Ray-based design and analysis of metalenses

Abstract

The present disclosure describes systems and methods for designing metalenses. The method includes receiving a selection of a meta-atom type and determining a layout of a plurality of meta-atoms of the meta-atom type on the metalens. A first dimension of each meta-atom of the plurality of meta-atoms is expressed as a first function of a position of the corresponding meta-atom on the metalens. The method further includes determining a direction of a light ray exiting the metalens based at least in part on the first function.

Description

[Technical Field]

[0001] The present disclosure relates to optical lens design, and more particularly to ray-based design and analysis of metalenses. [Background technology]

[0002] Lenses are used in optical systems to focus or redirect light. Traditional lenses are formed using a smooth surface (e.g., glass or plastic). In contrast, metalenses are formed using an arrangement of subwavelength meta-atoms (which may also be referred to as pillars, nanopillars, or nanofins) on a surface. When light is directed across the metalens, the meta-atoms redirect and focus the light depending on the arrangement and dimensions of the meta-atoms. Summary of the Invention

[0003] The present disclosure describes systems and methods for designing metalenses. According to one embodiment, the method for designing a metalens includes receiving a selection of a meta-atom type and determining a layout of a plurality of meta-atoms of the meta-atom type on the metalens. A first dimension of each meta-atom of the plurality of meta-atoms is expressed as a first function of a position of the corresponding meta-atom on the metalens. The method further includes determining a direction of a light ray exiting the metalens based at least in part on the first function.

[0004] The method may include generating a lookup table for transfer functions of meta-atom types for a set of first dimension values ​​and determining efficiency of the light beam based at least in part on the lookup table. A second dimension of each meta-atom of the plurality of meta-atoms may be expressed as a second function of a position of the corresponding meta-atom on the metalens. The lookup table may indicate transfer functions of meta-atom types for a set of second dimension values. The direction of the light beam exiting the metalens may be based at least in part on the second function. Generating the lookup table may include determining a Jones matrix for the meta-atom types for the set of first dimension values. The method may include determining polarization of the light beam exiting the metalens based at least in part on the lookup table. The method may include updating the lookup table to have higher resolution based at least in part on the layout.

[0005] The first function may include discontinuities along the metalens, and the direction of the light rays exiting the metalens may be based on the positions of the discontinuities along the metalens.

[0006] According to another embodiment, a system for designing a metalens includes a memory and a processor communicatively coupled to the memory. The processor receives a selection of a meta-atom type and determines a layout of a plurality of meta-atoms of the meta-atom type on the metalens. A first dimension of each meta-atom of the plurality of meta-atoms is expressed as a first function of a position of the corresponding meta-atom on the metalens. The processor further determines a direction of a light ray exiting the metalens based at least in part on the first function.

[0007] The processor may generate a lookup table for transfer functions of meta-atom types for a set of first dimension values ​​and determine the efficiency of the light beam based at least in part on the lookup table. A second dimension of each meta-atom of the plurality of meta-atoms may be expressed as a second function of the position of the corresponding meta-atom on the metalens. The lookup table may indicate the transfer functions of the meta-atom types for a set of second dimension values. The direction of the light beam exiting the metalens may be based at least in part on the second function. Generating the lookup table may include determining a Jones matrix for the meta-atom types for the set of first dimension values. The processor may determine the polarization of the light beam exiting the metalens based at least in part on the lookup table. The processor may update the lookup table to have higher resolution based at least in part on the layout.

[0008] The first function may include a discontinuity along the metalens, and the direction of a light ray exiting the metalens may be based on its position along the discontinuity of the metalens.

[0009] According to another embodiment, a non-transitory computer-readable medium stores instructions for designing a metalens that, when executed by a processor, cause the processor to generate a lookup table for a transfer function of a meta-atom type and to determine a first function representing first dimensions of multiple meta-atoms of the meta-atom type as a function of positions of the multiple meta-atoms on the metalens, The processor further determines characteristics of light rays exiting the metalens based at least in part on the lookup table and the first function.

[0010] The properties may include the energy of the light beam exiting the metalens.

[0011] The processor may determine a second function representing a second dimension of the plurality of meta-atoms as a function of positions of the plurality of meta-atoms on the metalens, and a characteristic of the light beam exiting the metalens may be based at least in part on the second function.

[0012] The first function may include discontinuities along the metalens.

