Terahertz wave lens and method for manufacturing terahertz wave lens

Abstract

Provided are a terahertz wave lens and a method for manufacturing a terahertz wave lens. The terahertz wave lens focuses or collimates terahertz waves. The terahertz wave lens includes a substrate having a surface formed with a concave-convex structure that changes the phase of the terahertz waves. The concave-convex structure has a plurality of pillars arranged periodically. The concave-convex structure has a plurality of regions each having a plurality of pillars. The height and diameter of the pillars in the thickness direction of the substrate differ for each region. The distance (period) between the centers of pillars adjacent to each other is constant. The outer end portions of the concave-convex structure in the thickness direction are located on the same plane.

Description

TECHNICAL FIELD

[0001] The present application relates to a lens for terahertz waves and a method for manufacturing a lens for terahertz waves. BACKGROUND

[0002] In recent years, a technique using electromagnetic waves (terahertz waves) in a terahertz band capable of performing safe and high-precision analysis has attracted attention. In order to use terahertz waves, a condensing optical system (lens or the like) for collimating or condensing terahertz waves is required. In order to avoid the large size of the condensing optical system, it is preferable to use a small lens as much as possible. In the related art, as a lens that is small in size while being capable of achieving a relatively high NA compared to a generally used spherical mirror, a planar lens (superlens) having a fine concave-convex structure (dielectric concave-convex structure arrangement) formed on a surface of a substrate is known.

[0003] For example, in Patent Literature 1 (Japanese Patent No. 6356557), a technique is disclosed in which an SOI substrate in which a resist layer composed of SiO2 and a silicon layer composed of Si are sequentially formed on a Si substrate is prepared, a mask corresponding to a concave-convex pattern is formed on a surface of the silicon layer of the SOI substrate, and a portion of the silicon layer not covered with the mask is removed by etching, thereby forming the above-described concave-convex structure. In addition, in Patent Literature 2 (Japanese Patent Application Laid-Open No. 2007-57622), a technique is disclosed in which a concave-convex structure obtained by forming a modulation spatial structure in height on a substrate using a method combining laser interference and laser processing is used. SUMMARY

[0004] According to the technique described in Patent Literature 1, etching is stopped at a stage at which the resist layer is exposed, and thus the height (i.e., etching depth) of the concave-convex structure can be made uniform. However, SiO2 used as the resist layer has a property of absorbing light in the terahertz region, and thus is not suitable for an optical element for terahertz waves. In addition, in the technique described in Patent Literature 2, a high-brightness processing laser and a mask for interference or the like are required, and there is a problem in that the process for forming the concave-convex structure is complicated. In addition, since the height (position of the outermost surface) of the concave-convex structure becomes irregular, there is a problem in that aberration is easily generated.

[0005] An object of one aspect of the present application is to provide a lens for terahertz waves that can be made small in size and suppress generation of aberration, and a method for manufacturing the same.

[0006] The terahertz wave lens of one aspect of the present application is a terahertz wave lens that condenses or collimates terahertz waves, and includes a substrate having a surface on which a concave-convex structure that changes the phase of terahertz waves is formed, the concave-convex structure having a plurality of concave-convex structure portions composed of convex portions or concave portions arranged periodically, the concave-convex structure having a plurality of regions in which the plurality of concave-convex structure portions are respectively arranged, the height of the substrate in the thickness direction of the concave-convex structure portion and the width in the direction orthogonal to the thickness direction being different for each region, the distance between the centers of the concave-convex structure portions adjacent to each other being constant, and the outer end portions of the concave-convex structure in the thickness direction being located on the same plane.

[0007] In the above-described terahertz wave lens, the height and the width of the concave-convex structure portion that constitutes the concave-convex structure are different for each region. Thereby, it is possible to impart a phase difference that is different for each region to the transmitted terahertz waves. Further, by using a substrate on which a concave-convex structure is formed on a surface, it is possible to reduce the thickness of the lens compared to a spherical mirror or the like, and thus it is possible to achieve miniaturization of the lens. Furthermore, by making the height positions of the outer end portions of the concave-convex structure in the thickness direction uniform, it is possible to suppress the generation of aberration. Further, in the above-described terahertz wave lens, by making the distance between the centers of the concave-convex structure portions adjacent to each other (i.e., the arrangement interval (period) of each concave-convex structure portion) constant, the design of the arrangement of the concave-convex structure portions becomes easy.

[0008] The concave-convex structure portion can be either a convex portion or a concave portion, and the larger the width of the concave-convex structure portion, the lower the height of the concave-convex structure portion. According to the above-described structure, it is possible to easily form a concave-convex structure in which the height and the width of the concave-convex structure portion are different for each region by utilizing the micro-loading effect in etching.

[0009] The concave-convex structure portion can be either a convex portion or a concave portion, and the larger the width of the concave-convex structure portion, the lower the height of the concave-convex structure portion. According to the above-described structure, it is possible to easily form a concave-convex structure in which the height and the width of the concave-convex structure portion are different for each region by utilizing the micro-loading effect in etching.

[0010] The plurality of regions can be composed of N regions (N is an integer of 2 or more) of a first region to an Nth region arranged in a prescribed direction, and the effective refractive index of each of the plurality of regions can gradually decrease as it goes from the first region to the Nth region. According to the above-described structure, it is possible to cause the terahertz wave lens to function as a refractive index distribution type lens by arranging the plurality of regions in such a manner that the effective refractive index gradually decreases as it goes from the first region to the Nth region.

[0011] The height of the concave-convex structure portion belonging to each region can increase as it goes from the first region to the Nth region. According to the above-described structure, compared to a case in which only the width of the concave-convex structure portion is different for each region, it is possible to efficiently generate a phase difference between regions.

[0012] The concave-convex structure portion can be a convex portion, or can be a concave-convex structure portion having a height between the height of the concave-convex structure portion corresponding to the nth region (n is an arbitrary integer from 1 to N-1) and the height of the concave-convex structure portion corresponding to the (n+1)th region, in the vicinity of the boundary between the nth region and the (n+1)th region. According to the above structure, the change in the height of the concave-convex structure portion can be moderated by forming a concave-convex structure portion (convex portion) having an intermediate height in the boundary between the nth region and the (n+1)th region. Thus, the change in the phase difference can be moderated in the boundary between the regions. As a result, a lens with high precision can be obtained.

[0013] The plurality of regions can also have a first phase difference region set in such a manner that the phase difference between regions adjacent to each other is a first phase difference, and a second phase difference region set in such a manner that the phase difference between regions adjacent to each other is a second phase difference smaller than the first phase difference. According to the above structure, the phase distribution design can be flexibly performed compared to the case where the phase difference between regions is equalized.

[0014] The concave-convex structure portion can be a convex portion, and at least one region in which the width of the concave-convex structure portion in the concave-convex structure is equal to or greater than a predetermined threshold value can be a second phase difference region. Alternatively, the concave-convex structure portion can be a concave portion, and at least one region in which the width of the concave-convex structure portion in the concave-convex structure is equal to or less than a predetermined threshold value can be a second phase difference region. Alternatively, at least the first region can constitute a second phase difference region. According to the above structure, for example, in the case where the concave-convex structure is formed by etching, the micro-loading effect is relatively significant, and it is difficult to accurately manufacture a portion having a width and a height corresponding to a predetermined phase distribution. By narrowing the interval of the phase difference between regions, the deviation (manufacturing error) from the designed value of the phase distribution can be compensated.

[0015] The concave-convex structure portion can have a plurality of repeating units each including a plurality of regions, and the plurality of repeating units can be arranged in a predetermined direction. At least one of the plurality of repeating units can be configured to have a phase distribution having a width greater than 2π. In order to appropriately obtain a lens effect, it is preferable that the repeating unit have a phase distribution having a width of 2π or more. On the other hand, due to the manufacturing error caused by the above-described micro-loading effect, there is a problem that the width of the phase distribution of the repeating unit can be less than 2π. According to the above structure, the possibility that the actual phase distribution has a width less than 2π can be reduced in the repeating unit configured to have a phase distribution having a width greater than 2π.

[0016] The height and width of the concave-convex structure portion corresponding to each of the plurality of regions can also be dimensions that suppress the reflection of terahertz waves at the interface between the concave-convex structure and air. According to the above structure, since a reflection preventing layer does not need to be separately provided outside the concave-convex structure portion, the terahertz wave lens can be prevented from being upsized, and the reflection of terahertz waves at the interface between the concave-convex structure and air is suppressed.

[0017] The manufacturing method of the terahertz wave lens according to one aspect of the present application is a manufacturing method of a terahertz wave lens that condenses or collimates terahertz waves, and includes: a first step of determining a pattern of a concave-convex structure that changes the phase of terahertz waves; a second step of forming an etching mask corresponding to the pattern on the surface of a flat substrate; a third step of forming the concave-convex structure having a plurality of concave-convex structure portions composed of convex portions or concave portions periodically arranged on the surface of the substrate by performing anisotropic etching of the substrate while the etching mask is formed on the surface of the substrate; and a fourth step of removing the etching mask from the surface of the substrate, the concave-convex structure having a plurality of regions in which a plurality of concave-convex structure portions are arranged, the height of the concave-convex structure portion in the thickness direction of the substrate and the width in the direction orthogonal to the thickness direction being different for each region, and the distance between the centers of the concave-convex structure portions adjacent to each other being constant.

[0018] According to the above manufacturing method, the terahertz wave lens having the above effects can be manufactured. Furthermore, by etching the surface of the substrate using the etching mask, the height position of the portion covered by the etching mask (i.e., the portion not removed by etching) can be made constant and uniform. Furthermore, by utilizing the microloading effect in etching, a structure in which the height and width of the concave-convex structure portion are both different for each region can be easily manufactured.

