus adjustable super-structure lens is characterized in that the plurality of nano-antennas on the third super-structure surface are arranged periodically, and the plurality of nano-antennas on the third super-structure surface are different in size.
The long axes of the nano antennas on the first super-structure surface are perpendicular to the corresponding basal layers, the long axes of the nano antennas on the second super-structure surface are perpendicular to the corresponding basal layers, and the long axes of the nano antennas on the third super-structure surface are perpendicular to the corresponding basal layers.
The adjustable super lens of full space focus, wherein, the second super structure surface set up in first super structure surface with between the third super structure surface, just a plurality of nanometer antennas on first super structure surface with a plurality of nanometer antennas on third super structure surface set up relatively, a plurality of nanometer antennas on second super structure surface with a plurality of nanometer antennas on first super structure surface or a plurality of nanometer antennas on third super structure surface set up relatively.
The full-space focal point adjustable super-structure lens is characterized in that the nano antennas are cylindrical.
The full-space focus adjustable super-structure lens is characterized in that the substrate layer is made of silicon dioxide, and the nano antennas are made of one or more of titanium dioxide, gallium nitride and silicon.
A design method of the full-space focus-adjustable super-structure lens comprises the following steps:
obtaining a first plane coordinate corresponding to each nano antenna on the first super-structured surface, a second plane coordinate corresponding to each nano antenna on the second super-structured surface and a third plane coordinate corresponding to each nano antenna on the third super-structured surface, which are predetermined, and determining an emergent wave phase corresponding to each nano antenna on the first super-structured surface, each nano antenna on the second super-structured surface and each nano antenna on the third super-structured surface according to the first plane coordinate, the second plane coordinate and the third plane coordinate; wherein, the phase of the outgoing wave corresponding to each nano antenna on the first superstructure surface satisfies the formula: p is 1 ＝-a((x 1 +d) 2 +y 1 2 ) The phase of the outgoing wave corresponding to each nano antenna on the second superstructure surface satisfies the formula: p 2 ＝a((x 2 +d) 2 +y 2 2 )(a(x 2 2 +y 2 2 ))φ 1 The phase of the outgoing wave corresponding to each nano antenna on the third metamaterial surface satisfies the formula: p 3 ＝-(a(x 3 2 +y 3 2 ))φ 2 Wherein a and d are constants, x 1 And y 1 A first planar coordinate, x, corresponding to each nano-antenna of the first nanostructured surface 2 And y 2 A second planar coordinate, x, corresponding to each nano-antenna of the second nanostructured surface 3 And y 3 A third planar coordinate, phi, corresponding to each nano-antenna of the third meta-surface 1 And phi 2 Is an angle phi in a cylindrical coordinate system 1 ＝tan -1 (y 2 /x 2 )，φ 2 ＝tan -1 (y 3 /x 3 )；
Determining a first antenna radius corresponding to each nano antenna on the first super-structured surface, a second antenna radius corresponding to each nano antenna on the second super-structured surface and a third antenna radius corresponding to each nano antenna on the third super-structured surface according to the emergent wave phases corresponding to each nano antenna on the first super-structured surface, each nano antenna on the second super-structured surface and each nano antenna on the third super-structured surface and a predetermined correspondence relationship between the antenna radius and the emergent wave phase;
and designing the full-space focus adjustable super-structure lens according to the first antenna radius, the first plane coordinate, the second antenna radius, the second plane coordinate, the third antenna radius and the third plane coordinate.
The design method of the full-space focus adjustable super-structure lens comprises the following steps of:
emitting waves with preset frequency from a fourth superstructure surface consisting of nano antennas with different radiuses to obtain emitted wave phases corresponding to the nano antennas with different radiuses;
and determining the corresponding relation between the radius of the antenna and the phase of the emergent wave according to the nano antennas with different radii and the corresponding phases of the emergent wave.
