CN117741839A - Hybrid integrated superlens and design method and processing method thereof - Google Patents
Hybrid integrated superlens and design method and processing method thereof Download PDFInfo
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Abstract
The invention belongs to the field of superlens simulation design, and relates to a superlens with a multi-step structure and a nano structure integrated in a mixed mode, a design method and a processing method thereof. The hybrid integrated superlens includes: multi-step structures and nanostructures; wherein the multi-step structure comprises: a plurality of phase design steps for changing the phase of the incident light, wherein the heights of adjacent phase design steps are different; the height of the phase design steps is related to the function realized by the hybrid integrated superlens; the nanostructure is disposed on the other side of the same substrate as the multi-step structure. In the invention, the multi-step structure and the nano structure of the hybrid integrated superlens are arranged on two different surfaces of the same substrate, and the processing processes of the two surfaces can be separated without mutual influence. The nano structure arranged on the plane has more uniform etching depth, higher precision, higher arrangement freedom degree and stronger phase regulation capability.
Description
Technical Field
The invention belongs to the field of super lens simulation design, and particularly relates to a hybrid integrated super lens, a design method and a processing method thereof.
Background
The super surface is a two-dimensional array structure composed of electromagnetic resonance units with sub-wavelength scale. The wave band selection, polarization control and wave front regulation of electromagnetic radiation can be realized on the ultra-thin scale of electromagnetic wavelength magnitude by manually designing the shape and the size of the electromagnetic resonance unit and the macroscopic sequence of the two-dimensional array. The super lens is a planar lens for regulating light rays by utilizing a super surface. Compared with a planar substrate superlens, the superlens with the mixed integration of the supersurface and other structures has great advantages in miniaturization and chromatic aberration correction, and becomes a research trend in superlens academic and industry.
The related art designs a stepped substrate super surface by taking a multi-step structure as a super surface substrate, and the processing method of the super surface is to carry out gray scale exposure etching on a planar substrate to obtain the stepped substrate, deposit a structural layer on the stepped substrate, and finally photoetching to form a nano structure arranged on the stepped substrate. The substrate of the stepped substrate supersurface is planar at different heights and can be processed using existing semiconductor planar processing techniques.
However, the method is to deposit the structural layer on the stepped substrate, so that the thickness of the structural layer at different heights of the substrate may be uneven, and the etching depth of the nano structure may be inconsistent during lithography, thereby increasing the process difficulty and affecting the optical performance of the superlens. In addition, the stepped substrate may limit the freedom of arrangement of the nanostructures, thereby affecting the phase modulation capability of the superlens.
Disclosure of Invention
In order to solve the problems, the invention aims to provide a hybrid integrated superlens, a design method and a processing method thereof. The hybrid integrated superlens comprises a multi-step structure and a nano structure; the multi-step structure comprises a plurality of phase design steps for changing the phase of incident light, wherein the heights of adjacent phase design steps in the plurality of phase design steps are different; the nano structures are highly consistent and are arranged on the other surface of the same substrate as the multi-step structure. The multi-step structure and the nano structure are respectively arranged on two different surfaces of the same substrate by the hybrid integrated superlens, and the processing technology of the two surfaces can be separated without mutual influence; the nano structure arranged on the plane has more uniform etching depth, higher precision, higher arrangement freedom degree and stronger phase regulation capability.
According to a first aspect of the present invention, there is provided a hybrid integrated superlens comprising a multi-step structure and a nanostructure; the multi-step structure comprises a plurality of phase design steps for changing the phase of incident light, wherein the heights of adjacent phase design steps in the plurality of phase design steps are different; the nano structures are highly consistent, are arranged on the other surface of the same substrate as the multi-step structure, and are used for modulating the phase of incident light.
Preferably, the nanostructure is a cylindrical structure, a hollow structure or a nested structure.
Preferably, the column structure is a cylinder or a square column;
the hollow structure is a hollow cylinder or a hollow square cylinder;
the nested structure is a cylinder nested cylinder or a square cylinder nested square cylinder.
According to another aspect of the present invention, there is provided a design method of a hybrid integrated superlens according to any one of the above, comprising the steps of:
(1) Determining a working wave band of the hybrid integrated superlens, wherein the middle wavelength of the working wave band is used as the main wave length of the working wave band, and the middle wavelength of the working wave band is the average value of the minimum value and the maximum value of the working wave band;
(2) The phase required for a ray having the dominant wavelength to pass through a phase design step in the substrate is calculated by the following formula:
φ c (x,y)＝mod(φ design (x,y),2π)
wherein (x, y) is a coordinate determined by a coordinate system established with the center of the substrate as the origin, phi c (x, y) represents the phase required for light rays having the dominant wavelength to pass through the phase design step in the substrate, phi design (x, y) represents the phase required for the dominant wavelength of the operating band;
(3) Calculating the step structure height of the phase design step in the substrate by the following formula:
Wherein h (x, y) represents the step height of the phase design step in the substrate; lambda (lambda) c A dominant wavelength representative of the operating band; phi (phi) c (x,y,λ c ) Indicating a wavelength lambda c The phase required when the light of (a) passes through the phase design step in the substrate; n is n c Indicating a substrate to wavelength lambda c Refractive index of the light ray of (a);
(4) The phase required for the light of other wavelengths in the operating band to pass through the phase design step in the substrate is calculated by the following formula:
wherein h (x, y) represents the step height of the phase design step in the substrate; n (λ) represents the refractive index of the substrate for light of said other wavelengths in said operating band; λ represents other wavelengths in the operating band; phi (phi) substrate (x, y, λ) represents the phase required for light of other wavelengths in the operating band to pass through the phase design step in the substrate;
(5) The phase required for the nanostructure is calculated by the following formula:
φ total (x,y,λ)＝mod(φ substrate (x,y,λ)+φ nanostructure (x,y,λ),2π)
wherein phi is total (x, y, λ) represents a design chromatic aberration phase; phi (phi) nanostructure (x, y, λ) represents the phase required for the nanostructure;
(6) Retrieving and selecting a group of nanostructures with phases closest to the phases required by the nanostructures from a nanostructure database, and covering the nanostructures with full 2 pi phases; the method comprises the following steps: inquiring each nanostructure phase from a nanostructure database; calculating the difference value between each nanostructure phase and the nanostructure required phase, and determining the nanostructure corresponding to the nanostructure phase with the smallest nanostructure required phase difference value as the nanostructure with the closest nanostructure phase to the nanostructure required phase;
(7) And (3) determining the distribution of the multi-step structure according to the height of the multi-step structure calculated in the step (3), and forming the hybrid integrated superlens by the shape and the size of the nano structure selected in the step (6).
