Optical design methods

Abstract

To provide an optical design method that facilitates an optical design of a structure using a diffractive optical element together with a conventional lens.SOLUTION: An optical design method comprises: a determination step; an acquisition step; and a design step. The determination step is configured to determine an optical characteristic of a diffractive optical element 1 to be used together with a conventional lens 2. The acquisition step is configured to acquire optical action information on the diffractive optical element 1 on the basis of the optical characteristic. The design step is configured to design the conventional lens 2 on the basis of the optical action information. For example, the optical design method is characterized in that the diffractive optical element 1 is a meta lens or flat optics. For example, the optical design method is characterized in that the determination step includes determining the optical characteristic by using an equivalent refractive index method on the basis of an optical design of a structure using binary optics together with the conventional lens 2.SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] This invention relates to an optical design method.

Background Art

[0002] In recent years, the development of diffractive optical elements has attracted attention. A diffractive optical element (DOE: Diffractive Optical Element) is an element that controls light using the diffraction effect, and exhibits element characteristics different from those of conventional lenses that control light using the refraction effect or the reflection effect. It is known that a diffractive optical element can correct chromatic aberration when used in combination with a conventional lens, and an optical system with a compact and lightweight configuration can be designed. As disclosed technologies related to diffractive optical elements, for example, Patent Documents 1 to 3, and Non-Patent Documents 1 to 3, etc. can be cited. In the following description, information indicating the degree of change in the state of a light beam when a conventional lens or a diffractive optical element refracts or reflects light is expressed as "optical action information". Also, for example, as an example of optical action information, it may be expressed using wavefront information indicating the characteristics of the transmission wavefront or the reflection wavefront of a conventional lens or a diffractive optical element.

[0003] As diffractive optical elements, for example, a Fresnel lens and binary optics (BO: Binary Optics) on a multi-stage staircase have been proposed and adopted. As an optical design method for a configuration using binary optics and a conventional lens in combination, the equivalent refractive index method (also called the high refractive index method) may be used. In the above optical design method, for example, the diffracted light of a diffractive optical element is expressed, and using that information, ray tracing is performed on a conventional lens using optical design software. As optical design software, "CODE V (registered trademark)", "ZEMAX (registered trademark)", "OSLO", etc. are commercially available. In the above software, the equivalent refractive index method is mainly used, and a calculation example thereof is disclosed in, for example, Non-Patent Document 1.

[0004] Here, "metalens" (also called "flat optics"), which can be classified as a type of diffractive optical element, are attracting particular attention among diffractive optical elements, and are being actively researched and developed. A characteristic of metalens is that, unlike binary optics which have a multi-stage step shape, they produce the desired diffraction effect by forming a fine pattern below the wavelength on a flat substrate such as glass.

[0005] A metalens is a structure that has a lens-like function, formed by creating a fine pattern in a single exposure and etching process, such as a metasurface. A characteristic of metalenses is their flat shape. Therefore, compared to binary optics, they allow for a more compact configuration, and various applications are expected. Examples of fine patterns formed as metalenses include those disclosed in Patent Document 1.

[0006] For example, Figures 11(a) to 11(d) are schematic diagrams showing the relationship between conventional lenses, Fresnel lenses, binary optics, and metalenses, with Figure 11(a) showing the structure of a conventional lens, Figure 11(b) showing a Fresnel lens, Figure 11(c) showing a binary optics, and Figure 11(d) showing a metalens.

[0007] In the metalens shown in Figure 11(d), the first pattern P1, the second pattern P2, and the third pattern P3 are examples of different types of fine patterns. The configurations show that the area occupied by the element material, such as glass, is larger in the order of the first pattern P1, the second pattern P2, and the third pattern P3, and the "effective refractive index" disclosed in Patent Document 1 tends to be higher in the same order. When referring to Figure 11(d), which shows a cross-sectional view of the metalens, each pattern P1, P2, and P3 is compared based on area, but in reality, they can be compared based on the volume of each pattern.

[0008] Each pattern P1, P2, and P3 is designed to be smaller than or equal to the wavelength of the optical system being used. To reduce the difficulty of processing the fine patterns, a larger pitch for each dimension and width is preferable. For example, when using a metalens for transmission, if diffracted light, like that of a diffraction grating, is generated from the metalens, the transmittance of light that is transmitted without diffraction (zero-order light) decreases. Therefore, when processing fine patterns, it is necessary to optimize the trade-off between processing difficulty and the transmittance of zero-order light depending on the application. For example, when the angle of first-order diffracted light from a diffraction grating is perpendicularly incident, it is 90 degrees when the pitch and wavelength are equal. However, considering oblique incidence, if transmittance is prioritized, a pitch of about half the wavelength or less is preferable.

[0009] Furthermore, Patent Document 1 proposes a metalens with a pattern that takes into account the effect of so-called "microloading," where the etched shape changes due to differences in pattern density during etching. Figure 11(d) shows an example where only the third pattern P3 is affected by "microloading," specifically when the height is low. In addition, using a metalens makes it possible to avoid the "shadowing effect," which is a problem in binary optics, and to form images with excellent optical performance that are free of flare.

