JP5256452B2 - Reflective diffraction grating hologram and X-ray focusing system - Google Patents

Description

  The present invention relates to a reflective diffraction grating hologram and an X-ray condensing system. In particular, the present invention relates to a diffraction grating having a grating period larger than twice the wavelength of an incident wave and a reflected wave as a hologram. The present invention relates to a reflection diffraction grating hologram and an X-ray condensing system capable of easily generating X-rays having orbital angular momentum.

  The main cause of the magnetism of a substance is largely due to the existence of spin angular momentum possessed by the atomic nucleus and electrons constituting the substance. X-rays with orbital angular momentum (hereinafter referred to as “X-rays with angular momentum”; see Non-Patent Document 1) cause an interaction with this spin angular momentum, so that magnetism and atoms have been conventionally used. X-rays having angular momentum have been used effectively for analysis of a three-dimensional array image. However, since X-rays with angular momentum can only be produced at the synchrotron radiation facility, it is difficult to perform such an analysis in the laboratory.

  Therefore, it is desired to develop an X-ray condensing system for generating X-rays with angular momentum easily in a laboratory and irradiating the X-rays with angular momentum on a substance as a subject. .

  On the other hand, it has been shown that it is possible to generate visible light having angular momentum by using a so-called transmissive fork type diffraction grating. The transmissive fork type diffraction grating in the case of visible light can be created as a hologram by using the interference pattern on the incident surface formed by irradiating non-polarized light and angular momentum light simultaneously. Further, since the wavelength is as long as about μm, it is possible to directly draw.

  However, in the case of X-rays, since it is difficult to generate angular momentum light at the laboratory level, it is possible to directly use the interference pattern on the incident surface that is formed by simultaneously irradiating non-polarized light and angular momentum light. There is a problem that direct drawing is difficult because the wavelength is as short as about nm.

  Here, the hologram is a recording of an interference pattern of two light waves, a normal laser beam emitted from a light source and an arbitrary light emitted from a reference light source, on an incident surface. When the same laser light as the original laser light is incident on the hologram thus created, the same light as that emitted from the reference light source is reproduced.

  The reproduction of light by this hologram needs to be performed with light having substantially the same wavelength as when it was created. For this reason, the interval between the fringes of the hologram is almost in the order of the wavelength of light, and there is a problem that when reproducing soft X-rays, it becomes in the order of nanometers.

  By the way, when producing a diffraction grating having a small grating period using visible light, ultraviolet light is usually used. This diffraction grating can be made by irradiating a hologram with ultraviolet light from two directions and recording an interference pattern on the incident surface. In the diffraction grating formed by interfering with ultraviolet rays, the number of engravings is 2400 lines / mm, and the grating period (interval between engravings) is limited to about 400 nm.

  In the case of X-rays, since the wavelength is as short as 1/1000 of visible light, it is difficult to process the diffraction grating, and even if a transmission-type fork-type diffraction grating can be created by special fine processing such as an ion beam. However, there is a problem that only a diffraction grating having a size as small as about μm can be produced.

A technique for generating X-rays having angular momentum using a transmission type diffraction grating hologram as such a conventional fork type diffraction grating is known. This transmission type fork type diffraction grating is produced by using a special processing technique, and its size is small on the order of μm.
“MEASURING THE ORBITAL ANGULAR MOMENTUM OF SINGLE PHOTONS”, http // www.physics.gla.ac.uk / Optics / projects / singlePhotonOAM / “Advanced Photon Functional Device Development Research Group” HP, http://wwwapr.kansai.jaea.go.jp/jaea/j/01/group/dev/#report

  However, the above-described conventional technique for generating X-rays having angular momentum with the transmissive fork type diffraction grating has the following problems.

  Here, problems of the conventional transmission type diffraction grating will be described with reference to FIG. FIG. 6 is a conceptual diagram for explaining a diffracted wave generation system 100 including a transmissive diffraction grating created with visible light. As shown in FIG. 6, the diffracted wave generation system 100 includes a laser light source 101 disposed at a point A, a transmissive diffraction grating 102, and a reference light source 103 for generating arbitrary light. .

First, normal laser light Ψ ¹ is generated from the laser light source 101 disposed at the point A, and arbitrary light Ψ ² is generated from the reference light source 103 disposed at the point B, and the hologram is irradiated with these lights. . The laser beam ψ ¹ travels from the point A by a distance r ₁ and is incident on the origin O on the surface of the transmission type diffraction grating 102. On the other hand, the light Ψ ² travels from the point B by a distance r ₂ and is incident on the origin O on the surface of the transmission type diffraction grating 102.