Preferably, in step (2), the phase required for the dominant wavelength of the operating band is calculated, including the steps of:
s1: determining a focal length of the hybrid integrated superlens;
s2: calculating the phase required by the dominant wavelength of the working wave band according to the dominant wavelength of the working wave band and the focal length of the hybrid integrated superlens;
the phase phi required for the dominant wavelength of the operating band is calculated by the following formula design (x, y) performing calculation:
wherein f represents the focal length of the optical lens generated by the hybrid integrated superlens; lambda (lambda) c Indicating the dominant wavelength of the operating band.
Preferably, the method for establishing the nanostructure database comprises the following steps:
(1) Integrating supers according to a hybridMinimum wavelength lambda of working band of lens min And a maximum wavelength lambda max Determining that the period of the nanostructure database is within the rangeAnd a height range of the nanostructure +.>Wherein lambda is 0 Is the dominant wavelength, n s Refractive index of base material, n p Refractive index of the nanostructure material;
(2) When the process is reached to the minimum processable size CD, the period is determined as p=p0, wherein: the range of P0 isWhen the diameter of the nanostructure changes, the range Var_D= [ CD, P0-CD]；
(3) And respectively carrying out parameter scanning on the nanostructure diameter D and the height H of the nanostructure under the period P and the period, wherein the scanning steps of the nanostructure diameter and the height are not less than 10, so as to obtain the phases and the transmittance of different nanostructure diameters under the period and the height at different wavelengths, thereby establishing the nanostructure database.
Preferably, in step (1), the base material of the hybrid integrated superlens is determined according to the type of the operating band.
Preferably, when the operating band is a wavelength range of infrared light, the base material is chalcogenide glass, zinc sulfide, zinc selenide, crystalline germanium, or crystalline silicon;
when the operating band is a wavelength range of visible light, the base material is silicon nitride, titanium oxide, gallium nitride, gallium phosphide, hydrogenated amorphous silicon, sapphire, or silicon oxide.
According to another aspect of the present invention, there is provided a method for processing a hybrid integrated superlens according to any one of the above, comprising the steps of:
(1) Carrying out gray scale exposure etching on a substrate to obtain a multi-step structure of the hybrid integrated superlens;
(2) Coating photoresist on the other surface of the same substrate with the multi-step structure;
(3) Exposing the photoresist to form the nanostructure;
(4) And etching and removing the residual photoresist to obtain the hybrid integrated superlens.
In general, compared with the prior art, the above technical solution conceived by the present invention mainly has the following technical advantages:
(1) Compared with the nano structures arranged on the stepped substrate, the nano structures arranged on the flat substrate surface have higher arrangement freedom degree in design according to avoiding the step edge when being arranged, and can realize smaller structure period. The super-surface phase composed of the nano-structures arranged in the way has stronger phase regulation capability, can better correct aberration in an optical system, and has wider application fields.
(2) According to the hybrid integrated superlens, the multi-step structure and the nano structure are respectively arranged on two different surfaces of the same substrate, the gray scale exposure etching process of the multi-step structure and the photoetching process of the nano structure can be separated and do not influence each other, and the damage to the existing structure caused by secondary processing on the same surface is avoided. The hybrid integrated superlens also uses the existing semiconductor process, but is simpler than the processing process of the stepped substrate supersurface, and is easier to mass produce and popularize.
(3) Compared with the nano structure arranged on the stepped substrate, the nano structure arranged on the flat substrate surface can carry out the photoetching process without depositing the structural layer, so that the error caused by uneven thickness of the structural layer deposited on the stepped substrate is avoided, the problem of different etching depths possibly caused by photoetching on the stepped substrate is solved, and the accuracy and uniformity of the etching depth of the nano structure are ensured.