[0010] Figure 12 shows a schematic diagram illustrating an example of the "Shadowing Effect." Light refracted by the stepped vertical section (L1 in Figure 12) is different from the light diffracted and used in binary optics, and becomes unwanted light, such as flare light when imaging occurs. Furthermore, it is difficult to apply an anti-reflective coating to the flat section of binary optics. Therefore, reflected light from the flat section (L2 in Figure 12) can also be generated as unwanted light, causing deterioration of optical properties. In contrast, metalens use diffracted light, including refraction and reflected light from the stepped structure, to create a fine pattern with a size smaller than the wavelength, resulting in the so-called "structural anti-reflective" characteristic. Therefore, metalens do not generate unwanted light that occurs in binary optics, making it possible to prevent the "Shadowing Effect." [Prior art documents] [Patent Documents]

[0011] [Patent Document 1] Japanese Patent Publication No. 2020-86055 [Patent Document 2] Japanese Patent Publication No. 2018-31896 [Patent Document 3] Japanese Patent Publication No. 2021-71727 [Non-patent literature]

[0012] [Non-Patent Document 1] O plus E January / February 2021 issue (No. 477), page 43 [Non-Patent Document 2] Optical Technology Contact, November 2021 issue, page 26. [Non-Patent Document 3] Nature Communications volume 6, Article number: 7069 (2015) [Overview of the project] [Problems that the invention aims to solve]

[0013] Here, a characteristic of metalens is that light is trapped (optically trapped) by the fine patterns of wavelengths smaller than the metalens that make up the metalens. In this respect, conventional optical design methods using the equivalent refractive index method do not take into account the representation of diffracted light. For this reason, it is difficult to design a configuration that uses both diffracting optical elements such as metalens and conventional lenses using conventional optical design methods using the equivalent refractive index method. "Optical trapping" will be discussed later.

[0014] To clarify the above basis, let's first explain "effective refractive index." For example, as described in Patent Document 1, the "effective refractive index" can be expressed by the density of glass per unit volume at the density of fine patterns below the wavelength, such as in a metalens. Based on this, we will explain the concept of "effective refractive index" using Figures 13(a) to 13(c). Note that the arrows shown in Figures 13(a) to 13(c) represent light.

[0015] First, as is well known, the speed V of light traveling through a certain material is related to the speed of light in a vacuum C and the refractive index N of that material by the following equation (1). V = C / N (1) From equation (1), the refractive index can be considered a coefficient that slows down the speed of light within a material. If the material is uniform, the above consideration is sufficient. However, for example, in a configuration of air and material 9 with refractive index N as shown in Figure 13(a), if we consider the combined speed of light C of both, it can be considered to be the average of their respective speeds. Therefore, we will consider the "effective refractive index" as the coefficient that determines that speed.

[0016] For example, as shown in Figure 13(a), if the air and material 9 with refractive index N have the same width, the average value is sufficient. However, as shown in Figure 13(b), if the air and material 9 with refractive index N have different widths, the "effective refractive index" is determined by multiplying the weights according to the ratio of those widths.

[0017] For example, when the width between the air and material 9 with refractive index N in Figures 13(a) and 13(b) is large compared to the transmitted wavelength, the phenomenon can be understood as a prism (although a lens can be considered to be composed of multiple different prisms) where the wavefront changes in one direction, with respect to the speed of light, rather than considering the two regions together. This can be seen as binary optics, where each region has a different speed. On the other hand, in the case of fine patterns smaller than the wavelength, such as in a metalens, it is not possible to distinguish between the two regions as described above. For this reason, the concept of "effective refractive index" is useful in considering the combined wavefront behavior of the ensemble average. Patent Document 1 proposes this "effective refractive index" while taking into account the effect of "microloading".

[0018] Furthermore, Figure 13(c), for example, shows an example of material 9 having two different fine pattern shapes. When material 9 is placed in air, the phase of light is slower in regions where the occupancy rate of the element material (e.g., glass) is high compared to regions where the occupancy rate of the element material is low. That is, the value of the "effective refractive index" tends to be larger in proportion to the occupancy rate of the element material. This value of the "effective refractive index" determined by material 9 will be called the "linear component." In addition, when transmitting fine patterns smaller than the wavelength, such as in a metalens, it becomes necessary to consider the "nonlinear component," which will be explained below.

[0019] For example, Patent Document 1 discloses a method that considers only linear components and does not consider the "nonlinear components" that will be pointed out below. The reason why it is necessary to consider "nonlinear components" is that, for example, in a metalens, light is trapped like in an optical waveguide, and this effect causes light to be delayed and phase delayed, so the nonlinear components affect the effective refractive index. Because of the existence of such nonlinear components, it is considered difficult to use the equivalent refractive index method when performing optical design of metalens.

[0020] Here, the above optical trap will be described using the description in Patent Document 2. Patent Document 2 proposes an optical buffer element for a high-speed optical communication router, and utilizes the phenomenon of changing the relative permeability to become a "negative refractive index" by forming a metamaterial of a metal microstructure that resonates with the electromagnetic field of light. This metamaterial has a negative refractive index, and due to the negative Goos-Hanchen shift, it is possible to slow down the propagation speed of light. This phenomenon is called the "optical trap effect". For example, by placing a metamaterial on an optical waveguide, it becomes possible to cause a propagation delay of light. In this way, by loading a metamaterial structure onto a silicon optical waveguide, a variable delay buffer can be obtained, which uses the phenomenon of delay by an optical trap. Note that "delay" means slowing down the speed at which light travels, so the effective refractive index shows a high value.

[0021] Note that in Patent Document 2, the description is for a metamaterial. However, since a meta-lens, which is a metasurface, has a sub-wavelength fine pattern that acts as an optical waveguide and is formed of a sub-wavelength fine pattern, an optical trap similarly occurs. Therefore, in order to obtain the diffracted light of a meta-lens considering an optical trap, it is necessary to use an optical simulation of a vector model that calculates rigorously from Maxwell's equations, the finite element method (FEM), the finite-difference time-domain method (FDTD method), etc. Non-Patent Document 1 shows an example thereof.