Has the advantages that: the invention realizes focusing through the super-structure lens composed of three super-structure surfaces meeting specific phase distribution, can freely control the position of a focus in three dimensions of space, simultaneously realizes zooming and off-axis focusing functions, has small volume and is beneficial to integration, and the planar structure avoids the generation of spherical aberration and chromatic aberration, increases the numerical aperture and improves the imaging resolution.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the structures shown in the drawings without creative efforts.
FIG. 1 is a schematic structural diagram of a full-space focus-adjustable super-structured lens provided in an embodiment of the present invention;
FIG. 2 is a perspective view of a metamaterial surface unit provided in an embodiment of the present invention;
fig. 3 is a graph of nano-antenna radius versus emergent wave phase and transmittance as provided in an embodiment of the present invention.
The various symbols in the drawings: 1. a first microstructured surface; 2. a second nanostructured surface; 3. a third microstructured surface; 11. a base layer; 12. a nano-antenna.
Detailed Description
The invention provides a full-space focus adjustable super-structure lens and a design method thereof, the super-structure lens realizes focusing through a first super-structure surface, a second super-structure surface and a third super-structure surface, the planar structure of the super-structure lens avoids the generation of spherical aberration and chromatic aberration, the numerical aperture is increased, the full-space focus can be freely adjusted by controlling three super-structure surfaces to meet corresponding phase distribution, the size of the super-structure lens is small, and the integration is facilitated. In order to make the objects, technical solutions and effects of the present invention clearer and clearer, the present invention is further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not limit the invention.
In the embodiments and claims, the terms "a" and "an" can mean "one or more" unless the article is specifically limited.
In addition, if there is a description relating to "first", "second", etc. in the embodiments of the present invention, the description of "first", "second", etc. is for descriptive purposes only and is not to be construed as indicating or implying relative importance or to implicitly indicate the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In addition, technical solutions between the embodiments may be combined with each other, but must be based on the realization of the technical solutions by a person skilled in the art, and when the technical solutions are contradictory to each other or cannot be realized, such a combination should not be considered to exist, and is not within the protection scope of the present invention.
Referring to fig. 1-2, the present invention provides a full-space focus adjustable super-structured lens.
As shown in FIG. 1, the invention provides aThe full-space focal point adjustable super-structure lens can be applied to optical devices such as multi-focal plane microscope and bifocal objective lenses, can realize free adjustment of the full-space focal point by controlling three super-structure surfaces to meet corresponding phase distribution, avoids spherical aberration and chromatic aberration due to the planar structure of the super-structure lens, increases the numerical aperture, is small in size and is beneficial to integration. Wherein the super-structured lens includes: the antenna comprises a first super-structure surface 1, a second super-structure surface 2 and a third super-structure surface 3, wherein the first super-structure surface 1, the second super-structure surface 2 and the third super-structure surface 3 are respectively composed of a substrate layer 11 and a plurality of nano antennas 12 arranged on the substrate layer 11, and the phase of an emergent wave corresponding to each nano antenna 12 of the first super-structure surface 1 meets the formula: p 1 ＝-a((x 1 +d) 2 +y 1 2 ) The phase of the outgoing wave corresponding to each nano-antenna 12 of the second metamaterial surface 2 satisfies the formula: p 2 ＝a((x 2 +d) 2 +y 2 2 )(a(x 2 2 +y 2 2 ))φ 1 The phase of the outgoing wave corresponding to each nano antenna 12 of the third metamaterial surface 3 satisfies the formula: p 3 ＝-(a(x 3 2 +y 3 2 ))φ 2 Wherein a and d are constants, x 1 And y 1 A first plane coordinate, x, corresponding to each nano-antenna 12 of the first nanostructured surface 1 2 And y 2 A second planar coordinate, x, corresponding to each nano-antenna 12 of the second nanostructured surface 2 3 And y 3 A third plane coordinate, phi, corresponding to each nano-antenna 12 of the third meta-surface 3 1 And phi 2 Is an angle phi in a cylindrical coordinate system 1 ＝tan -1 (y 2 /x 2 )，φ 2 ＝tan -1 (y 3 /x 3 ). Compared with the traditional focus-adjustable optical lens based on a micro lens, the super-structured lens based on the super-structured surface has stable phase modulation, the planar structure surface generates spherical aberration and chromatic aberration, and the numerical aperture is increased.