Drawings
FIG. 1 shows a schematic structural view of a stepped substrate supersurface;
fig. 2 a shows a schematic structural diagram of a first implementation of the hybrid integrated superlens according to embodiment 1 of the present invention;
fig. 2 b shows a schematic structural diagram of a second implementation of the hybrid integrated superlens provided by embodiment 1 of the present invention;
fig. 2 c shows a schematic structural diagram of a third implementation of the hybrid integrated superlens according to embodiment 1 of the present invention;
fig. 3 a shows a schematic structural diagram of a cylindrical nanostructure in a hybrid integrated superlens according to embodiment 1 of the present invention;
fig. 3 b shows a schematic structural diagram of a square pillar nanostructure in a hybrid integrated superlens according to embodiment 1 of the present invention;
Fig. 3 c shows a schematic structural diagram of the hollow cylindrical nanostructure in the hybrid integrated superlens according to embodiment 1 of the present invention;
fig. 3 d shows a schematic structural diagram of a nanostructure of a hollow square column in a hybrid integrated superlens according to embodiment 1 of the present invention;
fig. 3 e shows a schematic structural diagram of a nanostructure of a cylinder-nested cylinder in a hybrid integrated superlens according to embodiment 1 of the present invention;
fig. 3 f shows a schematic structural diagram of a nanostructure of square-column nested square-columns in a hybrid integrated superlens according to embodiment 1 of the present invention;
FIG. 4 is a flow chart showing a design method of a hybrid integrated superlens according to embodiment 2 of the present invention;
FIG. 5 is a flow chart showing a hybrid integrated superlens processing method according to embodiment 3 of the present invention;
fig. 6 is a schematic diagram showing the height of a multi-step structure of a divergent lens designed according to the design method of the hybrid integrated superlens in the design method of the hybrid integrated superlens according to embodiment 2 of the present invention;
fig. 7 a is a schematic diagram showing the phase required for the nanostructure at a wavelength of 8 μm of a divergent lens designed according to the design method of the hybrid integrated superlens in the design method of the hybrid integrated superlens according to embodiment 2 of the present invention;
Fig. 7 b is a schematic diagram showing the phase required for the nanostructure at 10 μm of the wavelength of the divergent lens designed according to the design method of the hybrid integrated superlens in the design method of the hybrid integrated superlens according to embodiment 2 of the present invention;
fig. 7 c shows a schematic diagram of the phase required for the nanostructure at a wavelength of 12 μm of a divergent lens designed according to the design method of the hybrid integrated superlens in the design method of the hybrid integrated superlens according to embodiment 2 of the present invention;
fig. 8 is a schematic diagram showing a structure of a refractive-superlens optical system in which a refractive-superlens optical system phase correction plate is arranged according to a design method of a hybrid integrated superlens in the design method of a hybrid integrated superlens according to embodiment 2 of the present invention;
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention. In addition, the technical features of the embodiments of the present invention described below may be combined with each other as long as they do not collide with each other.
The invention provides a hybrid integrated superlens, comprising: multi-step structures and nanostructures;
the multi-step structure includes: a plurality of phase design steps for changing the phase of the incident light, wherein the heights of adjacent phase design steps are different; the height of the phase design step is related to the function achieved by the superlens;
the nano structure is consistent in height and arranged on the other surface of the same substrate as the multi-step structure, and is used for modulating the phase of incident light.
The invention relates to a design method of a hybrid integrated superlens, which comprises the following steps:
determining a working wave band of the hybrid integrated superlens, determining a base material of the hybrid integrated superlens according to the working wave band, and selecting an intermediate wavelength from the working wave band as a main wavelength of the working wave band;
calculating a phase required for a dominant wavelength of the operating band, the phase being related to a function implemented by the superlens;
the phase required for the light rays with the dominant wavelength to pass through the phase design step in the substrate is calculated according to the obtained phase required for the dominant wavelength by the following formula:
φ c (x,y)＝mod(φ design (x,y),2π)
Wherein phi is c (x, y) represents the phase required for light rays having the dominant wavelength to pass through the phase design step in the substrate, phi design (x, y) represents the phase required for the dominant wavelength of the operating band;
the step structure height of the phase design step in the substrate is calculated based on the refractive index of the substrate material for the light having the dominant wavelength, the phase required for the light having the dominant wavelength to pass through the phase design step in the substrate, and the dominant wavelength of the operating band by the following formula:
wherein h (x, y) represents the step height of the phase design step in the substrate; lambda (lambda) c A dominant wavelength representative of the operating band; phi (phi) c (x, y) represents the phase required for the light ray having the dominant wavelength to pass through the phase design step in the substrate; n is n c Representing the refractive index of the substrate for light having said dominant wavelength;
the steps of adjacent phase design steps in the substrate are different in height, so that the multi-step structure is formed;
the step height of the step is designed based on other wavelengths in the operating band, the refractive index of the substrate to light of the other wavelengths in the operating band, and the phase in the substrate. The phase required for the light of other wavelengths in the operating band to pass through the phase design step in the substrate is calculated by the following formula:
Wherein h (x, y) represents the step height of the phase design step in the substrate; n (λ) represents the refractive index of the substrate for light of the other wavelengths in the operating band; λ represents other wavelengths in the operating band; phi (phi) substrate (x, y, λ) represents the phase required for the other wavelengths of light in the operating band to pass through the phase design step in the substrate.
Determining the designed chromatic aberration phase of the hybrid integrated superlens, and calculating the phase required by the nanostructure according to the phase required by the light rays with other wavelengths in the working wave band when passing through the phase design step in the substrate and the determined designed chromatic aberration phase by the following formula:
φ total (x,y,λ)＝mod(φ substrate (x,y,λ)+φ nanostructure (x,y,λ),2π)
wherein phi is total (x, y, λ) represents a design chromatic aberration phase; phi (phi) nanostructure (x, y, λ) represents the phase required for the nanostructure.
Retrieving and picking a group of nanostructures from a nanostructure database, the nanostructures having phases closest to the desired phase of the nanostructure and capable of covering all 2 pi phases, comprising:
inquiring each nanostructure phase from a nanostructure database;
and calculating the difference value between each nanostructure phase and the nanostructure required phase, and determining the nanostructure corresponding to the nanostructure phase with the smallest nanostructure phase difference value as the nanostructure with the closest nanostructure phase to the nanostructure required phase.