[0019] In the first step, the pattern of the concave-convex structure can be determined so that the plurality of regions are composed of N (N is an integer of 2 or more) regions of a first region to an Nth region arranged in a predetermined direction, and the etching amount per unit region of each of the plurality of regions gradually increases from the first region to the Nth region. According to the above structure, a plurality of regions in which the effective refractive index gradually decreases from the first region to the Nth region can be formed, and a terahertz wave lens that functions as a refractive index distribution type lens can be obtained.

[0020] The first step can further include: a step of acquiring information indicating the relationship between the width of the concave-convex structure portion and the etching depth; and a step of determining the width of the concave-convex structure portion arranged in each region based on the information indicating the relationship and a design value of the predetermined phase distribution. According to the above structure, the width of the concave-convex structure portion of each region can be determined by taking into account the relationship between the width of the concave-convex structure portion and the etching depth (i.e., the magnitude of the influence of the microloading effect), and the occurrence of manufacturing errors (deviation from the design value) caused by the microloading effect can be suppressed.

[0021] In the first step, the width of the concave-convex structure portion arranged in each region can be determined in such a manner that a plurality of regions have a first phase difference region and a second phase difference region. The first phase difference region is a region set in such a manner that the phase difference between regions adjacent to each other becomes a first phase difference, and the second phase difference region is a region set in such a manner that the phase difference between regions adjacent to each other becomes a second phase difference smaller than the first phase difference. According to the above structure, the phase distribution design can be flexibly performed compared to a case where the phase difference between regions is equalized.

[0022] In the first step, the width of the concave-convex structure portion arranged in each region can be determined in such a manner that at least one region in which the width of the concave-convex structure portion in the concave-convex structure is equal to or greater than a predetermined threshold value becomes the second phase difference region. In addition, in the first step, the width of the concave-convex structure portion arranged in each region can be determined in such a manner that at least one region in which the width of the concave-convex structure portion in the concave-convex structure is equal to or less than a predetermined threshold value becomes the second phase difference region. In addition, in the first step, the width of the concave-convex structure portion arranged in each region can be determined in such a manner that at least the first region constitutes the second phase difference region. According to the above structure, for a portion in which the micro-loading effect is relatively significant and it is difficult to accurately manufacture the concave-convex structure portion having a width and a height corresponding to a phase distribution designed in advance, the deviation (manufacturing error) from the designed value of the phase distribution can be compensated for by narrowing the pitch of the phase difference between regions.

[0023] In the first step, the width of the concave-convex structure portion arranged in each region can be determined in such a manner that a plurality of repeating units each including a plurality of regions are arranged in a predetermined direction, and at least one of the repeating units has a phase distribution having a width greater than 2π. According to the above structure, the terahertz wave lens can be obtained in which the possibility that the actual phase distribution has a width less than 2π is reduced in the repeating unit configured in such a manner as to have a phase distribution having a width greater than 2π.

[0024] In the first step, the width of the concave-convex structure portion arranged in each region can be determined in such a manner that the height and the width of the concave-convex structure portion corresponding to a plurality of regions become sizes capable of suppressing the reflection of terahertz waves at the interface between the concave-convex structure and air. According to the above structure, since a reflection preventing layer does not need to be separately provided outside the concave-convex structure portion, a terahertz wave lens capable of preventing the enlargement of the terahertz wave lens and suppressing the reflection of terahertz waves at the interface between the concave-convex structure and air can be obtained.

[0025] According to one aspect of the present application, a terahertz wave lens capable of achieving miniaturization and suppressing the generation of aberration and a manufacturing method thereof can be provided. Attached Figure Description

[0026] Figure 1 This is a side view of a lens for terahertz waves in one embodiment.

[0027] Figure 2 yes Figure 1 A top view of terahertz waves using a lens.

[0028] Figure 3 A is a top view showing a portion of the concave-convex structure of a lens used for terahertz waves.

[0029] Figure 3 B is a side cross-sectional view of a part of the concave-convex structure.

[0030] Figure 4 It is a diagram showing the height and diameter of the supports contained in each region of the concave-convex structure.

[0031] Figure 5 This diagram illustrates the manufacturing process of lenses used for terahertz waves.

[0032] Figure 6 This is a diagram illustrating an example of the relationship between the support radius (gap between supports) and the support height based on the micro-load effect.

[0033] Figure 7 It is a graph representing the phase deviation (deviation from the design value) caused by the non-uniformity of the support height.

[0034] Figure 8 This is a diagram illustrating the phase distribution design of this embodiment, the conventional phase distribution design, and the ideal phase distribution.

[0035] Figure 9 This is a diagram schematically representing a portion of the concave-convex structure corresponding to the phase distribution design.

[0036] Figure 10 It is a top view showing part of the concave-convex structure near the boundary of adjacent areas.

[0037] Figure 11 It is an SEM image of a part of the uneven structure near the boundary of adjacent regions.

[0038] Figure 12 A is a top view showing a portion of the concave-convex structure in a modified example.

[0039] Figure 12 B is a side cross-sectional view of a portion of the concave-convex structure in this modified example.

[0040] Figure 13 A diagram showing the height and width of the holes contained in each region of the convex-concave structure of the modified example.

[0041] Figure 14 is a plan view showing a part of the relief structure of the modification in the vicinity of the boundary of the regions adjacent to each other.

[0042] Figure 15 is a diagram schematically showing a part of the relief structure of the modification.

[0043] Figure 16 is a diagram showing the modification of the pillar.

[0044] Figure 17 is a diagram showing the modification of the hole portion. DETAILED DESCRIPTION

[0045] Hereinafter, an embodiment of the present application will be explained in detail with reference to the drawings. In the explanation of the drawings, the same or equivalent elements are denoted by the same reference numerals, and repeated explanation is omitted.

[0046] [TERAHERTZ-WAVE LENS]

[0047] As shown in Figure 1 , Figure 2 , Figure 3 A and Figure 3 B, a TeraHertz-wave lens 1 of one embodiment is a TeraHertz-wave optical element that can be used for electromagnetic waves in the TeraHertz band (hereinafter, "TeraHertz waves"). Specifically, the TeraHertz-wave lens 1 is a lens that transmits TeraHertz waves of a predetermined frequency and performs condensing or collimation without depending on the direction of polarized light. The TeraHertz-wave lens 1 is formed as a flat optical element (so-called metalens) using a fine dielectric relief structure arrangement. In this embodiment, as one example, the predetermined frequency is 2.4 THz (wavelength 125 μm), and the focal distance of the TeraHertz-wave lens 1 is 40 mm.

[0048] The TeraHertz-wave lens 1 includes a circular plate-shaped substrate 2. The substrate 2 is formed of a transparent material (e.g., silicon or the like) in the TeraHertz region. In this embodiment, the substrate 2 is formed of high-resistance silicon. In this embodiment, as one example, the diameter of the substrate 2 is 45 mm. The thickness of the substrate 2 is, for example, about 0.5 mm to 1 mm. On one main surface (surface) of the substrate 2 intersecting the thickness direction D of the substrate 2, a fine relief structure 3 is formed. The relief structure 3 functions as a phase modulation layer that changes the phase of TeraHertz waves transmitted through the relief structure 3.

[0049] The relief structure 3 has a plurality of pillars 31 (relief structure portions) arranged periodically. As Figure 3 A and Figure 3As shown in Figure B, in this embodiment, as an example, the support column 31 is constructed as a cylindrical protrusion erected on the surface of the substrate 2 (bottom 3b described later). Figure 3 As shown in Figure A, multiple supports 31 are arranged periodically. Specifically, the multiple supports 31 are arranged such that the distance (period p) between the centers of adjacent supports 31 is fixed, covering the entire concave-convex structure 3. In this embodiment, the multiple supports 31 are arranged in a grid pattern. The period p is set such that it is a period (subwavelength period) smaller than the wavelength of the terahertz wave of the object being acted upon (125 μm in this embodiment). In this embodiment, the period p is 30 μm as an example. As described above, the concave-convex structure 3 consists of periodic structures of equal area (in this embodiment, a square area containing one support 31 in the center). Figure 3 A is formed by the area enclosed by the dashed line.

[0050] The outer end 3a of the concave-convex structure 3 in the thickness direction D is formed by the upper surfaces of multiple pillars 31. The outer end 3a of the concave-convex structure 3 (i.e., the upper surfaces of the multiple pillars 31) lies on the same plane. The concave-convex structure 3 has a bottom 3b located inside the outer end 3a between the multiple pillars 31 (i.e., the portion where pillars 31 are not formed). The length in the thickness direction D between the upper surface (outer end 3a) of the pillar 31 and the bottom 3b of the pillar 31 is defined as the height h of the pillar 31 (refer to...). Figure 3 B).

[0051] like Figure 2 As shown, the uneven structure 3 has a structure in which repeating units RU are arranged in a plane, capable of imparting a phase difference of 2π (in radians (rad). In the following description, the unit of phase difference (rad) is appropriately omitted.) or more. In this embodiment, the uneven structure 3 has a plurality of repeating units RU1 to RU arranged radially (in a predetermined direction) from the center P of the substrate 2 as viewed from the thickness direction D towards the outer edge of the substrate 2. K Here, K is the number of repetitions (i.e., the number of repeating units RU contained in the concave-convex structure 3), which is an integer greater than 2. The first repeating unit RU1, including the center P, is a circular region centered on the center P. The second and subsequent repeating units RU2 to RU1... K It is a ring-shaped region centered on center P. The width (radial length) of the multiple repeating units RU gradually decreases with distance from center P. Based on this repeating structure, a phase difference of "2π×K" can be imparted radially from center P of substrate 2, similar to a Fresnel lens. That is, by utilizing substrate 2, which includes a flat surface with fine concave-convex structures 3, miniaturization can be achieved by reducing the lens thickness compared to spherical lenses and Fresnel lenses. Furthermore, a lens with high NA is realized.

