JP2022168217A - Diffraction optical element - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a diffraction optical element capable of further reducing 0-order diffraction light.

SOLUTION: A diffraction optical element 10 includes a diffraction layer 15 having a high refractive index portion 11 in which a plurality of protrusions 11a are disposed side by side in a cross section shape and a low refractive index portion 14 having a lower refractive index than the high refractive index portion 11 and including a recess 12 at least formed between the protrusions 11a. Each protrusion 11a has a saw-tooth-shape or a shape imitating a saw-tooth-shape by a multi-step contour shape. A slope inclining against a sheet face of the diffraction optical element 10 with the saw-tooth shape or the shape imitating the saw-tooth-shape by the multi-step contour shape has a concave curved surface concave toward the protrusions 11a.

SELECTED DRAWING: Figure 5

COPYRIGHT: (C)2023,JPO&INPIT

Description

The present invention relates to a diffractive optical element.

In recent years, the need for sensor systems has increased, such as the need for personal authentication to avoid security risks due to the spread of networks, the trend toward automatic driving of automobiles, and the spread of the so-called "Internet of Things". there is There are various types of sensors, and the information they detect is also diverse. One of them is to irradiate the object with light from a light source and obtain information from the reflected light. . For example, a pattern authentication sensor, an infrared radar, and the like are examples.

The light source of these sensors has a wavelength distribution, brightness, and spread according to the application. Visible light to infrared wavelengths are often used. In particular, infrared rays are not easily affected by external light, are invisible, and are widely used because they can be used to observe the inside of objects. there is As for the types of light sources, LED light sources, laser light sources, and the like are often used. For example, a laser light source with little spread of light is preferably used to detect a distant place, and an LED light source is preferably used to detect a relatively close place or to irradiate an area with a certain extent of spread. be done.

By the way, the size and shape of the target irradiation area does not necessarily match the spread (profile) of the light from the light source. There is a need. Recently, a diffusion plate called a Light Shaping Diffuser (LSD) has been developed that can shape the shape of light to some extent.
Another means for shaping light is a diffractive optical element (DOE). This applies the diffraction phenomenon when light passes through a place where materials with different refractive indices are arranged periodically. Although DOEs are designed primarily for light of a single wavelength, in theory they can be shaped into almost any shape. Further, in the above-described LSD, the light intensity in the irradiation area has a Gaussian distribution, whereas in the DOE, it is possible to control the uniformity of the light distribution in the irradiation area. Such characteristics of the DOE are advantageous in terms of high efficiency by suppressing irradiation to unnecessary areas and miniaturization of the device by reducing the number of light sources (see, for example, Patent Document 1).
In addition, DOE can be used with both parallel light sources such as lasers and diffuse light sources such as LEDs, and can be applied to a wide range of wavelengths from ultraviolet light to visible light and infrared light. .

When the DOE is used to uniformly irradiate a predetermined area with light, the 0th-order diffracted light may be concentrated, for example, near the center of the irradiated area, which may be a hindrance. This tendency was particularly strong when the light source was a laser. Conventionally, when an attempt was made to reduce the 0th-order diffracted light, the required 1st-order diffracted light also decreased accordingly. Therefore, it has been desired to reduce the 0th-order diffracted light while suppressing the decrease in the necessary 1st-order diffracted light.

It is said that by blazing the grating surface of the DOE, a specific wavelength can be efficiently concentrated into a specific order for diffraction. It has been conventionally practiced to configure as follows (for example, Patent Document 1).

However, there is still a lot of unnecessary 0th-order diffracted light with only the sawtooth (blaze) shape, and it has been desired to further reduce the 0th-order diffracted light.

JP-A-09-230121

SUMMARY OF THE INVENTION An object of the present invention is to provide a diffractive optical element capable of further reducing 0th-order diffracted light.

The present invention solves the above problems by means of the following solutions. In order to facilitate understanding, reference numerals corresponding to the embodiments of the present invention are used for explanation, but the present invention is not limited to these.

A first invention is a diffractive optical element (10) for shaping light, comprising a high refractive index portion (11) in which a plurality of convex portions (11a) are arranged side by side; ), and a diffraction layer (15) having a low refractive index portion (14) including recesses (12) formed at least between the protrusions (11a); The portion 11a) has a multistep shape formed by a plurality of stepped portions with different heights, and the high refractive index portion (11) has the largest deepest surface area per unit area and the largest This is the diffractive optical element (10) in which the area of the surface next to the upper surface is the smallest.

A second invention is the diffractive optical element (10) according to the first invention, wherein the area of the uppermost surface of the high refractive index portion (11) is the area of the lowermost surface of the high refractive index portion. A diffractive optical element (10) characterized by having an area of 0.6 to 0.9 times.

A third aspect of the invention is the diffractive optical element (10) according to the first aspect or the second aspect, wherein the high refractive index portion (11) extends from the deepest surface to the uppermost surface per unit area. The diffractive optical element (10) is characterized in that the area of each stepped portion gradually decreases toward the surface of .

A fourth aspect of the invention is a diffractive optical element (10) for shaping light, comprising: a high refractive index portion (11) in which a plurality of convex portions (11a) are arranged side by side in a cross-sectional shape; A diffraction layer (15) having a low refractive index portion (14) having a lower refractive index than the portion (11) and including a recess (12) formed at least between the protrusions (11a); The convex portion (11a) has a sawtooth shape or a shape imitating a sawtooth shape with a multistep contour shape, and the sawtooth shape or a sawtooth shape imitating a multistep contour shape of the diffractive optical element (10) The slope inclined with respect to the sheet surface is a diffractive optical element (10) having a concave curved surface recessed toward the convex portion (11a).

According to a fifth aspect of the invention, in the diffractive optical element (10) according to the fourth aspect, the convex portion (11a) has a plurality of stepped portions having different heights on at least one side of the side surface thereof. The diffractive optical element (10 ).

A sixth aspect of the invention is the diffractive optical element according to the fourth aspect or the fifth aspect, wherein the convex portion forms the sawtooth shape on at least one side of its side surface shape by a plurality of steps having different heights. It is a diffractive optical element characterized by having a multi-step shape similar to the diffractive optical element, and having the largest area per unit area of the deepest surface and the smallest area of the surface next to the uppermost surface.

A seventh invention is the diffractive optical element (10) according to the fifth invention or the sixth invention, wherein the height per step of the stepped portion is constant, and the width of the stepped portion varies depending on the location. A diffractive optical element (10) characterized in that the concave curved surface is simulated by being different.

