A large numerical aperture broadband achromatic plane lens and its design method

Abstract

The present invention discloses a large numerical aperture broadband achromatic plane lens and a design method thereof. The achromatic plane lens comprises a composite substrate with a variable optical thickness and a meta-lens composed of target nano-units in sequence along the light propagation direction; the phase of the target nano-unit is a non-negative number, and the optical thickness of the composite substrate is determined according to the target phase of the plane lens and the target nano-unit; the composite substrate comprises a stepped substrate. The embodiment of the present invention realizes a wider range of broadband achromatic focusing, reduces the difficulty of processing, and can be widely used in the field of optical imaging technology.

Description

Technical Field

[0001] The invention relates to the technical field of optical imaging, and in particular to a large numerical aperture broadband achromatic plane lens and a design method thereof. Background Art

[0002] A metasurface is an ultra-thin two-dimensional array plane composed of metal or dielectric subwavelength micro-nano units arranged in a certain sequence. By designing and adjusting the geometric parameters and arrangement of the nanounits, the amplitude, phase, polarization, etc. of light can be controlled, thereby realizing functions such as light beam deflection, focusing, and polarization conversion. A metasurface used for beam focusing is usually called a metalens. Compared with traditional optical devices, it can provide more accurate and efficient phase control and obtain any transmitted or reflected light wavefront. In addition, metalenses have the advantages of small size and easy integration, and have broad application prospects in portable electronic devices, super-resolution microscopes, and other fields.

[0003] Traditional lenses are often accompanied by chromatic aberration and are difficult to use in imaging systems. Therefore, achromatic lenses play a pivotal role in the imaging optical path. Most existing meta-lenses often only work on one or several wavelengths, and the effects of other wavelengths are often unsatisfactory. In addition, most meta-lenses are polarization-dependent, which has strict requirements on the incident light and is easily affected by stray light of different polarization states. These have greatly limited the practical application of meta-lenses, and broadband achromatic meta-lenses have become an urgent need.

[0004] Traditional broadband achromatic metalens uses nanounits of various shapes to achieve the reference phase and phase dispersion required for the target optical band, so that all wavelengths meet the corresponding phase within a certain phase error range, and ultimately achieve achromatic focusing of the entire optical band.

[0005] Traditional broadband achromatic meta-lenses rely on nano-units to control phase and provide phase dispersion. Since the nano-units of planar meta-lenses can only provide normal phase dispersion with positive values, the hyperbolic phase equation curves of each wavelength need to be mathematically transformed to make their phase dispersion positive, and the phase dispersion at the center is the largest, and the phase dispersion at the edge is 0 or close to 0. This position is the physical limit of the achromatic lens. The area, numerical aperture, and operating bandwidth of the lens are limited by the formula R*NA*Δω≤2cΔφ (where R is the radius of the lens, NA is the numerical aperture, Δω is the operating bandwidth, c is the speed of light in a vacuum, and Δφ is the phase dispersion). Therefore, in order to increase the area, numerical aperture, and operating bandwidth of the lens, nano-units that can provide larger phase dispersion are required, which will result in the designed nano-units not only having very complex shapes, but also having large heights, making the processing difficulty increase dramatically. Summary of the invention

[0006] In view of this, in order to solve one of the above problems, an embodiment of the present invention aims to provide a large numerical aperture broadband achromatic plane lens and a design method thereof, so as to achieve a wider range of broadband achromatic focusing and reduce the difficulty of processing.

[0007] On the one hand, an embodiment of the present invention provides a large numerical aperture, broadband, achromatic plane lens, which includes a composite substrate with variable optical thickness and a meta-lens composed of target nano-units in sequence along the direction of light propagation; the phase of the target nano-unit is a non-negative number, and the optical thickness of the composite substrate is determined according to the target phase of the plane lens and the target nano-unit; the composite substrate includes a stepped substrate.

[0008] Optionally, the material of the composite substrate includes optical glass or optical film.

