Control of antiblaze angle in stepped diffraction gratings and related applications

Abstract

A stepped diffraction grating and a method for manufacturing the same are disclosed. Multiple parallel grating lines are formed on the substrate surface by forming multiple laminated layers made of a light-transmitting material. In cross-section, each grating line has an upper layer having an upper surface with a first end and a second end, a bottom layer having a bottom surface in contact with the substrate surface and an upper surface having a first end and a second end, an ascending step portion extending at an ascending step angle between 10 and 60 degrees, and a descending step portion extending at a descending step angle between the ascending step angle and 89 degrees.

Description

【Technical Field】 【0001】 This application claims priority to U.S. Provisional Application No. 63 / 472,463, filed Jun. 12, 2023, and U.S. Patent Application No. 18 / 670,486, filed May 21, 2024, the entire contents of each of which are incorporated herein by reference. 【0002】 This disclosure generally relates to optical structures, and more particularly to diffraction gratings. 【Background Art】 【0003】 Diffraction gratings, such as input gratings of optical waveguides, can be manufactured to have a grating line structure on the sub-micron order in order to diffract light with very high uniformity. However, due to their fine scale and structure, the individual lines of the diffraction grating are prone to deformation during the manufacturing process. Further, as part of the manufacturing process, when a further material layer is coated on a grating manufactured on a very fine scale, the coating thickness may be non-uniform at each part of the grating line due to the grating structure. 【0004】 Furthermore, when light is incident on the input grating of the waveguide, the light is coupled into the waveguide and undergoes total internal reflection within the waveguide body. During the internal reflection, the light may be reflected to the opposite side of the input grating, and as a result, a part of the internally reflected light may be coupled and emitted in the reverse direction from the waveguide, which may reduce the efficiency of the waveguide. 【0005】 Typically, the manufacturing goal of a blaze diffraction grating is to achieve a grid line having a blaze plane oriented toward the substrate surface at a predetermined ascending step angle and an anti-blaze plane (opposite the blaze plane) oriented perpendicular to the substrate surface. If the anti-blaze plane is formed at a non-perpendicular angle to the substrate surface, this is usually due to an imperfection in the manufacturing process. For example, international patent application PCT / GB2014 / 050019, filed on January 6, 2014, and published as WO2014 / 108670A1, states that it is desirable to form a grid line or "groove" having an anti-blaze angle perpendicular to the substrate surface. 【0006】 The drawings are not always drawn to scale, and similar numbers may represent the same components from different perspectives. To facilitate the identification of specific elements or functions, the most significant digit of the reference number is the number of the drawing in which that element first appears. The attached drawings below show some non-exclusive examples. [Brief explanation of the drawing] 【0007】 [Figure 1] This shows a plan view of a stepped diffraction grating with multiple parallel grid lines, illustrating the principles related to several examples. [Figure 2] This diagram shows a cross-sectional view of the grid lines of a stepped diffraction grating with a 90-degree downward step section, along plane A, illustrating the principles relevant to several examples. [Figure 3] Figure 2 shows a cross-sectional view of the grid lines that have been deformed during manufacturing, illustrating the principles involved in several examples. [Figure 4] Figure 2 shows a cross-sectional view of a grid line covered with a uniform coating, illustrating the principles relevant to several examples. [Figure 5] Figure 2 shows a cross-sectional view of a grid line covered with a non-uniform coating, illustrating the principles relevant to several examples. [Figure 6] Figure 2 shows the angles of ascending and descending stairs in a cross-sectional view of the grid lines, illustrating the principles relevant to several examples. [Figure 7] Cross-sectional views of grid lines with descending stair angles of less than 90 degrees are shown in several examples. [Figure 8] Cross-sectional views of grid lines with a 60-degree downward staircase angle are shown in several examples. [Figure 9] The diagrams show cross-sectional views of grid lines with stepped staircase sections having a staircase angle of less than 90 degrees in several examples. [Figure 10] Cross-sectional views of masters and processing stamps for forming grid lines are shown for several examples. [Figure 11] A method 1100 for manufacturing stepped diffraction gratings is shown in several examples. [Figure 12] Cross-sectional views of grid lines with non-vertical layer surfaces are shown in several examples. [Figure 13] The images show cross-sectional views of the grid lines in Figure 12, covered with a uniform coating, in several examples. [Figure 14] This diagram shows a cross-sectional view of light incident on a waveguide with an input grating and reflected within the waveguide, illustrating the relevant principles with several examples. [Figure 15] Figure 14 shows a cross-sectional view of light incident on the waveguide, reflected along the first inverse coupling path, and exiting the waveguide, illustrating the principles related to several examples. [Figure 16] Figure 14 shows a cross-sectional view of light incident on the waveguide, reflected along the second inverse coupling path, and exiting the waveguide, illustrating the principles relevant to several examples. [Figure 17] The graphs show two performance indices, FOM1 and FOM2, against the descending step angle tested in simulations of stepped diffraction gratings in several examples. [Figure 18] Plan views of stepped diffraction gratings with parallel grating lines configured to propagate light along a single light propagation path are shown in several examples. [Figure 19] Plan views of stepped diffraction gratings having parallel grating lines configured to propagate light along multiple light propagation paths are shown in several examples. [Modes for carrying out the invention] 【0008】 This specification describes examples of stepped diffraction gratings having controlled descending steps and methods for manufacturing the same. The grating lines of a stepped diffraction grating are usually formed in a substantially triangular shape, having a base placed on the substrate surface, an ascending step section rising toward the apex at an ascending step angle, and a descending step section extending upward from the base toward the apex at a right angle (90 degrees, also referred to herein as a vertical angle). However, the examples described herein describe grating lines having descending steps with a descending step angle of less than 90 degrees (also referred to herein as inclined, tilted, or oblique). Methods for manufacturing grating lines of a stepped diffraction grating having descending steps with a descending step angle of less than 90 degrees are also described. 【0009】 Several embodiments described herein attempt to address one or more of the above-mentioned technical problems by providing a grid line having an inclined descending step. Deformation of the grid line during manufacturing, for example, deformation of the upper or descending step, or both, that occurs when removing a processing stamp used to imprint the grid line shape onto a molding material, can be reduced by making the inclination of the sides of the grid line gentler. For example, when a coating such as a coating of a reflective material or a high refractive index material, or a multilayer laminate of a dielectric material is formed on the upper surface of the grid line, the inclined shape of the grid line can improve the uniformity of the coating or reduce or eliminate irregularities in the coating. Finally, when a stepped diffraction grating with an inclined descending step of the grid line is used as an input grating to a waveguide, the amount of light that is inversely coupled and emitted from the waveguide may be reduced at certain wavelengths and certain descending step angles. This can increase the amount of light that propagates to the target position within the waveguide body or reduce the appearance of ghost images caused by light that is inversely coupled and emitted from the waveguide and then reflected back to another position within the waveguide. 【0010】 Figure 1 shows an overhead plan view of an example of a stepped diffraction grating 102 consisting of multiple parallel grid lines 200. Diffraction gratings can be used in many useful applications in the field of optics, including the operation of redirecting light in relation to waveguides. 【0011】 The example of the stepped diffraction grating 102 shown in Figure 1 is shown to have only a small number of grating lines 200 for simplification and visual clarity. However, it should be understood that some examples of stepped diffraction gratings 102 described herein may have hundreds or even thousands of grating lines 200. For example, some stepped diffraction gratings 102 have a period on the nanometer scale, such as 300 nm (the sum of the width of the grating lines 200 and the width of the groove between adjacent grating lines 200). This means that a stepped diffraction grating 102 with a width of 5 mm may have more than 15,000 grating lines 200. The nanometer-scale structures and manufacturing techniques described herein attempt to address one or more of the technical challenges that arise in such situations. 【0012】 Figure 2 shows a cross-sectional view of the grid lines 200 of a stepped diffraction grating 102, where the angle of the descending steps is vertical, passing through plane A in Figure 1. Plane A is perpendicular to the multiple parallel grid lines 200 of the stepped diffraction grating 102. 