In a specific application process, the phase of the outgoing wave corresponding to each nano antenna 12 of the first metamaterial surface 1 meets the requirementThe formula: p 1 ＝-a((x 1 +d) 2 +y 1 2 ) The phase of the outgoing wave corresponding to each nano-antenna 12 of the second nanostructured surface 2 satisfies the formula: p 2 ＝a((x 2 +d) 2 +y 2 2 )(a(x 2 2 +y 2 2 ))φ 1 The phases of the outgoing waves corresponding to the nano-antennas 12 of the third nanostructured surface 3 satisfy the formula: p is 3 ＝-(a(x 3 2 +y 3 2 ))φ 2 When light waves or electromagnetic waves enter the super-structure lens, the wavefront of the incident waves is controlled by the first super-structure surface 1, the second super-structure surface 2 and the third super-structure surface 3 to realize light field focusing, and when the first super-structure surface 1, the second super-structure surface 2 and the third super-structure surface 3 are rotated to change the relative rotation angle among the three super-structure surfaces, the control mode of the three super-structure surfaces on the wavefront of the incident waves can be changed, so that the position of a focusing light spot can be changed, the position of a focus can be freely controlled in three dimensions of space, and two functions of zooming and off-axis focusing can be realized simultaneously. The inventors have found that when the diameter of the three-piece nanostructured surface in this embodiment is 1mm, longitudinal modulation of the focal spot on the order of centimeters can be achieved, while the off-axis offset distance of the focal spot is maximally up to the radius of the nanostructured surface.
With continued reference to fig. 1 and fig. 2, the nano-antennas 12 of the first meta-surface 1 are arranged periodically, so that the phase of the outgoing wave corresponding to each nano-antenna 12 of the first meta-surface 1 satisfies the following formula: p 1 ＝-a((x 1 +d) 2 +y 1 2 ) The dimensions of the several nano-antennas 12 of the first nanostructured surface 1 are different. When designing the metamaterial lens, in this embodiment, the correspondence between the size of the nano-antenna and the phase of the outgoing wave is predetermined, and then the corresponding size is determined according to the phase of the outgoing wave that each nano-antenna 12 of the first metamaterial surface 1 needs to satisfy. In an embodiment, the nano-antennas 12 of the first meta-surface 1 are cylindrical structures, the heights of the nano-antennas 12 of the first meta-surface 1 are the same, and the different sizes of the nano-antennas 12 of the first meta-surface 1 specifically refer to the number of the nano-antennas 12 of the first meta-surface 1The radii of the dry nano-antennas 12 are different, when designing the metamaterial lens, the corresponding relationship between the radius of the nano-antennas and the phase of the outgoing wave is predetermined, and then the corresponding radius is determined according to the phase of the outgoing wave which needs to be satisfied by each nano-antenna 12 of the first metamaterial surface 1, so that the first metamaterial surface 1 which satisfies the phase distribution formula can be obtained.