[0009] Optionally, the material of the target nano-unit includes optical glass or optical film.

[0010] Optionally, the structure of the target nano-unit includes any one or more of a circular, annular, square, 45° rotated square, cross, 45° rotated cross, circular hole square, square hole circular, rectangular or elliptical.

[0011] On the other hand, an embodiment of the present invention provides a design method for a large numerical aperture broadband achromatic plane lens, comprising:

[0012] Determine the phase and transmittance of a preset nanometer unit set for a preset light wavelength according to a numerical simulation method, and form a database;

[0013] Determine the range of the maximum phase dispersion and the aspect ratio of each nanounit in the preset nanounit set according to the database, and update the database according to the maximum phase dispersion and the aspect ratio;

[0014] Calculating the target phase of the preset light wavelength at different positions of the plane lens, determining the target nanometer unit according to the target phase and the database, and determining the target height of the optical thickness variable composite substrate at different positions according to the propagation phase formula, the target phase and the target nanometer unit;

[0015] A composite substrate of a target height is prepared by etching a substrate, the target nanometer unit is prepared by a graphical arrangement method, and the composite substrate of the target height and the target nanometer unit are assembled into an achromatic plane lens.

[0016] Optionally, determining the phase and transmittance of a preset nanounit set for a preset light wavelength according to a numerical simulation method specifically includes:

[0017] Determine the total degree of freedom of each nanounit in a preset nanounit set and the preset light wavelength;

[0018] Determine the parameter range and interval according to the total degree of freedom of each nanounit;

[0019] The numerical simulation method is used to simulate and scan the parameters of each degree of freedom of each nano unit to determine the phase and transmittance of each nano unit with each degree of freedom parameter for a preset light wavelength.

[0020] Optionally, updating the database according to the maximum phase dispersion and the aspect ratio specifically includes:

[0021] If the maximum phase dispersion corresponds to several nanounits, the nanounit with the smallest aspect ratio is selected;

[0022] If the same aspect ratio corresponds to several nanounits, select the nanounit with a phase coverage of 0-2π;

[0023] If the phase coverage 0-2π corresponds to several nanounits, the nanounit with the highest transmittance is selected.

[0024] Optionally, the calculating the target phase of the preset light wavelength at different positions of the plane lens, determining the target nanometer unit according to the target phase and the database, and determining the target height of the optical thickness variable composite substrate at different positions according to the propagation phase formula, the target phase and the target nanometer unit specifically includes:

[0025] Calculate the target phase of the preset light wavelength at different positions according to the phase curve of the plane lens;

[0026] determining a target nanounit according to the target phase and the database;

[0027] Determining the phase dispersion and phase distribution of the optical thickness variable composite substrate at different positions according to the target phase and the target nanometer unit;

[0028] The target height of the composite substrate at different positions is determined according to the propagation phase formula and the phase dispersion and phase distribution of the composite substrate at different positions.

[0029] Optionally, the step of preparing the target nanounit by a graphical arrangement method specifically includes:

[0030] The target nano-unit is prepared by any one or more of electron beam direct writing, ultraviolet lithography or laser direct writing.

[0031] Optionally, the step of preparing a composite substrate of a target height by etching the substrate specifically includes:

[0032] Designing a substrate with a preset thickness;

[0033] Etching is performed on the substrate to obtain a composite substrate with a target height.