The nanostructure database stores the corresponding relation between the nanostructure and the nanostructure phase.
Forming the hybrid integrated superlens according to the shape and the size of the multi-step structure and the shape and the size of the nano structure obtained through calculation;
performing full spectrum simulation on the formed hybrid integrated superlens to obtain a simulation result;
when the obtained simulation result can realize the function which can be realized by the optical lens and is generated by the hybrid integrated super lens, determining that the hybrid integrated super lens obtained by design meets the function requirement of the optical lens.
The invention discloses a hybrid integrated superlens processing method, which is used for processing any hybrid integrated superlens, and comprises the following steps:
carrying out gray scale exposure etching on a substrate to obtain a multi-step structure of the hybrid integrated superlens;
coating photoresist on the other surface of the same substrate with the multi-step structure;
exposing the photoresist to form the nanostructure;
and etching and removing the residual photoresist, and processing to obtain the superlens with the multi-step structure and the nano structure mixed and integrated.
Referring to the schematic structural diagram of the stepped substrate subsurface shown in fig. 1, the nanostructures 102 are disposed on the stepped substrate 101 of the stepped substrate subsurface; the stepped substrate super surface has the defects of high process difficulty, limited functions realized by super surface energy and the like.
Based on this, various embodiments of the present application provide a hybrid integrated superlens, and related design method and processing method, designing a hybrid integrated superlens with a multi-step structure and a nanostructure, where the multi-step structure includes a plurality of phase design steps with different heights for changing the phase of incident light, and the nanostructure is disposed on the other surface of the same substrate as the multi-step structure, so that the superlens with the multi-step structure and the nanostructure hybrid integrated can perform a similar function as the supersurface of the stepped substrate, but the superlens sets the multi-step structure and the nanostructure on two different surfaces of the same substrate respectively, so that the mass production and popularization are easier compared with the processing technology of the stepped substrate supersurface; and compared with the stepped substrate super surface capable of realizing the same effect, the super lens with the mixed integration of the multi-step structure and the nano structure has stronger phase regulation capability and more functions.
The following are specific examples
Example 1
Referring to the schematic structural diagram of a hybrid integrated superlens with different shapes shown in fig. 2, this embodiment proposes a hybrid integrated superlens, including: a multi-step structure 103 and a nanostructure 102.
The multi-step structure 103 includes: a plurality of phase design steps for changing the phase of the incident light, wherein the heights of adjacent phase design steps are different; the height of the phase design step is related to the function achieved by the hybrid integrated superlens.
The nanostructures 102 are highly uniform and disposed on the other side of the same substrate as the multi-step structure.
The hybrid integrated superlens as shown in a of fig. 2, the hybrid integrated superlens proposed by the present embodiment can form an achromatic divergent lens of the far infrared band (8 μm to 12 μm). The multi-step structure of the diverging lens is similar in shape to the concave lens.
The hybrid integrated superlens as shown in b in fig. 2, which is proposed by the present embodiment, can form an achromatic converging lens of the far infrared band (8 μm to 12 μm). The multi-step structure of the achromatic negative lens is similar in shape to that of a convex lens.
The hybrid integrated superlens as shown in c of fig. 2, which is proposed in the present embodiment, may form a phase compensation plate of a refractive-superlens hybrid optical system. The phase compensation plate is in a multi-step structure.
In one embodiment, the nanostructure is a cylindrical structure, a hollow structure, or a nested structure.
The nanostructure is used for modulating the phase of incident light.
See schematic structural diagram of the nanostructure shown as a in fig. 3, which is a cylinder.
See schematic structural diagram of the nanostructure shown in b in fig. 3, which is a square cylinder.
See schematic structural diagram of the nanostructure shown as c in fig. 3, which is a hollow cylinder.
See schematic structural diagram of the nanostructure shown as d in fig. 3, which is a hollow square cylinder.
See the schematic structure of the nanostructure shown as e in fig. 3, which is a cylinder nested cylinder.
See the schematic structural diagram of the nanostructure shown as f in fig. 3, which is a square cylinder nested square cylinder.
The embodiment provides a hybrid integrated superlens, which comprises the multi-step structure and the nano structure.
In summary, the present embodiment proposes a hybrid integrated superlens, which is designed with a multi-step structure and a nano-structure, wherein the multi-step structure includes a plurality of phase design steps with different heights for changing the phase of the incident light, and the nano-structure is disposed on the other surface of the same substrate as the multi-step structure, so as to design the hybrid integrated superlens with the same function as the super surface of the stepped substrate, but with simpler processing technology, and thus, the hybrid integrated superlens is easier to mass produce and popularize.
Example 2
Before the design method of the hybrid integrated superlens provided in this embodiment is performed, the following steps are required to be executed first, and a nanostructure database is established:
minimum wavelength lambda according to the operating band of hybrid integrated superlens min And a maximum wavelength lambda max Determining that the period of the nanostructure database is within the rangeAnd height range of nanostructures +.>Wherein lambda is 0 Is the dominant wavelength, n s Refractive index of base material, n p Is the refractive index of the nanostructure material. When the minimum process workable size (Critical dimension, CD) is reached, the cycle is determined to be P=P0 (where P0 is within the range +.>) When the diameter of the nanostructure changes, the range Var_D= [ CD, P0-CD]. And respectively carrying out parameter scanning on the nanostructure diameter D and the height H of the nanostructure under the period P and the period, wherein the scanning steps of the nanostructure diameter and the height of the nanostructure diameter are not less than 10, so that the Phase (lambda) and the Transmittance transmissibility (lambda) of different nanostructure diameters under the period and the height of the nanostructure diameter at different wavelengths are obtained, and a nanostructure database is built. The nanostructure database records information such as period (P), structure geometry, material, height, transmittance, phase, etc. of each nanostructure.