Similar to the first meta-surface 1, the nano-antennas 12 of the second meta-surface 2 are arranged periodically, so that the phase of the outgoing wave corresponding to each nano-antenna 12 of the second meta-surface 2 satisfies the following formula: p 2 ＝a((x 2 +d) 2 +y 2 2 )(a(x 2 2 +y 2 2 ))φ 1 The dimensions of the several nano-antennas 12 of the second nanostructured surface 2 are different. When designing the metamaterial lens, in this embodiment, the correspondence between the size of the nano-antenna and the phase of the outgoing wave is predetermined, and then the corresponding size is determined according to the phase of the outgoing wave that needs to be satisfied by each nano-antenna 12 of the second metamaterial surface 2. In a specific embodiment, the plurality of nano antennas 12 of the second metamaterial surface 2 are cylindrical structures, the heights of the plurality of nano antennas 12 of the second metamaterial surface 2 are the same, and the different sizes of the plurality of nano antennas 12 of the second metamaterial surface 2 specifically mean that the radii of the plurality of nano antennas 12 of the second metamaterial surface 2 are different, when designing a metamaterial lens, a corresponding relationship between the radius of the nano antennas and an emergent wave phase is predetermined, and then a corresponding radius is determined according to the emergent wave phase that each nano antenna 12 of the second metamaterial surface 2 needs to satisfy, so that the second metamaterial surface 2 that satisfies a phase distribution formula can be obtained.
Similar to the first super surface 1 and the second super surface 2, the nano antennas 12 of the third super surface 3 are arranged periodically, so that the phase of the outgoing wave corresponding to each nano antenna 12 of the third super surface 3 satisfies the formula: p 2 ＝a((x 2 +d) 2 +y 2 2 )(a(xx 2 +y 2 2 ))φ 1 The dimensions of the nano-antennas 12 of the third nanostructured surface 3 are different. When designing a metamaterial lens, the correspondence between the size of the nano-antenna and the phase of the outgoing wave is predetermined in this embodiment, and thenAnd determining the corresponding size according to the emergent wave phase which needs to be met by each nano antenna 12 of the third metamaterial surface 3. In a specific embodiment, the plurality of nano antennas 12 of the third nanostructure surface 3 are cylindrical structures, the heights of the plurality of nano antennas 12 of the third nanostructure surface 3 are the same, and the different sizes of the plurality of nano antennas 12 of the third nanostructure surface 3 specifically mean that the radii of the plurality of nano antennas 12 of the third nanostructure surface 3 are different, when designing the nanostructure lens, the corresponding relationship between the radius of the nano antennas and the phase of the outgoing wave is predetermined, and then the corresponding radius is determined according to the phase that each nano antenna 12 of the third nanostructure surface 3 needs to satisfy, so that the third nanostructure surface 3 that satisfies the phase distribution formula can be obtained.
With continued reference to fig. 1 and fig. 2, the long axes of the nano-antennas 12 of the first super-structured surface 1 are perpendicular to the corresponding substrate layers 11, the long axes of the nano-antennas 12 of the second super-structured surface 2 are perpendicular to the corresponding substrate layers 11, and the long axes of the nano-antennas 12 of the third super-structured surface 3 are perpendicular to the corresponding substrate layers 11. The base layer 11 is made of silicon dioxide, and the nano antennas 12 are made of one or more of titanium dioxide, gallium nitride and silicon. Fig. 3 is a graph of a relationship between a radius of a nano antenna of the metamaterial lens, a phase of an outgoing wave, and a transmittance, and it can be seen from fig. 3 that the metamaterial lens provided by this embodiment can realize a phase change of an incident wave from-pi to pi, and the transmittance of a wave transmitted through a surface of the metamaterial is more than 80%, which indicates that the nano antenna does not interfere with the efficiency of the metamaterial lens.
In this embodiment, the positions of the first, second and third surfaces 1, 2 and 3 may be set as required, and in a specific embodiment, the second surface 2 is set between the first surface 1 and the third surface 3, the nano-antennas 12 of the first surface 1 and the nano-antennas 12 of the third surface 3 are set opposite to each other, and the nano-antennas 12 of the second surface 2 and the nano-antennas 12 of the first surface 1 or the nano-antennas 12 of the third surface 3 are set opposite to each other.
In another embodiment, the first nanostructured surface 1 is disposed between the second nanostructured surface 2 and the third nanostructured surface 3, and the nano-antennas 12 of the second nanostructured surface 2 and the nano-antennas 12 of the third nanostructured surface 3 are disposed opposite to each other, and the nano-antennas 12 of the first nanostructured surface 1 and the nano-antennas 12 of the second nanostructured surface 2 or the nano-antennas 12 of the third nanostructured surface 3 are disposed opposite to each other.