A transmission type diffraction grating 102 is obtained by recording the interference patterns of the ^two lights Ψ ¹ and Ψ ² on the incident surface. When the transmission type diffraction grating 102 is irradiated with the original laser beam ψ ¹ from the point A, the laser beam ψ ¹ is emitted in the direction of a extending the original laser beam ψ ¹ and the original beam ψ ² is extended. Light Ψ ² goes out in the direction of b. In the interference pattern on the transmission type diffraction grating 102, the wave where both Ψ ¹ and Ψ ² are both peaks is transmitted.

In the case of the transmissive diffraction grating 102 created with ultraviolet light, the hologram is irradiated with ultraviolet light Ψ ¹ and Ψ ² from the laser light source 101 disposed at the point A and the reference light source 103 disposed at the point B. The interference pattern on the incident surface can be recorded. In the transmissive diffraction grating 102 produced by interfering with ultraviolet light, as described above, the number of engraved lines is 2400 lines / mm, and the grating period is limited to about 400 nm.

  The above-described conventional transmission fork type diffraction grating is prepared so as to be applicable even at wavelengths of the X-ray level using a special processing technique. However, since the number of diffracted waves entering the grating period is about 1 in the conventional transmissive fork type diffraction grating, it is not possible to make a diffraction grating with the same grating period and wavelength of the diffracted wave. However, it is difficult in the X-ray region, and there is a problem that only small items can be made. Therefore, in the case of the X-ray region, the size of the diffraction grating is about 1 μm, and there is a problem that a strong diffracted wave cannot be obtained.

  Further, in the case of a transmission type diffraction grating, unnecessary 0th order light is also transmitted, so that the 0th order light becomes stronger than the diffracted wave, and X-rays having angular momentum can be efficiently used. There is also a problem that it cannot be obtained.

  Further, in the case of the transmission type, even if the direction of the diffraction grating is changed in principle, diffracted waves having different orders of sign are generated separately on the left and right of the 0th order light that travels straight, so that diffracted waves having different orders of sign are generated. There is a problem that it is difficult to use both in the same place.

  The present invention has been made in view of the above-described conventional problems, and the object thereof is to generate X-rays having an orbital angular momentum as a diffracted wave and weaken unnecessary zeroth-order light or A reflection diffraction grating hologram that can be completely erased, can easily change the exit direction of a diffraction wave, can be enlarged, and can be easily created, and an X comprising the reflection diffraction grating hologram It is to provide a line condensing system.

  In order to solve the above problems, the reflective diffraction grating hologram of the present invention has a plurality of convex portions and concave portions arranged alternately and regularly on the incident surface side of the incident wave, and is closest to the incident surface side. Based on the wavefront when the grating period, which is the sum of the spacing between the convex portions and the spacing between the concave portions, is greater than twice the wavelength of the incident wave and the diffracted wave, and the diffracted wave has an orbital angular momentum, The plurality of convex portions and concave portions are formed, and the incident wave is reflected.

  According to the configuration, the incident surface of the reflective diffraction grating hologram has a plurality of convex portions and concave portions regularly and alternately arranged on the incident surface side of the incident wave. Further, in the case of a reflection type diffraction grating hologram, when a plurality of convex portions and concave portions reflect incident waves (for example, when a lamina type diffraction grating or the like is used), the height of the concave portion and the convex portion is determined. By appropriately adjusting the grating depth (the same description is omitted hereinafter) which is the difference (difference between the lowermost part of the concave part and the uppermost part of the convex part), the zero-order reflected wave is weakened or completely extinguished. Can do.

  The case where only a plurality of convex portions reflect incident waves, or the case where only a plurality of concave portions reflect incident waves (for example, when a blazed diffraction grating is used) is also included in the scope of the present invention. . Further, unlike the transmission type diffraction grating, the reflection type diffraction grating can change the direction of the zero-order light by changing the direction of the diffraction grating, and diffracted waves having different orders of sign are emitted in the same direction. be able to.

  In addition, the concave and convex portion on the incident surface side is formed so that the grating period is considerably larger than the wavelength of the diffracted wave (the grating period is larger than twice the wavelength). In this case, the diffracted wave can be reproduced by forming the diffracted wave so as to satisfy the diffraction condition that the integral multiple of the beat interval generated by the superposition of the incident wave and the diffracted wave is equal to the grating period. Therefore, the diffraction grating can be enlarged and can be easily created.