【0013】 The grid line 200 has, in cross-section, a bottom layer 202 formed on the substrate surface 208, an intermediate layer 204 formed on the upper surface 210 of the bottom layer 202, and an upper layer 206 formed on the upper surface 212 of the intermediate layer 204. The upper surface 214 of the upper layer 206 defines the height of the grid line. Each layer 202, 204, and 206 has a left side that forms an ascending staircase and a right side that forms a descending staircase. The number of layers forming the steps of the grid line can be at least two or any number greater than that. However, it should be understood that the more steps there are, the closer the stepped grid line approaches a true blaze structure (i.e., a structure with straight inclined surfaces that form an ascending staircase). 【0014】 In some examples, the grating lines 200 are formed from a light-transmissive material such as a transparent or translucent polymer. The light-transmissive material can be selected based on factors such as the mechanical properties during molding and curing and its refractive index. In some examples, the light-transmissive material may be a resin polymer, for example, a resin polymer added with nanoparticles and the like. 【0015】 During operation, the grating lines 200 cooperate with other grating lines 200 of the stepped diffraction grating 102 to change the direction of light by diffracting the passing light. Some aspects of the operation when the stepped diffraction grating 102 and the individual grating lines 200 diffract light will be described later with reference to FIGS. 14 to 16. 【0016】 FIG. 3 shows a cross-section of the grating lines as in FIG. 2, showing the state in which the grating lines are deformed during the manufacturing process. The deformation can occur from various processes used to form the grating lines on the nanometer scale. In this example, a deformation 302 has occurred in the uppermost layer of the grating lines, a part of the uppermost layer has been displaced to the right, and a recess 304 has been formed under the uppermost layer. This deformation 302 can occur when the material for forming the grating lines is subjected to a shearing force when the mold is peeled off upward from the substrate surface in a certain situation. 【0017】 FIG. 4 shows the grating lines 200 covered with a uniform coating 402. The coating 402 may be deposited on the upper side of the grating lines 200 after the formation of the grating lines 200, where the upper side can be regarded as all the surfaces exposed to the environment above the grating lines (for example, the upper surfaces 210, 212, 214, and the left and right surfaces of each layer 202, 204, 206). The coating 402 may be a coating of a reflective material, a coating of a high refractive index material (such as titanium dioxide (TiO2)), a coating of other functional materials, a multilayer laminate such as an alternating layer of TiO2 and SiO2, or a multilayer laminate of functional materials. 【0018】 The coating 402 shown in Figure 4 is close to an ideal coating in that it is relatively uniform across the upper side of the grid lines 200. However, in practice, when depositing material coatings at the nanometer scale, which characterize some of the grid lines described herein, achieving high uniformity in the distribution and thickness of the coating 402 presents a technical challenge. 【0019】 Figure 5 shows a non-uniform coating 402 deposited on the grid lines 200, which is a more typical actual manufacturing result. The coating material may be excessively thick on the 90-degree cliffs formed by the descending steps, because at least some of the coating material is deposited on the vertical side of the descending steps. Furthermore, the coating material tends to accumulate in sharp concave corners and deposit more thinly on vertical surfaces, which can result in depressions such as depression 502. One or both of these non-uniformities can be exacerbated by deformations such as deformation 302 and depression 304 shown in Figure 3, resulting from defects that occurred during manufacturing. Such non-uniformities can lead to a decrease in coating performance. 【0020】 Figure 6 shows the grid lines 200 and illustrates the concepts of ascending and descending stair angles. As defined herein, the ascending stair angle 606 of the grid lines 200 can be considered as the angle formed between the line 614 passing through the first end 602 of the top surface 210 of the bottom layer 202 and the first end 604 of the top surface 214 of the upper layer 206 and the substrate surface 208. As defined herein, the descending stair angle 608 of the grid lines 200 can be considered as the angle formed between the line 616 passing through the second end 612 of the top surface 210 of the bottom layer 202 and the second end 610 of the top surface 214 of the upper layer 206 and the substrate surface 208. (In Figure 6, it should be noted that line 616 is offset from the descending stair side of grid line 200 to improve visibility without affecting the descending stair angle 608.) As used herein, the term “layer edge angle” generally refers to the measured angle from the upper edge of the bottom layer of the stepped sidewall to the upper edge of the top layer of the stepped sidewall, and includes both the ascending stair angle and the descending stair angle described above. 【0021】 In some cases, the ascending stair angle, descending stair angle, or both may be calculated using different reference points than those described above. For example, the angle from a lower point on the substrate surface (e.g., the lowest point of the bottom layer, or the horizontal midpoint between two adjacent grid lines of the bottom layer) to a higher point on the top surface of the upper layer (e.g., the horizontal midpoint on the top surface of the upper layer) may be measured. Also, in each example, these angles may be measured using any partial combination of the lower and higher points described above, and it should be understood that the ascending stair angle and descending stair angle may use different higher points, lower points, or both in their measurements. In some cases, the ascending stair angle and descending stair angle may be measured by a line passing through the horizontal midpoint of two of the stair treads (e.g., the top surface of the bottom layer and the top surface of the upper layer). In some cases, such as when the height and width of the steps are uniform, the same angle value may be obtained from these measurements, but in other cases, such as when the height and width of the steps are uneven, the choice of angle measurement method may affect the measured angle value. In this specification, the ascending stair angle values ​​and descending stair angle values ​​are calculated as floor end angles, unless otherwise specified. 【0022】 Figure 7 shows an example of a grid line 700 having a descending stair angle 608 of less than 90 degrees. As described above, a grid line 700 having a non-vertical descending stair angle 608 exhibits a more inclined shape, which can address one or more of the technical challenges described above. 【0023】 The ascending stair section 702 of the grid line 700 has a stepped shape in cross-section, while the descending stair section 704 is straight in cross-section. In some examples, even if the processing stamp used to imprint the grid line 700 on the molding material has a stepped shape for the descending stair section, the manufacturing process may result in the descending stair section being straight, which is more likely to occur when the angle of the descending stair is very close to 90 degrees. Examples of grid lines having inclined surfaces in one or more layers will be described later with reference to Figures 12 and 13. 【0024】 Figure 8 shows the ascending stair angle 606 and descending stair angle 608 for grid line 800 where the descending stair section is a straight line. Similar to Figure 6, the ascending stair angle 606 is defined by a line passing through the first edge of the top surface of the bottom layer and the first edge of the top surface of the upper layer. In this example, the descending stair angle 608 is defined by the straight line of the descending stair section. 【0025】 In this example, at grid line 800, the descending step angle 608 is approximately 60 degrees. In each example described herein, the descending step angle 608 can vary from slightly less than 90 degrees (e.g., 85 degrees) to an angle as shallow as the ascending step angle 606. When the ascending step angle 606 and the descending step angle 608 are the same, light may not be properly redirected within the waveguide body, as will be discussed later with reference to Figures 14-16. This effect becomes more pronounced as the ascending step angle 606 and the descending step angle 608 become closer, and in some examples, this constitutes a practical constraint on the shallowness of the descending step angle 608. 【0026】 Figure 9 shows a grid line 900 having stepped shapes in both the ascending and descending stair sections. In this example, each layer 202, 204, and 206 has an ascending stair section 912, 910, and 908 (i.e., the left face in this figure) perpendicular to the substrate surface 208 at its first end (i.e., the left end in this figure). Furthermore, each layer 202, 204, and 206 has a descending stair section 906, 904, and 902 (i.e., the right face in this figure) perpendicular to the substrate surface 208 at its second end (i.e., the right end in this figure). The ascending stair angle 606 is defined by the top of each first end, and the descending stair angle 608 is defined by the top of each second end. For example, it is defined by a line passing through the second end 612 of the upper surface 210 of the bottom layer and the second end 610 of the upper surface 214 of the upper layer. 【0027】 Figure 10 shows the components used in the manufacture of a stepped diffraction grating according to the examples described herein. The components shown in Figure 10 will be described with reference to the exemplary method 1100 shown in the flowchart of Figure 11. 【0028】 Figure 11 shows an exemplary method 1100 for manufacturing a stepped diffraction grating with a controlled descending step angle. While the exemplary method 1100 shows a specific sequence of operations, this sequence is modifiable as long as it does not deviate from the scope of the disclosure. For example, some of the operations presented may be performed in parallel, or in a different order, provided that this does not substantially affect the functionality of method 1100. In other examples, separate components of an example apparatus or system implementing method 1100 may perform functions substantially simultaneously or in a specific order. 【0029】 In operation 1106, one or more grid lines are formed as masters. These masters are used to form molds. Masters can be, for example, hard masters or soft masters. Operation 1106 includes substeps 1102 and 1104. 