Light-based design and analysis of meta-lenses

Abstract

The present disclosure describes systems and methods for designing meta-lenses. 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 a meta-lens. A first size of each meta-atom of the plurality of meta-atoms is represented as a first function of a position of a corresponding meta-atom on the meta-lens. The method further includes determining a direction of light exiting the meta-lens 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 metasurfaces. Background Art

[0002] Lenses are used in optical systems to focus or redirect light. Conventional lenses are formed using smooth surfaces (e.g., glass or plastic). In contrast, metasurfaces use an arrangement of subwavelength meta-atoms (also referred to as pillars, nanocolumns, or nanofins) on a surface to form. When light passes through a metasurface, the meta-atoms redirect and focus the light based on the arrangement and size of the meta-atoms. Summary of the Invention

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

[0004] The method may include generating a look-up table of transfer functions of the meta-atom type for a set of values of the first dimension; and determining, at least in part based on the look-up table, an efficiency of the ray. A second dimension of each of the plurality of meta-atoms may be represented as a second function of a position of a corresponding meta-atom on the metasurface. The look-up table may indicate transfer functions of the meta-atom type for a set of values of the second dimension. The direction of the ray exiting the metasurface may be at least in part based on the second function. Generating the look-up table may include determining a Jones matrix of the meta-atom type for a set of values of the first dimension. The method may include determining, at least in part based on the look-up table, a polarization of the ray exiting the metasurface. The method may include updating the look-up table to have a higher resolution, at least in part based on the layout.

[0005] The first function may include a discontinuity along the metasurface. The direction of the ray exiting the metasurface may be based on a position of the discontinuity along the metasurface.

[0006] According to another embodiment, a system for designing a metasurface 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 metasurface. A first dimension of each of the plurality of meta-atoms is represented as a first function of a position of a corresponding meta-atom on the metasurface. The processor further determines, at least in part based on the first function, a direction of a ray exiting the metasurface.

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

[0008] The first function may include a discontinuity along the meta-lens. The direction of the light rays exiting the meta-lens may be based on the position of the discontinuity along the meta-lens.

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

[0010] The characteristics may include the energy in the light rays exiting the meta-lens.

[0011] The processor may determine a second function that represents the second dimension of the plurality of meta-atoms as a function of the positions of the plurality of meta-atoms on the meta-lens. The characteristics of the light rays exiting the meta-lens may be at least in part based on the second function.

[0012] The first function may include a discontinuity along the meta-lens. Description of the Drawings

[0013] Based on the detailed description given below and the drawings of the embodiments of the present disclosure, the present disclosure can be more fully understood. The drawings are used to provide an understanding and recognition of the embodiments of the present disclosure and do not limit the scope of the present disclosure to these specific embodiments. Additionally, these drawings are not necessarily drawn to scale.

[0014] Figure 1A An example meta-lens is illustrated.

[0015] Figure 1B Illustrated is Figure 1A an example portion of the meta-lens of

[0016] Figure 2 An example system is illustrated.

[0017] Figure 3 Illustrates an example parametric function for metasurface lens design.

[0018] Figure 4 Illustrates Figure 3 an example representation of the metaatom design parameter distribution for parameterizing the function in

[0019] Figure 5 Illustrates an example metasurface lens with a superimposed equivalent grating.

[0020] Figure 6 Illustrates an example ray incident on the metasurface lens.

[0021] Figure 7 Illustrates an example ray incident on the metasurface lens.

[0022] Figure 8 Illustrates an example representation of the parametric function and the metasurface lens design parameter distribution.

[0023] Figure 9 is a flowchart of an example method for designing and analyzing a metasurface lens.

[0024] Figure 10 Depicts a diagram of an example computer system in which embodiments of the present disclosure may operate. Detailed Description

[0025] Aspects of the present disclosure relate to ray-based design and analysis of metasurface lenses. A metasurface lens is formed using an arrangement of subwavelength metaatoms (also referred to as pillars) on a surface. When light passes through the metasurface lens, the pillars redirect and focus the light according to the arrangement and size of the pillars.

[0026] Consider an example metasurface lens that includes a series of cylindrical pillars of equal height but different widths. Such a metasurface lens 100 is shown in Figure 1A . A portion 102 of the metasurface lens 100 is shown in more detail in Figure 1B . As shown in Figure 1A and Figure 1B , the metasurface lens 100 includes an arrangement of pillars 104 (e.g., cylindrical pillars) on the surface of the metasurface lens 100. When light passes through the metasurface lens 100, one or more of the pillars 104 impart a phase to the light. The magnitude of the phase depends on the width of the pillar 104 through which the light passes in the lens. By appropriately selecting the distribution of the pillar widths on the surface of the metasurface lens 100, the metasurface lens 100 can focus the light. The metasurface lens 100 can be used as an independent single element or can be incorporated as a component of a subassembly that also includes other non-metasurface lens optical elements.