[0013] The present disclosure will be more fully understood from the detailed description given below and from the accompanying drawings of embodiments of the present disclosure. The drawings are used to provide an understanding and understanding of embodiments of the present disclosure and do not limit the scope of the present disclosure to these particular embodiments. Additionally, the drawings are not necessarily drawn to scale. [Brief explanation of the drawings]

[0014] [Figure 1A] FIG. 1 illustrates an exemplary metalens. [Figure 1B] FIG. 1B illustrates an exemplary portion of the metalens of FIG. 1A. [Figure 2] FIG. 1 illustrates an exemplary system. [Figure 3] FIG. 10 illustrates an example parameterization function for metalens design. [Figure 4] FIG. 4 illustrates an exemplary depiction of meta-atom design parameter distributions for the parameterization functions of FIG. 3. [Figure 5] FIG. 10 illustrates an exemplary metalens that includes a superimposed equivalent grating. [Figure 6] FIG. 10 illustrates an exemplary light ray incident on a metalens. [Figure 7] FIG. 10 illustrates an exemplary light ray incident on a metalens. [Figure 8] FIG. 10 shows exemplary depictions of parameterization functions and metalens design parameter distributions. [Figure 9] 1 is a flowchart of an exemplary method for designing and analyzing a metalens. [Figure 10]1 is a schematic diagram of an exemplary computer system in which embodiments of the present disclosure may function. DETAILED DESCRIPTION OF THE INVENTION

[0015] Aspects of the present disclosure relate to ray-based design and analysis of metalenses. Metalenses are formed using an arrangement of subwavelength meta-atoms (which may be referred to as pillars) on a surface. When light is directed across the metalens, the pillars redirect and focus the light depending on the arrangement and dimensions of the pillars.

[0016] Consider an exemplary metalens that includes a series of cylindrical pillars of equal height but varying widths. Such a metalens 100 is shown in FIG. 1A . A portion 102 of the metalens 100 is shown in more detail in FIG. 1B . As seen in FIGS. 1A and 1B , the metalens 100 includes an array of pillars 104 (e.g., cylindrical pillars) on the surface of the metalens 100. As light traverses the metalens 100, a phase is imparted to the light by one or more of the pillars 104. The magnitude of the phase depends on the width of the pillars 104 where the light traverses the lens. By appropriately selecting the distribution of pillar widths across the surface of the metalens 100, the metalens 100 can focus light. The metalens 100 may be used as a stand-alone single element, or may be incorporated as one component of a subassembly that further includes other non-metalens optical elements.

[0017] In order for the light exiting the metalens 100 to be free from artifacts propagated by the discrete nature of the pillars 104, the separation between the pillars 104 can be on the order of the wavelength of light or less. As a result, ray-based methods for analysis and optimization have not previously been considered appropriate. Instead, wave-based methods, which involve modeling the propagation of electromagnetic fields, are used. However, these wave-based methods are slower and more cumbersome to use.

[0018] The present disclosure describes a ray-based system that can be used to design and analyze optical systems incorporating one or more metalenses. The ray-based system may be used for imaging or illumination systems consisting entirely of metalenses, or for systems that incorporate a mixture of metalenses and traditional refractive, reflective, or diffractive optical elements. Generally, the system receives a selection of a meta-atom type. The system then determines a function that represents a parameter (e.g., width) of the meta-atoms of the meta-atom type across the surface of the metalens as a function of the position of the meta-atom on the surface of the metalens. The system further generates a lookup table that provides values ​​for the transfer function of the meta-atom type for a set of parameter values. The system can then use the function and lookup table to perform ray-based design and analysis of metalenses. For example, the system can use the function and lookup table to determine the direction and efficiency (e.g., energy) of light rays exiting a metalens.

[0019] In certain embodiments, the system provides several technical advantages. For example, the system may implement ray-based techniques that are suitable for metalens design and analysis. The use of lookup tables may increase the speed of ray-based analysis by avoiding the expensive process of determining or calculating transfer functions for each ray as the ray is being traced. Furthermore, by expressing meta-atom parameters as functions, the need to calculate parameters for meta-atoms individually may be avoided. As a result, the system may enable ray-based design and analysis to become a viable option for metalens designers.

[0020] In many imaging applications, there is an extended object to be imaged, and this object irradiates (or scatters) light over a range of wavelengths. In such applications, tradeoffs may be made in the design of a metalens to achieve the best average performance over the extended object and wavelength range. In the context of imaging systems consisting of traditional refractive, reflective, or diffractive elements, ray-based tools for optimization and analysis have been successfully developed and used for countless designs.

[0021] To use such methods for the design and analysis of metalenses, there are two pieces of information that can be used: 1. Ray direction after the metasurface. In general, there may not be a single ray direction, but a set of discrete ray directions (or orders) propagating in different directions, analogous to the different diffraction orders in a conventional grating or diffractive optical element. 2. The amount of energy propagated (also called efficiency) at each of these orders is determined by the details of the phase carried by the meta-atoms in the vicinity of the ray. The system is capable of computing each of these two pieces of information, which can be tightly coupled with their representation as a function of the meta-atom parameters (sometimes referred to as parameterization).

[0022] Figure 2 shows an exemplary system 200. As seen in Figure 2, system 200 includes one or more devices 204, a network 206, and a design device 208. Generally, system 200 implements ray-based techniques for designing and analyzing metalenses or optical systems that include metalenses.