Of course, in the present invention, a third super structure surface 3 may also be disposed between the first super structure surface 1 and the second super structure surface 2, and the nano antennas 12 of the first super structure surface 1 and the nano antennas 12 of the second super structure surface 2 are disposed oppositely, and the nano antennas 12 of the third super structure surface 3 are disposed oppositely to the nano antennas 12 of the first super structure surface 1 or the nano antennas 12 of the second super structure surface 2.
Based on the above-mentioned full-space focus adjustable super-structure lens, an embodiment of the present invention further provides a design method of the full-space focus adjustable super-structure lens, including:
s1, obtaining a first planar coordinate corresponding to each nano antenna on the first nanostructure surface, a second planar coordinate corresponding to each nano antenna on the second nanostructure surface, and a third planar coordinate corresponding to each nano antenna on the third nanostructure surface, which are predetermined, and determining an outgoing wave phase corresponding to each nano antenna on the first nanostructure surface, each nano antenna on the second nanostructure surface, and each nano antenna on the third nanostructure surface according to the first planar coordinate, the second planar coordinate, and the third planar coordinate; wherein, the phase of the outgoing wave corresponding to each nano antenna on the first superstructure surface satisfies the formula: p 1 ＝-a((x 1 +d) 2 +y 1 2 ) The phase of the outgoing wave corresponding to each nano antenna on the second superstructure surface satisfies the formula: p 2 ＝a((x 2 +d) 2 +y 2 2 )(a(x 2 2 +y 2 2 ))φ 1 Said third superstructure tableThe phase of the emergent wave corresponding to each nano antenna of the surface meets the formula: p 3 ＝-(a(x 3 2 +y 3 2 ))φ 2 Wherein a and d are constants, x 1 And y 1 A first planar coordinate, x, corresponding to each nano-antenna of the first nanostructured surface 2 And y 2 A second planar coordinate, x, corresponding to each nano-antenna of the second nanostructured surface 3 And y 3 A third planar coordinate, phi, corresponding to each nano-antenna of the third meta-surface 1 And phi 2 Is an angle phi in a cylindrical coordinate system 1 ＝tan -1 (y 2 /x 2 )，φ 2 ＝tan -1 (y 3 /x 3 )；
S2, determining a first antenna radius corresponding to each nano antenna on the first nanostructure surface, a second antenna radius corresponding to each nano antenna on the second nanostructure surface, and a third antenna radius corresponding to each nano antenna on the third nanostructure surface according to the emergent wave phases corresponding to each nano antenna on the first nanostructure surface, each nano antenna on the second nanostructure surface, and a predetermined correspondence between the antenna radius and the emergent wave phase;
and designing the full-space focus adjustable super-structure lens according to the first antenna radius, the first plane coordinate, the second antenna radius, the second plane coordinate, the third antenna radius and the third plane coordinate.