[0052] Each of the repeating units RU has a plurality of regions (1st region to Nth region) arranged in a radial direction from the center P side of the substrate 2 to the outer edge side. Here, N is the number of regions included in one repeating unit RU, and is an integer of 2 or more. In the present embodiment, N is 9 as one example. That is, each of the repeating units RU has nine regions Al to A9. As shown in A, in each of the regions Al to A9, a plurality of pillars 31 are periodically arranged. Figure 3 A

[0053] The height h in the thickness direction D and the width (in the present embodiment, the diameter d (refer to A)) in the direction orthogonal to the thickness direction D of the plurality of pillars 31 arranged in the same region are uniform in design. That is, in the same region, the plurality of pillars 31 having the uniform height h and diameter d are periodically arranged. On the other hand, the height h and diameter d of the pillars 31 differ from each other between the different regions in the same repeating unit RU. That is, the height h and diameter d of the pillars 31 differ for each region. Figure 3

[0054] As shown in A, the diameter d of the pillars 31 belonging to each of the regions Al to A9 is adjusted in such a manner that the filling rate of the material (in the present embodiment, high-resistance silicon) of the substrate 2 in each of the regions Al to A9 (that is, the area occupied by the pillars 31 per unit area) becomes smaller as going from the region Al to the region A9. That is, the diameter d of the pillars 31 belonging to each of the regions Al to A9 becomes smaller as going from the region Al to the region A9. In the regions in which such pillars 31 are formed, the average refractive index (effective refractive index) of the portion of the pillars 31 (the portion formed of the material of the substrate 2, that is, high-resistance silicon) and the surrounding air layer (a layer having a low refractive index compared to the material of the substrate 2) is averaged. By adjusting the diameter d of the pillars 31 belonging to each of the regions Al to A9 (that is, the filling rate of silicon in each of the regions Al to A9) as described above, the effective refractive index of each of the regions Al to A9 gradually becomes smaller as going from the region Al to the region A9. By making the effective refractive index different for each region, a phase difference can be imparted between the regions. Figure 4

[0055] ​​Furthermore, as one moves from region A1 towards region A9, the height h of the supports 31 belonging to each of regions A1 to A9 increases. As described above, the height position (position in the thickness direction D) of the upper surfaces (outer end 3a) of the multiple supports 31 is uniform. Therefore, as one moves from region A1 towards region A9, the height position of the bottom 3b of each region A1 to A9 moves inward toward the substrate 2. By making the effective refractive index of each region A1 to A9 different according to the diameter d of the supports 31 as described above, and further by making the thickness of the uneven structure 3 (i.e., the height h of the supports 31) different for each region, a greater phase difference between regions can be achieved.

[0056] The height h of the support pillar 31 is set, for example, to be approximately one wavelength (125 μm) of the terahertz wave that is the target of the operation. However, due to the micro-load effect generated during the etching process described later, the height h of the support pillar 31 varies for each region A1 to A9. In this embodiment, as an example, in each repeating unit RU, the maximum value of the height h of the support pillar 31 (i.e., the height h of the support pillar 31 belonging to region A9) is approximately 120 μm, and the minimum value of the height h of the support pillar 31 (i.e., the height h of the support pillar 31 belonging to region A1) is approximately 95 μm. Furthermore, the maximum value of the diameter d of the support pillar 31 (i.e., the diameter d of the support pillar 31 belonging to region A1) is approximately 25 μm, and the minimum value of the diameter d of the support pillar 31 (i.e., the diameter d of the support pillar 31 belonging to region A9) is approximately 13 μm.

[0057] like Figure 5 As shown, the aforementioned uneven structure 3 can be fabricated, for example, using photolithography. First, a substrate 2 with a flat surface before the uneven structure 3 is formed is prepared (S1). Next, a photoresist R is coated on the surface of the substrate 2 (S2). Then, a photomask M is formed using a pattern corresponding to a plurality of circular patterns (i.e., patterns corresponding to the areas occupied by the plurality of pillars 31) with a pre-designed diameter d and distribution, and the photoresist R on the substrate 2 is exposed (S3). Thus, when the photoresist R is negative, the exposed portion of the photoresist R remains; when the photoresist R is positive, the exposed portion of the photoresist R is removed. When the photoresist R is negative, a photomask M formed to allow light to pass through the pattern only at positions corresponding to the plurality of circular patterns can be used. On the other hand, when the photoresist R is positive, a photomask M formed to block light only at positions corresponding to the plurality of circular patterns can be used. Through the above processing, an etching mask is formed using the photoresist R left on substrate 2.

[0058] Next, anisotropic etching (anisotropic dry etching) is performed using the photoresist R remaining on the substrate 2 as an etching mask (S5). Thus, the portions of the substrate 2 (silicon regions) not covered by the photoresist R are removed. In addition, Figure 5 is a diagram schematically showing the order of fabrication of the concave-convex structure 3, and is illustrated so that the etching depth is constant regardless of the diameter of the pillars 31. However, in reality, the shallower the gap between the pillars 31 adjacent to each other, the shallower the etching depth. This phenomenon is generally called microloading effect. In the present embodiment, as described above, the concave-convex structure 3 has, in each of the regions Al to A9, a group of pillars 31 configured in such a manner that not only the diameter d but also the depth (height h) is different. The group of pillars 31 thus configured is formed by utilizing the microloading effect. That is, the diameter d of the pillars 31 belonging to each of the regions Al to A9 is determined on the basis of taking into account the influence of the microloading effect. Thus, it is possible to set the desired phase difference (i.e., the phase difference determined by the combination of the diameter d and the height h of the pillars 31) in each of the regions Al to A9. That is, in each of the regions Al to A9, the diameter d of the pillars 31 belonging to each of the regions Al to A9 is determined in such a manner that the combination of the diameter d and the height h of the pillars 31 required to obtain the desired phase difference is obtained.

[0059] Next, the photoresist R remaining on the substrate 2 is removed (S6). Through the above processing, the above-described concave-convex structure 3 is formed on the surface of the substrate 2, and the lens 1 for terahertz waves is obtained.

[0060] Reference Figure 6 and Figure 7 will be described in more detail. Figure 6 shows the relationship between the radius of the pillars 31 and the etching depth (height) obtained by the inventor of the present application through experiments using a prescribed etching condition. More specifically, Figure 6 shows the results (etching depth) of etching performed with respect to a plurality of changes in the radius of the pillars included in the range of 5 μm to 12.5 μm using an etching condition in which the etching depth becomes 125 μm in the case where the radius of the pillars 31 is 5 μm (i.e., in the case where the gap between the adjacent pillars 31 is 20 μm). It is understood that, under the etching condition used in the present experiment, the microloading effect (i.e., the proportion of the amount of change in the height of the pillars to the amount of change in the radius of the pillars) becomes significant in the range where the radius of the pillars 31 is 9 μm or more (i.e., the gap between the pillars 31 is 12 μm or less).

[0061] By performing etching (trial) on the same work object (substrate 2) in advance using the same etching conditions as the predetermined etching performed in the above manufacturing process (S5), it is possible to grasp in advance Figure 6 the relationship between the diameter d of the pillar 31 (i.e., the gap between the pillars 31) and the micro-loading effect. Note that this relationship is uniquely grasped by making the period p of the pillars 31 of the concave-convex structure 3 constant as in the present embodiment. Specifically, as described above, the degree of the micro-loading effect depends on the gap between the pillars 31 adjacent to each other. On the other hand, in the present embodiment, since the period p of the pillars 31 of the concave-convex structure 3 is constant, the relationship "gap between adjacent pillars 31 = period p - diameter d" holds. Thus, it is possible to correspond the degree of the micro-loading effect to the diameter d of the pillar 31 one-to-one.

[0062] Figure 7 The dotted line in FIG. 12 indicates the phase difference calculated assuming that the height h (i.e., etching depth) is constant (125 μm) regardless of the radius of the pillar 31. That is, the phase difference is calculated without considering the influence of the micro-loading effect. Figure 7 The dotted line in FIG. 12 indicates the phase difference calculated assuming that the height h (i.e., etching depth) is constant (125 μm) regardless of the radius of the pillar 31. That is, the phase difference is calculated without considering the influence of the micro-loading effect. Figure 7 The phase difference in FIG. 12 is the phase difference in the case where the phase of the region in which the pillars 31 having a radius of 5 mm and a height of 125 μm are periodically arranged is taken as a reference (0 rad).

[0063] On the other hand, Figure 7 The solid line in FIG. 12 indicates the phase difference calculated considering the influence of the micro-loading effect. That is, the phase difference is calculated using the relationship shown in FIG. 11 and the height h of the pillar 31 obtained from the radius of the pillar 31. Figure 6 The solid line in FIG. 12 indicates the phase difference calculated considering the influence of the micro-loading effect. That is, the phase difference is calculated using the relationship shown in FIG. 11 and the height h of the pillar 31 obtained from the radius of the pillar 31.

[0064] For example, in the case where the material of the concave-convex structure (i.e., the region to be removed by etching) is different from the material of the substrate serving as the base, etching is stopped at the surface of the substrate, and thus the height of each pillar constituting the concave-convex structure becomes constant. In such a case, the micro-loading effect does not need to be considered. However, in the case where the concave-convex structure is formed on the surface of the substrate itself as in the present embodiment, there are regions where the micro-loading effect is significant (in the example of FIG. 12, regions where the gap is 12 μm or less) and regions where the micro-loading effect is not significant (in the example of FIG. 12, regions where the gap is 12 μm or more) in an alternating manner. Figure 6 In the example of FIG. 12, the difference in the height h (etching depth) of the pillar 31 occurs between the regions Al to A9. That is, as shown in FIG. 13, when the diameter d of the pillar 31 belonging to each of the regions Al to A9 is set so that the phase difference of each of the regions Al to A9 becomes a desired value, without considering the micro-loading effect (i.e., based on the dotted line in FIG. 12), the actually obtained phase difference of each of the regions Al to A9 (i.e., the solid line in FIG. 12) is different from the desired value. Figure 6 Figure 7 Figure 7 Figure 7 ​​​deviate from the desired value.