[0022] Furthermore, the "nonlinear component" of the phase change due to the "optical trapping effect" will be described using the results of optical simulation of the vector model for fine patterns with dimensions below the wavelength, as described in Non-Patent Document 3. Fig. 1 of Non-Patent Document 3 discloses the results of optical simulation of the vector model showing the relationship between the transmittance and phase when changing the cylindrical diameter of the "meta-atoms" of the fine pattern. As the calculation conditions, the wavelength is 1550 nm, the material is amorphous silicon with a refractive index of 3.43, the height of the cylinder is 940 nm, and FDTD is used based on the above conditions (although described as hexagonal and square lattice periodic HCTAs, the shape after pattern transfer and etching is circular, so it is expressed as "cylinder" here).

[0023] Note that the horizontal axis in Fig. 1 of Non-Patent Document 3 is the cylinder diameter. However, since the "effective refractive index" is determined by the volume of the cylinder and the height is constant, Fig. 14(a) shows the newly obtained relationship between the phase on the vertical axis when the horizontal axis is the square of the cylinder radius. If only the "linear component" is considered, the "effective refractive index" also changes linearly, so the phase when changing to the square of the cylinder radius also changes linearly. However, as shown in Fig. 14(a), the change in phase is non-linear rather than linear. Thus, the "effective refractive index" of fine patterns with dimensions below the wavelength is determined by both the "linear component" and the "nonlinear component".<所

[0024] Also, Patent Document 3 mentions an optical system with a configuration using a metalens and a conventional lens together. Although there is a description of "the same phase delay profile", there is no description of how to actually perform the optical design, and it is difficult to solve the above-mentioned problems.

[0025] In addition, Non-Patent Document 2 discloses a technique related to the optical design of a metalens using a supercomputer. However, there is no description of the optical design of a configuration using a metalens and a conventional lens together, and it is difficult to solve the above-mentioned problems.

[0026] Therefore, even if we take into account the technologies disclosed in the aforementioned Patent Documents 1-3 and Non-Patent Documents 1-3, Metalens Therefore, it is difficult to simplify the optical design of a configuration that uses conventional lenses in combination.

[0027] Therefore, the present invention was devised in view of the above-mentioned problems, and its purpose is as follows: Metalens The objective is to provide an optical design method that facilitates the optical design of configurations that use conventional lenses in combination with other lenses. [Means for solving the problem]

[0028] The optical design method according to the first invention comprises a determination step of determining the optical properties of a metalens for use in combination with a conventional lens, and based on the optical properties, Using optical simulations of vector models The process includes an acquisition step of acquiring optical action information of the metalens, and a design step of designing the conventional lens based on the optical action information, wherein the decision step is an optical design of a configuration using binary optics and the conventional lens in combination. The optical design is designed using optical design software. Based on this, the method is characterized by determining the optical properties of the metalens by matching the effective refractive index with respect to the height of the steps formed in the binary optics to the effective refractive index of the fine pattern formed in the metalens.

[0034] The 2 The optical design method according to the invention is the first 1 The invention is characterized in that the design step includes designing an aspherical lens having optical action information equivalent to the optical action information, and designing the conventional lens based on the aspherical lens.

[0035] The 3 The optical design method according to the invention is the first 1 In the invention, the design step is characterized by including obtaining approximate information using polynomial approximation for the optical operation information, and designing the conventional lens based on the approximate information.

[0036] The 4The optical design method relating to the invention is described in the first invention to the second invention. 3 In any of the inventions, the invention further comprises an evaluation step of evaluating the shape of the fine pattern in the metalens based on the optical action information.

[0037] The 5 The optical design method according to the invention is the first 4 In the invention, the evaluation step is characterized by determining whether the phase change with respect to the change in the shape of the fine pattern is less than or equal to the manufacturing error of the metalens, and if the result of the determination exceeds the manufacturing error, changing at least one of the shape of the fine pattern, pitch, fill factor, and material used for the metalens.

[0038] The 6 The optical design method relating to the invention is described in the first invention to the second invention. 5 In any of the inventions, the acquisition step is characterized by including acquiring the optical action information for each of the target wavelengths.

[0039] The 7 The optical design method relating to the invention is described in the first invention to the second invention. 6 In any of the inventions, the optical action information is characterized by including wavefront information that shows the characteristics of the transmitted wavefront or reflected wavefront of the metalens. [Effects of the Invention]

[0040] First Invention ~ 7 According to the invention, the acquisition step involves acquiring optical action information of the metalens based on its optical properties. The design step involves designing a conventional lens based on the optical action information. Therefore, it is possible to design a conventional lens that is suitable for the optical action information of the metalens. This makes it possible to simplify the optical design of a configuration that uses both a metalens and a conventional lens.

[0044] Furthermore, the 1st to 7th inventionsAccording to the invention, the acquisition step includes acquiring optical action information using an optical simulation of a vector model. Therefore, optical action information can be acquired while considering the nonlinear components of the metalens. This makes it possible to improve the design accuracy in optical design.

[0046] In particular, the 2 According to the invention, the design step involves designing an aspherical lens having optical action information equivalent to that of an optical action information. Therefore, conventional optical design methods that take into account the characteristics of aspherical lenses can be used. This makes it possible to further simplify the optical design of configurations that use both a metalens and a conventional lens.