[0027] To make the light leaving the meta-lens 100 not affected by the artifacts imparted by the discrete nature of the pillars 104, the spacing between the pillars 104 can be on the order of the optical wavelength or less. Therefore, ray-based analysis and optimization methods were previously considered inappropriate. Instead, wave-based methods are used, which involve modeling the propagation of electromagnetic fields. However, these wave-based methods are slower and more cumbersome to use.

[0028] The present disclosure describes a ray-based system that can be used to design and analyze optical systems incorporating one or more meta-lenses. The ray-based system can be used for imaging systems or illumination systems consisting only of meta-lenses, or for hybrid systems incorporating meta-lenses and conventional refractive, reflective, or diffractive optical elements. Generally, the system receives a selection of meta-atom types. The system then determines functions that represent the parameters (e.g., width) of the meta-atoms of the meta-atom type on the surface of the meta-lens as a function of the position of the meta-atoms on the surface of the meta-lens. The system also generates a look-up table that provides values for the transfer function of the meta-atom type for a set of values of the parameters. The system can then use these functions and the look-up table to perform ray-based design and analysis of the meta-lens. For example, the system can use these functions and the look-up table to determine the direction and efficiency (e.g., energy) of the light rays leaving the meta-lens.

[0029] In some embodiments, the system provides several technical advantages. For example, the system can implement ray-based techniques that are applicable to meta-lens design and analysis. Using a look-up table can improve the speed of ray-based analysis by avoiding the expensive process of determining or calculating the transfer function ray-by-ray when the rays are traced. In addition, representing the meta-atom parameters as functions can avoid the need to individually calculate the parameters of the meta-atoms. Therefore, the system can allow ray-based design and analysis to be a viable option for meta-lens designers.

[0030] For many imaging applications, there is an extended object to be imaged, and this object emits (or scatters) light within a certain wavelength range. For such applications, trade-offs can be made in the design of the meta-lens to achieve optimal average performance over the extended object and wavelength range. In the context of imaging systems composed of conventional refractive, reflective, or diffractive elements, ray-based optimization and analysis tools have been developed and successfully used in countless designs.

[0031] To use this method for the design and analysis of meta-lenses, two pieces of information can be used:

[0032] 1. The direction of the light rays after the meta-surface. Generally, instead of a single ray direction, a set of discrete ray directions (or orders) propagate in different directions, similar to the different diffraction orders in a conventional grating or diffractive optical element.

[0033] 2. The amount of energy (also known as efficiency) propagated at each of these orders is determined by the details of the phase imparted by the meta-atoms near the light rays.

[0034] The system can calculate each of these two pieces of information, which can be closely related to the expression of the meta-atom parameters as a function (this can be called parameterization).

[0035] Figure 2 An example system 200 is illustrated. As Figure 2 shown, 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 meta-lenses or optical systems including meta-lenses.

[0036] User 202 can use device 204 to initiate a meta-lens design or analysis process. For example, user 202 can use device 204 to select the meta-atom type or the meta-lens shape. User 202 can also use device 204 to set limits or bounds on certain parameters (e.g., length, width, height, etc.) of the meta-atoms of the meta-lens. Device 204 can transmit these selections and settings to design device 208 to initiate a meta-lens design or analysis process. Device 204 is any suitable device for communicating with the components of system 200 via network 206. By way of example and not limitation, device 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 is any suitable network operable to facilitate communication between the components of system 200.

[0037] Design device 208 can be a computer system (e.g., Figure 10 the computer system 1000 shown). Design device 208 performs ray-based techniques for designing or analyzing meta-lenses. Generally, design device 208 can be a computer system (e.g., Figure 10 the computer system 1000), which determines functions that represent the parameters (e.g., width, length, height, etc.) of the meta-atoms of a meta-atom type as a function of the position of the meta-atoms on the meta-lens. Design device 208 also determines a look-up table of the transfer functions of the meta-atom type. Design device 208 can then use these functions and the look-up table to perform ray-based design or analysis (e.g., determining the direction of the light rays leaving the meta-lens). As Figure 2 shown, design device 208 includes a processor 210 and a memory 212 that can perform the actions or functions of design device 208 described herein. Processor 210 and memory 212 can be Figure 10The processing device 1002 and the memory 1004 of the computer system 1000 shown.