In an eighth invention, in the diffractive optical element (10) according to the seventh invention, the x-axis is set in the direction in which the convex portions (11a) are arranged, and the direction in which the slopes increase is the plus of the x-axis. , the y-axis perpendicular to the sheet surface of the diffractive optical element (10) is set, the direction in which the convex portion (11a) projects is the positive direction of the y-axis, and the tip of the convex portion (11a) Let L be the total number of steps counted including , let f be the rate of decrease in width for each level, and let lv be the number of steps of the target step when counted with the lowest position of the recess (12) being 0. , when the height per step of the stepped portion is a constant value h and the width ratio of the level zero is C, the concave vertex of the level zero and each convex portion in the cross section of the concave curved surface modeled by the multi-step shape The curve that is the locus of the vertices of
Let S be the ratio of the x-coordinate to the pitch,
x′=0.5×f×lv ² +C×lv
S=P/{tw+Σx′i}
Σ is i=0 to L−1
When the top x, y coordinates of the staircase shape are
x=0.5×f×lv ² +C×lv
y = lv x h
A diffractive optical element (10) characterized by:

A ninth invention is the diffractive optical element (10) according to any one of the first invention to the eighth invention, wherein the high refractive index portion (11) A boundary between the convex portion (11a) and the concave portion (12) when viewed from the direction forms a diffraction grating having a pattern including at least one of a curved line and a polygonal line connecting a plurality of line segments. is a diffractive optical element (10).

A tenth invention is the diffractive optical element (10) according to any one of the first invention to the eighth invention, wherein the high refractive index portion (11) A grating cell array type (also referred to as "grating cell array type" or "GCA type") diffraction grating formed in a grid-like pattern in which a plurality of unit cells in which the same uneven shape is arranged side by side when viewed from the direction are tiled. A diffractive optical element (10) characterized by forming

According to the present invention, it is possible to suppress the reduction in the diffraction efficiency of the first-order light and reduce the zero-order light.

FIG. 4 is a plan view showing an example of a diffractive optical element in which the uneven shape of the diffraction grating seen from the normal direction of the sheet surface is formed in a regular or irregular pattern including curved lines at the boundaries between the convex portions and the concave portions. A plan view showing an example of a diffractive optical element in which the concave-convex shape of the diffraction grating seen from the normal direction of the sheet surface is formed in a lattice-like pattern in which a plurality of unit cells in which the same concave-convex shape is arranged side by side are tiled. is. 1B is a perspective view showing an example of a partial periodic structure in the example of the irregular type diffractive optical element shown in FIG. 1A; FIG. 1C is a perspective view showing an example of a partial periodic structure in the example of the GCA-type diffractive optical element shown in FIG. 1B; FIG. FIG. 2B is a cross-sectional view of the diffractive optical element cut at the position of arrows GG' in FIG. 2A; It is a figure explaining a diffraction optical element. 4A and 4B are diagrams for explaining a concave curved surface of a convex portion 11a in the diffractive optical element 10; FIG. It is the figure which showed the diffraction optical element 10 of this embodiment in comparison with the conventional form. FIG. 6B is a view showing the curve of the original design pattern superimposed on the view of FIG. 6A; FIG. 2 shows a diffractive optical element 10 having an 8-level multi-stage shape; It is a figure explaining the curve in the cross section of a concave curved surface, and a multistep shape. It is a figure which shows the specific example of the cross-sectional shape of 8 levels. In FIG. 9, the values of x and y are also written. It is a figure which shows the specific example of the cross-sectional shape of 4 levels. In FIG. 10, the values of x and y are also written. It is a figure explaining the intensity|strength measurement method of 0th-order diffracted light. FIG. 10 is a diagram showing a diffractive optical element of a comparative example; FIG. 5 is a diagram showing the results of measuring the intensity of 0th-order diffracted light for the diffractive optical element 10 of the present invention and a comparative example; It is a figure which shows the shape of Example 2 which changed the height per step. It is a figure which put together the result of a simulation. It is a figure which shows the example which imitated sawtooth shape by 16 steps|paragraphs. It is a graph of zero-order light intensity when C is changed when f=−0.02, t=0.8, and a pitch of 3284 nm with a diffraction angle of 15° of the diffraction grating. It is a graph of the zero-order light intensity when f is changed when C=0.25, t=0.8, and the pitch is 3284 nm with the diffraction angle of the diffraction grating being 15°. It is a graph of zero-order light intensity when t is changed when f=-0.02, C=0.25, and a pitch of 3284 nm with a diffraction angle of the diffraction grating of 15°. It is a graph of zero-order light intensity when C is changed when f=−0.02, t=0.8, and a pitch of 3284 nm with a diffraction angle of 15° of the diffraction grating. It is a graph of zero-order light intensity when f is changed when C=0.18, t=0.8, and a pitch of 3284 nm with a diffraction angle of the diffraction grating of 15°. It is a graph of zero-order light intensity when t is changed when f=−0.02, C=0.18, and a pitch of 3284 nm with a diffraction angle of 15° of the diffraction grating. FIG. 10 is a diagram showing the cross-sectional shape and simulation results of a diffractive optical element having a configuration in which the trajectory connecting the vertices of the present invention is a concave curved surface; FIG. 3 is a diagram showing a cross-sectional shape of a diffractive optical element having a theoretical structure in which vertices are arranged in a straight line and simulation results; Contrary to the present invention, it is a diagram showing a cross-sectional shape and simulation results of a diffractive optical element in which the trajectory connecting the vertices has a configuration of a convex curved surface. FIG. 5 is a plan view showing a diffractive optical element having a conventional structure and a diffractive optical element of the present invention side by side for comparison. FIG. 26 is a diagram showing the ratio of each surface shown in FIG. 26 to the area of the 4-level diffractive optical element according to the conventional ideal design of FIG. 26(a); FIG. 4 is a diagram showing the ratio of each surface to the area of an 8-level diffractive optical element according to a conventional ideal design; 26B is a diagram showing the ratio of each surface shown in FIG. 26 to the area of the 4-level diffractive optical element of the present invention shown in FIG. 26B. FIG. FIG. 4 is a diagram showing the ratio of each surface to the area of the 8-level diffractive optical element of the present invention; 26(a) and 26(b), the diffractive optical element is actually manufactured and the zero-order light is measured. It is a figure which shows the area ratio of three types of diffractive optical elements. FIG. 2 is a view of an ideally designed diffractive optical element viewed from the direction normal to the sheet surface; FIG. 2 is a view of a type 1 diffractive optical element viewed from the normal direction of the sheet surface; It is the figure which looked at the diffraction optical element of type2 from the normal line direction of a sheet surface. FIG. 4 is a diagram numerically showing simulation results of three types of diffractive optical elements; FIG. 4 is a graph showing simulation results of three types of diffractive optical elements; FIG. 3 shows an example of a black and white (grayscale) image acquired from a laser microscope; It is a figure which shows the result of having binarized the black-and-white image acquired from a laser microscope. FIG. 10 is a diagram showing an example in which level-3 is painted out; FIG. 10 is a diagram showing an example in which level-2 is filled; FIG. 10 is a diagram showing an example in which level-1 is filled; FIG. 10 is a diagram showing an example in which level-0 is painted out;

BEST MODE FOR CARRYING OUT THE INVENTION The best mode for carrying out the present invention will be described below with reference to the drawings.