[0065] Thus, in the present embodiment, the information indicating the relationship between the radius (or diameter d) of the pillar 31 and the height h of the pillar 31 obtained by etching is obtained in advance Figure 6 the information indicating the above relationship and the design value of the phase distribution (i.e., the phase difference assigned to each of the regions Al to A9) determined in advance, the diameter d of the pillar 31 belonging to each of the regions Al to A9 is determined. That is, the diameter d of the pillar 31 belonging to each of the regions Al to A9 is determined in such a manner that the phase difference of each of the regions Al to A9 determined by the combination of the height h and the diameter d of the pillar 31 belonging to each of the regions Al to A9 becomes the desired value (design value). Further, in the above manufacturing process, the photo mask M reflecting the diameter d of the pillar 31 belonging to each of the regions Al to A9 thus determined is used to form the etching mask (the photoresist R left on the surface of the substrate 2) Figure 5 anisotropic dry etching (S5 of FIG. 3) is performed, and finally the etching mask (S6 of FIG. 3) is removed. Thus, the terahertz lens 1 having the phase distribution in accordance with the design can be obtained. That is, in each of the repeating units RU, the regions Al to A9 having the phase distribution in accordance with the design can be formed. Figure 5 Figure 5 is a graph indicating the phase distribution design of the present embodiment, the conventional phase distribution design, and the ideal phase distribution.

[0066] The ideal phase distribution indicated by the one-dot chain line in FIG. 4 is determined based on the wavelength λ (125 μm in the present embodiment) of the terahertz wave to be the object of the action, the focal distance f (40 mm in the present embodiment) of the lens, the distance r from the center (center P) of the lens, and the following equation (1). The ideal phase distribution determined by the following equation (1) is wrapped around the phase every 2π (≈ 6.28 rad). In addition, Figure 8 The phase difference indicated by the one-dot chain line in FIG. 4 is the value in the case where the phase difference at the boundary of each of the repeating units of every 2π is taken as the reference (= 0). Figure 8 Figure 8

[0067] In the conventional phase distribution design indicated by the broken line in FIG. 4, 2π is divided into about eight regions in such a manner as to approximate the ideal phase distribution, and appropriate subwavelength structures are assigned to the regions, respectively. That is, in each of the repeating units of every 2π, eight regions having different phase differences are formed at a pitch of π / 4.

[0068] In the conventional phase distribution design indicated by the broken line in FIG. 4, 2π is divided into about eight regions in such a manner as to approximate the ideal phase distribution, and appropriate subwavelength structures are assigned to the regions, respectively. That is, in each of the repeating units of every 2π, eight regions having different phase differences are formed at a pitch of π / 4. Figure 8 In the conventional phase distribution design indicated by the broken line in FIG. 4, 2π is divided into about eight regions in such a manner as to approximate the ideal phase distribution, and appropriate subwavelength structures are assigned to the regions, respectively. That is, in each of the repeating units of every 2π, eight regions having different phase differences are formed at a pitch of π / 4.

[0069] Figure 8 ​​In the phase distribution design of the present embodiment, as described above, nine regions Al to A9 having different phase differences are formed. Specifically, a repeating unit RU (one group of the plurality of regions Al to A9) has a first phase difference region set in such a manner that the phase difference between regions adjacent to each other is π / 4 (a first phase difference), and a second phase difference region set in such a manner that the phase difference between regions adjacent to each other is a phase difference smaller than π / 4 (a second phase difference). In the present embodiment, as one example, regions in which the micro-loading effect is not significant (in the present embodiment, as one example, regions A3 to A9) constitute the first phase difference region, and regions in which the micro-loading effect is significant (in the present embodiment, as one example, regions Al, A2) constitute the second phase difference region.

[0070] A region in which the micro-loading effect is significant, for example, refers to a region in which the diameter d of the pillar 31 is equal to or greater than a predetermined threshold value Δd (i.e., a region in which the gap between pillars 31 is not necessarily below a certain value). For example, in the example of Fig. 2, as described above, in a region in which the radius of the pillar 31 is equal to or greater than 9 μm (i.e., the diameter d is equal to or greater than 18 μm), the micro-loading effect is significant. In such a case, the threshold value Δd can be set to 18 μm, for example. Figure 6

[0071] As described above, in the phase distribution design of the present embodiment, in a region in which the micro-loading effect is significant, the number of phase divisions is increased compared to a region in which the micro-loading effect is not significant, as opposed to being equally divided in a conventional phase distribution design. In a region in which the micro-loading effect is relatively significant, it is difficult to accurately manufacture a portion of the pillar 31 having a diameter d and a height h corresponding to the designed phase distribution, and the deviation (manufacturing error) from the designed value of the phase distribution can be compensated for by narrowing the pitch of the phase difference between regions.

[0072] In addition, as described above, the width (radial length) of the plurality of repeating units RU gradually decreases as it moves away from the center P. That is, the respective widths of the plurality of regions included in the repeating unit RU gradually decrease as it moves away from the center P. Therefore, for example, in a repeating unit RU existing near the outer edge of the substrate 2, in which the width is very small, even in a region in which the diameter d of the pillar 31 is equal to or greater than the threshold value Δd, there are cases in which it is difficult to increase the number of phase divisions. In such a repeating unit RU, the number of phase divisions is not necessarily increased in a region in which the diameter d of the pillar 31 is equal to or greater than a certain value. For example, the repeating unit RU near the outer edge of the substrate 2 can also be constituted by eight regions having a phase difference of π / 4, which is designed in accordance with a conventional phase distribution design.

[0073] ​Further, in the phase distribution design of the present embodiment, the repeating unit RU is configured in such a manner that the phase distribution has a width greater than 2π. Specifically, in the conventional phase distribution design, the phase difference of the region having the largest phase difference (a region corresponding to the regions Al, A2 in the phase distribution design of the present embodiment) is made to coincide with 2π so as to approximate an ideal phase distribution that is wound every 2π (i.e., a phase distribution having a width of 2π). In contrast, in the phase distribution design of the present embodiment, the height h and the diameter d of the pillar 31 belonging to the region Al having the largest phase difference are adjusted in such a manner that the phase difference of the region Al is made greater than 2π. In order to obtain a proper lens effect, it is preferable that the repeating unit RU have a phase distribution having a width of 2π or more. On the other hand, due to the manufacturing error caused by the above-described micro-loading effect, there can be a case where the width of the phase distribution of the repeating unit RU is less than 2π. Therefore, in the present embodiment, the repeating unit RU is configured in such a manner that the repeating unit RU has a phase distribution having a width greater than 2π. Thereby, it is possible to reduce the possibility that the width of the actual phase distribution of the repeating unit RU is less than 2π.

[0074] In the present embodiment, as one example, the region A2 is set to have a phase difference of π / 8 with respect to the region A3, and the region Al is set to have a phase difference of a size between π / 8 and π / 4 with respect to the region A2. Thereby, the repeating unit RU has a phase distribution having a width greater than 2π as the entire regions Al to A9.

[0075] Figure 9 is a diagram schematically showing the correspondence between the concave-convex structure 3 formed based on the above-described phase distribution design and the phase difference (phase distribution). In Figure 9 , the diameter d of the pillar 31 is made greater than actually illustrated. Therefore, Figure 9 the number of the pillars 31 (the number in the radial direction of the substrate 2) belonging to each of the regions Al to A9 illustrated in Figure 9 is different from the actual number. Actually, in each of the regions Al to A9, there are more pillars 31 than Figure 9 illustrated. As illustrated in

[0076] Figure 10 is a plan view showing a portion of the concave-convex structure 3 in the vicinity of the boundary between the region A n (the nth region) and the region A n+1 (the (n+1)th region) in one repeating unit RU. Here, n is an arbitrary integer from 1 to N-1. Here, let the diameter of the pillar 31 corresponding to the region A n be d n , and let the diameter of the pillar 31 corresponding to the region An+1 The corresponding diameter d of the support 31 n+1 Let region A n The gap between adjacent internal support columns 31 is G. n Let region A n+1 The gap between adjacent internal support columns 31 is G. n+1 Let region A n Internal pillar 31 and area A n+1 The gap between the internal support columns 31 is G. m When, the following equations (2) to (4) hold true.

[0077] G n =pd n (2)

[0078] G n+1 =pd n+1 (3)

[0079] G m =p-(d n / 2+d n+1 / twenty four)

[0080] Here, the diameter d n Greater than diameter d n+1 Therefore, the gap G n G n+1 G m The size relationship is "G" n <G m <G n+1 That is, the period p of the multiple pillars 31 is constant throughout the entire concave-convex structure 3, therefore in region A n With region A n+1 Between them, region A is formed. n Gap G n With region A n+1 Gap G n+1 The size of the gap G between them m Therefore, in region A n With region A n+1 The magnitude of the micro-loading effect generated near the boundary becomes the value in region A. n The micro-load effect generated internally and in region A n+1 The magnitude of the micro-load effects generated within the region A is determined by the magnitude of these effects. As a result, in regions A adjacent to each other... n With region A n+1 Near the boundary, a region A is formed. n The corresponding height of pillar 31 and area A n+1 The height of the corresponding support 31 is between the heights of the support 31. In other words, in region A nnear the boundary of the region A n+1 , the height position of the bottom 3b of the inside of the region A n , and the height position of the bottom 3b of the inside of the region A n+1 . The bottom 3b is a bottom 3b of the height position between the height position of the bottom 3b of the inside of the region A Figure 11 is a SEM image of a part of the concave-convex structure near the boundary of the regions adjacent to each other. It is grasped from this SEM image that near the portion where the diameter of the pillar changes (i.e., the boundary of the regions adjacent to each other), the height position of the bottom does not change sharply in steps but changes gently. According to the above-described structure, near the boundary of the region A n and the region A n+1 , it is possible to make the change in the height of the pillar 31 gentle. Thereby, near the boundary of the region switching, it is possible to make the change in the phase difference gentle (continuous). As a result, it is possible to obtain a lens of high precision.