[0038] The design device 208 may receive a meta-atom type 214 from the device 204. For example, a user may have selected the meta-atom type 214 using the device 204, and the device 204 may have transmitted the meta-atom type 214 to the design device 208. The meta-atom type 214 may indicate a particular characteristic of the meta-atom. For example, the meta-atom type 214 may indicate the shape of the meta-atom (e.g., cylindrical, square columnar, cross-shaped column, etc.). The selection of the meta-atom type 214 may indicate a desire to use meta-atoms of the selected meta-atom type 214 in the meta-lens.

[0039] The meta-atom type 214 may include one or more parameters 216. The parameters 216 may indicate any suitable characteristic of the meta-atom of the meta-atom type 214. For example, the parameters 216 may indicate the size of the meta-atom (e.g., length, width, height, radius, etc.). Instead of determining the value of the parameter 216 for each meta-atom individually, the design device 208 may determine a function 218 that represents the value of the parameter 216 as a function of the position of the meta-atom on the surface of the meta-lens (this may be referred to as the parameterization of the parameter 216).

[0040] By the method described in this disclosure, the design device 208 does not individually control the meta-atom parameters 216 of each meta-atom of the meta-lens. This would result in too many degrees of freedom and lead to inefficient and potentially unstable optimization or analysis. Instead, the meta-atom parameters 216 are parameterized by a function 218 (e.g., a smooth continuous function), and the function 218 determines the value of the meta-atom parameter 216 at any point on the surface of the meta-lens. For example, a polynomial may be used for such parameterization, but any suitable set of functions 2118 may be used. For a rotationally symmetric meta-lens, the parameterization may be considered as a function of the radial position on the surface of the meta-lens, but a more general free-form parameterization may also be used. Ray tracing may use the function 218, and the optimizer may change the function 218 or the parameter 216 during optimization or analysis.

[0041] Figure 3 and Figure 4 Illustrates an example of parameterization. In this example, a single meta-atom parameter 216 (e.g., width) is considered, but these concepts may be extended to a family of meta-atoms specified by more than one parameter 216.

[0042] The parameterization function 218 of the meta-atom parameter 216 is referred to as p(x,y) (where x and y represent the coordinates of points on the meta-lens), and is represented by Figure 3 the curve 302 in. The curve 302 shows the value of p(x,y) for a fixed x. The meta-atom parameter 216 typically has a range of allowable values. InFigure 3 Among them, the minimum and maximum values within the allowable value range are respectively represented as p0 and p1. These values usually come from manufacturing considerations (for example, there are the minimum and maximum pillar diameters that can be manufactured).

[0043] In order for the meta-lens to perform well, the design may not need to use all the allowable values of parameter 216. The value range of parameter 216 actually used is represented by p min and p max . These values satisfy the following conditions: p min > p0; p max < p1; p min < p max . In other words, as shown in Figure 4 , both p min and p max can be between p0 and p1. Therefore, the meta-atom parameter 216 itself [denoted as P(x, y)] as a function of the position on the meta-lens is considered to be given by

[0044] P(x,y) = p min + mod{[p(x,y) - p min , (p max - p min )} (1)

[0045] where mod is the modulo operator. Given the parameterization p(x,y) as shown by curve 302 in Figure 4 and the values of p min and p max as shown in the figure, the final distribution of the meta-atom parameter 216 P(x,y) is represented by a discontinuous curve 402 with values between p min and p max . Curve 402 shows the values of P(x,y) with a fixed x. The value of P(x,y) changes on the surface of the meta-lens.

[0046] To understand how to effectively use ray tracing to analyze and optimize a system incorporating a meta-lens, it can be noted that Figure 4 the curve 402 in

[0047] is similar to a conventional diffractive optical element.

[0048] Therefore, the function min [p(x,y) - p max / (p min ) (2)

[0049] can be similar to the phase function conventionally used to specify a conventional diffractive optical element. Therefore, the standard techniques for ray tracing diffractive elements can be applied to such a meta-lens.

[0050] In other words, the distribution of meta - atoms on the meta - lens, in particular the discontinuities in the meta - atom parameters 216, act like a diffraction grating. Figure 1A The grating - like nature of the meta - lens 100 shown is clarified in Figure 5 where circles 502 are drawn at the positions of the discontinuities in the pillar width. These circles 502 then determine the local equivalent grating pitch, which can be the radial distance between the circles 502.

[0051] Light incident on the grating can be coupled into multiple orders. Typically, there is one order of primary interest (referred to as the design order). Other orders outside of the design order can also be analyzed to determine where the light from these other orders will fall on the image or target surface (this light is typically considered stray light). After knowing the directions of the light rays entering the different orders, the efficiency (or amount of energy) associated with each order can be determined.

[0052] The grating structure may not always be as clear as in the case of the pillar width shown in Figure 5 where a discontinuous change in the pillar width from narrow to wide can be clearly seen. If the pillars are rectangular and the pillar parameter is the rotation angle of the rectangular pillar (so p0 = 0 and p1 = π), the grating structure will be more difficult to resolve from a figure similar to Figure 5 shown. The methods described in this disclosure are equally applicable to such meta - atom families or types.