[0047] In particular, the 3 According to the invention, the design step obtains approximate information from the optical action information using polynomial approximation. Therefore, conventional optical design methods based on the approximate information can be used. This makes it possible to further simplify the optical design of configurations that use both metalens and conventional lenses.

[0048] In particular, the 4 According to the invention, the evaluation step evaluates the shape of the micro-pattern in the metalens based on optical action information. Therefore, changes to the shape of the micro-pattern can be considered during the optical design process. This makes it possible to reduce the time spent on optical design.

[0049] In particular, the 5 According to the invention, the evaluation step determines whether the phase change due to the change in the shape of the fine pattern is less than or equal to the manufacturing tolerance of the metallens. Therefore, optical design can be carried out taking into account the manufacturing tolerance of the metallens. This makes it possible to further improve the design accuracy in optical design.

[0050] In particular, the 6According to the invention, the acquisition step includes acquiring optical action information for each of the target wavelengths. This makes it possible to further facilitate optical design suitable for the application.

[0051] In particular, the 7 According to the invention, the optical operation information includes wavefront information that indicates the characteristics of the transmitted or reflected wavefront of the metalens. Therefore, it becomes possible to design an optical configuration using a metalens and a conventional lens in combination using a method similar to that used in conventional optical design. [Brief explanation of the drawing]

[0052] [Figure 1] Figure 1 is a schematic diagram showing an example of a configuration that uses a diffractive optical element in combination with a conventional lens. [Figure 2] Figure 2 is a flowchart showing an example of an optical design method in the first embodiment. [Figure 3] Figure 3 is a flowchart showing an example of the decision step, acquisition step, and design step in the first embodiment. [Figure 4] Figure 4 is a schematic diagram showing an example of a configuration when designing an optical system using binary optics in combination with conventional lenses. [Figure 5] Figure 5 is a schematic diagram illustrating the relationship between binary optics and metalens. [Figure 6] Figure 6(a) is a schematic diagram showing an example of a step in binary optics; Figure 6(b) is an enlarged schematic diagram of the dashed frame in Figure 6(a); Figure 6(c) is a schematic diagram of a metalens having the same effective refractive index as in Figure 6(b); and Figure 6(d) is a schematic diagram showing the area around Figure 6(c). [Figure 7] Figures 7(a) to 7(c) are schematic diagrams showing an example of a configuration when optically designing using both aspherical lenses and conventional lenses. [Figure 8] Figure 8 is a flowchart showing an example of the decision step, acquisition step, and design step in the second embodiment. [Figure 9]Figure 9 is a schematic diagram showing an example of a Fizeau interferometer. [Figure 10] Figure 10 is a flowchart showing an example of the decision step, acquisition step, and design step in the third embodiment. [Figure 11] Figure 11(a) is a schematic diagram showing an example of a conventional lens, Figure 11(b) is a schematic diagram showing an example of a Fresnel lens, Figure 11(c) is a schematic diagram showing an example of binary optics, and Figure 11(d) is a schematic diagram showing an example of a metalens. [Figure 12] Figure 12 is a schematic diagram illustrating an example of the "Shadowing Effect" that occurs in binary optics. [Figure 13] Figures 13(a) to 13(c) are schematic diagrams showing examples of effective refractive indices. [Figure 14] Figure 14(a) is a graph showing the relationship between the volume of the fine pattern shape and its phase, and Figure 14(b) is a graph showing the relationship between the result of differentiating the curve in Figure 14(a) with respect to the square of the radius and the absolute value of the phase change. [Modes for carrying out the invention]

[0053] The following describes an example of an optical design method as an embodiment of the present invention, with reference to the drawings. Note that the configurations in each figure are schematically represented for illustrative purposes, and the shape, thickness, etc., of each configuration may differ from those shown in the figures.

[0054] (First Embodiment) Figure 1 is a schematic diagram showing an example of a configuration using a diffractive optical element 1 and a conventional lens 2 in combination. Figure 2 is a flowchart showing an example of an optical design method in this embodiment.

[0055] The optical design method in this embodiment is used to realize an optical design that uses a diffractive optical element 1 and a conventional lens 2 in combination, as shown in Figure 1, for example. In this optical design method, based on a configuration in which, for example, an aperture 3, a diffractive optical element 1, and a conventional lens 2 are arranged in that order, information regarding the focusing 5 when parallel light 4 from an object at infinity is incident can be obtained.

[0056] The diffractive optical element 1 refers to an element also called a phase-modulated optical element, such as a metalens 11 or flat optics. The conventional lens 2 has different characteristics from the diffractive optical element 1 and refers to lenses such as refractive lenses, divergent lenses, and reflective lenses.

[0057] The optical design method in this embodiment comprises, for example, a determination step S1, an acquisition step S2, and a design step S3, as shown in Figure 2, and may also include, for example, an evaluation step S4. Furthermore, the optical design method may include, for example, a preparation step S0 for determining the specifications to be designed.

[0058] The determination step S1 determines the optical properties of the diffractive optical element 1 for use in combination with the conventional lens 2. In the determination step S1, the type and shape of the lens associated with the optical properties of the diffractive optical element 1, such as a metalensor 11, may also be determined. The optical properties include parameters such as wavelength, focal length, F-number, and various allowable aberrations, and are input into known optical design software for optical tracking, which will be described later.