  Moreover, the uneven | corrugated | grooved part by the side of an entrance plane is formed with the shape of a some convex part and a recessed part based on the wave surface in case a diffracted wave has an orbital angular momentum.

  Further, in the reflection type diffraction grating hologram of the present invention, in addition to the above configuration, the shape of the plurality of convex portions and concave portions is the wavelength of the diffracted wave, the grating period, and the sine of the exit angle of the diffracted wave. Preferably, it is formed along a trajectory drawn by the intersection of a half line extending along the wavefront from the center axis of rotation of the wavefront of the wave when extended to a length equal to the product. According to the above configuration, if a normal plane wave is incident, a diffracted wave having an orbital angular momentum can be generated.

  In order to solve the above problems, the reflective diffraction grating hologram of the present invention has a plurality of convex portions and concave portions arranged alternately and regularly on the incident surface side of the incident wave. When the number of diffracted waves entering the lattice period, which is the sum of the distance between the nearest convex parts and the distance between the concave parts, is an integer larger than 1, and the diffracted wave has an orbital angular momentum Based on the wavefront, the shapes of the plurality of convex portions and concave portions are formed, and the incident wave is reflected.

  According to the above configuration, the number of diffracted waves entering the grating period, which is the sum of the distance between the nearest convex parts and the distance between the concave parts on the incident surface side, is 1 in the concave and convex parts on the incident surface side. It is formed so as to satisfy the diffraction condition of being an integer larger than that. Therefore, by adjusting the grating period, a desired diffracted wave can be reproduced even if the number of waves entering the grating period is different from one. Other configurations are the same as those described above.

In order to solve the above problems, the reflective diffraction grating hologram of the present invention has a plurality of convex portions and concave portions arranged alternately and regularly on the incident surface side of the incident wave. The grating period a, which is the sum of the distance between the nearest convex parts and the distance between the concave parts, is larger than twice the wavelength of the incident wave and the reflected wave, and the diffracted wave makes the incident surface an XY plane. When it is assumed that the light is emitted from the origin O in the XYZ Cartesian coordinate system on the XZ plane with the initial phase φ _{0, the} emission angle β, and the wave number k (= 2π / asin β), the plurality of convex portions And the shape of the recess is formed along a locus drawn by the intersection of the incident surface and a half line extending along the wavefront from the rotation center axis of the wavefront of the wave when the wavelength of the diffracted wave is extended to asin β. With
The trajectory is expressed by the following formula (1) where m (m ≠ 0) and n are integers.

... (1)
A trajectory drawn by a point P (x, y) that satisfies the above condition, and is characterized by reflecting the incident wave.

  According to the above configuration, the integer m (m ≠ 0) is the orbital angular momentum of the diffracted wave,

  This corresponds to the case of. Further, the shapes of the plurality of convex portions and concave portions are formed in accordance with a trajectory that satisfies the above formula (1). Therefore, if a normal plane wave is incident, a diffracted wave having an orbital angular momentum can be generated. Other configurations are the same as those described above.

  As described above, X-rays having orbital angular momentum can be generated as diffracted waves, unnecessary zero-order light can be weakened or completely extinguished, and the exit direction of diffracted waves can be easily changed, Further, it is possible to provide a reflection type diffraction grating hologram that can be enlarged and can be easily produced.

  In addition to the above configuration, the reflective diffraction grating hologram of the present invention is preferably a lamina type in which the cross-sectional shape of the plurality of convex portions in the concave-convex direction is a rectangular shape. As described above, the application range of the present invention is not limited to the lamina type diffraction grating, but includes other types of reflection type diffraction gratings such as a blazed diffraction grating.

  Further, in addition to the above configuration, the reflection diffraction grating hologram of the present invention includes the convex portion so that the reflected waves from the plurality of convex portions and the reflected waves from the plurality of concave portions are 180 degrees different from each other. It is preferable that the depth of the lattice, which is a difference in height from the concave portion, is determined.

  According to the above configuration, the zero-order reflected wave can be weakened or completely extinguished by appropriately setting the grating depth. For example, if the grating depth is set so that the reflected waves from the plurality of convex portions and the reflected waves from the plurality of concave portions are 180 degrees different from each other, if both reflected waves interfere with each other, the principle of wave superposition Since they cancel each other, the zero-order reflected wave can be completely canceled.