[0023] User 202 can use instrument 204 to initiate a metalens design or analysis process. For example, user 202 can use instrument 204 to select a meta-atom type or a metalens shape. User 202 can further use instrument 204 to set limits or boundaries on certain parameters (e.g., length, width, height, etc.) of the meta-atoms of the metalens. Instrument 204 can communicate these selections and settings to design instrument 208 to initiate the metalens design or analysis process. Instrument 204 can be any suitable device for communicating with components of system 200 over network 206. By way of example, but not by way of limitation, instrument 204 can be a computer, laptop, wireless or cellular phone, electronic notebook, personal digital assistant, tablet, or any other device capable of receiving, processing, storing, or transmitting information with other components of system 200. Network 206 can be any suitable network operable to facilitate communication between components of system 200.

[0024] The design instrument 208 may be a computer system (e.g., computer system 1000 shown in FIG. 10 ). The design instrument 208 implements ray-based techniques for designing or analyzing metalenses. In general, the design instrument 208 can be a computer system (e.g., computer system 1000 of FIG. 10 ) that determines a function representing a parameter (e.g., width, length, height, etc.) of a meta-atom of a meta-atom type as a function of the position of the meta-atom on the metalens. The design instrument 208 further determines a lookup table for a transfer function of the meta-atom type. The design instrument 208 can then use the function and the lookup table to perform ray-based design or analysis (e.g., determining the direction of a ray leaving the metalens). As can be seen in FIG. 2 , the design instrument 208 includes a processor 210 and a memory 212 that can perform the operations or functions of the design instrument 208 described herein. The processor 210 and the memory 212 can be the processing instrument 1002 and the memory 1004 of the computer system 1000 shown in FIG. 10 .

[0025] Design instrument 208 may receive meta-atom type 214 from instrument 204. For example, a user may have selected meta-atom type 214 using instrument 204, and instrument 204 may have communicated meta-atom type 214 to design instrument 208. Meta-atom type 214 may indicate a particular characteristic of a meta-atom. For example, meta-atom type 214 may indicate the shape of the meta-atom (e.g., cylindrical pillar, square pillar, cross pillar, etc.). The selection of meta-atom type 214 may indicate a desire to use a meta-atom having the selected meta-atom type 214 in a metalens.

[0026] Meta-atom type 214 may include one or more parameters 216. Parameters 216 may indicate any suitable characteristics of meta-atoms of meta-atom type 214. For example, parameters 216 may indicate the size of the meta-atom (e.g., length, width, height, radius, etc.). Rather than determining the value of parameters 216 individually for each meta-atom, design equipment 208 may determine a function 218 that represents the value of parameters 216 as a function of the position of the meta-atom on the surface of the metalens (this is sometimes referred to as parameterizing parameters 216).

[0027] Using the techniques described in this disclosure, design instrument 208 does not control meta-atom parameters 216 individually for each meta-atom of the metalens. This would introduce too many degrees of freedom, leading to inefficient and potentially unstable optimization or analysis. Instead, meta-atom parameters 216 are parameterized by function 218 (e.g., a smooth and continuous function), and this function 218 determines the value of meta-atom parameters 216 at any point on the surface of the metalens. For example, a polynomial may be used for this parameterization; however, any suitable set of functions 218 may be used. For rotationally symmetric metalenses, the parameterization may be considered to be solely a function of radial position on the surface of the metalens, although more general freeform-like parameterizations may also be used. Ray tracing may use this function 218, and an optimizer may vary function 218 or parameters 216 during optimization or analysis.

[0028] 3 and 4 show an example of parameterization. In this example, a single meta-atom parameter 216 (e.g., width) is considered, but the concept may be extended to meta-atom species defined by multiple parameters 216.

[0029] The parameterization function 218 for the meta-atom parameters 216 is referred to as p(x,y), where x and y represent the coordinates of a point on the metalens, and is represented by curve 302 in FIG. 3. Curve 302 shows the value of p(x,y) for a constant x. Typically, there is a range of acceptable values ​​for the meta-atom parameters 216. The minimum and maximum values ​​in this range of acceptable values ​​are represented in FIG. 3 as p0 and p1, respectively. These values ​​will typically result from manufacturing considerations (e.g., there are minimum and maximum pillar diameters that can be produced).

[0030] For the metalens to function well, the design may not need to use the full range of allowed values ​​for parameter 216. The range of values ​​for parameter 216 that is actually used may be p min and p max These values ​​are expressed as follows: min >p0;p max <p1;およびp min <p max In other words, as can be seen in Figure 4, p min and p max can be between p0 and p1. The meta-atom parameters 216 themselves as a function of position on the metalens [referred to as P(x,y)] are then P(x,y)=p min +mod{[p(x,y)-p min ],(p max -p min )} (1) where mod is the modulo operator. The parameterization p(x,y) shown in FIG. 4 by curve 302 and the parameterization p(x,y) as shown in FIG. min and p max Given the values ​​of and, the resulting distribution of the meta-atom parameters P(x,y) is min and p max y) with a constant x. The value of P(x,y) varies across the surface of the metalens.