[0053] Returning to Figure 2 , the design device 208 can determine or generate a look - up table 220 of the transfer function of the meta - atom type 214. Typically, by determining or generating the look - up table 220, the design device 208 pre - computes the transfer function of the meta - atom type 214. In some embodiments, the values in the look - up table 220 can then be referenced or used during ray tracing to increase the speed of the ray - tracing process.

[0054] When determining the directions of the light rays of the respective orders, the parameterization of the meta - atom parameters 216 can be used, and information about the phase imparted by the pillars may not be required, because the direction of the light rays from the diffraction grating can depend only on the grating pitch and not on the details of the phase change occurring within one period. However, to know how the energy of the incident light is distributed among the respective orders, the details of the phase change occurring within one period may be required. As schematically illustrated in Figure 6 , the meta - lens 602 can impart one or more phases to the light rays 604 incident on the meta - lens 602. Before determining the energy of the respective orders 606 leaving the meta - lens 602, it may be necessary to know the phase added due to the meta - lens 602.

[0055] The meta-lens 602 typically does not transmit all incident light - the sum of the energies of all orders 606 is typically not equal to the energy of the incident light ray 604. The amount of light lost may also be required at this stage (for transmissive meta-lenses 602, lost from absorption or reflection, or for reflective meta-lenses 602, lost from absorption and transmission). The added phase and the lost light together constitute the transfer function of the meta-lens 602.

[0056] The transfer function is typically a function of the direction of the input light ray 604 (angle of incidence), wavelength, and in some cases polarization. Additionally, it is also a function of the meta-atom parameters 216. Various methods can be used to determine this added phase, such as the finite-difference time-domain method (FDTD) or rigorous coupled-wave analysis (RCWA).

[0057] Although the transfer function can be calculated ray-by-ray as the rays are traced, the calculation of the transfer function can be costly, and this method can slow down the ray tracing unacceptably. The design device 208 pre-computes the values of the transfer function for discrete sets of these parameters (as a function of all relevant parameters, i.e., angle of incidence, wavelength, polarization, and meta-atom parameters 216). The pre-computed data of the transfer function is stored in the look-up table 220. During ray tracing, when a ray is incident on the meta-lens, the value of the transfer function can be interpolated from the values in the look-up table 220. The algorithm for performing the interpolation can also be included in the look-up table 220. The amount of time required to calculate the transfer function over the relevant ranges of the incident ray direction, wavelength, polarization, and meta-atom parameters 216 can be large, but using the look-up table 220 can be very fast.

[0058] This method does allow the design device 208 to start with a relatively coarse grid in the sampling of the various parameters included in the look-up table 220, then move to a finer grid as the design progresses and the range of parameter values for a particular design (such as the incident ray direction) is better understood.

[0059] The user 202 selects the type of meta-atom 214 to be used in the design, and the design device 208 pre-computes the transfer function 214 for that type of meta-atom. For example, the type of meta-atom 214 can be cylindrical columns of equal height but different widths. The design device 208 can calculate the transfer function for this type of meta-atom 214, which is a function of the incident ray direction, wavelength, polarization, and column width. The data of the transfer function can be included in the look-up table 220 for the type of meta-atom 214. If the user 202 decides to use a different type of meta-atom 214 (e.g., rectangular columns), then the design device 208 will calculate the look-up table 220 for that type of meta-atom 214 (as a function of the length and width of the column, as well as the incident ray direction, wavelength, and polarization).

[0060] Not all of the parameters on which the transfer function can depend can be built into the lookup table 220. For example, if the system operates at only one wavelength, the transfer function can be computed only for that wavelength. Similarly, if a particular meta-atom type 214 does not change the polarization state of the incident light, the lookup table 220 for the transfer function need not include polarization.

[0061] After the lookup table 220 has been pre-computed, Fourier optics can be used with the parameterized functional form of the cylinder to estimate the amount of energy (or efficiency) entering each order. The design device 208 can model the meta-lens as a comb function convolved with one period of the transfer function. The far field resulting from sending a plane wave through this structure is the product of a different comb function in Fourier space with the Fourier transform of one period of the transfer function.

[0062] As described above, the parameterized function [p(x, y) - p min / (p max - p min ) is considered an alternative to the phase function used in ray tracing of conventional diffraction. Thus, can be the local grating vector (whose magnitude is the local grating frequency, which is equal to 1 divided by the local grating period). In the following discussion, a coordinate system is chosen (without loss of generality) such that the Y axis is parallel to the local grating vector (and thus in this coordinate system, ). Hereinafter, the local grating period is denoted by D.