(embodiment)
FIG. 1A is a plan view showing an example of a diffractive optical element in which the uneven shape of the diffraction grating seen from the normal direction of the sheet surface is formed in a regular or irregular pattern including curved lines at the boundaries between the convex portions and the concave portions. It is a diagram.
As an example, this embodiment can be applied to a diffractive optical element having a seemingly irregular uneven pattern as shown in FIG. 1A. In the following description, the diffractive optical element of the type shown in FIG. 1A is also called an irregular type. However, this irregular pattern may become a regular pattern depending on the target output pattern of the diffractive optical element. not something to do. In FIG. 1A, the irregular pattern is composed of curved lines, but depending on the target output pattern of the diffractive optical element, the pattern may be a polygonal line formed by connecting straight line segments or curved line segments. may also include Therefore, in the pattern of the irregular diffraction grating, the boundary between the convex portion and the concave portion connects the curved line and a plurality of line segments when viewed from the normal direction of the surface on which the uneven shape of the high refractive index portion (described later) is formed. and at least one of the polygonal lines.

FIG. 1B is an example of a diffractive optical element in which the concave-convex shape of the diffraction grating seen from the normal direction of the sheet surface is formed in a grid-like pattern in which a plurality of unit cells in which the same concave-convex shape is arranged side by side are tiled. It is a plan view showing the.
As another example, as shown in FIG. 1B, this embodiment can be applied to a diffractive optical element formed in a lattice pattern in which a plurality of unit cells in which the same concave-convex shape is arranged side by side are tiled. can. In the following description, the diffractive optical element of the type shown in FIG. 1B is also called a grating cell array type or a GCA type. In a grating cell array type diffractive optical element, the direction and angle of light diffracted by the diffraction grating is different for each unit cell, and diffractive optics that can obtain desired optical characteristics by tiling a large number of unit cells. elements are constructed. That is, in the grating cell array type diffractive optical element, the high refractive index portion is partitioned into a lattice when viewed from the normal direction of the surface on which the uneven shape is formed, and extends in a specific direction within the partition. The convex portions having the same shape are arranged side by side in a direction orthogonal to the specific extending direction, and the width and extending direction of the convex portions are different for each section.

FIG. 2A is a perspective view showing an example of a partial periodic structure in the example of the irregular diffractive optical element shown in FIG. 1A.
FIG. 2B is a perspective view showing an example of a partial periodic structure in the example of the GCA-type diffractive optical element shown in FIG. 1B.
FIG. 3 is a cross-sectional view of the diffractive optical element taken along arrows GG' in FIG. 2A.
In the following description, since it is necessary to grasp the cross-sectional shape peculiar to the GCA type, the description will be given mainly by taking the irregular type as an example. However, if the GCA type is cut at the position of the arrow GG' shown in FIG. 1A, it will have a similar cross-sectional shape, and as described above, the present invention can be similarly applied.
FIG. 4 is a diagram illustrating a diffractive optical element.
In addition, each figure shown below including FIG. 1 is a schematic diagram, and the size and shape of each part are shown exaggerated appropriately for easy understanding.
Also, in the following description, specific numerical values, shapes, materials, and the like are shown and described, but these can be changed as appropriate.

It should be noted that the terms used in the present invention to specify shapes and geometric conditions, and their degree, for example, terms such as "parallel", "perpendicular", "same", length and angle values, etc. Without being bound by a strict meaning, it is interpreted to include the extent to which similar functions can be expected.

In the present invention, "to shape light" means to control the traveling direction of the light so that the shape of the light projected onto the target object or target region (irradiation region) has an arbitrary shape. Say. For example, as shown in the example of FIG. 4, a light source unit 210 is prepared that emits light 201 (FIG. 4B) that forms a circular irradiation area 202 when directly projected onto a planar screen 200 . By transmitting this light 201 through the diffractive optical element 10 of the present invention, the irradiation area 204 can be made into a desired shape such as a square (FIG. 4A), a rectangle, a circle (not shown), or the like. It is said to "shape light".
By combining the light source unit 210 and at least one diffractive optical element 10 of the present embodiment, which is arranged at a position through which the light emitted by the light source unit 210 passes, the light can be irradiated in a shaped state. It can be an irradiation device.
In the present invention, the term "transparent" refers to a material that transmits at least the light of the wavelength used. For example, even if a material does not transmit visible light, if it transmits infrared light, it is treated as transparent when used for infrared applications.

The diffractive optical element 10 of this embodiment is a diffractive optical element (DOE) that shapes light. For example, the diffractive optical element 10 has a cross shape with respect to the light from the light source unit 210 that emits light with a wavelength of 500 nm. It is designed to spread the light in two intersecting bands.
The diffractive optical element 10 of this embodiment has different depths at positions A, B, C, and D shown in FIGS. 1A and 1B. That is, the diffractive optical element 10 has a multi-stage shape with four different heights. The diffractive optical element 10 usually has a plurality of regions having different periodic structures (partial periodic structures: regions E and F in FIGS. 1A and 1B, for example). 2A and 2B extract and show an example of the partial periodic structure.
As shown in FIG. 3, the diffractive optical element 10 has a high refractive index portion 11 in which a plurality of convex portions 11a are arranged side by side in a cross-sectional shape. In the GCA-type diffractive optical element, this high refractive index portion 11 extends in the depth direction of the cross section while maintaining the same cross-sectional shape. On the other hand, in an irregular-type diffractive optical element, if the cross-sectional position changes, the cross-sectional shape changes, and a large number of diffraction gratings with various cross-sectional shapes are arranged. In the irregular type, the cross-section for specifying the shape of the diffraction grating, that is, the cross-sectional structure for specifying the specific shape of the diffraction grating that affects the diffraction phenomenon of the diffracted light, is the law of the sheet surface. It is necessary to have a cross-sectional structure in a cross section cut in a direction orthogonal to a line (curved line or straight line) drawn by a boundary between a convex portion and a concave portion when viewed from the line direction.

The high refractive index portion 11 may be formed by etching quartz (SiO ₂ , synthetic quartz), for example. Alternatively, the high refractive index portion 11 may be obtained by forming a mold from a processed quartz material and curing the ionizing radiation-curable resin composition using the mold. Various techniques are known for producing an object having such a periodic structure using an ionizing radiation-curable resin composition, and the high refractive index portion 11 of the diffractive optical element 10 is produced using these known techniques. can be produced as appropriate.