[0034] The implementation of the embodiment of the present invention includes the following beneficial effects: In this embodiment, the achromatic plane lens includes a composite substrate with variable optical thickness and a meta-lens composed of target nano-units, the phase dispersion of the composite substrate with variable optical thickness is determined by the propagation phase, the phase dispersion of the target nano-unit is non-negative, and the composite substrate with variable optical thickness breaks through the limit point where the phase dispersion of the single-layer meta-lens is 0, so that the phase of the achromatic plane lens can be extended to a region with larger phase dispersion, and then combined with the target nano-unit, a larger phase dispersion can be achieved, thereby obtaining a broadband achromatic plane lens with a larger numerical aperture and area. In addition, based on the achromatic plane lens of the embodiment of the present invention, the target phase of the preset light wavelength at different positions of the plane lens is calculated, the target nano-unit is determined according to the target phase and the database, the target height of the composite substrate with variable optical thickness at different positions is determined according to the propagation phase formula, the target phase and the target nano-unit, the composite substrate with the target height is prepared by etching the substrate, the target nano-unit is prepared by a graphical arrangement method, and the composite substrate with the target height and the target nano-unit are assembled into an achromatic plane lens, which reduces the processing difficulty. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 is a schematic structural diagram of an achromatic plane lens provided by an embodiment of the present invention;

[0036] Figure 2 is a schematic structural diagram of a nano unit provided by an embodiment of the present invention;

[0037] Figure 3 is a schematic diagram of a unit structure of a nano unit provided by an embodiment of the present invention;

[0038] Figure 4 It is a schematic flow chart of the steps of a method for preparing an achromatic plane lens provided by an embodiment of the present invention;

[0039] Figure 5 This is a schematic diagram of an ideal phase of an achromatic plane lens for different wavelengths at different radial coordinates provided by an embodiment of the present invention;

[0040] Figure 6 This is a schematic diagram of an ideal phase of a target nanometer unit for different wavelengths at different radial coordinates provided by an embodiment of the present invention;

[0041] Figure 7 It is a schematic diagram of an ideal phase of a stepped substrate for different wavelengths at different radial coordinates provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0042] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. The step numbers in the following embodiments are only provided for the convenience of explanation and description, and the order between the steps is not limited in any way. The execution order of each step in the embodiment can be adaptively adjusted according to the understanding of those skilled in the art.

[0043] In the following description, reference is made to “some embodiments”, which describe a subset of all possible embodiments, but it will be understood that “some embodiments” may be the same subset or different subsets of all possible embodiments and may be combined with each other without conflict.

[0044] In the following description, the terms "first\second\third" involved are merely used to distinguish similar objects and do not represent a specific ordering of the objects. It can be understood that "first\second\third" can be interchanged with a specific order or sequence where permitted, so that the embodiments of the present invention described herein can be implemented in an order other than that illustrated or described herein.

[0045] Unless otherwise defined, all technical and scientific terms used in the embodiments of the present invention have the same meanings as those commonly understood by those skilled in the art of the present invention. The terms used in the embodiments of the present invention are only for the purpose of describing the embodiments of the present invention and are not intended to limit the present invention.

[0046] like Figure 1 As shown, an embodiment of the present invention provides a large numerical aperture broadband achromatic plane lens, which includes a composite substrate 1-2 with variable optical thickness and a meta-lens composed of target nano-units 1-1 in sequence along the light propagation direction; the phase of the target nano-unit 1-1 is a non-negative number, and the optical thickness 1-2 of the composite substrate is determined according to the target phase of the plane lens and the target nano-unit 1-1; the composite substrate 1-2 includes a stepped substrate.

[0047] It should be noted that the optical thickness variable composite substrate includes a substrate with an equivalent refractive index variable, and the optical thickness variable composite substrate includes but is not limited to a stepped substrate. For example, the stepped substrate can cover a larger range of phase dispersion and can achieve broadband achromatism with a numerical aperture of 0.99.

[0048] Specifically, see Figure 1 , the plane normal incident light, after passing through the achromatic plane lens in this embodiment, is focused to a point. The plane normal incident light passes through the stepped substrate to produce a phase dispersion with a larger numerical range, and after generating a non-negative phase dispersion of the target nanometer unit, the emitted light can obtain an ideal phase dispersion.