[0059] Acquisition step S2 acquires optical action information of the diffractive optical element 1 based on its optical properties. The optical action information includes, for example, information usable with known optical tracking optical design software. The optical action information includes, for example, wavefront information indicating the characteristics of the transmitted wavefront or reflected wavefront of the diffractive optical element 1.

[0060] Design step S3 involves designing the conventional lens 2 based on optical operation information. In design step S3, optical design is performed for the conventional lens 2, for example, using known optical tracking optical design software.

[0061] In this optical design method, by performing acquisition step S2 and design step S3 in particular, it is possible to design a conventional lens 2 that is suitable for the optical action information of the diffractive optical element 1. This makes it possible to simplify the optical design of a configuration that uses both the diffractive optical element 1 and the conventional lens 2.

[0062] The following describes in detail an example of an optical design method. In this explanation, a metalens 11 will be used as an example of a diffractive optical element 1.

[0063] Figure 3 is a flowchart showing an example of the decision step S1, acquisition step S2, and design step S3 in this embodiment. Figure 4 is a schematic diagram showing an example of a configuration when designing an optical system using binary optics 21 and a conventional lens 22 in combination.

[0064] <Decision Step S1> Determination step S1 determines the optical properties of the metalens 11 for use with the conventional lens 2. Determination step S1 determines the optical properties using the equivalent refractive index method based on an optical design of a configuration that uses, for example, binary optics 21 and the conventional lens 22 in combination. Here, we will explain the case where only the aberration of the on-axial field of view needs to be corrected. The type and number of conventional lenses 22 are arbitrary.

[0065] In decision step S1, a configuration using binary optics 21 and a conventional lens 22 in combination is designed using known optical design software for optical tracking, for example, as shown in Figure 4. In this case, the above configuration is designed based on the specifications determined in preparation step S0, for example. In decision step S1, the above configuration may be designed using, for example, the equivalent refraction method.

[0066] Subsequently, the optical properties corresponding to the linear components of the metalens 11 are derived from the binary optics 21. Here, for example, as shown in Figure 5, the effective refractive index with respect to the height of the steps formed in the binary optics 21 can be made to correspond to the effective refractive index of the fine pattern formed in the metalens 11. Based on this correspondence, an example of deriving the optical properties of the metalens 11 will be explained.

[0067] For example, as shown in Figure 6(a), if the step height d of the binary optics 21 is set to satisfy the relationship shown in equation (2) below, when plane wave light incident perpendicularly on the binary optics 21 is transmitted through it, a phase difference of αλ occurs due to the effect of the step height d. Nd-d = αλ ···(2) Here, the letters in equation (2) are as follows: λ: Wavelength of light N: Refractive index of the Binary Optics 21 material (e.g., relative refractive index to air) α: Arbitrary coefficient (varies depending on specifications)

[0068] According to equation (2) above, the height of each step in the binary optics 21 can be determined by setting the coefficient α to a different value to obtain a phase difference suitable for the specifications. For example, when α is set to 1, a step height d that satisfies a phase difference of 2π can be derived.

[0069] Next, as shown in Figure 6(b), for example, a region SB is defined on the stair surface where the step d is formed. The height d1 and width P of region SB can be set arbitrarily.

[0070] Next, as shown in Figure 6(c), for example, a convex portion SC having a volume equal to the volume of region SB is derived as a fine pattern formed on the metalens 11. For example, equation (3) below is used to derive the convex portion SC. P × d1 = a × b ... (3) Here, the letters in equation (3) are as follows: P: Width of area SB a: Width of the protruding part SC b: Depth of the recess In this case, the width P of region SB is the pitch Pm of the fine pattern formed on the metalens 11, and the depth b of the recess adjacent to the convex portion SC is equal to the sum of the step d and the height d1. Note that in equation (3) above, the length (depth of the paper) is shown as 1, but for example, the length of region SB may be multiplied on the left side and the length of convex portion SC on the right side.

[0071] By performing the calculation in equation (3) above over the entire stepped surface where the step d is formed, the fine pattern formed on the metalens 11 shown in Figure 6(d) can be derived. Note that the dashed frame in Figure 6(d) corresponds to Figure 6(c). The effective refractive index of the linear component in the derived fine pattern of the metalens 11 is equal to the effective refractive index of the linear component in the portion of the binary optics 21 where the step d is formed (for example, Figure 6(a)).

[0072] By performing the calculations in equations (2) and (3) above over the entire binary optics 21, the fine pattern formed on the metalens 11 can be derived. This allows the optical properties of the metalens 11 to be derived.

[0073] Furthermore, for example, as the fine patterns formed on the metalens 11, multiple types of fine patterns with different fill factors (similar to the ratio of the width a of the convex portion SC to the width of the concave portion) may be derived while keeping the pitch Pm of the fine patterns constant. In other words, when deriving the optical properties of the metalens 11 from the binary optics 21 described above, the properties can be derived by any method as long as fine patterns with equal effective refractive indices can be formed.

[0074] <Acquisition Step S2> Acquisition step S2 acquires optical action information of the metalens 11 based on its optical properties. In acquisition step S2, optical action information of the metalens 11 is acquired using, for example, an optical simulation of a vector model such as FDTD. This makes it possible to acquire optical action information that includes not only the effective refractive index of the linear component mentioned above, but also information of the nonlinear component. If the optical action information differs for multiple wavelengths, optical action information may be acquired for each wavelength. In acquisition step S2, when using an optical simulation of a vector model, parameters such as wavelength, focal length, F-number, and various allowable aberrations are input to acquire optical action information.