3, including the recesses 12 formed between the protrusions 11a and the spaces 13 near the tops of the protrusions 11a, air exists and has a higher refractive index than the high refractive index portion 11. is low refractive index portion 14. The periodic structure in which the high refractive index portions 11 and the low refractive index portions 14 are alternately arranged constitutes the diffraction layer 15 having the function of shaping light.

The convex portion 11a has a multi-stage shape with four steps having different heights on one side (the left side in FIG. 3) of the side shape. Specifically, the convex portion 11a has a level 3 stepped portion 11a-3 that protrudes most, a level 2 stepped portion 11a-2 that is one step lower than the level 3 stepped portion 11a-3, and a level 2 stepped portion 11a-2 A level 1 step portion 11a-1 that is one step lower than the level 1 step portion 11a-1 and a level 0 step portion 11a-0 that is one step lower than the level 1 step portion 11a-1 are provided on one side surface side. The other side (the right side in FIG. 3) of the side surface shape of the convex portion 11a is a side wall portion 11b that linearly connects from the level 3 step portion 11a-3 to the level 0 step portion 11a-0.

Here, the convex portion 11a of the present embodiment has a shape that imitates a sawtooth shape with a multistep contour shape, and is inclined with respect to the sheet surface of the sawtooth-shaped diffractive optical element 10 that imitates the multistep contour shape. The slope has a concave curved surface that is recessed toward the convex portion 11a. Here, "simulated by a multistep contour shape" means that in this embodiment, a line connecting the corners of the stepped portions constitutes a pseudo concave curved surface. It is not limited to the part, and may be a line connecting the centers of the surfaces of the stepped parts or a line connecting the corner parts. In addition, the wording “simulated” indicates that a concave curved surface was constructed in a pseudo manner. In this embodiment, when viewed macroscopically, the surface is a concave curved surface, but when viewed microscopically, it represents a stepped configuration. In other words, it may be said to be "approximate". In the example described so far, the morphology of four levels has been described, so the morphology is relatively roughly modeled. can be

5A and 5B are diagrams for explaining the concave curved surface of the convex portion 11a in the diffractive optical element 10. FIG.
FIG. 6A is a diagram showing the diffractive optical element 10 of this embodiment in comparison with a conventional form. FIG. 6A(a) shows a cross section of a conventional diffractive optical element cut at the position of arrows HH in FIG. 6A(b). FIG. 6A(b) is a plan view of a conventional diffractive optical element viewed from the normal direction of the sheet surface. FIG. 6A(c) is a plan view of the diffractive optical element 10 of the present embodiment viewed from the normal direction of the sheet surface. FIG. 6A(d) is a diagram in which FIG. 6A(b) and FIG. 6A(c) are superimposed.
In a conventional diffractive optical element, the depth (height) of each step is constant, and the width is also constant, as indicated by the chain double-dashed line in FIG. Therefore, in the cross section shown in FIG. 5, the slope L0 connecting the corners of the steps of the conventional diffractive optical element was flat (straight in cross section).
On the other hand, in the diffractive optical element 10 of the present embodiment, the slope L connecting the corners of the stepped portions is a concave curved surface (concave curve in cross section) recessed toward the convex portion 11a. In order to imitate the concave curved surface described above, the depth (height) of each step may be changed, the width of each step may be changed, or both of these may be combined. However, considering the manufacturing method of manufacturing the stepped portions by etching, the simplest manufacturing method is to change the width of each stepped portion.
Therefore, in the diffractive optical element 10 of this embodiment, the width of each stepped portion is gradually narrowed as the depth of the recessed portion becomes shallower in order to imitate the concave curved surface described above. Therefore, as shown in FIGS. 5 and 6, the width of the convex portion 11a is also narrowed as a whole.

In the irregular-type diffractive optical element 10, as shown in FIG. 1A, in terms of design, there are many curved portions where the lines drawn by the boundaries between the convex portions and the concave portions are curved. As described above, the cross-sectional structure that affects the optical characteristics of the diffractive optical element is the cross-sectional structure in the direction perpendicular to this curve (the normal direction). However, in the actual diffractive optical element 10, the line drawn by the boundary between the convex portion and the concave portion is approximated to a curved line by a fine polygonal line shape, particularly a polygonal line shape connecting straight lines in two orthogonal directions as shown in FIG. 6A. They are often made into shapes. This is mainly due to manufacturing convenience.
In this case, if the cross-sectional structure shown in FIG. 5 is examined by cutting the cross-section as shown in FIG. The width becomes wider or narrower than the width to be examined, and correct examination cannot be performed.
FIG. 6B is a diagram showing curves of the original design pattern superimposed on the diagram of FIG. 6A. FIG. 6B(b) is a diagram in which the curve of the ideal design pattern is superimposed on FIG. 6A(b), and FIG. It is the figure which overlapped with the curved line of the design pattern. In FIG. 6B(c), the solid line is the curve of the ideal design pattern, and the dashed line is the curve of the design pattern of this embodiment.
FIG. 6B clearly shows that the width of each step gradually narrows as the depth of the recess becomes shallower. Thus, when examining the width of each step in an actually manufactured diffractive optical element, a design curve is obtained from the curve connecting the vertices as shown in FIG. It is important to consider the cross-sectional shape and width of the

Although the description so far has shown an example of a multi-stage shape with four levels, the number of stages may be larger.
FIG. 7 is a diagram showing a diffractive optical element 10 having an 8-level multi-stage shape.
When the number of steps is increased in this way, the accuracy of simulating the concave curved surface increases.

Here, the sawtooth-shaped slope has a shape that imitates a concave curved surface, and the shape of this curved surface will be described.
FIG. 8 is a diagram for explaining curves in a section of a concave curved surface and a multi-stage shape.
An x-y orthogonal coordinate system as shown in FIG. 8 is provided. That is, the x-axis is set in the direction in which the convex portions 11a are arranged, the direction in which the slanted surface becomes higher is the positive direction of the x-axis, the y-axis is set perpendicular to the sheet surface of the diffractive optical element 10, and the convex portions 11a are set. is set as the positive direction of the y-axis.
Let L be the total number of steps including the tip of the convex portion 11a. Let f be the width reduction rate for each level. Further, let lv be the number of steps of the target stepped portion when the lowest position of the concave portion is 0 and the coefficient is set, h is the height per step of each stepped portion, and C is the width ratio of level zero. . Then, the curve in the cross section of the concave curved surface modeled by the multi-step shape (the curve that is the locus of the concave vertex of level zero and the vertex of each convex portion) is represented by the following equation.
Let S be the ratio of the x-coordinate to the pitch,
x′=0.5×f×lv ² +C×lv
S=P/{tw+Σx′i}
Σ is i=0 to L−1
Then, the top x and y coordinates of the staircase shape are expressed as follows.
x=S×(0.5×f×lv ² +C×lv)
y = lv x h
When the number of levels in the multistage shape is n and the width of the highest level is tw, the pitch is
0.5×f×(n-1)2+C×(n-1)+tw
is normalized.
The width ratio C of level zero indicates the ratio of the width of level zero, which is the lowest position of the recess, to the width of one step when the width of each step is constant in the conventional case.
Here, for the height h of each stepped portion, good results can be obtained by setting h=ht×1.05 to h=ht×1.15 with respect to the theoretical value ht. The theoretical value ht=wavelength/{level number (refractive index−1)}.