[0049] Phase dispersion is the first-order differential term of the phase equation with respect to frequency. By Taylor expanding φ(x, y, ω), we can obtain Where ω0 is the reference circular frequency, let Then Δφ is called phase dispersion. In the selected nanounit, if the phase response of the nanounit to different optical frequencies has a certain linearity, then the change in phase as the frequency increases can be considered as the phase dispersion that the nanounit can achieve.

[0050] Optionally, the material of the composite substrate includes optical glass or optical film.

[0051] Specifically, the material of the target nano-unit includes but is not limited to optical glass or optical film. The optical film includes but is not limited to titanium dioxide and the like. The optical glass includes but is not limited to semiconductors such as silicon and the like.

[0052] Optionally, the material of the target nano-unit includes optical glass or optical film.

[0053] Specifically, the material of the nano-unit includes an optical dielectric material. Considering the transmittance of the final structure to the normal incident light, a full dielectric structure can be used. The material of the target nano-unit includes but is not limited to optical glass or optical film. The optical film includes but is not limited to titanium dioxide, etc. The optical glass includes but is not limited to semiconductors such as silicon.

[0054] Optionally, the structure of the target nano-unit includes any one or more of a circular, annular, square, 45° rotated square, cross, 45° rotated cross, circular hole square, square hole circular, rectangular or elliptical.

[0055] It should be noted that the structure of the target nanounit includes polarization-insensitive structures, such as circular, annular, square, 45° rotated square, cross, 45° rotated cross, circular square with hole, square with hole; the structure of the target nanounit includes polarization-sensitive structures, such as rectangular or elliptical.

[0056] See also Figure 2 and Figure 3 The nano unit includes a substrate and a unit structure. The repetition period of the substrate is U, the height of the unit structure is H, and the shape of the unit structure includes a circle with a diameter of D, a ring with an outer diameter of D1 and an inner diameter of D2, a square with an edge length of A, a 45° rotated square with an edge length of B, and a cross with a length of L and a width of W. The shape of the unit structure also includes a 45° rotated cross, a circular hole square, and a square hole circular. The unit structure of the above-mentioned nano unit is a symmetrical structure, that is, the nano unit has the same effect on incident light of different linear polarization states, so the focusing lens meets the polarization insensitivity condition and has no stringent requirements on the polarization state of the incident light.

[0057] The implementation of the embodiments of the present invention includes the following beneficial effects: In this embodiment, the achromatic plane lens includes a composite substrate with variable optical thickness and a meta-lens composed of target nano-units, the phase dispersion of the composite substrate with variable optical thickness is determined by the propagation phase, the phase dispersion of the target nano-unit is a non-negative number, and the composite substrate with variable optical thickness breaks through the limit point that the phase dispersion of the single-layer meta-lens is 0, so that the phase of the achromatic plane lens can be extended to a region with larger phase dispersion, and then combined with the target nano-unit, a larger phase dispersion can be achieved, thereby obtaining a broadband achromatic plane lens with a larger numerical aperture and area.

[0058] See also Figure 4 The embodiment of the present invention provides a method for designing a large numerical aperture broadband achromatic plane lens, comprising steps S100 to S400.

[0059] S100, determining the phase and transmittance of a preset nanometer unit set for a preset light wavelength according to a numerical simulation method, and forming a database.

[0060] Specifically, numerical simulation includes but is not limited to using the time-domain finite difference method, the finite element difference method, the coupled wave analysis method, etc. to obtain electromagnetic field data such as the intensity, polarization, phase, and transmittance of the outgoing light wave, thereby establishing a database of the phase and transmittance generated by the nanounits in response to incident light under specific conditions.

[0061] Optionally, the phase and transmittance of the preset nanounit set for the preset light wavelength are determined according to a numerical simulation method, specifically including steps S110 to S130:

[0062] S110, determining the total degree of freedom of each nanounit in a preset nanounit set and a preset light wavelength;

[0063] S120, determining a parameter range and interval according to the total degree of freedom of each nanometer unit;

[0064] S130, using a numerical simulation method to simulate and scan the parameters of each degree of freedom of each nano unit, and determine the phase and transmittance of each nano unit with each degree of freedom parameter for a preset light wavelength.