Wherein, the structural mode includes but is not limited to: nano-cylinders, nano-square cylinders, nano-hollow square cylinders, nano-cylinder nested cylinders and nano-square cylinder nested square cylinders.
For example, for the phase compensation plate of the refractive-superlens hybrid optical system, the operating band is selected to have a dominant wavelength of 4.8 μm and the base material is selected to be silicon. The nanostructure database is selected from the nanostructure databases of P=1.3 μm, H=4.8 μm and D from 0.7 μm to 1.2 μm, the nanostructure square column, the nanoring column and the nanostructure square ring column.
After the nanostructure database is built, the following hybrid integrated superlens design method may be continuously executed, referring to a flowchart of a hybrid integrated superlens design method shown in fig. 4, and the embodiment proposes a hybrid integrated superlens design method, which includes the following specific steps:
step 400, determining an operating band of the hybrid integrated superlens, determining a base material of the hybrid integrated superlens according to the operating band, and selecting an intermediate wavelength from the operating band as a main wavelength of the operating band.
When the operating band is the wavelength range of infrared light, materials for the substrate may be selected, including but not limited to: chalcogenide glass, zinc sulfide, zinc selenide, crystalline germanium, and crystalline silicon.
When the operating band is the wavelength range of visible light, materials that may be selected for the substrate include, but are not limited to: silicon nitride, titanium oxide, gallium nitride, gallium phosphide, hydrogenated amorphous silicon, sapphire and silicon oxide.
When the hybrid integrated superlens to be designed is used as a phase compensation plate for the mid-infrared band (3.7-4.8 μm), since the operating band is 3.7-4.8 μm, then the mid-wavelength (4.25 μm) of 3.7-4.8 μm can be selected as the dominant wavelength.
Step 401, calculating the step shape and size of the multi-step structure based on the obtained dominant wavelength of the working band, and determining the nano structure forming the super surface.
In the above step 401, in order to calculate the step shape and size forming the multi-step structure based on the obtained dominant wavelength of the operating band, the following steps (1) to (4) may be performed:
(1) Calculating the phase required by the dominant wavelength of the working wave band;
(2) Calculating the phase required by the light rays with the dominant wavelength when passing through the phase design steps in the substrate according to the obtained phase required by the dominant wavelength;
(3) Calculating a substrate height of the phase design step in the substrate based on the refractive index of the substrate for the light having the dominant wavelength, the phase required for the light having the dominant wavelength to pass through the phase design step in the substrate, and the dominant wavelength of the operating band; wherein, the substrate heights of adjacent phase design steps in the substrate are different, so as to form the multi-step structure;
(4) And calculating the phase required by the light rays with other wavelengths in the working wave band when the light rays with other wavelengths pass through the phase design step in the substrate based on the other wavelengths in the working wave band, the refractive index of the substrate for the light rays with other wavelengths in the working wave band and the substrate height of the phase design step in the substrate.
In the above step (1), the phase required for the dominant wavelength of the operating band is calculated, including the following steps (11) to (12):
(11) Determining a focal length of the hybrid integrated superlens;
(12) Calculating the phase required by the dominant wavelength of the working wave band according to the dominant wavelength of the working wave band and the focal length of the hybrid integrated superlens;
the phase phi required for the dominant wavelength of the operating band is calculated by the following formula design (x, y) performing calculation:
wherein f represents the focal length of the optical lens generated by the hybrid integrated superlens; lambda (lambda) c Indicating the dominant wavelength of the operating band.
Of course, any other existing phase calculation method may be used to calculate the phase required for the dominant wavelength of the operating band, which is not described herein.
In step (2) above, the phase required for the light having the dominant wavelength to pass through the phase design step in the substrate is calculated:
The phase required for a ray having the dominant wavelength to pass through a phase design step in the substrate is calculated by the following formula:
φ c (x,y)＝mod(φ design (x,y),2π)
wherein phi is c (x, y) represents the phase required for light rays having the dominant wavelength to pass through the phase design step in the substrate, phi design (x, y) represents the phase required for the dominant wavelength of the operating band.
Calculating the step structure height of the phase design step in the substrate by the following formula:
wherein h (x, y) represents the step height of the phase design step in the substrate; phi (phi) c (x, y) represents the phase required for the light ray having the dominant wavelength to pass through the phase design step in the substrate; n is n c Indicating the refractive index of the substrate for light having said dominant wavelength.
In the step (4), the other wavelengths in the operating band refer to the wavelengths remaining in the operating band except the wavelength selected as the dominant wavelength.
The phase required for the light of the other wavelengths in the operating band to pass through the phase design step in the substrate is then calculated by the following formula:
wherein h (x, y) represents the step height of the phase design step in the substrate; n (λ) represents the refractive index of the substrate for light of the other wavelengths in the operating band; λ represents other wavelengths in the operating band; phi (phi) substrate (x, y, λ) represents the phase required for the other wavelengths of light in the operating band to pass through the phase design step in the substrate.