Further, the widths d0 to d7 of each stepped portion (level) are defined as a ratio of the pitch as follows.
di=C+i×f
However, i is an integer of 0-6.
where f<0.

Further, in a diffractive optical element having a maximum diffraction angle of 10° or more,
−20≦C/f≦−6,
Desirably,
-16≤C/f≤-10.5
-0.0275≤f≤-0.0125
when
0.13≦C≦0.4
and when C is in this range, preferably
-0.0225≤f≤-0.0125
is.
When t is the ratio of the width of the highest level to the width of the zero level, which is the deepest plane,
0.5≦t≦0.9
and
0.6≤t≤0.8
is desirable.

Specific examples are given below.
FIG. 9 is a diagram showing a specific example of 8-level cross-sectional shapes. Values of x' and y are also written in the table written together in the lower part of FIG. This x' indicates the horizontal position of the top when looking at the cross section of the staircase structure, y indicates the vertical position, and the cross-sectional shape (step structure) coordinate data ( vertex coordinates). Also in the following figures, the values in the tables written together with the graphs indicate the coordinate data in the graphs.
In the example of FIG. 9, wavelength 850 nm, pitch = 3284 nm (diffraction angle 15°), 8 levels, f = -0.02, C = 0.25, t = 0.8, h = 850/8*1.1. *(n-1), n=1.5. In this case, C/f=-12.5.
x′=0.5×f×lv ² +C×lv
From the equation by, the width from the zero level to the highest level is 1.4542, and the width of each level is the width derived from the x value times 3284/1.4542. The zero-order light intensity at this time is 0.15776%, which is sufficiently small.

FIG. 10 is a diagram showing a specific example of a four-level cross-sectional shape. In FIG. 10, the values of x and y are also written.
In the example of FIG. 10, wavelength 850 nm, pitch = 3284 nm (diffraction angle 15°), 4 levels, f = -0.02, C = 0.2, t = 0.8, h = 850/4*1.1. (n-1.0), n=1.5. In this case, C/f=-10.
x′=0.5×f×lv ² +C×lv
From the equation by, the width from the zero level to the highest level is 0.662, and the width of each level is the width derived from the x value times 3284/0.662. The zero-order light at this time is sufficiently small at 0.2803%.

Next, the results of actually measuring the intensity of the 0th-order diffracted light for the above embodiment and the comparative example will be shown.
FIG. 11 is a diagram for explaining a method for measuring the intensity of 0th-order diffracted light.
In order to measure the intensity of the 0th-order diffracted light, first, as shown in FIG. Only light in a specific range that passes is allowed to reach the sensor S, and the power meter M measures the intensity in the presence of the diffractive optical element 10 .
Next, as shown in FIG. 11(b), only the diffractive optical element 10 is removed from the state of FIG. 11(a), and the intensity without the diffractive optical element 10 is measured. The intensity of the 0th-order diffracted light can be obtained by (intensity with the diffractive optical element 10)/(intensity without the diffractive optical element 10).
The light source LS used for the measurement was of two types, a laser light source and a halogen light source, and had a wavelength of 850 nm.

The intensity of the 0th-order diffracted light was measured for the diffractive optical element 10 of the present invention by the method described above. As the diffractive optical element 10 of the present invention, the 4-level element shown in FIGS. 3 and 5 and the 8-level element shown in FIGS. 7 and 8 were measured.
The 4-level product of the diffractive optical element 10 of the present invention has a height h of 470 nm per step. This value corresponds to h=ht×1.106. Also, C=0.1825 and f=-0.02. It should be noted that the pitch varies depending on the part as shown in FIGS. 1 and 6, so it is difficult to specify.
In addition, in the diffractive optical element 10 of the present invention, the line connecting the stepped portions forms a concave curved line in the cross section.

For comparison with the diffractive optical element 10 of the present invention, 4-level products and 8-level products were also prepared as comparative examples.
FIG. 12 is a diagram showing a diffractive optical element of a comparative example.
As a comparative example, as shown in FIG. 12, the line connecting the stepped portions is a straight line in the cross section. Two types of comparative examples, 4-level and 8-level, were also prepared. The height h per step was the same as the product of the present invention.
FIG. 13 is a diagram showing the results of measuring the intensity of 0th-order diffracted light for the diffractive optical element 10 of the present invention and the comparative example. In FIG. 13, the data indicated by circles and squares indicate the data of the laser light source, and the data indicated by the curve indicate the data of the halogen light source.
As shown in FIG. 13, regardless of whether the light source is a laser light source or a halogen light source, the intensity of the 0th-order diffracted light is significantly lower in the present invention than in the comparative example. Therefore, it has been proved by actual measurement that the intensity of the 0th-order diffracted light can be reduced by configuring the portion corresponding to the slanted surface of the sawtooth shape as a concave curved surface.

Next, a simulation was performed to investigate the effects of the present invention in more detail.
The analysis simulation of the diffraction efficiency used calculations based on rigorous coupled-wave analysis (RCWA).RCWA is mathematically reduced to solving a matrix eigenvalue problem and a linear equation. Moreover, the simulation result of the electromagnetic field analysis based on this RCWA basically agrees with the reality, except for the shape error in the actual product.
Note that the simulation this time did not take into account the three-dimensional shape shown in FIG. 2A, but was calculated assuming that it is one-dimensional and has an infinite length in the depth direction as shown in FIG. 2B.