[0065] Specifically, the degree of freedom refers to the number of geometric parameters required to fully describe the geometric characteristics of the periodically arranged nanounits, such as the height H, the repetition period U, the shape of the nanounits, the rotation direction, the dimensions in each orientation, etc. For example: the circle is the diameter D, the ring is the outer diameter D1 and the inner diameter D2, the square is the edge length A, the 45° rotated square is the edge length B, and the cross is the length L and width W.

[0066] Specifically, the total degrees of freedom of a single nanounit are first determined, and the required incident light band is set. Then, the range and interval of the geometric parameters of each degree of freedom are set. Finally, the numerical simulation method is used to simulate and scan the geometric parameters of each degree of freedom of the nanounit to obtain a database of phase and transmittance generated by a single nanounit under different geometric parameters for the incident light band.

[0067] S200, determining the range of the maximum phase dispersion and the aspect ratio of each nanounit in the preset nanounit set according to the database, and updating the database according to the maximum phase dispersion and the aspect ratio.

[0068] Specifically, the phase of the nanounit is analyzed to determine the maximum phase dispersion and the range of the aspect ratio of the nanounit that can be achieved by various nanounits. Then, the height and repetition period with the best phase and transmittance are selected according to the maximum phase dispersion, aspect ratio, repetition period and transmittance, and the data is updated in the phase and transmittance database.

[0069] The aspect ratio of a nanometer unit refers to the ratio of the longitudinal dimension of a nanometer unit to its lateral characteristic dimension. For current micro-nano manufacturing, if this value exceeds a certain value, the difficulty of manufacturing will increase dramatically. The aspect ratio of the nanometer unit selected in the present invention is less than 10, which is relatively adapted to the general requirements of manufacturing.

[0070] First, the transmission phase obtained by scanning various shapes under different geometric parameters is normalized to be between 0-2π, and then a set of optimal height and repetition period combinations are found in the database. At this fixed height and repetition period, the phase and transmittance database of each shape nanounit covering 0-2π is obtained. With this repetition period as the interval, the target lens is discretized into a phase grid composed of multiple points. The sampling point (x, y) is the center coordinate of the grid, and the center of the lens is defined as the origin (0, 0).

[0071] Optionally, updating the database according to the maximum phase dispersion and the aspect ratio specifically includes steps S210 to S230:

[0072] S210, if the maximum phase dispersion corresponds to a plurality of nanounits, selecting the nanounit with the smallest aspect ratio;

[0073] S220, if the same aspect ratio corresponds to several nano-units, select a nano-unit with a phase coverage of 0-2π;

[0074] S230 , if the phase coverage 0-2π corresponds to a number of nano-units, select the nano-unit with the highest transmittance.

[0075] First, among the nanounits whose maximum phase dispersion can reach the required value, the one with the smallest aspect ratio is selected; then, under this aspect ratio, the phase of the nanounit is selected to cover a repetition period of 0-2π; if there are multiple repetition periods that meet the conditions, the one with the higher overall transmittance of the nanounit is selected.

[0076] S300, calculating the target phase of the preset light wavelength at different positions of the plane lens, determining the target nanometer unit according to the target phase and the database, and determining the target height of the optical thickness variable composite substrate at different positions according to the propagation phase formula, the target phase and the target nanometer unit.

[0077] Specifically, the target phase of the preset light wavelength at different positions of the plane lens is first calculated, and then the target nanounit is determined based on the target phase and the parameters of each nanounit in the database. Finally, the target height of the composite substrate with variable optical thickness at different positions is determined based on the propagation phase formula, the target phase and the target nanounit.

[0078] Optionally, the calculating of the target phase of the preset light wavelength at different positions of the plane lens, determining the target nanometer unit according to the target phase and the database, and determining the target height of the optical thickness variable composite substrate at different positions according to the propagation phase formula, the target phase and the target nanometer unit specifically includes steps S310 to S330:

[0079] S310, calculating target phases of preset light wavelengths at different positions according to the phase curve of the plane lens.