[0081] [Modified Example of Concave-Convex Structure]

[0082] Next, a modified example (concave-convex structure 3A) of the concave-convex structure will be described with reference to Figure 12 A ~ Figure 16 . The concave-convex structure 3A has a plurality of hole portions 32 (concave-convex structure portions) instead of a plurality of pillars 31, unlike the concave-convex structure 3. The structure of the concave-convex structure 3A other than the above is the same as that of the concave-convex structure 3. That is, the concave-convex structure 3A, like the concave-convex structure 3, has a plurality of repeating units RU and a plurality of regions A1 to A9 included in each repeating unit RU. Further, the phase distribution design of each of the regions A1 to A9 of the concave-convex structure 3A is the same as that of the concave-convex structure 3 described above. That is, the concave-convex structure 3A realizes the same phase distribution as that of the concave-convex structure 3 described above by providing hole portions (concave portions) instead of pillars (convex portions) on the surface of the substrate 2.

[0083] In the present embodiment, as one example, the hole portions 32 are constituted by cylindrical concave portions (bottomed holes) provided on the surface of the substrate 2. As shown in Figure 12 A, the plurality of hole portions 32 are periodically arranged. Specifically, the plurality of hole portions 32 are arranged in such a manner that the distance (period p) between the centers of the hole portions 32 adjacent to each other becomes constant throughout the concave-convex structure 3A. The period p is set in such a manner that it becomes a period (subwavelength period) smaller than the wavelength of the terahertz wave which is the object of the operation (125 μm in the present embodiment). The concave-convex structure 3A is constituted by a periodic structure (a square region (a region of A enclosed by a broken line) including one hole portion 32 in the central portion in the present embodiment) of equal areas. Figure 12

[0084] ​In the uneven structure 3A, the portion of the substrate 2 on the surface where no holes 32 are provided constitutes the outer end portion 3a of the uneven structure 3A in the thickness direction D. The outer end portion 3a of the uneven structure 3A is located on the same plane. Specifically, the outer end portion 3a of the uneven structure 3A is continuously formed along the same plane. In the uneven structure 3A, the bottom of each hole 32 constitutes the bottom 3b of the uneven structure 3A. The length in the thickness direction D between the outer end portion 3a and the bottom (bottom 3b) of the hole 32 is defined as the height h of the hole 32 (refer to...). Figure 12 B).

[0085] The height h in the thickness direction D and the width (in this embodiment, the diameter d) in the direction orthogonal to the thickness direction D of the plurality of holes 32 arranged in the same area (refer to...) Figure 12 A)) The design is consistent. That is, within the same region, multiple holes 32 with uniform height h and diameter d are periodically arranged. On the other hand, between different regions of the same repeating unit RU, the height h and diameter d of the holes 32 are different from each other. That is, the height h and diameter d of the holes 32 are different for each region.

[0086] like Figure 13 As shown, in the uneven structure 3A, the diameter d of the holes 32 belonging to each of regions A1 to A9 is adjusted so that the fill rate of the substrate 2 material (high-resistivity silicon in this embodiment) in each of regions A1 to A9 decreases as the area moves from region A1 to region A9. That is, the diameter d of the holes 32 belonging to each of regions A1 to A9 increases as the area moves from region A1 to region A9. In the region where such holes 32 are formed, terahertz waves sense the averaged refractive index (effective refractive index) of the portion where holes 32 are not formed (the portion formed by high-resistivity silicon, which is the material of substrate 2) and the air layer (a layer with a lower refractive index compared to the material of substrate 2) within the holes 32. By adjusting the diameter d of the aperture 32 belonging to each of regions A1 to A9 (i.e., the silicon filling rate of each of regions A1 to A9) as described above, the effective refractive index of each of regions A1 to A9 gradually decreases as one moves from region A1 to region A9. By making the effective refractive index different for each region, a phase difference can be imparted between regions.

[0087] Furthermore, as one moves from region A1 towards region A9, the height h of the aperture 32 in each of regions A1 to A9 increases. That is, as one moves from region A1 towards region A9, the height position of the bottom 3b of each region A1 to A9 moves inward toward the substrate 2. By making the effective refractive index of each region A1 to A9 different according to the diameter d of the aperture 32, as described above, and further by making the thickness of the uneven structure 3A (i.e., the height h of the aperture 32) different for each region, a greater phase difference between regions can be achieved.

[0088] The height h of the hole portions 32 is set to, for example, about 1 wavelength (125 μm) of the terahertz waves that are the action targets. However, the height h of the hole portions 32 differs for each of the regions Al to A9 due to a micro-loading effect that occurs at the time of etching processing to be described later. In the present embodiment, as one example, the maximum value of the height h of the hole portions 32 (i.e., the height h of the hole portions 32 belonging to the region A9) is about 125 μm, and the minimum value of the height h of the hole portions 32 (i.e., the height h of the hole portions 32 belonging to the region Al) is about 95 μm in each of the repeating units RU. Further, the maximum value of the diameter d of the hole portions 32 (i.e., the diameter d of the hole portions 32 belonging to the region A9) is about 25 μm, and the minimum value of the diameter d of the hole portions 32 (i.e., the diameter d of the hole portions 32 belonging to the region Al) is about 11 μm.

[0089] The concave-convex structure 3A can be produced using the photolithography technique described above, like the concave-convex structure 3. That is, the concave-convex structure 3A can be produced in the order shown below, like the concave-convex structure 3. In the concave-convex structure 3, the portions other than the portions corresponding to the pillars 31 are removed by etching, in contrast to which, in the concave-convex structure 3A, the portions corresponding to the hole portions 32 are removed by etching. Figure 5

[0090] In the case of using the concave-convex structure 3A, like in the case of using the concave-convex structure 3, a design that takes into account the micro-loading effect (design of the diameter d of the hole portions 32 belonging to each of the regions Al to A9) can also be performed. Specifically, instead of the information indicating the relationship between the radius of the pillars 31 and the etching depth (height of the pillars 31 obtained by etching) shown in FIG. 8, information indicating the relationship between the radius (or diameter d) of the hole portions 32 and the etching depth (height of the hole portions 32 obtained by etching) is obtained in advance by experiment or the like. Then, based on the information indicating the above-described relationship and the design values of the phase distribution (i.e., the phase differences assigned to each of the regions Al to A9) determined in advance, the diameter d of the hole portions 32 belonging to each of the regions Al to A9 is determined. That is, the diameter d of the hole portions 32 belonging to each of the regions Al to A9 is determined in such a manner that the phase difference of each of the regions Al to A9 determined by the combination of the height h and the diameter d of the hole portions 32 belonging to each of the regions Al to A9 becomes a desired value (design value). Then, in the above-described production process, an etching mask (photoresist R left on the surface of the substrate 2) Figure 6 Figure 5 Figure 5 Figure 5 ​​​​S6). Thus, the terahertz-wave lens 1 having a phase distribution in accordance with the design can be obtained. That is, in each of the repeating units RU, the regions Al to A9 having a phase distribution in accordance with the design can be formed.

[0091] Figure 14 is a plan view schematically showing a part of the relief structure 3A near the boundary between the region A n (the nth region) and the region A n+1 (the nth+l region). Here, n is an arbitrary integer from 1 to N-1. In the relief structure 3A, the regions (i.e., the inside of each of the hole portions 32) removed by etching are spatially separated. That is, in the relief structure 3 of the pillar structure, the regions removed by etching are continuous, in contrast to which, in the relief structure 3A of the hole portion structure, the regions removed by etching are separated from each other. Therefore, unlike the relief structure 3 (refer to Figure 10 ), in the relief structure 3A, the hole portions 32 having an intermediate height are not formed near the boundary between the regions A n and the region A n+1 . Thus, the relief structure 3A cannot obtain the effect of smoothing the change in the phase difference between the regions adjacent to each other within one of the repeating units RU as in the relief structure 3 described above.

[0092] On the other hand, at the boundary between the repeating units RU adjacent to each other (i.e., the boundary where the repeating units RU are switched), it is preferable that the phase difference be changed sharply in a stepwise manner as in the boundary portion between the repeating units RU of the ideal phase distribution shown in Figure 8 . Thus, according to the relief structure 3A, a more preferable change in the phase difference (i.e., a change in a stepwise manner) can be realized at the boundary between the repeating units RU adjacent to each other.

[0093] Figure 15 is a plan view schematically showing a part of the relief structure 3A near the boundary between the region A Figure 15 . In Figure 15 , the number of the hole portions 32 belonging to each of the regions Al to A9 (the number formed in the radial direction of the substrate 2) is different from the actual number. Actually, in each of the regions Al to A9, a larger number of the hole portions 32 than that shown in Figure 15 is included.

[0094] Next, a structure for realizing a function of suppressing reflection of terahertz waves at the interface of the concave-convex structure 3, 3A and air (i.e., the surface along the outer side end portion 3a) (hereinafter referred to as "non-reflection function") is described. Such a structure is realized by taking advantage of the fact that the diameter d of the concave-convex structure portion (pillar 31 or hole portion 32) can be varied not only in each of the regions Al to A9 but also the height h can be varied. In the following description, the case where the concave-convex structure 3A shown in Fig. 1 is used is described. Figure 15

[0095] In the following description, the meanings of the respective parameters are as described below.

[0096] • λ: wavelength of the terahertz waves that are the object of action

[0097] • p: period of the hole portions 32 (distance between the centers of adjacent hole portions 32)

[0098] • r1: hole portion radius of the region Al (radius of the hole portion 32)

[0099] • r i : hole portion radius of the region Ai (i > 2)

[0100] • h1: height of the region Al (height of the hole portion 32 included in the region Al)

[0101] • h i : height of the region Ai (height of the hole portion 32 included in the region Ai)

[0102] • n Air : refractive index of the air layer

[0103] • n sub : refractive index of the portion filled with the material of the substrate 2 (high-resistance silicon) (i.e., the portion of the substrate 2 in which the concave-convex structure 3A (hole portion 32) is not formed)

[0104] • n eff1 : effective refractive index of the region Al

[0105] • n effi : effective refractive index of the region Ai

[0106] In the case where it is determined that the hole portion radius r1 has an arbitrary value, by setting the height h1 based on the following equation (5), the non-reflection function can be realized in the region Al.