The simulation was performed under the following conditions.
Wavelength: 850nm
Refractive index n of high refractive index portion: 1.5
Refractive index of low refractive index part: 1.0
Pitch: 2 types, 2 μm and 4 μm Number of levels: 8 levels

As a comparative example, a comparative example 1 was first obtained in which the theoretical height ht=212.5 nm for the height per step. Comparative Example 2 was obtained by setting the height per step h=ht×1.106=235 nm. This height h=ht×1.106=235 nm is the same as that used in the previous actual measurement.
In addition, two types of examples were prepared as examples in which the portion corresponding to the inclined surface, which is the product of the present invention, has a concave curved surface. First of all, Example 1 was prepared by increasing the width of the deep portion in the same manner as the previous measured products. In addition, in Example 2, the portion corresponding to the slant surface has a concave curved surface by gradually decreasing the height of the deep portion without changing the width.
FIG. 14 is a diagram showing the shape of Example 2 in which the height per step is changed.
As described above, a concave curved surface can also be simulated by changing the height of each step as shown in FIG.

FIG. 15 is a diagram summarizing the simulation results. In the simulation, the first-order diffracted light is also obtained as a reference value.
From the simulation results, it was found that the 0th-order diffracted light can be greatly reduced if the portion corresponding to the slope is a concave curved surface.

Note that the number of steps (number of levels) when the sawtooth shape is pseudo-reproduced by the multi-step shape is not limited to the above four steps and eight steps.
FIG. 16 is a diagram showing an example of simulating a sawtooth shape with 16 stages. By increasing the number of steps, it is possible to approach a smoother slope, and it is possible to make the slope almost stepless, ie, substantially curved. From the results of the actual measurements and simulations described above, it can be said that even if the slope is smooth, the intensity of the 0th-order diffracted light can be reduced if the slope is a concave curved surface.

Next, simulation results for explaining the effects of the width change rate C at level zero, the width reduction rate f for each level, and the width ratio t at the highest level will be shown.
(8-level)
17 to 19 show the results of simulating an 8-level structure represented by the following formula with a wavelength of 850 nm and a refractive index of the diffractive optical element of 1.5. The theoretical value of the height of one step is ht=212.5 nm, and h=ht×1.1=223.125 nm. t is the ratio of the width of the top surface (level-7) to the bottom (level-0). The formula uses the following formula, which is the same as the formula described above.
Let S be the ratio of the x-coordinate to the pitch,
x′=0.5×f×lv ² +C×lv
S=P/{tw+Σx′i}
Σ is i=0 to L−1
Then, the top x and y coordinates of the staircase shape are expressed as follows.
x=S×(0.5×f×lv ² +C×lv)
y = lv x h
FIG. 17 is a graph of the zero-order light intensity when C is changed with f=−0.02, t=0.8, and a pitch of 3284 nm with a diffraction angle of the diffraction grating of 15°. It can be seen that when 0.21≦C≦0.40, the zero-order light is low and is 0.5% or less.
FIG. 18 is a graph of zero-order light intensity when f is changed with C=0.25, t=0.8, and a pitch of 3284 nm with a diffraction angle of 15° of the diffraction grating. It can be seen that when −0.0225≦f≦−0.0125, the zero-order light is low and is 0.5% or less.
FIG. 19 is a graph of zero-order light intensity when t is changed when f=−0.02, C=0.25, and a pitch of 3284 nm with a diffraction angle of the diffraction grating of 15°. It can be seen that when t is 0.5 to 0.9, the zero-order light is small and becomes 0.5% or less.

From these results, a suitable range of C/f at 8-level can be obtained. Here, a range in which the zero-order light intensity is 1% or less is set as a suitable range of C/f.
From the results of FIG. 17, it can be seen that when 0.18<C, the zero-order light is 1% or less. In the example of FIG. 17, since f=-0.02, it is desirable that C/f<-9.
Further, from the results of FIG. 18, it can be seen that the zero-order light is 1% or less when −0.0275<f<−0.005. In the example of FIG. 18, since C=0.25, it is desirable that -50<C/f<-9.
As a range common to these two ranges, a preferred range of C/f at 8-level is -50<C/f<-9.

(4-level)
20 to 22 show the results of simulating a 4-level structure represented by the following formula with a wavelength of 850 nm and a refractive index of the diffractive optical element of 1.5. The theoretical value of the height per step is ht=425 nm, and h=ht×1.1=467.5 nm. t is the ratio of the width of the top surface (level-3) to the bottom (level-0). The formula uses the following formula, which is the same as the formula described above.
Let S be the ratio of the x-coordinate to the pitch,
x′=0.5×f×lv ² +C×lv
S=P/{tw+Σx′i}
Σ is i=0 to L−1
Then, the top x and y coordinates of the staircase shape are expressed as follows.
x=S×(0.5×f×lv ² +C×lv)
y = lv x h
FIG. 20 is a graph of the zero-order light intensity when C is changed with f=−0.02, t=0.8, and a pitch of 3284 nm with a diffraction angle of 15° of the diffraction grating. It can be seen that when 0.13≦C≦0.33, the zero-order light is low and is 0.5% or less.
FIG. 21 is a graph of zero-order light intensity when f is changed with C=0.18, t=0.8, and a pitch of 3284 nm with a diffraction angle of 15° of the diffraction grating. It can be seen that when −0.0275≦f≦−0.0125, the zero-order light is low and is 0.5% or less.
FIG. 22 is a graph of zero-order light intensity when t is changed when f=−0.02, C=0.18, and a pitch of 3284 nm with a diffraction angle of the diffraction grating of 15°. It can be seen that when t is 0.3 to 0.9, the zero-order light is small and becomes 0.5% or less.

From these results, a suitable range of C/f at 4-level can be obtained. Here, a range in which the zero-order light intensity is 1% or less is set as a suitable range of C/f.
From the results of FIG. 20, it can be seen that when 0.1<C, the zero-order light is 1% or less. In the example of FIG. 20, since f=-0.02, it is desirable that -5<C/f.
Also, from the results of FIG. 21, it can be seen that the zero-order light is 1% or less when f<0. In the example of FIG. 21, since C=0.18, the range of C/f cannot be obtained from the condition of f<0, and any value is acceptable under this condition.
As a range common to these two ranges, a preferred range of C/f at 4-level is −5<C/f.

As described above, the preferred range of C/f at 8-level is -50<C/f<-9, and the preferred range of C/f at 4-level is -5<C/f. be. Therefore, as a range common to these, -5<C/f<-9 can be set as a preferable range of C/f.
Here, focusing on the reduction rate f, the reduction rate f has a relationship of inverse proportion to C/f. Therefore, when the above range is rewritten so that the decrease rate f becomes a numerator, it is desirable that the range be −0.2<f/C<−0.1. The rate of decrease f is the rate of decrease in width for each level and is a dimensionless value, and if C is constant, it is considered desirable that the rate of change in area is also within the above range. Therefore, it is desirable that the rate of reduction of the area of each stepped portion is in the range of -5% or more and -20% or less.