【0030】 As shown in Figure 10, the master 1002 is a durable structure that functions as a positive model for one or more grid lines of the stepped diffraction grating 102. The upper part 1008 of the master 1002 functions as a model for one or more grid lines. The master 1002 may be formed from a durable and etchable material (referred to herein as the master material), such as silicon, glass, or quartz. 【0031】 In substep 1102, the master material is etched to form grooves between adjacent parallel grid lines. In the first region 1012, the master material is etched from the grid height (i.e., the height of the upper surface 214 of the upper layer 206 from the substrate surface 208) down to the substrate surface 208 to form the descending step vertical surface 906 of the bottom layer 202. 【0032】 In method 1100, after substep 1102, substep 1104 is repeated for each additional layer above the bottom layer 202. In substep 1104, in the next region, the master material is etched up to the top surface of the previously formed layer to form a descending step surface for the next layer above the previously formed layer. Thus, for example, in the example shown in Figure 10, the first iteration of substep 1104 includes forming a descending step elevation 904 of the intermediate layer by etching up to the top surface 210 of the bottom layer 202 in the next region 1014. 【0033】 After the final iteration of substep 1104, method 1100 proceeds to operation 1108. In operation 1108, a processing stamp 1004 is formed on the master 1002. As shown in Figure 10, the processing stamp 1004 is a stamp or mold formed across the upper 1008 of the master 1002, with the lower 1010 of the processing stamp 1004 shaped as a negative of the upper 1008 of the master 1002. In some examples, the processing stamp 1004 is formed from a moldable material such as a polymer and is hardened or otherwise solidified with the upper 1008 of the master 1002 imprinted on the lower 1010 to maintain the shape of the processing stamp 1004. In some examples, after the solidification of the processing stamp 1004, the lower 1010 is covered with a thin layer of a harder material such as a metal layer 1006. In some examples, the metal layer 1006 is formed from an electroformable metal such as nickel. 【0034】 Following operation 1108, method 1100 proceeds to operation 1110. In operation 1110, a processing stamp 1004 is imprinted on the light-transmitting material to form grid lines 200. In some examples, a layer of a relatively flexible or moldable light-transmitting material, such as a viscous resin, is deposited on the waveguide substrate (such as a glass substrate). Next, the processing stamp 1004 is pressed down onto the layer of light-transmitting material to form grid lines 200 inside the underside 1010 of the processing stamp 1004. The light-transmitting material is then cured or solidified by other means. In some examples, the polymer resin can be cured by passing ultraviolet light upward through the glass substrate and the layer of light-transmitting material. In some examples, it should be understood that the layer of light-transmitting material is located between the glass waveguide and the bottom layer of grid lines 200, and the upper end surface of the layer of light-transmitting material constitutes the substrate surface 208. Furthermore, the structure formed by the combination of the glass substrate that forms the waveguide body 1406 (for example, Figures 14 to 16) and the stepped diffraction grating (and, if necessary, the layer of light-transmitting material between them) forms or functions as a waveguide. However, in the examples described, please understand that the glass substrate below the stepped diffraction grating (and, if necessary, the layer of light-transmitting material) is referred to as the "waveguide body". 【0035】 After the light-transmitting material has solidified, the processing stamp 1004 is peeled upward from the imprinted shape of the grid lines 200. This operation presents challenges in maintaining the structural integrity of the grid lines 200 at the nanometer scale. This is because sharp peaks and vertical surfaces tend to adhere to the inside of the mold formed by the underside 1010 of the processing stamp 1004, and as the processing stamp 1004 is peeled upward, parts of the grid lines 200 may be torn or deformed from the rest of the structure. Similarly, certain shapes tend to leave incomplete filling of the shape of the underside 1010 of the processing stamp 1004 or deform as the processing stamp 1004 is peeled upward. Figures 12 and 13 show examples of typical grid line shapes formed by these manufacturing techniques. 【0036】 For clarity and simplicity, Figure 10 shows the master 1002 and the processing stamp 1004 in the shape of a single grid line. However, it should be understood that in some examples, the master 1002 or the processing stamp 1004 or both are manufactured to encompass many or all of the grid lines of the stepped diffraction grating 102, and each operation of Method 1100 is performed in one step on a portion of the stepped diffraction grating 102 or on the stepped diffraction grating 102 as a whole. 【0037】 Figure 12 shows an example of grid lines 1200 formed by a manufacturing technique such as the exemplary method 1100. Even when a processing stamp 1004 having a surface perpendicular to each layer 202, 204, and 206 is used, in reality, due to imperfections originating from the stamping, the layers have upward staircase vertical surfaces 1208, 1210, and 1212 and downward staircase vertical surfaces 1202, 1204, and 1206 having an inclined shape in cross-section. As a result, the layer edge angles formed between the downward staircase vertical surfaces 1202, 1204, and 1206 and the substrate surface tend to be angles between the downward staircase angle and 90 degrees. In some cases, when the descending stair angle 608 is close to 90 degrees, and the degree of inclination generated in the descending stair elevations 1202, 1204, and 1206 by the engraving process is sufficiently large, the descending stair section of the grid lines may resemble a straight line where the layer end angle is equal to, or substantially equal to, the descending stair angle, as shown by grid line 700 in Figure 7 or grid line 800 in Figure 8. 【0038】 In some examples, the shape of the grid lines 1200 is intentionally sloped rather than being sloped as a result of imperfections in the stamping process. In operation 1110, the grid lines 1200 may be formed using a processing stamp 1004 having a sloped surface instead of a vertical surface. Peeling such a processing stamp 1004 upward may reduce the risk of damage or deformation of parts of the grid lines 1200 because the sloped surface reduces the tendency to adhere to the lower side 1010 of the processing stamp 1004, and also increases the degree of freedom in the angle when peeling the processing stamp 1004 upward from the cured light-transmitting material. 【0039】 Figure 13 shows the grid lines 1200 of Figure 12 covered with coating 402. Examples of coating 402 include reflective coatings of TiO2 or other reflective materials as described above (see Figures 4 and 5), or multilayer laminates of materials. In the example in Figure 13, the coating 402 is deposited relatively uniformly on the grid lines 1200, and the non-uniformity shown in Figure 5 is largely avoided. In some examples, the generally inclined sides of the grid lines 1200 do not have sharp concave corners or vertical surfaces, which makes it easier to achieve uniformity of the coating 402. 【0040】 Figure 14 shows the operation of an exemplary input grating 1402 used as an input grating to the waveguide body 1406, implemented as a stepped diffraction grating 102 according to the examples described herein. The exemplary components shown in Figures 14 to 16 may operate as part of an optical assembly such as an augmented reality display or other device that projects light onto the waveguide body 1406 using the exit pupil 1410 of the optical engine and the input grating 1402. The purpose of this device is to couple the projected light to the waveguide body 1406 so that the light propagates along the length of the waveguide body 1406 by total internal reflection (TIR). If the light does not couple to the waveguide body 1406 (i.e., low input coupling efficiency), or if the light is reverse-coupled from the waveguide and exits through the exit pupil 1410 of the optical engine (i.e., high reverse coupling efficiency), or both, the overall efficiency of the device may be reduced, or spurious reflections may occur that produce ghost images or other undesirable false images. Therefore, it is desirable that the configuration of the components shown in Figure 14 increases the input coupling efficiency and decreases the reverse coupling efficiency. 【0041】 Each component shown in Figures 14 to 16 is described in spatial terms based on their position in the figures; for example, "downward" refers to the direction toward the bottom of the figure. However, each component can be positioned in any orientation relative to a given environment, and it should be understood that in Figures 14 to 16, each component is shown in the side section view such that the waveguide body 1406 has a waveguide thickness 1408 that enables total internal reflection. Similarly, the input grating 1402 is located on the upper surface of the waveguide body 1406 (in this case, the surface opposite to the exit pupil 1410 of the waveguide body 1406), and the exit pupil 1410 of the optical engine is located at a distance of optical engine standoff 1418 from the lower surface of the waveguide body 1406 (in this case, the surface opposite to the input grating 1402 of the waveguide body 1406). The input grid 1402 has an input grid diameter 1404 (assuming a circular input grid), which is shown as the width of the input grid 1402 along the length of the waveguide body 1406 and defines the centerline 1420. The exit pupil 1410 has an exit pupil diameter 1414 (assuming a circular exit pupil 1410), which is shown as the width of the exit pupil 1410 along the length of the waveguide body 1406 and defines the centerline 1422. The centerlines 1420 and 1422 of the input grid 1402 and the exit pupil 1410 are offset by the optical engine offset 1416. The specific shapes, spacings, and dimensions of the various components illustrated and described herein are intended to be illustrative only. 