[0107]

[0108] Here, the effective refractive index n eff1 is determined based on the following equation (6) in accordance with the hole portion radius r1 of the region Al. ​

[0109]

[0110] That is, the height hi of the region Al for realizing the non-reflective function is determined in accordance with the hole radius ri. With the above in mind, the desired phase difference of the region Ai with respect to the region Al is obtained as follows and the hole radius r i .

[0111] First, the amount of phase modulation generated in the region Al is expressed by the following equation (7). Further, the amount of phase modulation generated in the region Ai is expressed by the following equation (8).

[0112] (n eff1 ·h1)+n sub (h i -h1) (7)

[0113] (n effi ·h i ) (8)

[0114] According to the above equations (7) and (8), the desired phase difference is expressed by the following equation (9).

[0115]

[0116] By transforming the above equation (9), the following equation (10) is obtained.

[0117]

[0118] Here, n effi is expressed as a function "neff(r i )" of the hole radius r i because it is expressed by the above equation (6). Further, the micro-loading effect of the region Ai (here, the difference between the height of the region Ai and the height of the region Al due to the micro-loading effect) can also be expressed as a function "M.l(r i )" of the hole radius r i of the region Ai. That is, it can be expressed as follows.

[0119] h i = h1 + M.1(r i ) (11)

[0120] Thus, the following equation (12) is obtained by the above equations (10) and (11).

[0121]

[0122] Here, h1 and n sub Since r is a constant, the left side of equation (12) above can be used as the value based on the hole radius r. i A function that determines the value of "G(r)" i )” indicates that the above formula (12) is expressed as in the following formula (13).

[0123]

[0124] Therefore, the hole radius r of region Ai can be set in a manner that satisfies the above equation (13). i In region Ai, there is a desired phase difference relative to region A1. And it achieves a non-reflective function. That is, in the above example, firstly, the combination of the aperture radius r1 and the height h1 of region A1 is determined in a manner that satisfies the above equation (5). The aperture radius r1 used to obtain the above combination is determined considering the micro-load effect. Specifically, it is possible to use information obtained in advance representing the relationship between the aperture radius and the etching depth (and Figure 6 The information shown corresponds to the information used to determine the hole radius r1. Next, the hole radii r1 of each region A2 to A9 are determined. i The determination is made in a manner that satisfies the above equation (13). Then, the hole radius r, which reflects this determination, is used. i The photomask M performs the above processing ( Figure 5 From S3 to S6), a terahertz wave lens 1 with non-reflective function in each region A1 to A9 can be obtained.

[0125] Furthermore, the case of using the concave-convex structure 3A is described here. Using the concave-convex structure 3, the same idea as described above can be used to achieve a non-reflective function in regions A1 to A9. Specifically, when using the concave-convex structure 3, an equation similar to the above equation (13) can be derived, with the radius of the support 31 in region Ai as the left-hand side. Then, the radius of the support 31 satisfying this equation is calculated for each region, and the above processing is performed using a photomask M that reflects the calculated radius of the support 31. Figure 5 From S3 to S6), a terahertz wave lens 1 with non-reflective function in each region A1 to A9 can be obtained.

[0126] [Effects]

[0127] In the above-described terahertz-wave lens 1, the height h and the diameter d of the concave-convex structure portion (the pillar 31 in the case of the concave-convex structure 3, and the hole portion 32 in the case of the concave-convex structure 3A) that configures the concave-convex structure 3, 3A are different for each of the regions Al to A9. Thereby, it is possible to impart a phase difference that is different for each of the regions Al to A9 to the terahertz wave transmitted from the substrate 2. Further, by using the substrate 2 on which the concave-convex structure 3, 3A is formed on the surface, it is possible to reduce the thickness of the lens compared to a spherical mirror or the like, and thus it is possible to achieve a reduction in the size of the lens. Furthermore, by making the height position of the outer end portion 3a of the concave-convex structure 3, 3A in the thickness direction D uniform, it is possible to suppress the occurrence of aberration.

[0128] Further, in the terahertz-wave lens 1, by making the distance (period p) between the centers of the concave-convex structure portions (the pillar 31 or the hole portion 32) that are adjacent to each other constant, the design of the arrangement of the concave-convex structure portions becomes easy. Specifically, in the case where the period p of the concave-convex structure portion is constant, the above-described periodic structure (in the present embodiment, a square region including one concave-convex structure portion in the central portion) whose area is constant can be arranged on a plane in principle (in the present embodiment, in a grid shape), and thus it is possible to easily design the layout of the concave-convex structure portion. On the other hand, in the case where the period p of the concave-convex structure portion is not constant (for example, in the case where the period p is made different in correspondence with the diameter d of the concave-convex structure portion), the size of the above-described periodic structure differs for each of the regions Al to A9. In this case, a gap (a gap between periodic structures of different sizes) can occur near the boundary of the region switching, and there is a problem that the effective refractive index (phase difference) in the portion of the gap deviates from the designed value. Further, in the case where periodic structures of different sizes are present in a staggered manner for each of the regions Al to A9, it is difficult to find an optimal arrangement of the periodic structures that does not generate such a gap (or has a very small gap). By making the period p constant, it is possible to avoid such a problem.

[0129] Further, in the case where the concave-convex structure portion is the pillar 31 (that is, in the case where the terahertz-wave lens 1 includes the concave-convex structure 3), the larger the diameter d of the pillar 31, the lower the height h of the pillar 31 (refer to FIG. 4). According to the above-described structure, it is possible to easily form the concave-convex structure 3 in which the height h and the diameter d of the pillar 31 differ for each of the regions Al to A9 by utilizing the micro-loading effect in etching. Figure 4 ). According to the above-described structure, it is possible to easily form the concave-convex structure 3 in which the height h and the diameter d of the pillar 31 differ for each of the regions Al to A9 by utilizing the micro-loading effect in etching.

[0130] Further, in the case where the concave-convex structure portion is the hole portion 32 (that is, in the case where the terahertz-wave lens 1 includes the concave-convex structure 3A), the larger the diameter d of the hole portion 32, the higher the height h of the hole portion 32 (refer to FIG. 5). According to the above-described structure, it is possible to easily form the concave-convex structure 3A in which the height h and the diameter d of the hole portion 32 differ for each of the regions Al to A9 by utilizing the micro-loading effect in etching. Figure 13). According to the above structure, the concave-convex structure 3A in which the height h and the diameter d of the hole portion 32 are different in each of the regions A1 to A9 can be easily formed by utilizing the micro-loading effect in etching.

[0131] Further, the plurality of regions included in one repeating unit RU are composed of nine regions of the region A1 to the region A9 arranged in a prescribed direction (the radial direction of the circular plate-shaped substrate 2 in this embodiment). Also, the effective refractive index of each of the plurality of regions A1 to A9 gradually decreases from the region A1 to the region A9. According to the above structure, the terahertz wave lens 1 can function as a refractive index distribution type lens by arranging the plurality of regions in such a manner that the effective refractive index gradually decreases from the region A1 to the region A9.

[0132] Further, the height h of the concave-convex structure portion (the pillar 31 or the hole portion 32) belonging to each of the regions A1 to A9 becomes higher as it goes from the region A1 to the region A9. According to the above structure, compared to the case where only the diameter d of the concave-convex structure portion is made different in each of the regions A1 to A9, it is possible to efficiently generate a phase difference among the regions A1 to A9.

[0133] Further, the plurality of regions A1 to A9 have a first phase difference region (the regions A3 to A9 in this embodiment) set in such a manner that the phase difference between regions adjacent to each other becomes a first phase difference and a second phase difference region (the regions A1 and A2 in this embodiment) set in such a manner that the phase difference between regions adjacent to each other becomes a second phase difference smaller than the first phase difference. According to the above structure, compared to the case where the phase difference between regions is made uniform (the conventional phase distribution design shown in FIG. 6), it is possible to flexibly perform phase distribution design. Figure 8

[0134] Further, in the case where the concave-convex structure portion is the pillar 31 (i.e., in the case where the terahertz wave lens 1 includes the concave-convex structure 3), it is also possible to make at least one region (the regions A1 and A2 in this embodiment) in which the diameter d of the pillar 31 in the concave-convex structure 3 is equal to or greater than a predetermined threshold value Δd, the second phase difference region. According to the same idea, in the case where the concave-convex structure portion is the hole portion 32 (i.e., in the case where the terahertz wave lens 1 includes the concave-convex structure 3A), it is also possible to make at least one region in which the diameter d of the hole portion 32 in the concave-convex structure 3A is equal to or less than a predetermined threshold value, the second phase difference region. According to the above structure, in the case where the micro-loading effect is relatively significant and it is difficult to accurately manufacture a portion having a diameter d and a height h corresponding to a previously designed phase distribution, it is possible to compensate for a deviation (manufacturing error) from the designed value of the phase distribution by narrowing the interval of the phase difference between regions.

[0135] ​Further, the height h and the diameter d of the concave-convex structure portion (the pillar 31 or the hole portion 32) corresponding to each of the plurality of regions Al to A9 are dimensions capable of suppressing reflection of terahertz waves at the interface of the concave-convex structure 3, 3A and air. According to the above structure, since a reflection preventing layer is not separately provided outside the concave-convex structure portion, it is possible to prevent the terahertz wave lens 1 from being upsized, and to suppress reflection of terahertz waves at the interface of the concave-convex structure 3, 3A and air.