Also, from FIG. 19, t is desirably 0.5 to 0.9 for 8-level, and from FIG. 22, t is desirably 0.3 to 0.9 for 4-level. t is the ratio of the width of the top surface (level-3) to the bottom (level-0). Therefore, it can be said that the area of the highest surface of the high refractive index portion is preferably 0.5 to 0.9 times the area of the lowest surface of the high refractive index portion.

Next, a diffractive optical element in which the trajectory connecting the vertices of the present invention has a configuration of a concave curved surface, a diffractive optical element in which the vertices are arranged in a straight line, which is a theoretical structure, and a Figs. 23 to 25 show the results of a simulation comparing a diffractive optical element in which the trajectory connecting the diffractive optical element has a configuration of a convex curved surface. In the simulations of FIGS. 23 to 25, f=−0.02, C=0.18, t=0.8, 3248 nm pitch (diffraction angle 15°).
FIG. 23 is a diagram showing the cross-sectional shape and simulation results of a diffractive optical element in which the trajectory connecting the vertices of the present invention has a configuration of a concave curved surface. In addition, in FIGS. 23 to 25, a straight line is also written with a dashed-dotted line so that the difference in cross-sectional shape can be easily understood.
As shown in FIG. 23, the structure according to the invention has a zero order of 0.26%.
FIG. 24 is a diagram showing a cross-sectional shape of a diffractive optical element having a configuration in which vertices are arranged in a straight line, which is a theoretical structure, and simulation results.
As shown in FIG. 24, the zero-order light is 0.88% when all stages are the same, which is a theoretical structure.
FIG. 25 is a diagram showing the cross-sectional shape and simulation results of a diffractive optical element in which the trajectory connecting the vertices has a configuration of a convex curved surface, contrary to the present invention.
As shown in FIG. 25, the zero-order light is 2.90% in the structure having a convex shape with respect to the slope of the blade of the saw, which is opposite to that of the present invention.
From the results shown in FIGS. 23 to 25, it can be confirmed that the zero-order light can be reduced in the diffractive optical element in which the trajectory connecting the vertices has a configuration of a concave curved surface as in the present invention.

Next, instead of the method of confirming the concave curved surface using the above formula, a method of making it easier to compare the structure of the present invention and the conventional structure will be described. In the configuration of the present invention, since the trajectory connecting the vertices forms a concave curved surface, the area of the upper surface of each step differs from step to step. A description focusing on this point will be given below.
FIG. 26 is a plan view showing a diffractive optical element having a conventional structure and a diffractive optical element of the present invention side by side for comparison. FIG. 26(a) shows data representing the 1st to 4th surfaces of the 4-level surfaces of a diffractive optical element designed by a method conventionally known as an ideal design. FIG. 26(b) is obtained by improving the shape of FIG. 26(a) based on the structure of the present invention. Individual surfaces are shown in the drawing with the lowest surface (level 0 stepped portion 11a-0: see FIG. 3) as the 0th surface and the highest surface (level 3 stepped portion 11a-3) as 3 surfaces.
FIG. 27A is a diagram showing the ratio of each surface shown in FIG. 26 to the area of the 4-level diffractive optical element according to the conventional ideal design of FIG. 26(a).
FIG. 27B is a diagram showing the ratio of each surface to the area of an 8-level diffractive optical element according to a conventional ideal design.
FIG. 28A is a diagram showing the ratio of each surface shown in FIG. 26 to the area of the 4-level diffractive optical element of the present invention shown in FIG. 26(b).
FIG. 28B is a diagram showing the ratio of each surface to the area of an 8-level diffractive optical element of the present invention.
27A, 27B and FIGS. 28A, 28B, area ratios were obtained for square regions with sides of 10 μm, 50 μm, and 100 μm of the diffractive optical element (DOE). As the size of the square area increases, the number of surfaces to be sampled increases, so there is a tendency to converge to a constant value.
As can be seen from FIGS. 27A and 27B, the ratio of each surface in the conventional ideal design is approximately 25% for each surface of 4-level, and 11% for each surface of 8-level. It can be seen that the proportions are approximately equal at ~14%.
On the other hand, as can be seen from FIGS. 28A and 28B, in the structure according to the present invention, the area of level-0, which is the lowest plane, is the largest, and the planes next to the highest plane (level-2, level-6) have the largest area. is the smallest area.
FIG. 29 shows the results of actual measurements of zero-order light obtained by actually manufacturing a diffractive optical element based on the data of FIGS. 26(a) and 26(b). Note that FIG. 29 also shows measured values for 4-level and 8-level.
As can be seen from FIG. 29, in both the 4-level and 8-level structures according to the present invention, the zero-order light is smaller than in the conventional structure.

In the example of FIG. 28A described above, when arranged in descending order of area, the order was level-0, level-1, level-3, and level-2 (hereinafter referred to as type 1). In the following, examples of the order of level-0, level-3, level-1, and level-2 (hereinafter referred to as type 2) are given in descending order of area, and the form of the ideal design that is the basis for these will be given. A comparison was made under the same conditions. In this comparison, the difference in height from level-0 to level-3, that is, the depth of unevenness (hereinafter also referred to as DOE height) is changed, and the influence of DOE height is also examined. The DOE height is usually determined according to the wavelength of light to be diffracted.

FIG. 30 is a diagram showing the area ratios of three types of diffractive optical elements.
FIG. 31 is a diagram of an ideally designed diffractive optical element viewed from the direction normal to the sheet surface.
FIG. 32 is a view of the diffractive optical element of type 1 viewed from the normal direction of the sheet surface.
FIG. 33 is a diagram of the type 2 diffractive optical element viewed from the normal direction of the sheet surface.
FIG. 34 is a diagram numerically showing simulation results of three types of diffractive optical elements.
FIG. 35 is a graph showing simulation results of three types of diffractive optical elements.
The simulations of FIGS. 34 and 35 were performed at a wavelength of 850 nm using rigorous coupled-wave analysis (RCWA).
As can be seen from FIGS. 34 and 35, the zero-order light intensity of the ideal design is smaller in the type 1 according to the present invention even when the DOE height is changed. Also, type 2 has a portion where the zero-order light intensity is smaller than that of the ideal design, depending on the DOE height.

In the above explanation, the explanation is mainly based on the simulation results. However, when the diffractive optical element is actually manufactured, it is necessary to obtain the area ratio of each step from the complex uneven shape of the actual product. In order to obtain the area ratio, the area of each step must be obtained. However, since the diffractive optical element to be manufactured often has minute and complicated concave and convex shapes, it is not easy to simply obtain the area. do not have. Therefore, one example of a method of obtaining the area ratio relatively easily is shown below. It should be noted that methods other than the method described below may be used to obtain the area ratio.