When designing a full-space focus-adjustable super-structured lens, in this embodiment, first planar coordinates corresponding to each nano-antenna of the first super-structured surface, second planar coordinates corresponding to each nano-antenna of the second super-structured surface, and third planar coordinates corresponding to each nano-antenna of the third super-structured surface are determined, and then the first planar coordinates, the second planar coordinates, and the third planar coordinates are respectively substituted into phase distribution formulas satisfied by the first super-structured surface, the second super-structured surface, and the third super-structured surface to determine each nano-antenna, and each third planar coordinate of the first super-structured surface,The outgoing wave phases corresponding to the nano-antennas on the second super-structured surface and the nano-antennas on the third super-structured surface; wherein, the phase of the outgoing wave corresponding to each nano antenna on the first superstructure surface satisfies the formula: p 1 ＝-a((x 1 +d) 2 +y 12 ) The phase of the outgoing wave corresponding to each nano antenna on the second superstructure surface satisfies the formula: p 2 ＝a((x 2 +d) 2 +y 2 2 )(a(x 2 2 +y 2 2 ))φ 1 The phase of the outgoing wave corresponding to each nano antenna on the third superstructure surface satisfies the formula: p 3 ＝-(a(x 3 2 +y 3 2 ))φ 2 Wherein a and d are constants, x 1 And y 1 A first planar coordinate, x, corresponding to each nano-antenna of the first nanostructured surface 2 And y 2 Second planar coordinates, x, corresponding to respective nano-antennas of a second nanostructured surface 3 And y 3 A third plane coordinate, phi, corresponding to each nano-antenna of the third metamaterial surface 1 And phi 2 Is an angle phi in a cylindrical coordinate system 1 ＝tan -1 (y 2 /x 2 )，φ 2 ＝tan -1 (y 3 /x 3 )。
Further, after obtaining the emergent wave phases corresponding to each nano antenna on the first metamaterial surface, each nano antenna on the second metamaterial surface, and each nano antenna on the third metamaterial surface, according to the emergent wave phases corresponding to each nano antenna on the first metamaterial surface, each nano antenna on the second metamaterial surface, and each nano antenna on the third metamaterial surface, and a predetermined correspondence between the antenna radius and the emergent wave phase, determining a first antenna radius corresponding to each nano antenna on the first metamaterial surface, a second antenna radius corresponding to each nano antenna on the second metamaterial surface, and a third antenna radius corresponding to each nano antenna on the third metamaterial surface. And finally, designing the full-space focus adjustable super-structure lens according to the first antenna radius, the first plane coordinate, the second antenna radius, the second plane coordinate, the third antenna radius and the third plane coordinate. The super-structure lens designed based on the method provided by the embodiment of the invention can realize free adjustment of a full-space focus, the planar structure of the super-structure lens avoids generation of spherical aberration and chromatic aberration, the numerical aperture is increased, and the super-structure lens is small in size and beneficial to integration.
In summary, the present invention provides a full-space focus adjustable super-structured lens and a design method thereof, including: first super structure surface, second super structure surface and third super structure surface, first super structure surface the second super structure surface and the third super structure surface by the stratum basale with set up in a plurality of nanometer antennas on the stratum basale constitute, the outgoing wave phase place that each nanometer antenna of first super structure surface corresponds satisfies the formula: p 1 ＝-a((x 1 +d) 2 +y 1 2 ) The phase of the outgoing wave corresponding to each nano antenna on the second superstructure surface satisfies the formula: p is 2 ＝a((x 2 +d) 2 +y 2 2 )(a(x 2 2 +y 2 2 ))φ 1 The phase of the outgoing wave corresponding to each nano antenna on the third superstructure surface satisfies the formula: p 3 ＝-(a(x 3 2 +y 3 2 ))φ 2 Wherein a and d are constants, x 1 And y 1 A first planar coordinate, x, corresponding to each nano-antenna of the first nanostructured surface 2 And y 2 A second planar coordinate, x, corresponding to each nano-antenna of the second nanostructured surface 3 And y 3 A third plane coordinate, phi, corresponding to each nano-antenna of the third metamaterial surface 1 And phi 2 Is an angle phi in a cylindrical coordinate system 1 ＝tan -1 (y 2 /x 2 )，φ 2 ＝tan -1 (y 3 /x 3 ). The super-structure lens can realize free adjustment of a full-space focus, avoids generation of spherical aberration and chromatic aberration due to the planar structure of the super-structure lens, increases the numerical aperture, has small volume and is beneficial to integration.
It is to be understood that the invention is not limited to the examples described above, but that modifications and variations may be effected thereto by those of ordinary skill in the art in light of the foregoing description, and that all such modifications and variations are intended to be within the scope of the invention as defined by the appended claims.