[0080] According to the Fresnel hyperbolic phase law of plane light at normal incidence, the Fresnel hyperbolic phase equation of the focusing plane lens is given: Where (x, y) is the position coordinate of each nanounit in the lens area, φ(x, y) is the phase of the nanounit, λ is the design wavelength, f is the design focal length, and C(λ, r) is the initial phase constant. Since the wavelength and circular frequency ω satisfy 2πc=λω, the above equation can be rewritten as

[0081] S320: Determine a target nano unit according to the target phase and the database.

[0082] S330, determining the phase dispersion and phase distribution of the composite substrate with variable optical thickness at different positions according to the target phase and the target nano-unit.

[0083] Phase dispersion is the first-order differential term of the phase equation with respect to frequency. The above Fresnel hyperbolic phase equation φ(x, y, ω) is Taylor expanded to obtain Where ω0 is the reference circular frequency, let Then Δφ is called phase dispersion. This is the so-called group delay. For the hyperbolic phase equation, The above Taylor expansion only takes the first two terms, so φ(x,y,ω)=φ(x,y,ω0)+Δφ(x,y,ω). In this formula, the first term on the right is the reference phase term that is only related to ω0, and the second term on the right is the phase dispersion term related to each frequency ω, which characterizes the change of the phase of other frequencies relative to the reference phase. In the selected nanounit, if the phase response of the nanounit to different optical frequencies has a certain linearity, then as the frequency continues to increase, the change in phase can be considered as the phase dispersion that the nanounit can achieve.

[0084] For the hyperbolic phase curve, Taylor expansion is performed and the first two terms are taken to express it as φ(x,y,ω)=φ(x,y,ω0)+Δφ(x,y,ω). For the broadband achromatic phase equation, the total phase can usually be divided into two terms like this. The first term on the right is the reference phase term, which is determined by the reference frequency ω0, and the second term is the phase dispersion term related to each frequency. The phase equation is decomposed according to the maximum phase dispersion that the nanounit can provide in the database, so that φ(x,y,λ)=φ1(x,y,λ)+φ2(x,y,λ)=φ1(x,y,λ0)+Δφ1(x,y,λ)+φ2(x,y,λ0)+Δφ2(x,y,λ), where φ1(x,y,λ) is the phase that the nanounit needs to satisfy, and its phase dispersion Δφ1(x,y,λ) needs to be a non-negative number, which is determined by the intrinsic properties of the nanounit. φ2(x,y,λ) is the phase that the composite substrate with variable optical thickness (such as a stepped substrate for example) needs to satisfy, and its phase dispersion Δφ2(x,y,λ) is a positive number with a large numerical range, which is calculated by the propagation phase formula.

[0085] According to the above calculation results, the optimal matching structure that satisfies φ1(x, y, λ) is retrieved in the database, and the corresponding size parameters are recorded. The most suitable nanounits are arranged on all corresponding sampling points (x, y) on the substrate, and a stepped substrate with a height distribution that satisfies φ2(x, y, λ) is obtained. Finally, a planar lens that can focus light in the entire target band is obtained. Since the design is based on the Fresnel hyperbolic phase, in principle the focused light spot can achieve the diffraction limit.

[0086] S340, determining the target height of the composite substrate at different positions according to the propagation phase formula and the phase dispersion and phase distribution of the composite substrate at different positions.

[0087] Specifically, for the same incident light wavelength, the phase dispersion distribution and phase response corresponding to different heights of the composite substrate are different.

[0088] Specifically, for a base with a height distribution (the height of each order from high to low is h0, h1, h2...), at a height of h i According to the propagation phase formula, the propagation phase corresponding to the wavelength λ after passing through the substrate is Furthermore, the phase dispersion value is: Where λ1 and λ2 are the minimum and maximum wavelengths in the design band, respectively. s is the refractive index of the substrate.