[0075] <Design Step S3> Design step S3 designs a conventional lens 2 based on optical action information. Design step S3 also designs an aspherical lens having optical action information equivalent to that of the conventional lens. The aspherical lens can be designed using, for example, known optical tracking optical design software.

[0076] Subsequently, a conventional lens 2 is designed based on the designed aspherical lens. The conventional lens 2 can be designed using, for example, known optical tracking optical design software. The designed conventional lens 2 may be identical to, for example, the conventional lens 22 designed in decision step S1, or it may have different characteristics. In design step S3, when using known optical design software, the conventional lens 2 is designed by inputting parameters such as wavelength, focal length, F-number, and various allowable aberrations.

[0077] Here, since the refractive index changes with wavelength, the effective refractive index for a particular shape also differs with wavelength. For this reason, if aberration correction is required for multiple wavelengths, in acquisition step S2, optical action information corresponding to each of the multiple wavelengths is obtained, and in design step S3, an aspherical lens corresponding to each piece of optical action information is designed.

[0078] For example, if three wavelengths are targeted, as shown in Figures 7(a) to 7(c), aspherical lenses 31, 32, and 33 corresponding to each of the three wavelengths are designed. Then, based on each of the aspherical lenses 31, 32, and 33, a common conventional lens 2 is designed, thereby realizing the design of a conventional lens 2 that corresponds to three wavelengths.

[0079] <Evaluation Step S4> For example, as shown in Figure 1, an evaluation step S4 may be performed after the design step S3. The evaluation step S4 determines whether the designed configuration satisfies the specifications determined in the preparation step S0, etc. If it satisfies the specifications, it ends; otherwise, the decision step S1 is performed again. Note that, for example, if the specifications are not met, the acquisition step S2 or the design step S3 may be performed again in the evaluation step S4.

[0080] According to this embodiment, for example, the following becomes possible. First, the design time for a single diffractive optical element 1, such as the metalens 11, can be shortened. If only the metalens 11 is to be used in the imaging system, optimization is required to bring the optical performance of the metalens 11 into specifications, which requires multiple calculations using vector model optical simulations that take several hours per condition. In contrast, according to this embodiment, the optical performance of the metalens 11 only needs to be within specifications when combined with the conventional lens 2, so it becomes unnecessary to perform multiple calculations using vector model optical simulations to converge the optical performance of the metalens 11. Therefore, the objective can be achieved by optimizing only the conventional lens 2.

[0081] In other words, according to this embodiment, acquisition step S2 acquires optical action information of the diffractive optical element 1 based on its optical properties. Furthermore, design step S3 designs a conventional lens 2 based on the optical action information. Therefore, a conventional lens 2 suitable for the optical action information of the diffractive optical element 1 can be designed. This makes it possible to simplify the optical design of a configuration using both the diffractive optical element 1 and the conventional lens 2.

[0082] Furthermore, according to this embodiment, the diffractive optical element 1 is a metalens 11 or a flat optics. Therefore, even when dealing with elements having complex optical properties such as metalens 11 or flat optics, it is possible to easily realize optical design.

[0083] Furthermore, according to this embodiment, the determination step S1 includes determining the optical properties using the equivalent refractive index method based on an optical design that uses both the binary optics 21 and the conventional lens 22. Therefore, the optical properties of the diffractive optical element 1, such as the metalens 11, can be determined using the conditions of other optical designs. This makes it possible to easily determine the optical properties of the diffractive optical element 1.

[0084] Furthermore, according to this embodiment, the determination step S1 includes determining the optical properties of the metalens 11 or flat optics that exhibit the same value as the effective refractive index in the linear component of the binary optics 21. Therefore, when determining the optical properties of the diffractive optical element 1, such as the metalens 11, it is possible to determine them without performing complex calculations. This makes it possible to easily determine the optical properties.

[0085] Furthermore, according to this embodiment, acquisition step S2 includes acquiring optical action information using an optical simulation of a vector model. Therefore, optical action information can be acquired while taking into account the nonlinear components of the diffractive optical element 1. This makes it possible to improve the design accuracy in optical design.

[0086] Furthermore, according to this embodiment, design step S3 involves designing an aspherical lens having optical action information equivalent to that of the optical action information. Therefore, conventional optical design methods that take into account the characteristics of aspherical lenses can be used. This makes it possible to further simplify the optical design of a configuration that uses both the diffractive optical element 1 and the conventional lens 2.

[0087] Furthermore, according to this embodiment, acquisition step S2 includes acquiring optical action information for each of the target wavelengths. This makes it possible to further facilitate optical design suitable for the application.

[0088] Furthermore, according to this embodiment, the optical operation information includes wavefront information that indicates the characteristics of the transmitted or reflected wavefront of the diffractive optical element 1. Therefore, it is possible to design an optical configuration using both the diffractive optical element 1 and the conventional lens 2 in a manner similar to that used in conventional optical design.

[0089] In the embodiments described above, the transmitted wavefront is used as part of the explanation of optical action information. However, even when using other optical action information such as the reflected wavefront, the same steps as described above can be performed based on known technology.

[0090] (Second Embodiment) Next, an example of the optical design method in the second embodiment will be described. Figure 8 is a flowchart showing an example of the decision step S1, acquisition step S2, and design step S3 in this embodiment. The difference between this embodiment and the embodiment described above is that optical operation information is measured. Details that are the same as those in the embodiment described above will be omitted from the explanation.