[0063] Consider a ray 702 incident on the meta-lens 704 as shown in Figure 7 . In Figure 7 , the field (U) after the meta-lens 704 can be equal to the product of the incident field and the meta-lens transfer function. is the amplitude transmittance of the meta-lens, which is a function of the meta-atom parameter 216, is the added phase, which is also a function of the meta-atom parameter 216, where for the considered meta-atom type 214, and can both be determined from the pre-computed lookup table 220.

[0064] Consider the incident field as a plane wave with amplitude A0 propagating along the optical direction cosines of (L, M, N). The field U(x, y) after the meta-lens 704 is given by

[0065]

[0066] where k = 2π / λ (and λ is the wavelength of light), and A0 is the complex amplitude.

[0067] One process for calculating the diffraction efficiency is to consider the incident light ray 702 as an infinite plane wave propagating in the direction of the light ray 702 and to consider the grating as an infinite linear grating, the parameters of which are derived from the local grating at the point where the light ray 702 is incident here. Thus, the far field after the meta-lens 704 is derived from standard Fourier optics.

[0068]

[0069] The form of the integral is the form of a Fourier transform, where the transform variable is (M - M′) / λ. The result of applying the convolution theorem is as follows:

[0070]

[0071] where L′ and M′ are the far-field directions, and δ is the Kronecker delta function (the term δ(L, L′) indicates that the grating of the grating vector in the Y direction does not change the X-direction cosine of the light ray). In the above expression, comb[(M - M′)D / λ] gives the directions of each order: M′ = M - mλ / D, where m is the order number. Then, the efficiency of any given order is obtained from the square of the magnitude of the term evaluated in the direction of that order in the brackets.

[0072] For meta-atoms, this can be taken a step further, where the phase is approximately linear in the meta-atom parameter 216. Maybe not, but at least it can be monotonic. In this case, a method similar to that of a blazed grating can be adopted, where a linear approximation of the phase (referred to as DE in the following equation) is used in the integral of the diffraction efficiency:

[0073]

[0074] In the above equation, t0 is the value of the meta-atom transmission evaluated for the ray being traced {for example, }.

[0075] Evaluating the integral, note that, Let M′ = M - mλ / D, and with a slight simplification, we get:

[0076]

[0077] The expression for the diffraction efficiency of the above mth order can be calculated as long as the look-up table 220 contains not only the phase as a function of the meta-atom parameter but also the derivative of that phase (if the phase derivative of the phase cannot be directly obtained in the look-up table 220, finite differences can be used). Although not explicitly stated in the equation for DE, the phase can also depend on the wavelength, the incident light ray direction, etc., and the derivative value suitable for the wavelength, direction, and polarization state of the ray being traced can be selected.

[0078] It may be reasonable to keep the transmission constant, as the impact of amplitude variations on efficiency is not as strong as that of phase variations. If this approximation does not work well in a given application, the integral given by equation (5) can be numerically evaluated in its full form. When the first-order terms are also included in (not just the constant term), an analogue of equation (7) can also be developed. By including the transmission of the meta-atoms in the analysis [even if it is just the simple approximation used in equation (7)], the optimizer is allowed to effectively balance the diffraction efficiency with the meta-atom transmission. For example, if the p and p min values that give the highest efficiency result in significant transmission losses of the meta-atoms, but different values of p max and p min and p max have lower efficiency but smaller transmission losses, then the optimizer can balance between efficiency and transmission loss to achieve maximum energy throughput.

[0079] Returning to Figure 2 , the design device 208 can use the function 218 to determine the layout 222 of the meta-lens. The meta-atoms in the layout 222 can be the selected type of meta-atoms 214. The parameters 216 (e.g., width) of the meta-atoms in the layout can have values determined according to the function 218. Then, the design device 208 can use ray tracing to analyze the meta-lens. For example, the design device 208 can use the function 218 to determine one or more ray directions 224 leaving the meta-lens. The design device 208 can also use the information in the look-up table 220 to determine the efficiency 226 of one or more orders of the rays passing through the meta-lens. In this way, the design device 208 can quickly evaluate how the rays leaving the meta-lens will travel (e.g., if the meta-lens focuses the rays as required).