[0031] To understand how ray tracing can be effectively used to analyze and optimize systems incorporating metalenses, it may be noted that curve 402 in FIG. 4 resembles a conventional diffractive optical element. Thus, the function [p(x,y)-p min ] / (p max -p min ) (2) can resemble the phase functions conventionally used to define conventional diffractive optical elements, and it follows that standard techniques for ray tracing diffractive elements may be applied to such metalenses.

[0032] Stated another way, the meta-atom distribution throughout the metalens, and specifically the discontinuities in the meta-atom parameters 216, behave like a diffraction grating. The grating-like nature of the metalens 100 shown in FIG. 1A is made clear in FIG. 5, where circles 502 are drawn at the locations of the discontinuities in the pillar width. These circles 502 therefore determine a local uniform lattice spacing, which may be the radial distance between the circles 502.

[0033] Light incident on a grating can couple into multiple orders. Typically, there will be one order (called the design order) that is the order of primary interest. Orders other than the design order may also be analyzed to determine where light from these other orders will fall on the image or target surface (such light is generally considered stray light). Knowing the ray directions into the different orders can determine the efficiency (or amount of energy) associated with each order.

[0034] The lattice structure may not always be as apparent as it is for the pillar widths shown in Figure 5, where the continuous change from narrow to wide pillar widths is clearly visible. If the pillars are assumed to be rectangular and the pillar parameters are the rotation angles of the rectangular pillars (so p0 = 0 and p1 = π), the lattice structure becomes more difficult to discern from a diagram similar to that shown in Figure 5. The methods described in this disclosure work equally well for such meta-atom species or types.

[0035] 2, design equipment 208 may determine or generate lookup table 220 for the transfer function of meta-atom type 214. Generally, by determining or generating lookup table 220, design equipment 208 pre-calculates the transfer function for meta-atom type 214. In certain embodiments, values ​​in lookup table 220 may then be referenced or used during ray tracing to improve the speed of the ray tracing process.

[0036] When determining the ray directions for the various orders, a parameterization of the meta-atom parameters 216 may be used, and information about the phase imparted by the pillars may not be needed, because the ray directions from a diffraction grating may depend only on the grating spacing and not on the details of the phase changes that occur within a period. However, details of the phase changes that occur within a period may be needed to know how the energy of the incident ray is distributed among the various orders. As shown schematically in FIG. 6 , a metalens 602 can impart one or more phases to light rays 604 that are incident on the metalens 602. The added phase due to the metalens 602 may need to be known before the energy of the various orders 606 exiting the metalens 602 can be determined.

[0037] Metalens 602 generally does not transmit all of the incident light, and the sum of all of the energies in the negative orders 606 generally does not add up to the energy of the incident light ray 604. The amount of optical loss (due to absorption or reflection for a transmissive metalens 602, or due to absorption and transmission for a reflective metalens 602) may also need to be accounted for at this stage. The added phase and optical loss together make up what is referred to as the transfer function for metalens 602.

[0038] The transfer function is generally a function of the direction (angle of incidence), wavelength, and possibly polarization of the input light ray 604. This is in addition to being a function of the meta-atom parameters 216. Various methods may be used to determine this added phase, such as finite-difference time domain (FDTD) or rigorous couple-wave analysis (RCWA).

[0039] Although a transfer function could be calculated for each ray as the ray is being traced, calculating the transfer function can be expensive, and such an approach can unacceptably slow down the ray tracing. Design equipment 208 pre-calculates transfer functions (as a function of all relevant parameters—incidence angle, wavelength, polarization, and meta-atom parameters 216) for a discrete set of values ​​for these parameters. The pre-calculated data for the transfer functions is stored in lookup table 220. During ray tracing, when a ray enters the metalens, a value for the transfer function may be interpolated from the values ​​in lookup table 220. An algorithm for performing the interpolation may also be included in lookup table 220. While the time it takes to calculate the transfer function over the relevant range of incident ray direction, wavelength, polarization, and meta-atom parameters 216 can be significant, using lookup table 220 can be very fast.

[0040] This approach allows the design equipment 208 to start with a relatively coarse grid when sampling the various parameters contained in the lookup table 220, and then progress to a finer grid as the design evolves and the range of values ​​for the parameters (such as incident ray direction) becomes better understood for the particular design.

[0041] User 202 selects a meta-atom type 214 to use in the design, and design equipment 208 pre-calculates a transfer function for that meta-atom type 214. For example, the meta-atom types 214 can be cylindrical pillars of equal height but different widths. Design equipment 208 can calculate the transfer function as a function of incident light direction, wavelength, polarization, and pillar width for the meta-atom type 214. The data for the transfer function may be included in a lookup table 220 for the meta-atom type 214. If user 202 decides to use a different meta-atom type 214 (e.g., a rectangular pillar), design equipment 208 will calculate lookup table 220 for this meta-atom type 214 (as a function of the pillar length and width as well as the incident light direction, wavelength, and polarization).