  As described above, the “height difference between the convex portion and the concave portion” is given by the difference between the lowermost portion of the concave portion and the uppermost portion of the convex portion.

  In addition to the above configuration, the reflection type diffraction grating hologram of the present invention is formed along a sine curve in which the shape of the cross section in the concave-convex direction of the convex part and concave part has the same period as the grating period. It is preferable.

  According to the said structure, the shape of the cross section of the uneven | corrugated | grooved part by the side of an entrance plane is formed along the sine curve with the same period as a grating | lattice period. Therefore, since the outgoing wave is analytically only the first-order wave, other diffraction waves such as the 0th-order diffracted wave (reflected wave) and the second-order are suppressed, and the first-order diffracted wave is efficiently obtained. be able to.

  In addition to the above configuration, the reflective diffraction grating hologram of the present invention includes a multilayer film in which large-mass atoms and small-mass atoms are alternately stacked at intervals at which the incident wave satisfies the Bragg reflection condition. It is preferably formed on the incident surface side.

  According to the above-described configuration, the multilayer film in which atoms having a large mass and atoms having a small mass are alternately stacked is formed on the incident surface side, and the distance between the multilayer films is determined so as to satisfy the Bragg reflection condition. . For this reason, X-rays can be reflected efficiently.

In addition to the above configuration, the reflective diffraction grating hologram of the present invention includes a position where a light source of an incident wave is placed, a condensing point where the diffracted wave converges, a straight line in the traveling direction of the incident wave, and the diffracted wave A radius of curvature in a plane that includes a Roland circle in which the circumference is drawn including an intersection with a straight line in the traveling direction of
The incident surface is preferably formed as a spherical surface having a radius of curvature in a plane orthogonal to the Rowland circle equal to the diameter of the Rowland circle.

  According to the above configuration, the entrance surface is formed as a spherical surface having the same radius of curvature in a plane including the Roland circle and the radius of curvature in a plane orthogonal to the Roland circle. For this reason, diffracted light can be efficiently converged on the condensing point, and since it is spherical, processing is easy. In this case, the circumferential direction of the Roland circle converges on the condensing point, but the direction perpendicular to the Roland circle does not converge on the condensing point.

  In addition to the above configuration, the reflective diffraction grating hologram of the present invention includes a position where a light source of an incident wave is placed, a condensing point where the diffracted wave converges, a straight line in the traveling direction of the incident wave, and the diffracted wave The radius of curvature in the plane including the Roland circle in which the circumference is drawn including the intersection with the straight line in the traveling direction is equal to the diameter of the Roland circle, and the radius of curvature in the plane orthogonal to the Roland circle is the Roland circle It is preferable that the incident surface is formed as a toroidal surface different from the diameter.

  In addition to the above configuration, the reflective diffraction grating hologram of the present invention includes a position where a light source of an incident wave is placed, a condensing point where the diffracted wave converges, a straight line in the traveling direction of the incident wave, and the diffracted wave The radius of curvature in the plane including the Roland circle in which the circumference is drawn including the intersection with the straight line in the traveling direction is equal to the diameter of the Roland circle, and the radius of curvature in the plane orthogonal to the Roland circle is the Roland circle It is preferable that the incident surface is formed as a spheroid having a diameter different from the diameter.

  According to the above configuration, the entrance surface has a different radius of curvature in a plane including the Roland circle and a radius of curvature in a plane orthogonal to the Roland circle. Therefore, even in the case of a divergent X-ray light source, the light can be adjusted so as to converge at both the circumferential direction of the Roland circle and the direction perpendicular to the Roland circle. Convergence efficiency is good.

  From the viewpoint of light collection efficiency, it is more preferable that the incident surface is formed as a spheroid.

  Note that the radius of curvature in the plane including the Roland circle is always equal to the diameter of the Roland circle. On the other hand, the radius of curvature in a plane orthogonal to the Roland circle does not necessarily have to be equal to the diameter of the Roland circle.

  In order to solve the above problems, an X-ray condensing system according to the present invention includes an X-ray source that generates X-rays as a light source for incident waves, and a diffraction grating for generating diffracted waves upon incidence of the incident waves. An X-ray condensing system comprising a hologram, wherein the diffraction grating hologram has a plurality of convex portions and concave portions arranged alternately and regularly on the incident surface side of the incident wave, Based on the wavefront when the grating period, which is the sum of the distance between the nearest convex parts and the distance between the concave parts, is larger than twice the wavelength of the incident wave and the reflected wave, and the diffracted wave has an orbital angular momentum A plurality of convex and concave shapes are formed, and the reflection type diffraction grating hologram reflects the incident wave, the position where the X-ray source is placed, a condensing point where the diffraction wave converges, And on the entrance surface of the diffraction grating hologram A radius of curvature in a plane including a Roland circle in which a circumference is drawn including an intersection of a straight line in the traveling direction of the incident wave and a straight line in the traveling direction of the diffracted wave is equal to the diameter of the Roland circle. It is said.