[0080] As described above, the ray direction 224 can depend only on the position of the discontinuities in the meta-atom parameters; the details of how the phase varies over each region can determine the efficiency 226. Therefore, the values of the meta-atom parameters 216 within each region can be adjusted to achieve maximum efficiency 226. This can include (i) allowing the values of p min and p max not to be fixed for the lens, but to vary within the lens, and (ii) allowing the meta-atom parameters 216 connecting p min to p max not to exactly follow the curve derived from p(x,y), but to deviate from that curve. These two options for further customizing the efficiency 226 are schematically illustrated in Figure 8 . The curve 302 of p(x,y) and the curve 402 of P(x,y) are shown in Figure 8 . In addition, p minand p max vary in the lens. In section 802 of curve 402, the value of P(x,y) can vary or deviate from the form of curve 302. Another possibility ( Figure 8 not shown) is to allow the desired design order to not be fixed over the entire part. For example, at the center of the part, the first order can be selected, but towards the edges, a switch can be made to using the second order.

[0081] When more than one parameter 216 is used to describe the meta - atom type 214 of interest, the methods described herein for a one - parameter 216 meta - atom can be applied with slight modification. For example, a family of rectangular meta - atoms can have meta - atom parameters 216 for the length and width of the rectangle. Two functions 218 may be required to parameterize the meta - atom - p1(x,y) and p2(x,y). Thus, the length and width of the meta - atom at a surface position (x,y) will be given by

[0082] Length(x,y)=p 1,min +mod{[p1(x,y)-p 1,min ,(p 1,max -p 1,min )}

[0083] Width(x,y)=p 2,min +mod{[p2(x,y)-p 2,min ,(p 2,max -p 2，min )}

[0084] In this case, the meta - lens still behaves very much like a grating, but now the grating structure comes from positions where the meta - atom parameters (e.g., length or width) have discontinuities here.

[0085] As previously mentioned, when the meta - atom changes the polarization state of light, the look - up table 220 can include not only a single added phase, but also the Jones matrix imparted by the meta - atom [as a function of wavelength, incident ray direction, and meta - atom parameter 216]. When a ray is incident on the meta - lens, the look - up table 220 will be used to determine the Jones matrix that should be applied to the ray, and the ray - tracing code will need to apply that Jones matrix.

[0086] The design device 208 can provide the following features:

[0087] · Parameterize the meta - atom structure to allow evaluation and analysis to be performed using relatively few parameters to specify the meta - lens, rather than directly dealing with individual meta - atoms, and use the modulo function to model discontinuities in the meta - lens parameters 216. This can greatly reduce the number of degrees of freedom.

[0088] · For the purpose of ray tracing, the macroscopic structure of the metasurface is treated similarly to diffraction so that light rays can be used for evaluation and analysis.

[0089] · Allow p min 、p max and the metaatom parameters to vary within each grating period to maximize efficiency (e.g., send as much light as possible to the desired order).

[0090] · Be able to start with a low-resolution look-up table 220, which can be constructed more quickly, and then increase the resolution after achieving a rough design. A higher-resolution look-up table 220 can be constructed for the values of the design parameters used in the rough design.

[0091] In an example operation, the design device 208 can use a ray-based method to design the metasurface. The user 202 can first select the type of metaatom 214 to be used in the design. The design device can pre-compute the look-up table 220 for that type of metaatom 214. A parameterization or function 218 can be selected for the metaatom parameters 216, which can be a polynomial function. Select the desired design order (usually the first order, but the desired design order can vary across the metasurface). The coefficients in the parameterization of the metaatom parameters 216 are adjusted or optimized so that the light rays behave as desired. For this step, make some reasonable guesses for p min and p max but these can be not allowed to change. In this step, the design device 208 can ignore the transmission of the metaatom and the efficiency of the metasurface. For this step, the light rays in the design order can be considered.

[0092] After achieving a metasurface with reasonable performance, the design device 208 can re-optimize the metasurface considering ray behavior and transmission / efficiency. That is, p min and p max can be allowed to vary, and the merit function can include components related to the total energy in the desired design order. At this stage, if the user 202 wants to try to optimize the final position of the stray light, the merit function can also include components related to the light rays in the non-design orders.

[0093] As a final step, other software tools performing more rigorous electromagnetic analysis can be used to analyze the metasurface, and / or the optimizer can fine-tune the design, which can include more rigorous electromagnetic analysis.

[0094] Figure 9 is a flowchart of an example method 900 for designing and analyzing a metasurface. In some embodiments, the design device 208 executes method 900.

[0095] At 902, the design device 208 receives a selection of a meta-atom type 214 and a grid arrangement (e.g., a square grid or a hexagonal grid) of meta-lenses. The user 202 may select the meta-atom type 214 and the grid arrangement. For example, the user 202 may select a meta-atom that is a cylindrical post arranged on a square grid.

[0096] At 904, the design device 208 generates a look-up table 220 of the transfer function of the meta-atom type 214 and the grid arrangement. At 906, the design device 208 receives a parameterized function type and a design order. The user 202 of the computer system may select the parameterized function type and the design order. For example, the user 202 may select a parameterized function type that is a polynomial and a design order equal to 1. The design device 208 parameterizes the meta-atom parameters 216 such that each parameter 216 is represented as a function 218 of the position of the meta-atom on the surface of the meta-lens.