【0042】 In Figures 14-16, please note that the input grating 1402 is not drawn to scale, but rather schematically. In some cases, the input grating 1402 is several orders of magnitude thinner than the waveguide body 1406. For example, the height of the input grating 1402 (including the height of each grating line and the thickness of the underlying layer of light-transmitting material acting as the substrate surface 208) may be less than 500 nm, while the waveguide thickness 1408 may exceed 500 μm. Therefore, the actual input grating 1402 drawn to scale is too thin to be seen, and in the figures, the diffracted light from the input grating 1402 is shown as occurring at the interface between the waveguide body 1406 and the input grating 1402. Furthermore, the length and width of the waveguide are larger than the size of the input grating, for example, the diameter 1404 of a circular input grating 1402. Furthermore, while the schematic depiction of the input grid 1402 shows triangular grid lines with a 90-degree downward staircase angle in cross-section, it should be understood that the principle shown in Figures 14 to 16 is applicable to any configuration of the input grid 1402, including examples with downward staircase angles of less than 90 degrees as described herein. 【0043】 The optical engine (not shown) includes a projector or other light source and projects light rays through or via the exit pupil 1410 of the optical engine. In Figures 14 to 16, the exit pupil 1410 of the optical engine is not shown to scale with respect to the waveguide 1406 and input grating 1402, but is depicted schematically. Light propagation from the optical engine to the waveguide and light propagation within the waveguide are shown by light rays. For convenience, the exit pupil 1410 of the optical engine is divided into a very small section, of which position 1412 is an example showing the light path from the exit pupil of the optical engine to the waveguide and the light path within the waveguide. A portion of the light projected from the optical engine passes through the light exit position 1412 of the exit pupil 1410 of the optical engine as a light ray 1424. Ray 1424 enters the bottom surface of the waveguide body 1406 at an incident angle of 1426 with respect to the vertical line (i.e., the normal to the bottom surface of the waveguide body 1406 in this example). Upon entering the waveguide body 1406, the light is refracted at a waveguide refraction angle of 1428 with respect to the vertical line, becoming ray 1430. It should be understood that optical paths from different exit positions within the exit pupil of the optical engine can be traced in the same way. 【0044】 Subsequently, the light ray 1430 interacts with the input grating 1402 at an incident angle equal to the waveguide refraction angle 1428. The design of the input grating 1402 (geometric shape and characteristics, etc.) affects the tendency of the light ray 1430 to diffract in various directions and return to the waveguide body 1406. In particular, the change in the descending step angle of the grating lines of the input grating affects the amount of light diffracted in various directions, as will be explained in the "Design" section below with reference to Figures 15 and 16. Note that in this example, the waveguide geometry and input grating design are chosen so that the input grating operates during reflection. Other waveguide geometries with input gratings that operate during transmission are also possible. 【0045】 In the ideal case, all light is diffracted from the input grating 1402 at the intended angle, i.e., the angle shown as the first angle 1432 of the diffracted ray 1434, based on the design of the input grating 1402. In reality, the light is diffracted from the input grating 1402 to multiple orders of diffraction, but ray 1434, in this example, represents the first-order diffracted light with the highest diffraction power and contributes to the input coupling efficiency. Next, ray 1434 contacts the bottom surface of the waveguide body 1406 at the first angle 1432. Since this first angle 1432 is sufficient to cause total internal reflection, the light is reflected again at the bottom surface of the waveguide body 1406 at the first angle 1432 as ray 1436. Ray 1436 travels toward the top surface of the waveguide and, upon contact with the input grating 1402 at the same first angle 1432, interacts with the input grating 1402 again and is diffracted to multiple orders of diffraction. In the ideal case, the zero-order ray 1438, diffracted at a first angle 1432, carries most of the optical power and propagates toward the bottom of the waveguide, from where it undergoes total internal reflection at the first angle 1432. In the ideal case, the light propagates along the length of the waveguide at a first angle 1432 as zero-order diffraction of ray 1436 at the input grating 1402, total internal reflection of ray 1438 at the bottom, zero-order diffraction of ray 1440 at the input grating 1402, total internal reflection of ray 1442 at the bottom, and so on. It should be understood that because the size of the input grating is small compared to the length and width of the waveguide, the total internally reflected rays from the bottom of the waveguide will, at some point along the length of the waveguide, be incident on the top of the waveguide where the input grating does not extend. The rays then move up and down within the waveguide via total internal reflections at the top and bottom of the waveguide, moving toward the right in Figure 14. The overall input coupling efficiency for a given incident angle 1426 from the optical engine exit pupil 1410 is determined by considering multiple optical paths from all minute elements of the optical engine exit pupil 1410 (e.g., each optical exit position 1412) at incident angle 1426, including re-interactions with the input grating 1402. The number of re-interactions with the input grating 1402 is determined by the optical path from the optical engine exit pupil 1410, and by the incident angle at the bottom of the waveguide, as well as the optical engine exit pupil size and the geometry of the input grating relative to the geometry of the waveguide.By applying an approach similar to that described herein, the overall input coupling efficiency can be determined as a function of the angle of incidence from the optical engine exit pupil 1410 across the entire field of view. 【0046】 Thus, Figure 14 illustrates the ideal case in which light projected from the optical engine is coupled to the waveguide body 1406. In this case, the projected light propagates along the length of the waveguide body 1406 in the direction of optical propagation 1444 by diffraction, total internal reflection, or both, to reach further optical components (such as an output grating, reflector, or simply the output end of the waveguide) configured to redirect the light elsewhere. In some examples, the input coupling efficiency of the configuration shown in Figure 14 is affected by factors such as the wavelength of the projected light and the angle of incidence 1426. However, the case shown in Figure 14 is considered ideal in terms of light incident on the waveguide re-coupling out of the waveguide. In contrast, Figures 15 and 16 show examples in which this ideal situation is not achieved. 【0047】 Figure 15 shows a cross-sectional view of the configuration in Figure 14, showing light incident on the waveguide body 1406, reflected, and exiting the waveguide body 1406 along the first reverse coupling path. Figure 15 shows a non-ideal case where some of the projected light exits the waveguide body 1406 via reverse coupling, and some of it returns towards the exit pupil 1410. This not only results in the loss of some of the projected light, but can also cause further spurious reflections that are reflected at various parts of the optical engine and return back into the waveguide body 1406, potentially leading to interference, ghost images that deviate from the intended image (and in some cases, images that are inverted from the intended orientation), and other visual false images. 【0048】 The projected light follows the same initial path as the light in Figure 14. For example, the projected light from the optical engine passes through the optical engine's exit pupil 1410 at the light exit position 1412 as ray 1424. Ray 1424 strikes the bottom surface of the waveguide body 1406 at an incident angle 1426. When the light enters the waveguide body 1406, it is refracted at a waveguide refraction angle 1428 to become ray 1430. 【0049】 Next, ray 1430 interacts with the input grating 1402, as described in relation to Figure 14. Some of the light is diffracted at an unintended angle, namely the same waveguide refraction angle 1428 as ray 1430, becoming ray 1502, while the remaining light is diffracted to other orders of diffraction, including ray 1434 shown in Figure 14. 【0050】 Ray 1502 intersects the bottom surface of the waveguide body 1406 at a waveguide refraction angle of 1428, thus avoiding total internal reflection. Instead, it exits the waveguide body 1406 in reverse coupling and, in the medium outside the waveguide, travels towards the exit pupil 1410 as ray 1504 at a refraction angle (equal to the incident angle 1426 in this example). Consequently, ray 1502 represents light that is lost from the waveguide body 1406 and cannot be used to form the intended image. Furthermore, ray 1504 may overlap with the exit pupil 1410 at the first return path position 1506. In this case, ray 1504 may travel towards the optical engine, be reflected by the optical engine, return towards the waveguide body 1406, and recombine with the waveguide body 1406 at a position different from the intended one. Thus, some of the light from each pixel of the image projected by the optical engine may follow the first inverse coupling path shown in Figure 15, be reflected by the optical engine (or other components), be inverted as a mirror image of the intended image, and recombine into the waveguide at a different position than the light that follows the desired path in Figure 14. This results in a "ghost image" at the output of the waveguide body 1406, which is mirrored and shifted from the intended position. Therefore, it is desirable to reduce the amount of light that follows the first inverse coupling path by adjusting the structure of the grid lines of the input grid 1402. 