After calculating the shape and size of the multi-step structure based on the obtained dominant wavelength of the operating band, the following steps (41) to (42) may be continuously performed, and based on the obtained dominant wavelength of the operating band, determining the nanostructure forming the hybrid integrated superlens:
(41) Determining the designed chromatic aberration phase of the hybrid integrated superlens, and calculating the phase required by the nano structure according to the phase required by the light rays with other wavelengths in the working wave band when passing through the phase design ladder in the substrate and the determined designed chromatic aberration phase;
(42) And retrieving and selecting a group of nanostructures with phases closest to the phases required by the nanostructures from a nanostructure database, wherein the nanostructures can cover the nanostructures with the phases of all 2 pi, and the nanostructure database stores the corresponding relation between the nanostructures and the phases of the nanostructures.
In the above step (41), the designed chromatic aberration phase of the hybrid integrated superlens corresponds to the realized function of the designed optical lens.
In one embodiment, the correspondence between the designed chromatic aberration phase of the hybrid integrated superlens and the formed optical lens of the hybrid integrated superlens may be expressed as follows:
Design chromatic aberration phase of hybrid integrated superlens 1 achromatic converging (positive) lens;
design chromatic aberration phase 2 achromatic diverging (negative) lens of hybrid integrated superlens;
design chromatic aberration of hybrid integrated superlens phase 3 a phase compensation plate of a refractive-superlens hybrid optical system.
Therefore, according to the optical lens to be formed of the hybrid integrated superlens, the designed chromatic aberration phase of the hybrid integrated superlens corresponding to the optical lens to be formed can be determined.
To calculate the phase required for the nanostructure, the phase required for the nanostructure is calculated by the following formula:
φ total (x,y,)＝mod(φ substrate (x,y,λ)+φ nanostructure (x,y,λ),2π)
wherein phi is total (x, y, λ) represents a design chromatic aberration phase; phi (phi) nanostructure (x, y, λ) represents the phase required for the nanostructure.
In the above step (42), in order to query the nanostructure database for the nanostructure whose phase is closest to the phase required for the nanostructure, the following steps (421) to (422) may be performed
(421) Inquiring each nanostructure phase from a nanostructure database;
(422) And calculating the difference value between each nanostructure phase and the nanostructure required phase, and determining the nanostructure corresponding to the nanostructure phase with the smallest nanostructure phase difference value as the nanostructure with the closest nanostructure phase to the nanostructure required phase.
In the step (422), when calculating the difference between the phase of each nanostructure and the phase required by the nanostructure, in one embodiment, the difference between the phase of each nanostructure and the phase required by the nanostructure may be directly calculated, that is: subtracting the phase required by the nanostructure from the nanostructure phase to obtain a difference between the nanostructure phase and the phase required by the nanostructure.
In another embodiment, the search for nanostructures may be performed using an optimization algorithm that minimizes the weighted error, the principle of which may be expressed by the following formula:
wherein delta (x, y) represents the difference between the phase of each nanostructure and the desired phase of the nanostructure,
(x,y,λ i ) Indicating a wavelength lambda i In the case of the phase required for the nanostructure,representing the j-th nanostructure in each nanostructure phase in the nanostructure database at wavelength lambda i Phase of the nanostructure below, c i Representing wavelength lambda i The weight coefficient at that time is usually 1.
And step 402, forming the hybrid integrated superlens according to the calculated shape and size of the multi-step structure and the calculated shape and size of the nano structure.
And 403, performing full spectrum simulation on the formed hybrid integrated superlens to obtain a simulation result.
Specifically, full spectrum simulation is performed on the designed hybrid integrated superlens by employing the minimum wavelength lambda in the operating band of the hybrid integrated superlens min To a maximum wavelength lambda max The spacing wavelength is not less than (lambda) max -λ min ) /10 light field propagation, thenAnd (5) weighting and superposing all the light fields to obtain a full spectrum simulation result.
Wherein the weight value used when all light fields are weighted and superimposed is the relative amplitude of each wavelength of the operating band (i.e. the square root of the ratio of the intensities of the light), and generally all weight coefficients are 1. For example, when the obtained hybrid integrated superlens is designed as a broad spectrum converging lens, it is determined whether or not the light passing through the hybrid integrated superlens is converged at the same point well as a condition whether or not the design satisfies the requirement.
Specifically, the convergence condition is a half width defined by a diffraction limit of twice or less of a half width of the optical focus in the optical axis direction, that isWherein (1)>The average wavelength of light incident on the hybrid integrated superlens, NA is the numerical aperture of an optical system formed by a multi-step structure and a nano structure on the other surface of the substrate, FWHM real For representing the half width of the optical focus in the direction of the optical axis.
And 404, determining that the designed hybrid integrated superlens meets the functional requirement of the optical lens when the obtained simulation result can realize the function which can be realized by the optical lens and is generated by the hybrid integrated superlens.
Otherwise, when the obtained simulation result fails to realize the function which can be realized by the optical lens to be generated by the hybrid integrated superlens, returning to the step 400, and attempting to design the hybrid integrated superlens by using other wavelengths as the dominant wavelength until the hybrid integrated superlens obtained by design is determined to meet the function requirement of the optical lens.
For example, the design method of the hybrid integrated superlens proposed in the present embodiment may be applied to design the following lenses:
1) The superlens is required to be used as a chromatic aberration-free and spherical aberration-free converging lens with a focal length of-10 mm and a caliber of 6mm in a far infrared band (8-12 μm). The dominant wavelength of 10 μm is selected, and the substrate material is silicon. The nanostructure databases are p=3 μm, h=8 μm nanopillars, nanopillars and nanopillar structures databases.
The heights corresponding to the multi-step structure can be obtained as shown in fig. 6 according to the following formulas Eq-1 to Eq-3. The color difference phases at 8 μm, 10 μm and 12 μm corresponding to the substrate height are obtained from the equation Eq-4, referring to a in FIG. 7, b in FIG. 7 and c in FIG. 7.