[0089] In a specific embodiment, Figure 6 is the phase that the nanounit needs to satisfy, and only three wavelengths in the target band are drawn. When the nanounit is selected from the above database, if multiple nanounits can simultaneously satisfy the phase of the phase surface of each wavelength at this position, the nanounit with the largest average transmittance in the band is selected to obtain higher focusing efficiency. This process is called phase matching. In this design, the phase that the nanounit needs to satisfy is:

[0090]

[0091] Figure 5 is the total phase curve, which is the algebraic sum of the phases satisfied by the nanounit and the step-type basis; Figure 7 is the phase that the stepped substrate needs to satisfy, and the height of the substrate at each position is determined according to the above propagation phase calculation method. Due to the introduction of the composite substrate with height distribution, the phase dispersion of light can be controlled in a larger range.

[0092] The diffraction limit refers to an ideal object point imaged by an optical system. Due to the limitation of diffraction, it is impossible to obtain an ideal point, but a diffuse spot is obtained. For a general circular aperture Fraunhofer diffraction, the diffuse spot is called an Airy disk. When two Airy disks are close to the limit distance that can be just resolved, the limit is the diffraction limit. According to the Rayleigh criterion, when the peak of the central bright spot of the diffraction pattern of a point target falls exactly on the first dark ring of the diffraction pattern of another point target, the two point targets are considered to be just resolved.

[0093] It should be noted that for each sampling point in the lens area, the theoretical phase required for incident light of each wavelength is calculated according to the above phase equation, and the difference is made with the phase in the above database; a difference library is constructed with the average value of the absolute value of the difference between the theoretical phase and the actual phase of the nanounit for each wavelength, and the minimum value is searched in the difference library, and the corresponding nanounit structure and size are used as the data that best fits the theoretical phase; according to this process, each sampling point can be matched with the most appropriate nanounit, and the matched nanounits will have phase matching errors, but as long as the errors are within the allowable range, they are acceptable. After obtaining the height of the substrate at different positions and the geometric parameters of the nanounits at each position, the following can be constructed: Figure 1 The flat lens shown.

[0094] S400, preparing a composite substrate of a target height by etching the substrate, preparing a target nanometer unit by a graphical arrangement method, and assembling the composite substrate of the target height and the target nanometer unit into an achromatic plane lens.

[0095] Optionally, the step of preparing a composite substrate of a target height by etching the substrate specifically includes:

[0096] S410, designing a base with a preset thickness;

[0097] S420, performing etching on the substrate to obtain a composite substrate of a target height.

[0098] Specifically, the substrate material with height distribution can be selected according to the wavelength range of the incident light. The material of the substrate includes but is not limited to silicon or silicon dioxide, and the substrate is patterned by one or more of focused ion beam, electron beam direct writing, ultraviolet lithography and laser direct writing.

[0099] Optionally, the step of preparing the target nanounit by a graphical arrangement method specifically includes:

[0100] S430, preparing the target nano-unit by any one or more of electron beam direct writing, ultraviolet lithography or laser direct writing.

[0101] Specifically, the material of the target nano-unit can be selected according to the wavelength range of the incident light, and the material of the target nano-unit includes but is not limited to silicon and titanium dioxide, etc. The patterning preparation method of the nano-unit is one or more of electron beam direct writing, ultraviolet lithography and laser direct writing. The meta-lens can be patterned by, but not limited to, electron beam etching, ultraviolet lithography, laser direct writing and other methods to arrange the nano-units.