【0051】 Various factors, including the structural details of each grid line of the input grid 1402, can affect the likelihood that light is diffracted from the input grid 1402 at a waveguide refraction angle of 1428 rather than a first angle of 1432 when light strikes the input grid 1402 at a waveguide refraction angle of 1428. The technical studies described in the following "Design" section show that changes in the grid line structure (in particular, changes in the descending step angle) can affect the amount of light reflected along the first inverse coupling path shown in Figure 15, and thus its contribution to the inverse coupling efficiency. The overall inverse coupling efficiency of this first inverse coupling path at a given incident angle 1426 from the optical engine exit pupil 1410 is determined by considering the optical path from all minute elements of the optical engine exit pupil 1410 at incident angle 1426. Similar methods to those described herein can be applied to determine the overall inverse coupling efficiency of this first inverse coupling path as a function of the incident angle from the optical engine exit pupil 1410 over the entire field of view. 【0052】 Figure 16 shows a cross-sectional view of the configurations in Figures 14 and 15, illustrating the light incident on the waveguide body 1406, reflected, and exiting the waveguide body 1406 along the second inverse coupling path. Thus, Figure 16 illustrates another non-ideal case in which a portion of the projected light exits the waveguide body 1406 via inverse coupling. While the first inverse coupling path in Figure 15 can be considered a non-ideal case resulting from zero-order diffraction by the input grating, the second inverse coupling path in Figure 16 can be considered a non-ideal case caused by both a positive first-order diffracted ray from the input grating 1402 and the subsequent re-interaction of the light with the input grating 1402, resulting in a negative first-order diffracted ray at a different location on the input grating 1402. 【0053】 In Figure 16, the projected light follows the same initial path as the light in Figures 14 and 15. A portion of the projected light from the optical engine passes through the light emission position 1412 of the exit pupil 1410 of the optical engine as ray 1424. Ray 1424 strikes the bottom surface of the waveguide body 1406 at an incident angle 1426. Upon entering the waveguide body 1406, the light is refracted at a waveguide refraction angle 1428 to become ray 1430. 【0054】 Then, ray 1430 interacts with the input grating 1402. Similar to Figure 14, a portion of the light is first diffracted as a positive first-order diffracted ray 1434 at the intended first angle 1432. Ray 1434 is again reflected at the first angle 1432 from the bottom surface of the waveguide body 1406 via total internal reflection as ray 1436. 【0055】 Ray 1436 is incident on the input grating 1402 at a first angle 1432 and diffracts into multiple diffraction orders, including a negative first-order diffracted ray 1604. Ray 1604 has the same unintended angle as the zero-order diffracted ray 1502 in Figure 15, i.e., a waveguide refraction angle of 1428. As a result, the diffracted ray 1604 exits the waveguide body 1406 in reverse coupling, refracts in the medium outside the waveguide at the refraction angle (incident angle 1426 in the illustrated example) to become ray 1606, which coincides with the exit pupil 1410 at the second return path position 1602. The reverse coupling efficiency of this second optical path indicates how much of the projected light follows the second reverse coupling path in Figure 16. For the same reasons as reducing the reverse coupling efficiency of the first path in Figure 15, it is desirable to reduce the reverse coupling efficiency of this second path, for example, by reducing the amount of light lost due to reverse coupling and reducing the likelihood of ghost images caused by this second reverse coupling path (in addition to the ghost images generated by the first reverse coupling path in Figure 15). The overall reverse coupling efficiency of this second reverse coupling path at a given incident angle 1426 from the optical engine exit pupil 1410 is determined by considering the optical path from all minute elements of the optical engine exit pupil 1410 at incident angle 1426. To determine the overall reverse coupling efficiency of this second reverse coupling path as a function of the incident angle from the optical engine exit pupil 1410 over the entire field of view, a method similar to that described herein can be applied. 【0056】 It should be understood that the reverse coupling paths shown in Figures 15 and 16 represent only a portion of the possible reverse coupling paths. Other reverse coupling paths involving different combinations of diffraction orders resulting from re-interaction with the input grating 1402 of light may also contribute to the reverse coupling efficiency. The efficiency of each reverse coupling path may be influenced by factors such as the specific angle achieved by the optical assembly, the dimensions and spacing of the waveguide body 1406 and other components, the wavelength of the propagated light, and the diameters of the input grating 1402 and the exit pupil 1410. 【0057】 design 【0058】 To clarify how different descending step angles of stepped grid lines affect the input coupling efficiency and inverse coupling efficiency of optical assemblies as shown in Figures 14 to 16 for light of various wavelengths, the behavior of various input grid structures was modeled. In one embodiment of the present invention, simulations were performed using an input grid 1402 with a descending step angle of 90 to 60 degrees for three different wavelengths of light (470 nm blue (B) light, 530 nm green (G) light, and 620 nm red (R) light) incident on the waveguide body 1406 at various incident angles 1426 (-12 degrees to 12 degrees). 【0059】 The modeled optical assembly has the following characteristics: TIFF2026520056000002.tif178170 【0060】 The performance of the optical assembly described above is quantified using the following different figures of merit (FOM): (a) input coupling efficiency as a function of wavelength and angle of incidence, (b) aggregated reverse coupling efficiency defined as the sum of reverse coupling efficiencies from multiple reverse coupling paths as a function of wavelength and angle of incidence, (c) FOM1, and (d) FOM2. FOM1 and FOM2 take into account the combined effects of all wavelengths and all angles of incidence within the field of view. FOM1 refers to the effective input coupling efficiency obtained by summing the input coupling efficiencies over wavelength and angle of incidence and normalizing this sum by the number of wavelengths and angles of incidence used in the simulation. FOM2 is defined as the ratio of the effective input coupling efficiency to the effective aggregated reverse coupling efficiency from multiple reverse coupling paths, summed over wavelength and angle of incidence. FOM1 and FOM2 are useful indicators for evaluating the overall performance of the designed optical assembly. 【0061】 Figure 17 graphs the latter two performance indices, FOM1 and FOM2, against the descending stair angle tested in the simulation. The axis for the descending stair angle 1706 spans from 90 degrees on the left to 60 degrees on the right. Graph 1710, showing FOM2 (mapped to the axis of FOM2 1704), peaks at 65 degrees, while graph 1708, showing FOM1, remains virtually unchanged. 【0062】 The simulation results reveal several notable findings regarding the variation in the descending step angle of each grid line in the input grid 1402. Firstly, a decrease in the descending step angle from 90 degrees results in a small change in input coupling efficiency, but this effect is modest across all simulated light wavelengths and incident angles for descending step angles between 90 and 60 degrees. This is reflected in the relatively flat variation of FOM1 1708 when the descending step angle is in the range of 90 to 60 degrees. Secondly, the aggregate inverse coupling efficiency decreases as the descending step angle decreases. This is demonstrated by a 30% improvement in FOM2 1710 with an approximately 2% decrease in FOM1 1708. 【0063】 In some examples, stepped diffraction gratings have grating lines in which the descending step angle, ascending step angle, or both vary in different regions of the stepped diffraction grating. For example, when light propagates mainly within the waveguide body 1406 from an input region (e.g., the region where the input diffraction grating is located) to one or more output regions (e.g., multiple regions where multiple output diffraction gratings are located), the intensity of the light tends to decrease as the light progresses along the light propagation path from the input region to one of the output regions. This means that as the light moves away from the input region and approaches the output region, a high input coupling efficiency (e.g., represented by FOM1 1708) becomes more important than a low reverse coupling efficiency (e.g., represented by FOM2 1710). Based on the above simulation results, according to the example simulation parameters listed in Table 1 above, the increase in input coupling efficiency is very small at a descending step angle close to 80 degrees, while a descending step angle of about 65 degrees results in a favorable ratio of input coupling efficiency to reverse coupling efficiency. Therefore, in some examples, a stepped diffraction grating is configured to propagate light along an optical propagation path that begins in a first region (e.g., a region near the input region) and ends in a second region (e.g., a region near the output region), and its parallel grating lines are configured to have a first descending step angle in the first region and a second descending step angle in the second region, with the first descending step angle being closer to 90 degrees than the second descending step angle. For example, a stepped diffraction grating may have grating lines with an angle of 90 degrees in the first region near the input region and an angle of 60 degrees in the second region near the output region. 【0064】 Figure 18 shows the stepped diffraction grating 102 of Figure 1, which has parallel grating lines 200 configured to propagate light along a first optical propagation path 1806. The first optical propagation path 1806 roughly corresponds to the optical propagation direction 1444 shown in Figure 14. The actual path along which light travels is a meandering path due to total internal reflection, as explained above with reference to Figures 14 to 16, but the optical propagation direction 1444 and the first optical propagation path 1806 indicate the overall direction in which light travels within the waveguide body 1406. 