[0136] Further, as described above, the manufacturing method of the terahertz wave lens 1 of the present embodiment includes: a first step of determining a pattern of the concave-convex structure 3, 3A (considering the design of the micro-loading effect described in Figure 6 and Figure 7 ); a second step of forming an etching mask (photoresist R) corresponding to the above pattern on the surface of the flat substrate 2 (refer to S2 to S4 of Figure 5 ); a third step of forming the concave-convex structure 3, 3A on the surface of the substrate 2 by performing anisotropic etching of the substrate 2 in a state where the etching mask is formed on the surface of the substrate 2 (refer to S5 of Figure 5 ); and a fourth step of removing the etching mask from the surface of the substrate 2 (refer to S6 of Figure 5 ). According to the above manufacturing method, it is possible to manufacture the terahertz wave lens 1 having the above-described effects. Further, by etching the surface of the substrate 2 using the etching mask, it is possible to make the height position (the outer end portion 3a) of the portion covered by the etching mask (i.e., the portion not removed by etching) constant and uniform. Further, by utilizing the micro-loading effect in etching, it is possible to easily manufacture a structure in which both the height h and the diameter d of the concave-convex structure portion differ for each region.

[0137] Further, in the above first step, the pattern of the concave-convex structure 3, 3A is determined in such a manner that the etching amount per unit region of each of the plurality of regions Al to A9 gradually increases from the region Al to the region A9. That is, in the case of using the concave-convex structure 3, the pattern of the concave-convex structure 3 is determined in such a manner that the diameter d of the pillar 31 decreases from the region Al to the region A9 (refer to Figure 4 ). Further, in the case of using the concave-convex structure 3A, the pattern of the concave-convex structure 3A is determined in such a manner that the diameter d of the hole portion 32 increases from the region Al to the region A9. According to the above structure, it is possible to form the plurality of regions Al to A9 in which the effective refractive index gradually decreases from the region Al to the region A9, and to obtain the terahertz wave lens 1 functioning as a refractive index distribution type lens.

[0138] Further, the above first step includes: obtaining information indicating the relationship between the diameter d of the concave-convex structure portion (the pillar 31 or the hole portion 32) and the etching depth (refer to Figure 6) and a design value of the phase distribution based on information representing the above-described relationship and a predetermined phase distribution (phase distribution design of the embodiment in Figure 8 According to the above-described structure, it is possible to determine the diameter d of the concave-convex structure portion in each of the regions A1 to A9 while taking into consideration the relationship between the diameter d of the concave-convex structure portion and the etching depth (i.e., the magnitude of the influence of the micro-loading effect), and to suppress the occurrence of a manufacturing error (deviation from the design value) due to the micro-loading effect.

[0139] Further, in the above-described first process, the diameter d of the concave-convex structure portion (the pillar 31 or the hole portion 32) arranged in each of the regions A1 to A9 is determined in such a manner that the plurality of regions A1 to A9 have a first phase difference region (a region in which the phase difference is set at a pitch of π / 4 in the present embodiment) and a second phase difference region (a region in which the phase difference is set to be narrower than π / 4). According to the above-described structure, it is possible to flexibly perform the phase distribution design compared to a case in which the phase difference between the regions A1 to A9 is made uniform.

[0140] Further, in the case where the concave-convex structure 3 is used, the diameter d of the pillar 31 arranged in each of the regions A1 to A9 can also be determined in the above-described first process in such a manner that at least one region (the regions A1 and A2 in the present embodiment) in which the diameter d of the pillar 31 in the concave-convex structure 3 is equal to or greater than a predetermined threshold value Δd becomes the second phase difference region. Further, in the case where the concave-convex structure 3A is used, the diameter d of the hole portion 32 arranged in each of the regions A1 to A9 can also be determined in the above-described first process in such a manner that at least one region in which the diameter d of the hole portion 32 in the concave-convex structure 3A is equal to or less than a predetermined threshold value becomes the second phase difference region. Further, the diameter d of the concave-convex structure portion (the pillar 31 or the hole portion 32) arranged in each of the regions A1 to A9 can also be determined in the above-described first process in such a manner that at least the region A1 constitutes the second phase difference region. According to the above-described structure, for a portion in which the micro-loading effect is relatively significant and it is difficult to manufacture the concave-convex structure portion having the diameter d and the height h corresponding to the predetermined phase distribution with high precision, it is possible to compensate for a deviation from the design value (manufacturing error) of the phase distribution by narrowing the pitch width of the phase difference between the regions A1 to A9.

[0141] Further, in the above-described first process, the diameter d of the concave-convex structure portion (the pillar 31 or the hole portion 32) arranged in each of the regions A1 to A9 is determined in such a manner that at least one of the plurality of repeating units RU becomes a phase distribution having a width greater than 2π. According to the above-described structure, it is possible to obtain the terahertz wave lens 1 in which the width of the actual phase distribution is less likely to be less than 2π, in the repeating unit RU configured in such a manner as to become a phase distribution having a width greater than 2π.

[0142] Further, in the above-mentioned first step, the diameter d of the concavo-convex structure portion arranged in each of the regions Al to A9 is determined in such a manner that the height h and the diameter d of the concavo-convex structure portion (the pillar 31 or the hole portion 32) corresponding to each of the regions Al to A9 become sizes capable of suppressing reflection of terahertz waves at the interface between the concavo-convex structure 3, 3A and air. According to the above-mentioned structure, the terahertz wave lens 1 capable of obtaining the above-mentioned reflection-free function in each of the regions Al to A9 can be obtained.

[0143] [Modified Example]

[0144] The above-mentioned preferred embodiments of the present application are described in detail, but the present application is not limited to the above-mentioned embodiments. For example, the materials and shapes of the respective structures are not limited to the above-mentioned examples.

[0145] Further, the pillar 31 of the concavo-convex structure 3 can not be cylindrical. For example, the concavo-convex structure 3 can include a prismatic pillar (for example, a quadrangular prism). In this case, the diameter d can be obtained using the width of the pillar as the length of one side of the pillar. Similarly, the hole portion 32 of the concavo-convex structure 3A can not be cylindrical. For example, the concavo-convex structure 3A can include a prismatic hole portion (for example, a quadrangular prism). In this case, the diameter d can be obtained using the width of the hole portion as the length of one side of the hole portion.

[0146] Further, the area equivalent periodic structure composed of a plurality of concavo-convex structure portions (pillars 31 or hole portions 32) is not necessarily a square region. For example, the plurality of concavo-convex structure portions can be arranged in a triangular lattice shape. In this case, the area equivalent periodic structure becomes a regular hexagonal region.

[0147] Further, the distance (period p) between the centers of the concavo-convex structure portions adjacent to each other is not necessarily constant. However, by making the distance between the centers of the concavo-convex structure portions constant, the above-mentioned advantage that the arrangement design of the concavo-convex structure portions becomes easy is obtained.

[0148] Further, the concavo-convex structure 3 can include a hole portion 32 instead of the pillar 31. Figure 16The illustrated pillar 31A has a cylindrical portion 31b as with the pillar 31, and has a portion 31a disposed between a portion of the substrate 2 other than the concavo-convex structure 3 (hereinafter, simply referred to as "substrate 2") and the portion 31b, and a portion 31c disposed outside (on the side opposite to the portion 31a side) of the portion 31b. The portion 31b is, as with the pillar 31, a portion that functions as the phase modulation layer R2. On the other hand, the portion 31a and the portion 31c are portions that function as the antireflection layers Rl, R3 by having a moth-eye structure. Specifically, the portion 31a is formed in a circular truncated cone shape that becomes sharp toward the portion 31b side from the substrate 2 side. The portion 31c is formed in a circular cone shape that becomes sharp toward the outside (air layer side) from the portion 31b side. With the portion 31a, it is possible to suppress reflection of terahertz waves at the boundary of the substrate 2 and the phase modulation layer R2. With the portion 31c, it is possible to suppress reflection of terahertz waves at the boundary of the phase modulation layer R2 and the air layer. In addition, the portion 31b can also be formed in a prismatic shape (for example, a quadrangular prism shape). In this case, the portion 31a can also be formed in a truncated prism shape, and the portion 31c can be formed in a pyramid shape.

[0149] Further, the concavo-convex structure 3A can also include Figure 17 The illustrated hole portion 32A has a cylindrical portion 32b as with the hole portion 32, and has a portion 32a disposed between a portion of the substrate 2 other than the concavo-convex structure 3A (hereinafter, simply referred to as "substrate 2") and the portion 32b, and a portion 32c disposed outside (on the side opposite to the portion 32a side) of the portion 32b. The portion 32b is, as with the hole portion 32, a portion that functions as the phase modulation layer R2. On the other hand, the portion 32a and the portion 32c are portions that function as the antireflection layers Rl, R3 by having a moth-eye structure. Specifically, the portion 32a is formed in a circular cone shape that becomes sharp toward the substrate 2 side from the portion 32b side. The portion 32c is formed in a circular truncated cone shape that becomes sharp toward the portion 32b side from the outside (air layer side). With the portion 32a, it is possible to suppress reflection of terahertz waves at the boundary of the substrate 2 and the phase modulation layer R2. With the portion 32c, it is possible to suppress reflection of terahertz waves at the boundary of the phase modulation layer R2 and the air layer. In addition, the portion 32b can also be formed in a prismatic shape (for example, a quadrangular prism shape). In this case, the portion 32a can also be formed in a truncated prism shape, and the portion 32c can be formed in a pyramid shape.

[0150] Moreover, in the above-described embodiment, the terahertz-wave lens 1 in which the plurality of repeating units RU are arranged in a concentric circular shape with respect to the lens center (center P) is exemplified, but the mode of the terahertz-wave lens of the present application is not limited to the above-described mode. For example, the terahertz-wave lens of the present application can also be a structure in which the lens function is exerted only in a single-axis direction like a cylindrical lens. For example, the repeating unit RU and the plurality of regions A1 to A9 included in the repeating unit RU can each be formed in a rectangular shape and arranged in the single-axis direction.