[0042] Not all parameters on which the transfer function may depend may be incorporated into the lookup table 220. For example, if the system is intended to function only at one wavelength, the transfer function may be calculated for only that one wavelength. Similarly, if a particular meta-atom type 214 does not change the polarization state of the incident light, then the lookup table 220 for the transfer function need not include polarization.

[0043] After lookup table 220 has been pre-calculated, Fourier optics can be used in conjunction with the functional form of the pillar parameterization to predict the amount of energy (or efficiency) down to various orders. Design instrument 208 can model the metalens as a comb function convolved with one period of a transfer function. The far field that results from sending a plane wave through this structure is then the product of the different comb functions in Fourier space and the Fourier transform of one period of the transfer function.

[0044] As discussed above, the parameterization function [p(x,y)-p min ] / (p max -p min ) is considered to be a proxy for the phase function used in conventional ray tracing for diffraction. Thus, (∂p / ∂x,∂p / ∂y) / (p max -p min ) may be the local lattice vector (whose magnitude is the local lattice frequency, equal to 1 divided by the local lattice period). In the following discussion, it is understood that the coordinate system is chosen (without loss of generality) so that the Y axis is parallel to the local lattice vector (hence, in this coordinate system, ∂p / ∂x=0). In the following, the local lattice period will be denoted by D.

[0045] Consider a ray of light 702 incident on a metalens 704, as shown in Figure 7. In Figure 7, the field after the metalens 704 (U) may be equal to the product of the incident field and the metalens transfer function.

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[0046] Considering the incident field to be a plane wave with amplitude A propagating in the cosine of the light direction of (L,M,N), the field U(x,y) after metalens 704 is then

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[0047] One procedure for calculating the diffraction efficiency is to treat the incident ray 702 as an infinite plane wave propagating in the direction of ray 702, and the grating as an infinite linear grating with parameters arising from the local grating at the point of incidence of ray 702. The far field after metalens 704 is thus derived from standard Fourier optics.

[0048]

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[0049] This is the phase difference in the meta-atom parameter 216.

number

[0050]

number

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[0051] To find the numerical value of the integral,

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[0052] Taking the transmission to be constant may be reasonable, since amplitude variations affect efficiency less strongly than phase variations. If this approximation proves not to work well for a given application, the integral given by equation (5) can be reduced to

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[0053] Returning to FIG. 2 , design instrument 208 can determine a layout 222 for the metalens using function 218. The meta-atoms in layout 222 can be of a selected meta-atom type 214. Parameters 216 (e.g., width) of the meta-atoms in the layout can have values ​​determined according to function 218. Design instrument 208 can then use ray tracing to analyze the metalens. For example, design instrument 208 can use function 218 to determine one or more ray directions 224 that exit the metalens. Design instrument 208 can further use information in lookup table 220 to determine efficiencies 226 of one or more orders of the light rays exiting the metalens. In this way, design instrument 208 can quickly assess how the light rays exiting the metalens will fare (e.g., if the metalens focuses the light rays as desired).

[0054] As explained above, the ray direction 224 may depend solely on the location of the discontinuities in the meta-atom parameters, and the details of how the phase varies across each zone can determine the efficiency 226. Therefore, within each zone, the value of the meta-atom parameters 216 can be adjusted to achieve maximum efficiency 226. This is achieved by: (i) adjusting the p min and p max is not constant for the lens, but varies across the lens; and (ii) p min p max , and allowing the meta-atom parameters 216 connected to p(x,y) to not adhere exactly to the curve derived from p(x,y), but to deviate from that curve. These two options for further adjusting the efficiency 226 are shown schematically in Figure 8. A curve 302 for p(x,y) and a curve 402 for P(x,y) are shown in Figure 8. Furthermore, min and p maxvaries across the lens. In portion 802 of curve 402, the values ​​of P(x,y) may vary or deviate from the shape of curve 302. One other possibility (not shown in FIG. 8) is to have the desired design order not fixed across the part. For example, at the center of the part, a first order may be selected, but towards the edge, this may be switched to use a second order.

[0055] When multiple parameters 216 are used to describe the meta-atom type 214 of interest, the methods described herein for meta-atoms of one parameter 216 may be applied with slight modifications. For example, a rectangular meta-atom species may have meta-atom parameters 216 for the length and width of the rectangle. There may be two functions 218—p1(x,y) and p2(x,y)—to parameterize the meta-atom. Thus, the length and width of the meta-atom at location (x,y) on the surface are given by Length(x,y)=p 1,min +mod{[p1(x,y)-p 1,min ],(p 1,max -p 1,min )} Width(x,y)=p 2,min +mod{[p2(x,y)-p 2,min ],(p 2,max -p 2,min )} is given by In this case, the metalens still behaves very much like a lattice, but now the lattice structure arises from locations where there are discontinuities in any meta-atom parameter (e.g., either length or width).