【0065】 In some examples, the grooves defined between two adjacent grid lines of a stepped diffraction grating have a generally constant width. In other examples, the width of these grooves may vary in different regions of the stepped diffraction grating, vary within a portion of the stepped diffraction grating (e.g., continuously), or vary across the entire region (e.g., across the optical propagation direction 1444). In some examples, the width of the grooves may vary in accordance with the change in the descending step angle. For example, as the descending step angle decreases, the descending step portion of each grid line may be extended further (e.g., to the right in the illustrated example) to keep the period of the stepped diffraction grating constant, thereby narrowing the grooves between the grid lines accordingly. Thus, for example, the period defined by the sum of the groove width and the grid line width may be kept constant, with wider grooves for grid lines having smaller descending step angles and narrower grooves for grid lines having larger descending step angles. 【0066】 Figure 19 shows a stepped diffraction grating 1912 having multiple sets of parallel grating lines configured to propagate light along multiple optical propagation paths. In a first region 1802 near the input (for example, the first region defines or is located near the input diffraction grating), the grating lines 200 have a first descending step angle (e.g., 90 degrees). As light propagates along the first optical propagation path 1806 perpendicular to the grating lines 200, the descending step angle may decrease continuously or remain constant until a new region is reached. 【0067】 At the end of the first optical propagation path 1806, in the second region 1804, the light strikes the second grid line group 1914, and the light is split into a second optical propagation path 1910 perpendicular to the first grid line group 200 and a third optical propagation path 1902 perpendicular to the second grid line group 1914. The second optical propagation path 1910 eventually exits the second region 1804 and strikes the third grid line group 1916, where the light is split again, and a portion of this light follows the fourth optical propagation path 1904 and proceeds toward the fourth region 1906. The third optical propagation path 1902 eventually reaches the third region 1908. 【0068】 Thus, the superimposed grid lines shown in Figure 19 generate the following multiple optical propagation paths for light traveling from the first region 1802. Specifically, individual optical propagation paths 1806, 1910, 1902, and 1904 are generated, as well as a path along the first optical propagation path 1806 and the third optical propagation path 1902, a path along the first optical propagation path 1806 and the second optical propagation path 1910, a path along the first optical propagation path 1806, the second optical propagation path 1910, and the fourth optical propagation path 1904, and a path along the second optical propagation path 1910 and the fourth optical propagation path 1904. In each of these cases, the light may travel from one region to another region further from the input (e.g., from region 1802 to region 2 to region 1804, from region 1802 to region 4 to region 1906, from region 2 to region 3 to region 1908, etc.), and the descending step angles of the grid lines in the two regions may differ such that the descending step angle of the grid line in the region closer to the input is closer to 90 degrees (e.g., 80 degrees or 90 degrees) compared to the grid line in the region further from the input (e.g., 60 degrees). 【0069】 Generally, the decrease in reverse coupling efficiency due to a smaller descending step angle is more pronounced for blue and green light than for red light, where the change in reverse coupling efficiency is relatively negligible. Specifically, the simulated blue light (wavelength 470 nm) and green light (530 nm) showed the minimum combined reverse coupling efficiency when the descending step angle was approximately 60 degrees. Furthermore, the decrease in combined reverse coupling efficiency with respect to the decrease in the descending step angle corresponds to the baseline of a descending step angle of 90 degrees. In the optimal case, FOM2 1710 increased by 30%, while FOM1 1708 remained almost constant (with only a 2% fluctuation), indicating that the effective reverse coupling efficiency decreased significantly compared to the effective input coupling efficiency. 【0070】 It should be understood that when the descending stair angle of the grid lines is smaller than the ascending stair angle, it tends to reverse the direction in which reflected light propagates along the length of the waveguide. When the descending stair angle is smaller than the ascending stair angle, the descending stair section functions as an ascending stair section instead, and the input grid sends most of the light to the wrong end of the waveguide. Furthermore, this behavior appears to some extent as the descending stair angle approaches the ascending stair angle, and simulation results suggest that the input coupling efficiency continuously decreases when the descending stair angle becomes small enough to fall below 60 degrees. Therefore, it is beneficial to select a descending stair angle that does not excessively reduce the input coupling efficiency but reduces the combined inverse coupling efficiency. 【0071】 Thus, in the design of the input grid for waveguides, a specific descending step angle can be selected based on factors such as the ascending step angle, the incident angle of the projected light from the optical engine, and the wavelength of the projected light. In the typical case where the ascending step angle is between 10 and 45 degrees, a descending step angle of 65 degrees can be selected to reduce the combined reverse coupling efficiency without significantly reducing the input coupling efficiency. Alternatively, a descending step angle of 80 degrees can be selected to maximize the input coupling efficiency while suppressing the reduction in reverse coupling efficiency. These results are expected to be applicable to various ranges of ascending step angles with appropriate modifications, for example, at least partially applicable to ascending step angles between 10 and 60 degrees, and very well applicable to ascending step angles between 20 and 25 degrees. 【0072】 The exemplary stepped diffraction gratings described herein may be formed using grid lines of uniform dimensions throughout the stepped diffraction grating, or different parts of the stepped diffraction grating may be formed using grid lines of different dimensions. For example, the descending step angle can be adjusted over the entire width of the stepped diffraction grating such that the grid lines at the near end of the stepped diffraction grating operate according to a first set of optical parameters, while the grid lines at the far end of the stepped diffraction grating operate according to a second set of optical parameters. Adjustment across different parts of the stepped diffraction grating is beneficial in some examples, for instance, when it is necessary to achieve uniformity of light emitted from the waveguide (i.e., output coupled) by having each part of the light output coupled from the waveguide over the entire width of the stepped diffraction grating, thereby increasing the output coupling efficiency at the far end compared to the near end. 【0073】 In some examples, the stepped diffraction grating may comprise diffraction elements formed using a different structure in which the cross-sectional shape passing through a plane parallel to the direction of light propagation is as described herein (for example, with defined ascending and descending steps). 【0074】 conclusion 【0075】 As described above, each example described herein attempts to address one or more technical challenges associated with stepped diffraction gratings. Deformation during the manufacturing of the grating lines can be reduced by a gentler slope on the sides of the grating lines. The sloped shape of the grating lines can improve the uniformity of the coating and reduce or eliminate protrusions in the coating. Finally, for certain wavelengths of light and descending step angles, the amount of light that is inversely coupled and emitted from the waveguide can be reduced. 【0076】 Accordingly, according to the examples described herein, stepped diffraction gratings and methods for manufacturing the same are provided, which include grating lines having a descending step angle of less than 90 degrees. 【0077】 Example 1 is a method for manufacturing a stepped diffraction grating, comprising forming a plurality of parallel grid lines on a substrate surface, wherein each grid line is formed by forming a plurality of laminated layers made of a light-transmitting material and extending from the substrate surface, and the laminated layers are formed such that, in a cross-section in a plane perpendicular to the plurality of parallel grid lines, each grid line has the following components: an upper layer having an upper surface separated from the substrate surface by the grid height and having a first end and a second end; a bottom layer having a bottom surface in contact with the substrate surface and an upper surface having a first end and a second end; an ascending step portion having an ascending step angle defined with respect to the substrate surface, the ascending step angle being between 10 and 60 degrees; and a descending step portion extending from the second end of the upper surface of the upper layer to the second end of the upper surface of the bottom layer, having a descending step angle defined with respect to the substrate surface, the descending step angle being greater than the ascending step angle and less than 80 degrees, the laminated layers are formed such that each grid line has 【0078】 In Example 2, the subject of Example 1 is further modified to include forming each grid line, which involves forming a grid line master, forming a processing stamp on the master, where the lower side of the processing stamp is shaped as the negative of the upper side of the master, and imprinting the processing stamp onto a light-transmitting material to form the grid line, wherein forming the grid line master involves etching the master material from the grid height to the substrate surface in a first region to form a descending step surface of the bottom layer extending from the second end of the upper surface of the bottom layer to the substrate surface, and repeating for each of one or more additional layers, including the upper layer, etching the master material to the upper surface of the previously formed layer in the next region to form a descending step surface of the additional layer above the previously formed layer. 