Here, a method for measuring the area of each level of the DOE using a laser microscope (manufactured by Keyence Corporation, VK-X250) will be described. This laser microscope has a height measurement accuracy and a repeatability of 3σ=12 nm, but an accuracy of several tens of nanometers is sufficient.
FIG. 36 is a diagram showing an example of a black and white (grayscale) image acquired from a laser microscope.
An image obtained from this laser microscope is a black and white image as shown in FIG. In addition, this black and white image can also be colored with a different color for each step height (not shown). It is enough to find the area for each colored color, but usually, even if the height of each step is the same level, the height is measured slightly different, so there is unevenness in color (change in chromaticity). Therefore, it is not suitable for calculating the area ratio as it is. Therefore, first, the image of FIG. 36 is subjected to black-and-white binarization (FIG. 37). For binarization, for example, commercially available image processing software can be used as appropriate, and it is preferable to select a threshold value that best expresses the characteristics of the microscope image while observing the processing result.
FIG. 37 is a diagram showing the result of binarizing a black-and-white image obtained from a laser microscope.

Next, using the binarized image, while referring to a separately obtained image colored with a different color for each height of each step, the white region is colored with, for example, an intermediate gradation color (gray color) for each step. ). For this filling process, for example, commercially available image processing software can be used as appropriate.
FIG. 38 is a diagram showing an example in which level-3 is filled.
FIG. 39 is a diagram showing an example in which level-2 is filled.
FIG. 40 is a diagram showing an example in which level-1 is filled.
FIG. 41 is a diagram showing an example in which level-0 is filled.
Using the row-wise fill image, count each filled gray pixel. For the process of counting the number of pixels for each color, for example, commercially available image processing software can be used as appropriate. In the example described above, since the colors are composed of three types of white, black, and gray, the number of gray pixels is counted.
For example, in the illustrated example, the count number for level-3 is 15167, the count number for level-2 is 24859, the count number for level-1 is 27541, and the count number for level-0 is 29391. . Since this number corresponds to the area, the area ratio can be obtained.
In the image output from the microscope, there are portions where the boundaries of each step are thick, and it is presumed that the thick portions are slopes. In the above-described area measurement method using image processing, by binarizing the image output from the microscope, the slope becomes black and is not included in the calculation of the area ratio. This is an advantage of this measurement method.

As described above, according to the present embodiment, the diffractive optical element 10 has a sawtooth-shaped slant surface as a concave curved surface, or a multi-step shape imitating a concave curved surface, so that the intensity of the 0th-order diffracted light is increased. can be reduced. Moreover, reduction in the diffraction efficiency of the primary light can be suppressed.

(deformed form)
Various modifications and changes are possible without being limited to the embodiments described above, and they are also within the scope of the present invention.

(1) In order to imitate a concave curved surface with a multi-step shape, an example of changing only one of the width or height of the multi-step shape has been described. Not limited to this, for example, both of these may be changed gradually.

(2) In the embodiments, the diffractive optical element is shown as a simple form composed only of the high refractive index portion. Not limited to this, for example, a transparent base material for forming the high refractive index portion may be provided, the low refractive index portion 14 may be made of resin, or a coating layer may be provided to cover the diffraction layer. good too.

(3) In the embodiments, a diffractive optical element configured in a multi-step shape has been mainly described, but the present invention is not limited to this. It may be a diffractive optical element configured with a continuous slope (curved surface) shape.

Although the embodiments and modifications can be used in combination as appropriate, detailed description thereof will be omitted. Moreover, the present invention is not limited to each embodiment described above.

10 diffractive optical element 11 high refractive index portion 11a convex portion 11a-0 level 0 step portion 11a-1 level 1 step portion 11a-2 level 2 step portion 11a-3 level 3 step portion 11b side wall portion 12 recess 13 space 14 low refraction index section 15 diffraction layer 200 screen 201 light 202 irradiation area 204 irradiation area 210 light source section

Claims (5)

A diffractive optical element that shapes light,
a high refractive index portion in which a plurality of protrusions are arranged side by side in a cross-sectional shape;
a low refractive index portion having a lower refractive index than the high refractive index portion and including at least concave portions formed between the convex portions;
a diffractive layer having
The convex portion has a sawtooth shape or a shape that imitates a sawtooth shape with a multi-step contour shape,
The slope inclined with respect to the sheet surface of the sawtooth-shaped diffractive optical element simulated by the sawtooth shape or the multi-step contour shape has a concave curved surface recessed toward the convex portion,
The convex portion has a multi-stage shape imitating the sawtooth shape with a plurality of steps having different heights on at least one side of the side shape,
At least one of the height and width of the step portion varies depending on the location to imitate the concave curved surface,
The stepped portion has a constant height per step,
A diffractive optical element that imitates the concave curved surface by varying the width of the stepped portion according to location. In the diffractive optical element according to claim 1,
The convex portion has a multi-stage shape imitating the sawtooth shape with a plurality of steps having different heights on at least one side of the side shape,
per unit area, the area of the deepest surface is the largest and the area of the surface next to the top surface is the smallest;
A diffractive optical element characterized by: In the diffractive optical element according to claim 1 or claim 2,
The x-axis is set in the direction in which the convex portions are arranged, and the direction in which the slopes increase is the positive direction of the x-axis,
setting a y-axis orthogonal to the sheet surface of the diffractive optical element, and setting the direction in which the convex portion protrudes as the positive direction of the y-axis;
Let L be the total number of stepped portions counted including the tip of the convex portion,
Let f be the width reduction rate for each level,
Let lv be the number of steps of the target stepped portion when counting the lowest position of the recessed portion as 0,
The height per step of the stepped portion is set to a constant value h,
When the width ratio of level zero is C,
A curve that is the trajectory of the concave vertex of level zero and the vertex of each convex portion in the cross section of the concave curved surface modeled by the multi-step shape is
Let S be the ratio of the x-coordinate to the pitch,
x′=0.5×f×lv ² +C×lv
S=P/{tw+Σx′i}
Σ is i=0 to L−1
When the top x, y coordinates of the staircase shape are
x=0.5×f×lv ² +C×lv
y = lv x h
be represented by
A diffractive optical element characterized by: In the diffractive optical element according to any one of claims 1 to 3,
The high refractive index portion has a pattern in which the boundary between the convex portion and the concave portion includes at least one of a curved line and a polygonal line connecting a plurality of line segments when viewed from the normal direction of the surface on which the uneven shape is formed. forming a diffraction grating;
A diffractive optical element characterized by: In the diffractive optical element according to any one of claims 1 to 4,
The high refractive index portion is of a grating cell array type formed in a grid-like pattern in which a plurality of unit cells having the same uneven shape arranged side by side when viewed from the normal direction of the surface on which the uneven shape is formed are tiled. forming a diffraction grating;
A diffractive optical element characterized by:

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