Based on the phase phi required by the dominant wavelength of the operating band design Further, the multi-step structure shape (x, y, h) on the substrate is calculated. Point-to-center wavelength λ on a substrate at coordinates (x, y) c Required phase phi c As shown in equation Eq-1:
φ c (x,y)＝mod(φ design (x,y),2π)(Eq-1)
when the desired phase is a diverging lens (focal length f), the design phase is as shown in equation Eq-2:
where mod (2π) is the remainder formula where a specific value is 2π. According to the phase phi required by the light with the dominant wavelength when passing through the phase design step in the substrate c The height h (x, y) at the (x, y) base coordinates can be determined by (x, y) and equation Eq-3:
wherein n is c Is the refractive index of the host wavelength of the substrate material. The thickness h (x, y) of the substrate can be used to calculate the other wavelength lambda c For example, eq-4:
where n (λ) is the refractive index of the base material at the wavelength λ.
In order to correct the chromatic aberration of 8 μm-12 μm, the phase of the nanostructure needs to satisfy the above formula for calculating the phase required for the nanostructure. Furthermore, according to the above formula for calculating the phase required by the nanostructure, the nanostructure units of different design positions of the whole hybrid integrated superlens can be obtained, and the phase discretization can refer to the above formula for searching the nanostructure and selecting an optimization algorithm for minimizing the weighting error.
And then, according to the formula for calculating the phase required by the nanostructure and the formula for searching the nanostructure, which can be an optimization algorithm for minimizing the weighting error, the arrangement of the nanostructure is obtained.
And finally, carrying out full spectrum simulation on the formed hybrid integrated superlens to obtain a focusing effect diagram under the full spectrum of 8-12 mu m, and verifying the focusing effect.
2) Phase correction plate of refraction-superlens optical system
The phase correction plate of the refraction-superlens optical system consists of a superlens and two refraction lenses, the working wave band is 8-12 mu m, the half field angle is 20 degrees, the F number is 0.8, and the total optical length is 85mm. This system configuration is shown in fig. 8, wherein the superlens is located in the middle of fig. 8; refractive lenses are located on the left and right sides of fig. 8; the multi-step structure phase of the phase correction plate of the refraction-superlens optical system is shown as the formula Eq-5,
wherein A, B, C, D each represents a phase distribution coefficient; ρ represents the radial coordinates of the surface of the phase correction plate of the refractive-superlens optical system, and R represents the normalized radius.
According to the formulas Eq-1, eq-3 and Eq-4 and the formulas for calculating the phase required by the nano structure, the step height of the multi-step structure of the correction plate can be obtained. According to the above formula for finding the nanostructure, which can be selected with an optimization algorithm that minimizes the weighting error, the desired theoretical phase diagrams of the nanostructure at 8 μm, 10 μm and 12 μm can be obtained.
In summary, the present embodiment provides a design method of a hybrid integrated superlens, which determines an operating band of the hybrid integrated superlens, and selects an intermediate wavelength as a dominant wavelength of the operating band according to the operating band; based on the obtained dominant wavelength of the working wave band, obtaining the shape and the size of the multi-step structure and the nano structure of the hybrid integrated superlens; forming the hybrid integrated superlens according to the shape and the size of the obtained multi-step structure and the shape and the size of the nano structure; and when the obtained simulation result can realize the functions required by the hybrid integrated superlens, determining that the designed hybrid integrated superlens meets the functional requirements of the optical lens, thereby obtaining the hybrid integrated superlens capable of realizing the target effect according to the functional requirements of the optical lens.
Example 3
Referring to the flowchart of the hybrid integrated superlens processing method shown in fig. 5, this embodiment proposes an all-medium hybrid integrated superlens processing method for processing the hybrid integrated superlens proposed in embodiment 1, where the processing method includes the following specific steps:
And 500, carrying out gray scale exposure etching on the substrate to obtain the multi-step structure of the hybrid integrated superlens.
And step 501, coating photoresist on the other surface of the same substrate with the multi-step structure.
And 502, exposing the photoresist to form the nanostructure.
And step 503, etching and removing the residual photoresist, and processing to obtain the superlens with the multi-step structure and the nano structure mixed and integrated.
In summary, in the processing method of the hybrid integrated superlens provided in the embodiment, since the hybrid integrated superlens has the multi-step structure and the nano structure respectively arranged on the two different surfaces of the same substrate, the processing processes of the two surfaces can be separated and are not affected, so that the processing process of the hybrid integrated superlens is simpler than the processing process of the supersurface of the stepped substrate, and is easier to mass production and popularization; simultaneously, compared with the nanostructure arranged on the stepped substrate, the nanostructure arranged on the plane has more uniform etching depth, higher precision, higher freedom degree of arrangement, stronger phase regulation capability, more functions and wider application scene.
It will be readily appreciated by those skilled in the art that the foregoing description is merely a preferred embodiment of the invention and is not intended to limit the invention, but any modifications, equivalents, improvements or alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (9)
1. The hybrid integrated superlens is characterized by comprising a multi-step structure and a nano structure; the multi-step structure comprises a plurality of phase design steps for changing the phase of incident light, wherein the heights of adjacent phase design steps in the plurality of phase design steps are different; the nano structures are highly consistent, are arranged on the other surface of the same substrate as the multi-step structure, and are used for modulating the phase of incident light.
2. The hybrid integrated superlens of claim 1, wherein the nanostructure is a cylindrical structure, a hollow structure, or a nested structure.