Claims (1)
1. A design method of a full-space focus adjustable super-structure lens is characterized in that the full-space focus adjustable super-structure lens comprises the following steps: the first, second and third super-structure surfaces are composed of a substrate layer and a plurality of nano-antennas arranged on the substrate layer, and the phase of an emergent wave corresponding to each nano-antenna on the first super-structure surface satisfies a formula:
the phase of the outgoing wave corresponding to each nano antenna on the second metamaterial surface satisfies the formula:
the nano antennas on the first super-structure surface are arranged periodically, and the sizes of the nano antennas on the first super-structure surface are different;
the nano antennas on the second metamaterial surface are arranged periodically, and the nano antennas on the second metamaterial surface have different sizes;
the nano antennas on the third super-structure surface are arranged periodically, and the sizes of the nano antennas on the third super-structure surface are different;
the long axes of the nano antennas on the first super-structure surface are vertical to the corresponding substrate layers, the long axes of the nano antennas on the second super-structure surface are vertical to the corresponding substrate layers, and the long axes of the nano antennas on the third super-structure surface are vertical to the corresponding substrate layers;
the second super-structure surface is arranged between the first super-structure surface and the third super-structure surface, the nano-antennas on the first super-structure surface and the nano-antennas on the third super-structure surface are oppositely arranged, and the nano-antennas on the second super-structure surface and the nano-antennas on the first super-structure surface or the nano-antennas on the third super-structure surface are oppositely arranged;
the nano antennas are cylindrical;
the base layer is made of silicon dioxide, the nano antennas are made of one or more of titanium dioxide, gallium nitride and silicon, and the design method comprises the following steps:
acquiring a first plane coordinate corresponding to each nano antenna on the first super-structure surface, a second plane coordinate corresponding to each nano antenna on the second super-structure surface and a third plane coordinate corresponding to each nano antenna on the third super-structure surface, which are determined in advance, and determining emergent wave phases corresponding to each nano antenna on the first super-structure surface, each nano antenna on the second super-structure surface and each nano antenna on the third super-structure surface according to the first plane coordinate, the second plane coordinate and the third plane coordinate; wherein, the phase of the outgoing wave corresponding to each nano antenna on the first superstructure surface satisfies the formula:
the phase of the outgoing wave corresponding to each nano antenna on the second superstructure surface satisfies the formula:
the phase of the outgoing wave corresponding to each nano antenna on the third superstructure surface satisfies the formula:
wherein, in the step (A),
and
is a constant number of times, and is,
and
a first planar coordinate corresponding to each nano-antenna of the first meta-surface,
and
second planar coordinates corresponding to respective nano-antennas of the second nanostructured surface,
and
a third planar coordinate corresponding to each nano-antenna of the third meta-surface,
and
is an angle in a cylindrical coordinate system,
，
；
determining a first antenna radius corresponding to each nano antenna on the first super-structured surface, a second antenna radius corresponding to each nano antenna on the second super-structured surface and a third antenna radius corresponding to each nano antenna on the third super-structured surface according to the emergent wave phases corresponding to each nano antenna on the first super-structured surface, each nano antenna on the second super-structured surface and each nano antenna on the third super-structured surface and a predetermined correspondence relationship between the antenna radius and the emergent wave phase;
designing the full-space focus adjustable super-structure lens according to the first antenna radius, the first plane coordinate, the second antenna radius, the second plane coordinate, the third antenna radius and the third plane coordinate;
the method for determining the corresponding relation between the antenna radius and the emergent wave phase comprises the following steps:
emitting waves with preset frequency from a fourth superstructure surface consisting of nano antennas with different radiuses to obtain emitted wave phases corresponding to the nano antennas with different radiuses;
determining the corresponding relation between the radius of the antenna and the phase of the emergent wave according to the nano antennas with different radii and the corresponding phases of the emergent wave;
the phase of the incident wave of the super-structured lens ranges from-pi to pi.
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