[0097] At 908, the design device 208 determines the layout 222 of the meta-lens. The design device 208 may determine a distribution function of the meta-atom parameters 216 of the selected meta-atom type 214 on the meta-lens. At 910, in order to determine the distribution function of the meta-atom parameters 216, the design device 208 changes the coefficients in the parameterized function 218 to optimize or improve the performance of the meta-lens in terms of light direction and efficiency. The design device 208 calculates the light direction based on the input from 906 (e.g., the parameterized function 218). The design device 208 determines the efficiency or energy based on the look-up table 220 from 904. At 912 (which is an optional step), the design device 208 analyzes and / or fine-tunes the meta-lens design through more rigorous electromagnetic analysis.

[0098] The design device 208 may use the parameterized function 218 and the design order to determine the direction 224 of the light leaving the meta-lens. In some embodiments, the design device 208 also uses the look-up table 220 to determine the energy or efficiency of the light leaving the meta-lens.

[0099] Figure 10 An example machine of a computer system 1000 is illustrated in which an instruction set for causing a machine to execute any one or more of the methods discussed herein may be executed. In an alternative implementation, the machine may be connected (e.g., networked) to other machines in a LAN, intranet, extranet, and / or the Internet. The machine may operate as a server or 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.

[0100] A machine can be a personal computer (PC), a tablet computer, a set-top box (STB), a personal digital assistant (PDA), a cellular phone, a network device, a server, a network router, a switch or a bridge, or any machine capable of executing a set of instructions (sequential, etc.) that specify actions to be taken by that machine. Additionally, although a single machine is illustrated, the term "machine" shall also be taken to include any collection of machines that individually or jointly execute a set (or multiple sets) of instructions to perform any one or more of the methods discussed herein.

[0101] Example 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)), a static memory 1006 (e.g., flash memory, static random access memory (SRAM), etc.), and a data storage device 1018, which communicate with each other via a bus 1030.

[0102] Processing device 1002 represents one or more processors, such as a microprocessor, a central processing unit, etc. More specifically, the processing device can 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 processor implementing a combination of instruction sets. Processing device 1002 can also be one or more dedicated processing devices, such as an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), a digital signal processor (DSP), a network processor, etc. Processing device 1002 can be configured to execute instructions 1026 for performing the operations and steps described herein.

[0103] Computer system 1000 may also include a network interface device 1008 for communicating via a network 1020. Computer system 1000 may also 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.

[0104] The data storage device 1018 may include a machine-readable storage medium 1024 (also referred to as a non-transitory computer-readable medium) having stored thereon a set or sets of instructions 1026 or software embodying any one or more of the methods or functions described herein. During execution of the instructions 1026 by the computer system 1000, the instructions may also reside, completely or at least partially, within the main memory 1004 and / or within the processing device 1002, which also constitutes a machine-readable storage medium.

[0105] In some implementations, the instructions 1026 include instructions for implementing the functions corresponding to the present disclosure. Although the machine-readable storage medium 1024 is shown as a single medium in the example implementation, the term "machine-readable storage medium" should be regarded as including a single medium or multiple media (e.g., a centralized or distributed database, and / or associated caches and servers) storing one or more sets of instructions. The term "machine-readable storage medium" should also be regarded as including any medium that is capable of storing or encoding a set of instructions for execution by a machine and causing the machine and the processing device 1002 to perform any one or more of the methods of the present disclosure. Thus, the term "machine-readable storage medium" should include, but is not limited to, solid-state memory, optical media, and magnetic media.

[0106] Some of the foregoing detailed descriptions are 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 art to most effectively convey the substance of their work to others skilled in the art. An algorithm may be a series of operations leading to a desired result. The operations are those requiring physical manipulation 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, etc.

[0107] However, it should be borne in mind that all such and similar terms are to be associated with appropriate physical quantities and are merely convenient labels applied to such quantities. Unless explicitly stated otherwise from the present disclosure, it should be understood that throughout the description, certain terms refer to the actions and processes of a computer system or similar electronic computing device that manipulates and transforms data represented as physical (electronic) quantities within the registers and memories of the computer system into other data similarly represented as physical quantities within the memories or registers or other such information storage devices of the computer system.

[0108] The present disclosure also relates to an apparatus for performing the operations herein. The apparatus can be specially constructed for the intended purpose, or it can include a computer selectively activated or reconfigured by a computer program stored in a computer. Such a computer program can be stored in a computer-readable storage medium, such as, but not limited to, any type of disk, including 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 the computer system bus.