【0079】 In Example 3, the subject of Example 2 is extended to include forming a metal layer on the underside of the processing stamp after the processing stamp has been formed. 【0080】 In Example 4, the theme of Examples 2 and 3 is that, in a cross-section in a plan view, the descending step surface of each layer determines the layer edge angle with respect to the substrate surface, and the layer edge angle is greater than the descending step angle and less than 90 degrees. 【0081】 In Example 5, the subject matter of Examples 1 to 4 is further expanded to include forming each grid line by depositing a coating on the grid line after forming multiple laminated layers. 【0082】 In Example 6, the subject matter of Example 5 is expanded to include the inclusion of a coating material having a high refractive index. 【0083】 In Example 7, the subject of Example 6 is expanded to include the fact that the material having a high refractive index includes titanium dioxide (TiO2). 【0084】 In Example 8, the subject matter of Examples 1 to 7 is expanded to include the light-transmitting material comprising a transparent or partially transparent resin. 【0085】 In Example 9, the theme of Examples 1 to 8 is that the substrate surface is the upper surface of the waveguide body. 【0086】 In Example 10, the subject matter of Examples 1-9 is expanded to include the fact that the angle of the ascending stairs is between 15 and 45 degrees. 【0087】 In Example 11, the subject matter of Examples 1 to 10 is expanded to include the fact that the angle of the ascending stairs is between 14 and 30 degrees. 【0088】 In Example 12, the subject matter of Examples 1 to 11 is expanded to include the fact that the angle of the ascending stairs is between 20 and 25 degrees. 【0089】 In Example 13, the theme of Examples 1 to 12 is expanded to include the fact that the descending staircase angle is between 60 and 89 degrees. 【0090】 In Example 14, the subject matter of Examples 1 to 13 is expanded to include the fact that the angle of the descending stairs is between 60 and 70 degrees. 【0091】 In Example 15, the theme of Examples 1 to 14 is expanded to include a descending staircase angle of 65 degrees. 【0092】 In Example 16, the theme of Examples 1 to 15 is expanded to include a descending staircase angle of 80 degrees. 【0093】 In Example 17, the theme of Examples 1 to 16 is that the lattice height is between 50 nm and 250 nm. 【0094】 In Example 18, the subject of Example 17 is further comprising a stepped diffraction grating having grooves between each pair of adjacent grating lines having a width between 10 nm and 130 nm. 【0095】 In Example 19, the subject matter of Examples 10 to 18 is expanded to include a configuration in which multiple laminated layers are composed of a bottom layer, an intermediate layer, and an upper layer, with each layer having a thickness between 20 nm and 80 nm. 【0096】 In Example 20, the subject of Example 19 is further described by a plurality of laminated layers comprising a bottom layer having a width between 250 nm and 350 nm in a planar cross-section, an intermediate layer having a width between 200 nm and 300 nm in a planar cross-section, and an upper layer having a width between 80 nm and 150 nm in a planar cross-section. 【0097】 In Example 21, the subject matter of Examples 1 to 20 is expanded to include the fact that multiple parallel grid lines have a common ascending stair angle and a common descending stair angle. 【0098】 In Example 22, the theme of Examples 1 to 21 is extended to include the fact that at least two of the multiple parallel grid lines have different ascending stair angles. 【0099】 In Example 23, the theme of Examples 1 to 22 is extended to include the fact that at least two of the multiple parallel grid lines have different descending stair angles. 【0100】 In Example 24, the subject of Example 23 is extended to include the stepped diffraction grating being configured to propagate light along a light propagation path that begins in a first region and ends in a second region, wherein the parallel grating lines have a first descending step angle in the first region and a second descending step angle in the second region, and the first descending step angle is closer to 90 degrees than the second descending step angle. 【0101】 Example 25 is a stepped diffraction grating comprising a plurality of parallel grid lines on the surface of a substrate, each grid line having a plurality of laminated layers made of a light-transmitting material and extending from the surface of the substrate, wherein each grid line has the following components in a cross-section in a plane perpendicular to the parallel grid lines: an upper layer having an upper surface separated from the substrate surface by the grid height and having a first end and a second end; a bottom layer having a bottom surface in contact with the substrate surface and an upper surface having a first end and a second end; an ascending step portion extending from the first end of the upper surface of the upper layer to the first end of the upper surface of the bottom layer and having an ascending step angle defined with respect to the substrate surface, the ascending step angle being between 10 and 60 degrees; and a descending step portion extending from the second end of the upper surface of the upper layer to the second end of the upper surface of the bottom layer and having a descending step angle defined with respect to the substrate surface, the descending step angle being greater than the ascending step angle and less than 80 degrees. The laminated layers are configured such that each grid line has 【0102】 In Example 26, the theme of Example 25 is extended to include the fact that, in a cross-sectional view in a plan view, the descending step surface of each layer determines the layer edge angle with respect to the substrate surface, and that the layer edge angle is greater than the descending step angle and less than 90 degrees. 【0103】 In Example 27, the subject matter of Examples 25-26 is extended to include coating on each grid line. 【0104】 In Example 28, the subject matter of Example 27 is expanded to include the inclusion of a material having a high refractive index in the coating. 【0105】 In Example 29, the subject of Example 28 is expanded to include the fact that the material having a high refractive index includes titanium dioxide (TiO2). 【0106】 In Example 30, the subject matter of Examples 25-29 is expanded to include the light-transmitting material comprising a transparent or partially transparent resin. 【0107】 In Example 31, the theme of Examples 25-30 is that the substrate surface is the upper surface of the waveguide body. 【0108】 In Example 32, the theme of Examples 25-31 includes the fact that the lattice height is between 50 nm and 250 nm. 【0109】 In Example 33, the subject of Example 32 is further comprising a stepped diffraction grating having grooves between each pair of adjacent grating lines having a width ranging from 10 nm to 130 nm. 【0110】 In Example 34, the subject matter of Example 33 is expanded to include a configuration in which multiple laminated layers are composed of a bottom layer, an intermediate layer, and an upper layer, with each layer having a thickness between 20 nm and 80 nm. 【0111】 In Example 35, the subject of Example 34 is further described by a plurality of laminated layers comprising a bottom layer having a width between 250 nm and 350 nm in a planar cross-section, an intermediate layer having a width between 200 nm and 300 nm in a planar cross-section, and an upper layer having a width between 80 nm and 150 nm in a planar cross-section. 【0112】 In Example 36, the subject matter of Examples 25-35 is expanded to include the fact that multiple parallel grid lines have a common ascending stair angle and a common descending stair angle. 【0113】 In Example 37, the theme of Examples 25-36 is extended to include the fact that at least two of the multiple parallel grid lines have different ascending stair angles. 【0114】 In Example 38, the theme of Examples 25-37 is extended to include the fact that at least two of the multiple parallel grid lines have different descending stair angles. 【0115】 In Example 39, the subject of Example 38 is extended to include the stepped diffraction grating being configured to propagate light along a light propagation path that begins in a first region and ends in a second region, wherein the parallel grating lines have a first descending step angle in the first region and a second descending step angle in the second region, and the first descending step angle is closer to 90 degrees than the second descending step angle. 【0116】 In Example 40, the subject matter of Examples 25-39 is expanded to include the fact that the angle of the ascending stairs is between 15 and 45 degrees. 【0117】 In Example 41, the subject matter of Examples 25-40 is expanded to include the fact that the angle of the ascending stairs is between 14 and 30 degrees. 【0118】 In Example 42, the subject matter of Examples 25-41 is expanded to include the fact that the angle of the ascending stairs is between 20 and 25 degrees. 【0119】 In Example 43, the subject matter of Examples 25-42 is expanded to include the fact that the descending staircase angle is between 60 and 89 degrees. 【0120】 In Example 44, the subject matter of Examples 25-43 is expanded to include the fact that the descending staircase angle is between 60 and 70 degrees. 【0121】 In Example 45, the theme of Examples 25-44 is expanded to include a descending staircase angle of 65 degrees. 【0122】 In Example 46, the theme of Examples 25-45 is expanded to include a descending staircase angle of 80 degrees. 【0123】 Example 47 is at least one machine-readable medium that stores instructions causing the processing circuit to perform a process that, when executed by the processing circuit, carries out one of the processes described in Examples 1 to 46. 【0124】 Example 48 is an apparatus comprising means for carrying out any of Examples 1 to 46. 【0125】 Example 49 is a system for implementing any of Examples 1 to 46. 【0126】 Example 50 is a method for carrying out any of Examples 1 to 46. 【0127】 It should be understood that the various aspects of the above-described method may be combined in various forms, either as a whole or as a partial combination.