[0056] As mentioned previously, when a meta-atom changes the polarization state of light, lookup table 220 can contain not only a single added phase, but also the Jones matrix [as a function of wavelength, incident ray direction, and meta-atom parameters 216] imparted by the meta-atom. When a ray enters the metalens, lookup table 220 will be used to determine the Jones matrix that should be applied to the ray, and the ray tracing code would need to apply this Jones matrix.

[0057] The design equipment 208 may provide the following features: Parameterizing the meta-atom structure, rather than addressing individual meta-atoms directly, to allow evaluation and analysis to be performed using relatively few parameters to define the metalens, and using modulo functions to model discontinuities in the metalens parameters 216, thereby significantly reducing the number of degrees of freedom. Treating the macrostructure of a metalens similarly to a diffractive structure for ray tracing purposes, so that rays are available for evaluation and analysis. To maximize efficiency, min , p max , and allowing the meta-atom parameters to vary within each lattice period (e.g., to send as much light as possible into the desired order). Starting with a lower resolution lookup table 220 that can be constructed more quickly, and then increasing the resolution once a rough design is achieved. A higher resolution lookup table 220 may be constructed for the design parameter values ​​that are being used for the rough design.

[0058] In an exemplary operation, design instrument 208 may design a metalens using a ray-based approach. User 202 may first select a meta-atom type 214 to use in the design. The design instrument may pre-calculate a lookup table 220 for this meta-atom type 214. A parameterization or function 218 may be selected for meta-atom parameters 216, which may be a polynomial function. A desired design order is selected (typically first order, although the desired design order may vary throughout the metalens). The coefficients in the parameterization of meta-atom parameters 216 are tuned or optimized so that the rays behave as desired. In this step, p min and p max Some reasonable guesses are made in , but these may not be allowed to vary. Design equipment 208 may not consider the transparency of the meta-atoms and the efficiency of the metalens in this step. Design order rays may be considered in this step.

[0059] After a reasonably high performance metalens is achieved, design equipment 208 can re-optimize the metalens, taking into account both ray behavior and transmission / efficiency, i.e., p min and p max may be allowed to vary, and the merit function may include a component related to the total energy of the desired design order. At this stage, if user 202 wants to optimize where stray light will end up, the merit function may further include a component related to rays of non-design orders.

[0060] As a final step, other software tools that perform more rigorous electromagnetic analysis may be used to analyze the metalens and / or an optimizer may fine-tune the design, which may include more rigorous electromagnetic analysis.

[0061] 9 is a flowchart of an exemplary method 900 for designing and analyzing a metalens. In one particular embodiment, the design equipment 208 performs the method 900.

[0062] At 902, design instrument 208 receives a selection of a meta-atom type 214 and a grid arrangement (e.g., a square grid or a hexagonal grid) for the metalens. User 202 may select meta-atom type 214 and grid arrangement. For example, user 202 may select meta-atoms that are cylindrical pillars arranged on a square grid.

[0063] At 904, design instrument 208 generates lookup table 220 for the transfer function and grid array of meta-atom type 214. At 906, design instrument 208 receives a parameterization function type and a design order. A user 202 of the computer system may select the parameterization function type and the design order. For example, user 202 may select a parameterization function type that is polynomial and a design order that is equal to 1. Design instrument 208 parameterizes the meta-atom parameters 216 such that each parameter 216 is expressed as a function 218 of the position of the meta-atom on the surface of the metalens.

[0064] At 908, design device 208 determines a layout 222 for the metalens. Design device 208 may determine a dispersion function of meta-atom parameters 216 for selected meta-atom types 214 on the metalens. At 910, to determine the dispersion function of the meta-atom parameters 216, design device 208 varies coefficients of parameterization function 218 to optimize or improve the performance of the metalens in terms of ray direction and efficiency. Design device 208 calculates the ray direction based on input from 906 (e.g., parameterization function 218). Design device 208 determines the efficiency or energy based on lookup table 220 from 904. At 912, which is an optional step, design device 208 analyzes and / or fine-tunes the metalens design using more rigorous electromagnetic analysis.

[0065] Design instrument 208 can use parameterization function 218 and the design order to determine the direction 224 of the light rays exiting the metalens. In some embodiments, design instrument 208 further uses lookup table 220 to determine the energy or efficiency of the light rays exiting the metalens.

[0066] 10 illustrates an exemplary machine of computer system 1000 having a set of executable instructions therein to cause the machine to perform any one or more of the methodologies discussed herein. In alternative embodiments, the machine may be connected (e.g., networked) to other machines in a LAN, an intranet, an extranet, and / or the Internet. The machine may function in the capacity of a server or a client machine in a client-server network environment, as a peer machine in a peer-to-peer (or distributed) network environment, or as a server or client machine in a cloud computing infrastructure or environment.