[0109] The algorithms and displays presented herein are not inherently related to any particular computer or other apparatus. Various other systems can be used in conjunction with the programs according to the teachings herein, or it may prove convenient to construct more specialized apparatus to perform the method. In addition, 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 described herein.

[0110] 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 may be used to program a computer system (or other electronic device) to perform a process according to the present disclosure. The machine-readable medium includes any mechanism for storing information in a machine (e.g., computer) readable form. For example, the machine-readable (e.g., computer-readable) medium includes a machine (e.g., computer) readable storage medium such as read-only memory (“ROM”), random access memory (“RAM”), magnetic disk storage media, optical storage media, flash memory devices, etc.

[0111] In the foregoing disclosure, implementations of the present disclosure have been described with reference to specific example implementations thereof. It will be apparent that various modifications can be made thereto without departing from the broader spirit and scope of the implementations of the present disclosure as set forth in the following claims. Where the present disclosure refers to some elements in the singular tense, more than one element may be depicted in the drawings and like elements may be labeled with like numerals. Accordingly, the present disclosure and the drawings are to be regarded in an illustrative rather than a restrictive sense.

Claims

1. A method for designing a metasurface lens, the method 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 metasurface lens, wherein a first dimension of each meta - atom of the plurality of meta - atoms is represented as a first function of a position of a corresponding meta - atom on the metasurface lens; And Determining at least in part a direction of light rays exiting the metasurface lens based on the first function.

2. The method according to claim 1, further comprising: Generating a look - up table of a transfer function of the meta - atom type for a set of values of the first dimension; And Determining at least in part an efficiency of the light rays based on the look - up table.

3. The method according to claim 2, wherein: A second dimension of each meta - atom of the plurality of meta - atoms is represented as a second function of a position of a corresponding meta - atom on the metasurface lens; The look - up table indicates the transfer function of the meta - atom type for a set of values of the second dimension; And The direction of the light rays exiting the metasurface lens is at least in part based on the second function.

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

5. The method according to claim 4, further comprising determining at least in part a polarization of the light rays exiting the metasurface lens based on the look - up table.

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

7. The method according to claim 1, wherein the first function includes a discontinuity along the metasurface lens.

8. The method according to claim 7, wherein the direction of the light rays exiting the metasurface lens is based on a position of the discontinuity along the metasurface lens.

9. A system for designing a metasurface lens, the system comprising: A memory; And A processor communicatively coupled to the memory, the processor being configured to: Receive a selection of a meta - atom type; Determine a layout of a plurality of meta - atoms of the meta - atom type on the metasurface lens, wherein a first dimension of each meta - atom of the plurality of meta - atoms is represented as a first function of a position of a corresponding meta - atom on the metasurface lens; And Determine at least in part a direction of light rays exiting the metasurface lens based on the first function.

10. The system according to claim 9, wherein the processor is further configured to: Generate a look - up table of a transfer function of the meta - atom type for a set of values of the first dimension; and Determine at least in part an efficiency of the light rays based on the look - up table.

11. The system according to claim 10, wherein: A second dimension of each meta - atom of the plurality of meta - atoms is represented as a second function of a position of a corresponding meta - atom on the metasurface lens; The look - up table indicates the transfer function of the meta - atom type for a set of values of the second dimension; And The direction of the light rays exiting the metasurface lens is at least in part based on the second function.

12. The system according to claim 10, wherein generating the look-up table further comprises determining the Jones matrix of the meta-atom type for the set of values of the first dimension.

13. The system according to claim 12, wherein the processor is further configured to determine the polarization of the light rays exiting the meta-lens at least in part based on the look-up table.

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

15. The system according to claim 9, wherein the first function includes a discontinuity along the meta-lens.

16. The system according to claim 15, wherein the direction of the light rays exiting the meta-lens is based on the position of the discontinuity along the meta-lens.

17. A non-transitory computer-readable medium storing instructions for designing a meta-lens, the instructions when executed by a processor cause the processor to: generate a look-up table of transfer functions of meta-atom types; determine a first function that represents a first dimension of a plurality of meta-atoms of the meta-atom type as a function of the positions of the plurality of meta-atoms on the meta-lens; and determine the characteristics of light rays exiting the meta-lens at least in part based on the look-up table and the first function.

18. The medium according to claim 17, wherein the characteristic includes the energy in the light rays exiting the meta-lens.

19. The medium according to claim 17, wherein the processor further determines a second function that represents a second dimension of the plurality of meta-atoms as a function of the positions of the plurality of meta-atoms on the meta-lens, wherein the characteristic of the light rays exiting the meta-lens is at least in part based on the second function.

20. The medium according to claim 17, wherein the first function includes a discontinuity along the meta-lens.

Images