[0151] Moreover, in the above-described embodiment, the terahertz-wave lens that functions as a convex lens is exemplified as one example of the terahertz-wave optical element, but the terahertz-wave lens provided with the substrate and the concave-convex structure described above can also function as a concave lens by adjusting the distribution of the effective refractive index of the concave-convex structure (i.e., the shape and arrangement of the plurality of concave-convex structure portions). Moreover, the terahertz-wave optical element provided with the substrate and the concave-convex structure described above is not limited to the terahertz-wave lens. For example, the terahertz-wave optical element of the present application can also be an optical element other than a lens such as a polarizing plate, a wavelength plate, a diffraction grating, and the like.

[0152] Explanation of Reference Signs

[0153] 1 Terahertz-wave lens (terahertz-wave optical element)

[0154] 2 Substrate

[0155] 3, 3A Concave-convex structure

[0156] 3a Outer side end portion

[0157] 31, 31A Pillar (concave-convex structure portion, convex portion)

[0158] 32, 32A Hole portion (concave-convex structure portion, concave portion)

[0159] A1 to A9 Regions

[0160] D Thickness direction

[0161] RU Repeating unit

Claims

1. A terahertz lens for condensing or collimating a terahertz wave, characterized by: a substrate having a surface formed with a concave-convex structure that changes a phase of a terahertz wave, the concave-convex structure having a plurality of concave-convex structure portions composed of convex portions or concave portions arranged periodically, the concave-convex structure having a plurality of regions each of which is arranged with a plurality of the concave-convex structure portions, a height in a thickness direction of the substrate of the concave-convex structure portion and a width in a direction orthogonal to the thickness direction of the concave-convex structure portion being different for each of the regions, a distance between centers of the concave-convex structure portions adjacent to each other being constant, outer end portions of the concave-convex structure in the thickness direction being located on the same plane, the plurality of regions being composed of N regions of a first region to an Nth region arranged in a prescribed direction, an effective refractive index of each of the plurality of regions gradually decreasing as going from the first region to the Nth region, the plurality of regions having a first phase difference region in which a phase difference between the regions adjacent to each other is set to be a first phase difference and a second phase difference region in which the phase difference between the regions adjacent to each other is set to be a second phase difference smaller than the first phase difference, in a case where the concave-convex structure portion is the convex portion, the region of the concave-convex structure in which the width of the concave-convex structure portion is equal to or greater than a first threshold value predetermined is the second phase difference region, and the region of the concave-convex structure in which the width of the concave-convex structure portion is smaller than the first threshold value is the first phase difference region, in a case where the concave-convex structure portion is the concave portion, the region of the concave-convex structure in which the width of the concave-convex structure portion is equal to or smaller than a second threshold value predetermined is the second phase difference region, and the region of the concave-convex structure in which the width of the concave-convex structure portion is greater than the second threshold value is the first phase difference region, and wherein N is an integer of 2 or greater.

2. The terahertz lens according to claim 1, characterized in that: the concave-convex structure portion is the convex portion, and the greater the width of the concave-convex structure portion, the lower the height of the concave-convex structure portion.

3. The terahertz lens according to claim 1, characterized in that: the concave-convex structure portion is the concave portion, and the greater the width of the concave-convex structure portion, the higher the height of the concave-convex structure portion.

4. The terahertz lens according to claim 1, characterized in that: the height of the concave-convex structure portion belonging to each of the regions increases as going from the first region to the Nth region.

5. The terahertz lens according to claim 2, characterized in that: the height of the concave-convex structure portion belonging to each of the regions increases as going from the first region to the Nth region.

6. The terahertz lens according to claim 3, characterized in that: the height of the concave-convex structure portion belonging to each of the regions increases as going from the first region to the Nth region.

7. The terahertz lens according to claim 4, characterized in that: the concave-convex structure portion is the convex portion, and the greater the width of the concave-convex structure portion, the lower the height of the concave-convex structure portion. ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ a concave-convex structure portion having a height between a height of the concave-convex structure portion corresponding to the n-th region and a height of the concave-convex structure portion corresponding to the n+1-th region is formed near a boundary between the n-th region and the n+1-th region, where n is an arbitrary integer from 1 to N-1.

8. The terahertz lens according to claim 5, wherein: the concave-convex structure portion is the convex portion, a concave-convex structure portion having a height between a height of the concave-convex structure portion corresponding to the n-th region and a height of the concave-convex structure portion corresponding to the n+1-th region is formed near a boundary between the n-th region and the n+1-th region, where n is an arbitrary integer from 1 to N-1.

9. The terahertz lens according to claim 6, wherein: the concave-convex structure portion is the convex portion, a concave-convex structure portion having a height between a height of the concave-convex structure portion corresponding to the n-th region and a height of the concave-convex structure portion corresponding to the n+1-th region is formed near a boundary between the n-th region and the n+1-th region, where n is an arbitrary integer from 1 to N-1.

10. The terahertz lens according to any one of claims 1 to 9, wherein: at least the first region constitutes the second phase difference region.

11. The terahertz lens according to any one of claims 1 to 9, wherein: the concave-convex structure has a plurality of repeating units each including one set of the plurality of regions, the plurality of repeating units are arranged in the prescribed direction, at least one of the plurality of repeating units is configured to have a phase distribution having a width greater than 2π.

12. The terahertz lens according to claim 10, wherein: the concave-convex structure has a plurality of repeating units each including one set of the plurality of regions, the plurality of repeating units are arranged in the prescribed direction, at least one of the plurality of repeating units is configured to have a phase distribution having a width greater than 2π.

13. The terahertz lens according to any one of claims 1 to 9, wherein: the height and the width of the concave-convex structure portion corresponding to the plurality of regions are dimensions capable of suppressing reflection of terahertz waves at an interface of the concave-convex structure and air.

14. The terahertz lens according to claim 10, wherein: the height and the width of the concave-convex structure portion corresponding to the plurality of regions are dimensions capable of suppressing reflection of terahertz waves at an interface of the concave-convex structure and air.

15. The terahertz lens according to claim 11, wherein: the height and the width of the concave-convex structure portion corresponding to the plurality of regions are dimensions capable of suppressing reflection of terahertz waves at an interface of the concave-convex structure and air.

16. The terahertz lens according to claim 12, wherein: the height and the width of the concave-convex structure portion corresponding to the plurality of regions are dimensions capable of suppressing reflection of terahertz waves at an interface of the concave-convex structure and air.

17. A method for manufacturing a lens for terahertz waves that condenses or collimates terahertz waves, characterized by, comprises: a first step of determining a pattern of a concavo-convex structure that changes a phase of a terahertz wave; a second step of forming an etching mask corresponding to the pattern on a surface of a flat substrate; a third step of forming the concavo-convex structure having a plurality of concavo-convex structure portions composed of periodically arranged convex portions or concave portions on the surface of the substrate by performing anisotropic etching of the substrate in a state where the etching mask is formed on the surface of the substrate; and a fourth step of removing the etching mask from the surface of the substrate, the concavo-convex structure has a plurality of regions each of which is arranged with a plurality of the concavo-convex structure portions, a height in a thickness direction of the substrate and a width in a direction orthogonal to the thickness direction of the concavo-convex structure portion are different for each of the regions, a distance between centers of the concavo-convex structure portions adjacent to each other is constant, in the first step, the pattern of the concavo-convex structure is determined in such a manner that: the plurality of regions is composed of N regions of a first region to an Nth region arranged in a prescribed direction, an etching amount per unit region of each of the plurality of regions gradually increases from the first region to the Nth region, where N is an integer of 2 or more, the first step includes: a step of acquiring information indicating a relationship between the width and an etching depth of the concavo-convex structure portion; and a step of determining the width of the concavo-convex structure portion arranged in each of the regions on the basis of the information indicating the relationship and a design value of a predetermined phase distribution, in the first step, the width of the concavo-convex structure portion arranged in each of the regions is determined in such a manner that the plurality of regions has a first phase difference region and a second phase difference region, the first phase difference region is a region set in such a manner that a phase difference between the regions adjacent to each other becomes a first phase difference, the second phase difference region is a region set in such a manner that the phase difference between the regions adjacent to each other becomes a second phase difference smaller than the first phase difference, in a case where the concavo-convex structure portion is the convex portion, in the first step, the width of the concavo-convex structure portion arranged in each of the regions is determined in such a manner that the region in which the width of the concavo-convex structure portion in the concavo-convex structure is equal to or greater than a predetermined first threshold value becomes the second phase difference region, and the region in which the width of the concavo-convex structure portion in the concavo-convex structure is smaller than the first threshold value becomes the first phase difference region, in a case where the concavo-convex structure portion is the concave portion, in the first step, the width of the concavo-convex structure portion arranged in each of the regions is determined in such a manner that the region in which the width of the concavo-convex structure portion in the concavo-convex structure is equal to or smaller than a predetermined second threshold value becomes the second phase difference region, and the region in which the width of the concavo-convex structure portion in the concavo-convex structure is greater than the second threshold value becomes the first phase difference region.

18. The method of manufacturing a lens for terahertz waves according to claim 17, wherein: In the first step, the width of the concave-convex structure portion arranged in each of the regions is determined in such a manner that at least the first region constitutes the second phase difference region.

19. The method of producing a terahertz lens according to claim 17, wherein: In the first step, the concave-convex structure has a plurality of repeating units each including one set of the plurality of regions, the plurality of repeating units are arranged in the prescribed direction, the width of the concave-convex structure portion arranged in each of the regions is determined in such a manner that at least one of the repeating units has a phase distribution having a width greater than 2π.

20. The method of producing a terahertz lens according to claim 18, wherein: In the first step, the concave-convex structure has a plurality of repeating units each including one set of the plurality of regions, the plurality of repeating units are arranged in the prescribed direction, the width of the concave-convex structure portion arranged in each of the regions is determined in such a manner that at least one of the repeating units has a phase distribution having a width greater than 2π.

21. The method of producing a terahertz lens according to any one of claims 17 to 20, wherein: In the first step, the width of the concave-convex structure portion arranged in each of the regions is determined in such a manner that the height and the width of the concave-convex structure portion corresponding to each of the plurality of regions are sizes capable of suppressing reflection of terahertz waves at the interface between the concave-convex structure and air.

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