[0102] The implementation of the embodiment of the present invention includes the following beneficial effects: based on the achromatic plane lens of the embodiment of the present invention, firstly, a phase and transmittance database of nano-units is established, then the target phase of a preset light wavelength at different positions of the plane lens is calculated, the target nano-unit is determined according to the target phase and the database, the target height of the optical thickness variable composite substrate at different positions is determined according to the propagation phase formula, the target phase and the target nano-unit, then the composite substrate of the target height is prepared by etching the substrate, the target nano-unit is prepared by a graphical arrangement method, and the composite substrate of the target height and the target nano-unit are assembled into an achromatic plane lens, thereby reducing the difficulty of processing.

[0103] The above is a specific description of the preferred implementation of the present invention, but the invention is not limited to the embodiments. Those skilled in the art may make various equivalent modifications or substitutions without violating the spirit of the present invention. These equivalent modifications or substitutions are all included in the scope defined by the claims of this application.

Claims

1. A design method for a large numerical aperture broadband achromatic plane lens, characterized in that: The achromatic plane lens comprises a composite substrate with variable optical thickness and a meta-lens composed of target nano-units in sequence along the light propagation direction; the phase of the target nano-unit is a non-negative number, and the optical thickness of the composite substrate is determined according to the target phase of the plane lens and the target nano-unit; the composite substrate comprises a stepped substrate; the design method comprises the following steps: Determine the phase and transmittance of a preset nanometer unit set for a preset light wavelength according to a numerical simulation method, and form a database; Determine the range of the maximum phase dispersion and the aspect ratio of each nanounit in the preset nanounit set according to the database, and update the database according to the maximum phase dispersion and the aspect ratio; Calculating the target phase of the preset light wavelength at different positions of the plane lens, determining the target nanometer unit according to the target phase and the database, and determining the target height of the optical thickness variable composite substrate at different positions according to the propagation phase formula, the target phase and the target nanometer unit; A composite substrate of a target height is prepared by etching a substrate, the target nanometer unit is prepared by a graphical arrangement method, and the composite substrate of the target height and the target nanometer unit are assembled into an achromatic plane lens.

2. The design method according to claim 1, characterized in that: The phase and transmittance of a preset set of nanometer units for a preset light wavelength are determined according to a numerical simulation method, specifically including: Determine the total degree of freedom of each nanounit in a preset nanounit set and the preset light wavelength; Determine the parameter range and interval according to the total degree of freedom of each nanounit; The numerical simulation method is used to simulate and scan the parameters of each degree of freedom of each nano unit to determine the phase and transmittance of each nano unit with each degree of freedom parameter for a preset light wavelength.

3. The design method according to claim 1, characterized in that: The updating of the database according to the maximum phase dispersion and the aspect ratio specifically includes: If the maximum phase dispersion corresponds to several nanounits, the nanounit with the smallest aspect ratio is selected; If the same aspect ratio corresponds to several nanounits, select the nanounit with a phase coverage of 0-2π; If the phase coverage 0-2π corresponds to several nanounits, the nanounit with the highest transmittance is selected.

4. The design method according to claim 1, characterized in that: The step of calculating the target phase of the preset light wavelength at different positions of the plane lens, determining the target nanometer unit according to the target phase and the database, and determining the target height of the optical thickness variable composite substrate at different positions according to the propagation phase formula, the target phase and the target nanometer unit specifically includes: Calculate the target phase of the preset light wavelength at different positions according to the phase curve of the plane lens; determining a target nanounit according to the target phase and the database; Determining the phase dispersion and phase distribution of the optical thickness variable composite substrate at different positions according to the target phase and the target nanometer unit; The target height of the composite substrate at different positions is determined according to the propagation phase formula and the phase dispersion and phase distribution of the composite substrate at different positions.

5. The design method according to claim 1, characterized in that: The method of preparing the target nanounit by a graphical arrangement method specifically includes: The target nano-unit is prepared by any one or more of electron beam direct writing, ultraviolet lithography or laser direct writing.

6. The design method according to claim 1, characterized in that: The method of preparing a composite substrate of a target height by etching the substrate specifically comprises: Designing a substrate with a preset thickness; Etching is performed on the substrate to obtain a composite substrate with a target height.

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