Claims

[Claim 1] A method for manufacturing a stepped diffraction grating, The step includes forming a plurality of parallel grid lines on the surface of the substrate, Each grid line is formed by forming multiple laminated layers made of a light-transmitting material that extend from the surface of the substrate. The laminated layer is formed such that, in a cross-section in a plane perpendicular to the plurality of parallel grid lines, each grid line comprises the following components: An upper layer having a top surface that is separated from the substrate surface by the lattice height, and having a first end and a second end, A bottom layer having a bottom surface in contact with the substrate surface and an upper surface having a first end and a second end, An ascending stair section, which extends from the first end of the upper surface of the upper layer to the first end of the upper surface of the bottom layer, and has an ascending stair angle defined with respect to the substrate surface, wherein the ascending stair angle is between 10 degrees and 60 degrees; A descending stair section, which extends from the second end of the upper surface of the upper layer to the second end of the upper surface of the bottom layer, and has a descending stair angle defined with respect to the substrate surface, wherein the descending stair angle is greater than the ascending stair angle and less than 80 degrees, The laminated layer is formed such that each grid line has method. [Claim 2] The method according to claim 1, Forming each grid line is Forming a master grid line, Forming a processing stamp on a master, where the lower side of the processing stamp is shaped as the negative of the upper side of the master, The process involves imprinting the aforementioned processing stamp onto the light-transmitting material to form the grid lines. Includes, Forming the master of the grid lines is In the first region, by etching the master material from the grid height to the substrate surface, a descending stepped surface is formed in the bottom layer, extending from the second end of the upper surface of the bottom layer to the substrate surface. For each of the one or more additional layers including the upper layer, the process of etching the master material in the following region up to the upper surface of the previously formed layer, thereby repeatedly forming a descending step surface of the additional layer above the previously formed layer, is performed. including, method. [Claim 3] The method according to claim 2, The further step includes forming a metal layer on the underside of the processing stamp after forming the processing stamp. method. [Claim 4] The method according to claim 2, In the cross-section in the aforementioned plane, the downward step surface of each layer determines the layer end angle with respect to the substrate surface. The aforementioned layer end angle is greater than the aforementioned ascending stair angle and less than 90 degrees. method. [Claim 5] The method according to claim 1, Forming each grid line is After forming the plurality of laminated layers, a coating is deposited on the grid lines. This also includes, method. [Claim 6] The method according to claim 5, The coating includes a material having a high refractive index. method. [Claim 7] The method according to claim 6, The aforementioned material having a high refractive index is titanium dioxide (TiO2). ２ ) including, method. [Claim 8] The method according to claim 1, The light-transmitting material includes a transparent or partially transparent resin. method. [Claim 9] The method according to claim 1, The substrate surface is the upper surface of the waveguide body. method. [Claim 10] The method according to claim 1, The angle of the ascending stairs is between 15 and 45 degrees. method. [Claim 11] The method according to claim 1, The angle of the ascending stairs is between 20 and 25 degrees. method. [Claim 12] The method according to claim 1, The angle of the descending stairs is greater than 60 degrees and less than 80 degrees. method. [Claim 13] The method according to claim 1, The angle of the descending stairs is greater than 60 degrees and less than 70 degrees. method. [Claim 14] The method according to claim 1, The angle of the descending stairs is 65 degrees. method. [Claim 15] The method according to claim 1, The lattice height is between 50 nm and 250 nm. method. [Claim 16] The method according to claim 15, The stepped diffraction grating further comprises grooves having a width between 10 nm and 130 nm between each pair of adjacent grating lines. method. [Claim 17] The method according to claim 16, The aforementioned plurality of laminated layers are composed of the bottom layer, the intermediate layer, and the upper layer. Each layer has a thickness between 20 nm and 80 nm. method. [Claim 18] The method according to claim 17, The aforementioned multiple laminated layers are The bottom layer having a width between 250 nm and 350 nm in the cross-section of the plane, The intermediate layer having a width between 200 nm and 300 nm in the cross-section of the plane, The upper layer having a width between 80 nm and 150 nm in the cross-section of the plane, Having, method. [Claim 19] The method according to claim 1, The plurality of parallel grid lines have a common ascending stair angle and a common descending stair angle. method. [Claim 20] The method according to claim 1, At least two of the aforementioned parallel grid lines have different ascending stair angles. method. [Claim 21] The method according to claim 1, At least two of the aforementioned parallel grid lines have different descending stair angles. method. [Claim 22] The method according to claim 21, The stepped diffraction grating is configured to propagate light along a light propagation path that begins in a first region and ends in a second region, and The aforementioned parallel grid lines are, The first region has a first descending stair angle, The second region has a second descending staircase angle, The first descending stair angle is closer to 90 degrees than the second descending stair angle. method. [Claim 23] A stepped diffraction grating, The substrate surface is provided with multiple parallel grid lines, Each grid line is made of a light-transmitting material and has multiple laminated layers extending from the surface of the substrate. The laminated layer is configured such that, in a cross-section in a plane perpendicular to the parallel grid lines, each grid line comprises the following components: An upper layer having a top surface that is separated from the substrate surface by the lattice height, and having a first end and a second end, A bottom layer having a bottom surface in contact with the substrate surface and an upper surface having a first end and a second end, An ascending stair section, which extends from the first end of the upper surface of the upper layer to the first end of the upper surface of the bottom layer, and has an ascending stair angle defined with respect to the substrate surface, wherein the ascending stair angle is between 10 degrees and 60 degrees; A descending stair section, which extends from the second end of the upper surface of the upper layer to the second end of the upper surface of the bottom layer, and has a descending stair angle defined with respect to the substrate surface, wherein the descending stair angle is greater than the ascending stair angle and less than 80 degrees, The laminated layer is configured such that each grid line has Stepped diffraction grating.

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