[0067] The machine may be a personal computer (PC), tablet PC, set-top box (STB), personal digital assistant (PDA), mobile phone, web appliance, server, network router, switch or bridge, or any machine capable of executing a set of instructions (sequential or otherwise arranged) that define operations to be taken by the machine. Additionally, although a single machine is shown, the term "machine" shall be deemed to further include any collection of machines that individually or together execute a set of instructions (or multiple sets) to perform any one or more of the methodologies discussed herein.

[0068] The exemplary computer system 1000 includes a processing device 1002, a main memory 1004 (e.g., read-only memory (ROM), flash memory, dynamic random access memory (DRAM) such as synchronous DRAM (SDRAM), static memory 1006 (e.g., flash memory, static random access memory (SRAM), etc.), and a data storage device 1018 that communicate with each other via a bus 1030.

[0069] Processing device 1002 represents one or more processors, such as a microprocessor or central processing unit. More specifically, processing device may be a complex instruction set computing (CISC) microprocessor, a reduced instruction set computing (RISC) microprocessor, a very long instruction word (VLIW) microprocessor, or a processor implementing other instruction sets or a combination of instruction sets. Processing device 1002 may also be one or more special-purpose processing devices, such as an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), a digital signal processor (DSP), or a network processor. Processing device 1002 may be configured to execute instructions 1026 to perform the operations and steps described herein.

[0070] Computer system 1000 may further include a network interface device 1008 for communicating over a network 1020. Computer system 1000 may further include a video display unit 1010 (e.g., a liquid crystal display (LCD) or a cathode ray tube (CRT)), an alphanumeric input device 1012 (e.g., a keyboard), a cursor control device 1014 (e.g., a mouse), a graphics processing unit 1022, a signal generation device 1016 (e.g., a speaker), a graphics processing unit 1022, a video processing unit 1028, and an audio processing unit 1032.

[0071] The data storage device 1018 may include a machine-readable storage medium 1024 (also known as a non-transitory computer-readable medium) having stored thereon one or more sets of instructions 1026, or software embodying any one or more of the methodologies or functions described herein. The instructions 1026 may further reside, completely or at least partially, within the main memory 1004 and / or within the processing device 1002 during execution of the instructions by the computer system 1000, with the main memory 1004 and the processing device 1002 further constituting machine-readable storage media.

[0072] In some embodiments, instructions 1026 include instructions for performing functions corresponding to the present disclosure. While machine-readable storage medium 1024 is shown to be a single medium in the exemplary embodiment, the term "machine-readable storage medium" should be considered to include a single medium or multiple media (e.g., a centralized or distributed database, and / or associated caches and servers) that store one or more sets of instructions. The term "machine-readable storage medium" should also be considered to include any medium capable of storing or encoding a set of instructions for execution by a machine and that cause the machine and processing device 1002 to perform any one or more of the methodologies of the present disclosure. Accordingly, the term "machine-readable storage medium" should be considered to include, but is not limited to, solid-state memory, optical media, and magnetic media.

[0073] Some portions of the foregoing detailed description are presented in terms of algorithms and symbolic representations of operations on data bits within a computer memory. These algorithmic descriptions and representations are the means used by those skilled in the data processing arts to most effectively convey the substance of their work to others skilled in the art. An algorithm may be a sequence of operations leading to a desired result. The operations require physical manipulations of physical quantities. Such quantities may take the form of electrical or magnetic signals capable of being stored, combined, compared, and otherwise manipulated. Such signals may be referred to as bits, values, elements, symbols, characters, terms, numbers, or the like.

[0074] It should be borne in mind, however, that all of these and similar terms are to be associated with the appropriate physical quantities and are merely convenient labels applied to these quantities. As will be apparent from this disclosure, unless specifically stated otherwise, throughout the description, certain terms will be understood to refer to operations and processes of a computer system or similar electronic computing device that manipulate and transform data represented as physical (electronic) quantities within the computer system's registers and memory into other data also represented as physical quantities within the computer system's memory or registers or other such information storage devices.

[0075] The present disclosure also relates to apparatus for performing the operations herein. The apparatus may be specially constructed for the intended purposes, or the apparatus may include a computer selectively activated or reconfigured by a computer program stored within the computer. Such computer programs may be stored on a computer-readable storage medium, such as any type of disk, including but not limited to, floppy disks, optical disks, CD-ROMs, and magneto-optical disks, read-only memory (ROM), random access memory (RAM), EPROM, EEPROM, magnetic or optical cards, or any type of medium suitable for storing electronic instructions, each coupled to a computer system bus.

[0076] The algorithms and displays presented herein are not inherently related to any particular computer or other apparatus. Various other systems can be used with programs in accordance with the teachings herein, although it may prove convenient to construct more specialized apparatus for performing the methods. Moreover, the present disclosure is not described with reference to any particular programming language. It will be understood that a variety of programming languages ​​can be used to implement the teachings of the present disclosure as described herein.