3. The hybrid integrated superlens of claim 2, wherein the cylinder structure is a cylinder or a square cylinder;
the hollow structure is a hollow cylinder or a hollow square cylinder;
the nested structure is a cylinder nested cylinder or a square cylinder nested square cylinder.
4. A method of designing a hybrid integrated superlens according to any of claims 1-3, comprising the steps of:
(1) Determining a working wave band of the hybrid integrated superlens, wherein the middle wavelength of the working wave band is used as the main wave length of the working wave band, and the middle wavelength of the working wave band is the average value of the minimum value and the maximum value of the working wave band;
(2) The phase required for a ray having the dominant wavelength to pass through a phase design step in the substrate is calculated by the following formula:
φ c (x,y)＝mod(φ design (x,y),2π)
wherein (x, y) is a coordinate determined by a coordinate system established with the center of the substrate as the origin, phi c (x, y) represents the phase required for light rays having the dominant wavelength to pass through the phase design step in the substrate, phi design (x, y) represents the phase required for the dominant wavelength of the operating band;
(3) Calculating the step structure height of the phase design step in the substrate by the following formula:
wherein h (x, y) represents the step height of the phase design step in the substrate; lambda (lambda) c A dominant wavelength representative of the operating band; phi (phi) c (x,y,λ c ) Indicating a wavelength lambda c The phase required when the light of (a) passes through the phase design step in the substrate; n is n c Indicating a substrate to wavelength lambda c Refractive index of the light ray of (a);
(4) The phase required for the light of other wavelengths in the operating band to pass through the phase design step in the substrate is calculated by the following formula:
wherein h (x, y) represents the step height of the phase design step in the substrate; n (λ) represents the refractive index of the substrate for light of said other wavelengths in said operating band; λ represents other wavelengths in the operating band; phi (phi) substrate (x, y, λ) represents the passage of light of other wavelengths in the operating band through the phase in the substrateThe phase required when the bits are stepped;
(5) The phase required for the nanostructure is calculated by the following formula:
φ total (x,y,λ)＝mod(φ substrate (x,y,λ)+φ nanostructure (x,y,λ),2π)
wherein phi is total (x, y, λ) represents a design chromatic aberration phase; phi (phi) nanostructure (x, y, λ) represents the phase required for the nanostructure;
(6) Retrieving and selecting a group of nanostructures with phases closest to the phases required by the nanostructures from a nanostructure database, and covering the nanostructures with full 2 pi phases; the method comprises the following steps: inquiring each nanostructure phase from a nanostructure database; calculating the difference value between each nanostructure phase and the nanostructure required phase, and determining the nanostructure corresponding to the nanostructure phase with the smallest nanostructure required phase difference value as the nanostructure with the closest nanostructure phase to the nanostructure required phase;
(7) And (3) determining the distribution of the multi-step structure according to the height of the multi-step structure calculated in the step (3), and forming the hybrid integrated superlens by the shape and the size of the nano structure selected in the step (6).
5. The method of designing a hybrid integrated superlens according to claim 4, wherein in step (2), the phase required for the dominant wavelength of the operating band is calculated, comprising the steps of:
S1: determining a focal length of the hybrid integrated superlens;
s2: calculating the phase required by the dominant wavelength of the working wave band according to the dominant wavelength of the working wave band and the focal length of the hybrid integrated superlens;
the phase phi required for the dominant wavelength of the operating band is calculated by the following formula design (x, y) performing calculation:
wherein f represents the focal length of the optical lens generated by the hybrid integrated superlens; lambda (lambda) c Indicating the dominant wavelength of the operating band.
6. The hybrid integrated superlens design method of claim 4, wherein the method for creating the nanostructure database comprises the steps of:
(1) Minimum wavelength lambda according to the operating band of hybrid integrated superlens min And a maximum wavelength lambda max Determining that the period of the nanostructure database is within the rangeAnd a height range of the nanostructure +.>Wherein lambda is 0 Is the dominant wavelength, n s Refractive index of base material, n p Refractive index of the nanostructure material;
(2) When the process is reached to the minimum processable size CD, the period is determined as p=p0, wherein: the range of P0 isWhen the diameter of the nanostructure changes, the range Var_D= [ CD, P0-CD]；
(3) And respectively carrying out parameter scanning on the nanostructure diameter D and the height H of the nanostructure under the period P and the period, wherein the scanning steps of the nanostructure diameter and the height are not less than 10, so as to obtain the phases and the transmittance of different nanostructure diameters under the period and the height at different wavelengths, thereby establishing the nanostructure database.
7. The method of designing a hybrid integrated superlens according to claim 4, wherein in step (1), the base material of the hybrid integrated superlens is determined according to the type of the operating band.
8. The method of designing a hybrid integrated superlens according to claim 7, wherein when the working band is a wavelength range of infrared light, the base material is chalcogenide glass, zinc sulfide, zinc selenide, crystalline germanium or crystalline silicon;
when the operating band is a wavelength range of visible light, the base material is silicon nitride, titanium oxide, gallium nitride, gallium phosphide, hydrogenated amorphous silicon, sapphire, or silicon oxide.
9. A method of manufacturing a hybrid integrated superlens according to any of claims 1-3, comprising the steps of:
(1) Carrying out gray scale exposure etching on a substrate to obtain a multi-step structure of the hybrid integrated superlens;
(2) Coating photoresist on the other surface of the same substrate with the multi-step structure;
(3) Exposing the photoresist to form the nanostructure;
(4) And etching and removing the residual photoresist to obtain the hybrid integrated superlens.
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