[0091] In the optical design method of this embodiment, the determination step S1 determines the optical properties by selecting a pre-formed diffractive optical element product 47. In addition, in the optical design method of this embodiment, the acquisition step S2 acquires optical operation information by measuring the optical operation information of the diffractive optical element product 47.

[0092] In other words, in this embodiment, when acquiring optical action information of the diffractive optical element 1, the optical simulation of the vector model described above is not used. Instead, the optical action information is measured using a physically existing diffractive optical element product 47. The design method and manufacturing method of the diffractive optical element product 47 are arbitrary. Therefore, in the decision step S1, for example, the optical characteristics can be determined by selecting a diffractive optical element product 47 that is suitable for the specifications from among several diffractive optical element products 47.

[0093] Acquisition step S2 involves measuring the optical action information of the diffractive optical element product 47 using a known interferometer, as shown in Figure 9, for example. In this case, wavefront information indicating the characteristics of the transmitted wavefront can be measured from the optical action information.

[0094] The interferometer shown in Figure 9 is a Fizeau interferometer that includes oscillators 41, 42, and 43 that output different oscillation wavelengths. When using this interferometer, interference fringes generated by the first light 46 and the second light 48, which have traveled through different optical paths, are detected by a CCD camera 50, and wavefront information indicating the characteristics of the transmitted wavefront of the diffractive optical element product 47 is obtained from the detection results. The first light 46 represents the light reflected by the reflective reference surface 45. The second light 48 represents the light that has been transmitted through the diffractive optical element product 47, focused, and then reflected by the concave mirror reflector 49.

[0095] In the optical design method of this embodiment, a pre-formed diffractive optical element product 47 is used. Therefore, in addition to the metalens 11 or flat optics described above, physically existing Fresnel lenses, binary optics 21, etc., can also be selected as the diffractive optical element 1.

[0096] According to this embodiment, acquisition step S2 includes measuring the optical action information of the diffractive optical element product 47. Therefore, compared to acquiring optical action information by simulation or the like, it is possible to acquire optical action information that takes into account even slight formation errors of the diffractive optical element product 47. This makes it possible to improve the design accuracy in optical design targeting the diffractive optical element product 47.

[0097] (Third embodiment) Next, an example of the optical design method in the third embodiment will be described. Figure 10 is a flowchart showing an example of the decision step S1, acquisition step S2, and design step S3 in this embodiment. The difference between this embodiment and the embodiment described above is that an aspherical lens is designed for each angle of view. Details that are the same as those described above will not be explained.

[0098] In the optical design method of this embodiment, acquisition step S2 acquires multiple optical action information for each field of view. Furthermore, in the optical design method of this embodiment, design step S3 designs multiple aspherical lenses associated with each of the multiple optical action information, and based on each aspherical lens, designs a common conventional lens 2. This makes it possible to further simplify the optical design suitable for the application.

[0099] (Fourth Embodiment) Next, an example of an optical design method in the fourth embodiment will be described. The difference between this embodiment and the embodiments described above is that polynomial approximation is used for the optical operation information. Details similar to those in the embodiments described above will be omitted from this description.

[0100] In the optical design method of this embodiment, design step S3 involves obtaining approximate information from the optical operation information using polynomial approximation, and designing the conventional lens 2 based on the approximate information.

[0101] In other words, in this embodiment, an aspherical lens is not designed for optical action information. Instead, approximate information is obtained using a polynomial approximation. As the polynomial approximation, Zernike polynomials can be used, or other known polynomial approximations such as Legendre polynomials, Chebyshev polynomials, Hermitian polynomials, Forbes polynomials, etc. may be used.

[0102] According to this embodiment, in design step S3, approximate information is obtained from the optical operation information using polynomial approximation. Therefore, a conventional optical design method that takes the approximate information into account can be used. This makes it possible to further simplify the optical design of a configuration that uses both the diffractive optical element 1 and the conventional lens 2.

[0103] (Fifth embodiment) Next, an example of the optical design method in the fifth embodiment will be described. The difference between this embodiment and the embodiments described above is that the shape of the fine pattern in the diffractive optical element 1 is evaluated. Details similar to those in the embodiments described above will be omitted from this description.

[0104] In the optical design method of this embodiment, evaluation step S4 evaluates the shape of the fine pattern in the diffractive optical element 1 based on optical operation information. In addition, in the optical design method of this embodiment, for example, evaluation step S4 determines whether the phase change due to the change in the shape of the fine pattern is less than or equal to the manufacturing error of the diffractive optical element 1. If the result of the determination exceeds the manufacturing error, at least one of the fine pattern shape, pitch Pm, fill factor, and material used for the diffractive optical element 1 is changed.

[0105] In other words, in this embodiment, in addition to evaluating the overall optical design, such as the result of design step S3, evaluation of the diffractive optical element 1 itself can also be performed. Note that evaluation step S4 may be performed after design step S3 or after acquisition step S2.

[0106] For example, if evaluation step S4 is performed after design step S3, evaluation step S4 may terminate the optical design method if the result of the judgment is less than or equal to the manufacturing tolerance. Also, for example, if evaluation step S4 is performed after acquisition step S2, evaluation step S4 may proceed to design step S3 if the result of the judgment is less than or equal to the manufacturing tolerance.

[0107] The manufacturing tolerance indicates the acceptable tolerance range relative to the standard and can be set arbitrarily according to the standard. For example, a finite value of 5% or less is used as the manufacturing tolerance for the phase change due to a change in the shape of a fine pattern.