[0077] The present disclosure may be provided as a computer program product, or software, which may include a machine-readable medium having stored thereon instructions that can be used to program a computer system (or other electronic device) to perform a process according to the present disclosure. A machine-readable medium includes any mechanism for storing information in a form readable by a machine (e.g., a computer). For example, machine-readable (e.g., computer-readable) media includes machine (e.g., computer) readable storage media such as read-only memory ("ROM"), random access memory ("RAM"), magnetic disk storage media, optical storage media, flash memory devices, and the like.

[0078] In the foregoing disclosure, embodiments of the present disclosure have been described with reference to detailed exemplary embodiments thereof. It will be apparent that various modifications may be made thereto without departing from the broader spirit and scope of the embodiments of the present disclosure, as set forth in the following claims. Where the present disclosure refers to certain elements in the singular tense, more than one element may be shown in the figures, and similar elements are labeled with similar numerals. Accordingly, the present disclosure and the drawings should be viewed in an illustrative, and not a limiting, sense.

Claims

1. 1. A method for designing a metalens, comprising: receiving a selection of a meta-atom type; determining a layout of a plurality of meta-atoms of the meta-atom type on the metalens, wherein a first dimension of each meta-atom of the plurality of meta-atoms is expressed as a first function of a position of the corresponding meta-atom on the metalens; determining a direction of a light ray exiting the metalens based at least in part on the first function; and A method comprising:

2. generating a lookup table for transfer functions of the meta-atom type for the set of values ​​of the first dimension; determining an efficiency of the light beam based at least in part on the look-up table; and The method of claim 1 further comprising:

3. a second dimension of each meta-atom of the plurality of meta-atoms expressed as a second function of the position of the corresponding meta-atom on the metalens; the lookup table indicates the transfer function of the meta-atom type for a set of values ​​of the second dimension; 3. The method of claim 2, wherein the direction of the light ray exiting the metalens is based at least in part on the second function.

4. The method of claim 2 , wherein generating the lookup table further comprises determining a Jones matrix for the meta-atom type for the set of values ​​of the first dimension.

5. 5. The method of claim 4, further comprising determining a polarization of said light ray exiting said metalens based at least in part on said lookup table.

6. The method of claim 2 , further comprising updating the lookup table to have a higher resolution based at least in part on the layout.

7. 10. The method of claim 1 , wherein the first function includes a discontinuity along the metalens.

8. 8. The method of claim 7, wherein the direction of the light ray exiting the metalens is based on a position of the discontinuity along the metalens.

9. 1. A system for designing a metalens, comprising: Memory and a processor communicatively coupled to the memory, receiving a selection of a meta-atom type; determining a layout of a plurality of meta-atoms of the meta-atom type on the metalens, wherein a first dimension of each meta-atom of the plurality of meta-atoms is expressed as a first function of a position of the corresponding meta-atom on the metalens; determining a direction of a light ray exiting the metalens based at least in part on the first function; and a processor configured to: A system comprising:

10. the processor: generating a lookup table for transfer functions of the meta-atom type for the set of values ​​of the first dimension; determining the efficiency of the light beam based at least in part on the look-up table; and The system of claim 9 , further configured to:

11. a second dimension of each meta-atom of the plurality of meta-atoms expressed as a second function of the position of the corresponding meta-atom on the metalens; the lookup table indicates the transfer function of the meta-atom type for a set of values ​​of the second dimension; 11. The system of claim 10, wherein the direction of the light ray exiting the metalens is based at least in part on the second function.

12. The system of claim 10 , wherein generating the lookup table further comprises determining a Jones matrix for the meta-atom type for the set of values ​​of the first dimension.

13. 13. The system of claim 12, wherein the processor is further configured to determine a polarization of the light ray exiting the metalens based at least in part on the lookup table.

14. The system of claim 10 , wherein the processor is further configured to update the lookup table to have a higher resolution based at least in part on the layout.

15. 10. The system of claim 9, wherein the first function comprises a discontinuity along the metalens.

16. 16. The system of claim 15, wherein the direction of the light ray exiting the metalens is based on a position of the discontinuity along the metalens.

17. A non-transitory computer-readable medium that, when executed by a processor, causes the processor to: generating a lookup table for a meta-atom type transfer function; determining a first function representing a first dimension of a plurality of meta-atoms of the meta-atom type as a function of positions of the plurality of meta-atoms on the metalens; determining a characteristic of a light beam exiting the metalens based at least in part on the lookup table and the first function; a non-transitory computer-readable medium storing instructions for designing a metalens;

18. 20. The medium of claim 17, wherein the property comprises the energy of the light ray exiting the metalens.

19. 18. The medium of claim 17, wherein the processor further determines a second function representing a second dimension of the plurality of meta-atoms as a function of the positions of the plurality of meta-atoms on the metalens, and wherein the characteristics of the light beam exiting the metalens are based at least in part on the second function.

20. 20. The medium of claim 17, wherein the first function comprises a discontinuity along the metalens.

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