[0108] Optical effect information can be shown, for example, in the relationship between the volume of the fine pattern in the metalens 11 and its phase, as shown in Figure 14(a). Furthermore, the graph in Figure 14(b), for example, shows the relationship between the result of differentiating the curve in Figure 14(a) with respect to the square of the radius and the absolute value of the phase change.

[0109] As shown in Figures 14(a) and 14(b), there is a region where the phase change is abrupt. If the cylinder diameter is set to correspond to this region, it will not be the desired cylinder diameter due to manufacturing errors, etc., and the phase will also change.

[0110] Therefore, when designing the fine pattern of the metalens 11, it is effective to avoid regions where the phase change is abrupt. However, if, for example, a region where the phase change is abrupt is not selected, it may not be possible to derive the optical properties corresponding to the linear component of the metalens 11 from the binary optics 21. In this case, it is also effective to avoid regions where the phase change is abrupt by changing the pitch Pm of the fine pattern.

[0111] In other words, this means considering regions where the phase changes abruptly, such as the area within the dashed circle in Figure 14(a). If the radius of the fine pattern in this region is approximately 213 nm (the horizontal axis in Figure 14(a) is the square of the radius), then if the refractive index and the shape of the fine pattern differ from the design due to material or manufacturing errors, the phase may change significantly from the design value, and it may not be possible to obtain the desired optical properties. Therefore, it is preferable that the vertical axis of Figure 14(b), which is the differential system of Figure 14(a), has a radius value of 0.05 (5%) or less.

[0112] Therefore, for example, the binary optics 21 shown in Figure 11(c) is a three-stage design, but in the case of more stages, such as eight stages (not shown), the step difference between stages becomes a small value. As a result, when converted to the metalens 11 in Figure 11(d), the radius may become such that the phase changes abruptly in the circular area of ​​Figure 14(a). In this case, the present invention can be effectively realized by partially changing the pitch Pm of the fine pattern in the metalens 11 to avoid abrupt phase changes. If optimization cannot be achieved by changing the pitch Pm of the fine pattern, the material may also be changed. If problems still persist, the design can be repeated up to the design of the binary optics 21.

[0113] According to this embodiment, evaluation step S4 evaluates the shape of the fine pattern in the diffractive optical element 1 based on optical action information. Therefore, changes to the shape of the fine pattern can be considered during the optical design process. This makes it possible to reduce the time spent on optical design.

[0114] Furthermore, according to this embodiment, evaluation step S4 determines whether the phase change due to the change in the shape of the fine pattern is less than or equal to the manufacturing error of the diffractive optical element 1. Therefore, optical design can be carried out taking into account the manufacturing error of the diffractive optical element 1. This makes it possible to further improve the design accuracy in optical design.

[0115] While several embodiments of the present invention have been described, these embodiments are presented as examples only and are not intended to limit the scope of the invention. These novel embodiments can be carried out in a variety of other forms, and various omissions, substitutions, and modifications can be made without departing from the spirit of the invention. These embodiments and their variations are included in the scope and spirit of the invention, as well as in the claims of the invention and its equivalents. [Explanation of symbols]

[0116] 1: Diffractive optical element 2: Conventional lens 3: Aperture 4: Parallel light 5: Light Concentration 11: Metalens 21: Binary Optics 22: Conventional lens 31: Aspherical lenses 32: Aspherical lenses 33: Aspherical lenses 41: Oscillator 42: Oscillator 43: Oscillator 45:Reflection reference surface 46:First light 47: Diffractive Optical Element Products 48:Second light 49: Concave mirror reflector 50: CCD camera S0: Preparation Step S1: Decision step S2: Acquisition Step S3: Design Step S4: Evaluation Step SB: area SC: protruding part d: step d1: Height

Claims

1. A decision step to determine the optical properties of a metalens for use in combination with a conventional lens, An acquisition step to acquire optical action information of the metalens using an optical simulation of a vector model based on the aforementioned optical properties, A design step of designing the conventional lens based on the aforementioned optical operation information, Equipped with, The determination step includes designing an optical design using optical design software for a configuration that combines binary optics and the conventional lens, and determining the optical properties of the metalens by corresponding the effective refractive index with respect to the height of the steps formed in the binary optics to the effective refractive index of the fine pattern formed in the metalens, based on the optical design. An optical design method characterized by the following.

2. The aforementioned design step is, Design an aspherical lens having optical action information equivalent to the aforementioned optical action information, Designing the conventional lens based on the aspherical lens. including The optical design method according to claim 1, characterized by the above.

3. The aforementioned design step is, Approximation information is obtained from the aforementioned optical operation information using polynomial approximation. Based on the aforementioned approximation information, the conventional lens is designed. including The optical design method according to claim 1, characterized by the above.

4. The invention further includes an evaluation step of evaluating the shape of the fine pattern in the metalens based on the optical action information. An optical design method according to any one of claims 1 to 3, characterized by the above.

5. The aforementioned evaluation step is, Determine whether the phase change with respect to the change in the shape of the fine pattern is less than or equal to the manufacturing error of the metallens. If the result of the above determination exceeds the manufacturing tolerance, change at least one of the shape, pitch, fill factor of the fine pattern, and the material used for the metalens. including The optical design method according to claim 4, characterized by the above.

6. The acquisition step includes acquiring the optical action information for each of the target wavelengths. An optical design method according to any one of claims 1 to 5, characterized by the above.

7. The optical action information includes wavefront information that shows the characteristics of the transmitted wavefront or reflected wavefront of the metalens. An optical design method according to any one of claims 1 to 6, characterized by the above.

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