  According to the above configuration, the position where the X-ray source is placed, the condensing point where the diffracted wave converges, the straight line of the traveling direction of the incident wave on the incident surface of the diffraction grating hologram, and the traveling direction of the diffracted wave The radius of curvature in the plane including the Roland circle in which the circumference is drawn including the intersection with the straight line is equal to the diameter of the Roland circle. For this reason, the orbital angular momentum X-rays generated by diffracting X-rays within the solid angle range where the incident surface of the diffraction grating is viewed from the X-ray source can be efficiently focused on the condensing point. Note that all of the diffraction grating holograms having the above-described configuration can be used in the X-ray condensing system of the present invention.

  In addition, although the basics of condensing are as described above, it is also possible to condense in a different arrangement from the above by combining the reflection type diffraction grating hologram of the present invention and other optical elements. It is included in the category of the invention.

  From the above, X-rays with orbital angular momentum can be generated as diffracted waves, unnecessary zero-order light can be weakened or completely extinguished, and the direction of emission of diffracted waves can be easily changed, Furthermore, it is possible to provide an X-ray condensing system including a reflection type diffraction grating hologram that can be enlarged and can be easily created.

  In addition, as described above, the reflective diffraction grating hologram of the present invention has a plurality of convex portions and concave portions arranged alternately and regularly on the incident surface side of the incident wave, and is closest to the incident surface side. Based on the wavefront when the grating period, which is the sum of the spacing between the convex portions and the spacing between the concave portions, is greater than twice the wavelength of the incident wave and the diffracted wave, and the diffracted wave has an orbital angular momentum, A plurality of convex and concave shapes are formed to reflect the incident wave.

  In addition, as described above, the reflective diffraction grating hologram of the present invention has a plurality of convex portions and concave portions arranged alternately and regularly on the incident surface side of the incident wave, and is closest to the incident surface side. In the wavefront when the number of diffracted waves entering the lattice period, which is the sum of the interval between the convex portions and the interval between the concave portions, is an integer larger than 1, and the diffracted wave has an orbital angular momentum. Based on this, the shapes of the plurality of convex portions and concave portions are formed, and the incident waves are reflected.

In addition, as described above, the reflective diffraction grating hologram of the present invention has a plurality of convex portions and concave portions arranged alternately and regularly on the incident surface side of the incident wave, and is closest to the incident surface side. The grating period a, which is the sum of the interval between the convex portions and the interval between the concave portions, is larger than twice the wavelength of the incident wave and the reflected wave, and the diffracted wave has XYZ orthogonal coordinates with the incident surface as the XY plane. When it is assumed that the light is emitted from the origin O in the system on the XZ plane, with the initial phase φ _{0, the} emission angle β, and the wave number k (= 2π / asin β), the plurality of convex portions and concave portions The shape is formed along a trajectory drawn by the intersection of a half line extending along the wavefront from the rotation center axis of the wavefront of the wave when the wavelength of the diffracted wave is extended to asin β, and the incident surface.
The trajectory is expressed by the following formula (1) where m (m ≠ 0) and n are integers.

... (1)
Is a locus drawn by a point P (x, y) that satisfies the above condition, and reflects the incident wave.

  Therefore, X-rays with orbital angular momentum can be generated as diffracted waves, unnecessary zero-order light can be weakened or completely extinguished, and the direction of emission of diffracted waves can be easily changed, Furthermore, it is possible to provide a reflection type diffraction grating hologram that can be enlarged and can be easily produced.

  In addition, as described above, the X-ray condensing system of the present invention includes an X-ray source that generates X-rays as a light source for incident waves, and a diffraction grating hologram for generating a diffracted wave upon incidence of the incident waves. The diffraction grating hologram includes a plurality of convex portions and concave portions arranged alternately and regularly on the incident surface side of the incident wave, and the closest to the incident surface side. Based on the wavefront when the grating period, which is the sum of the spacing between the convex portions and the spacing between the concave portions, is greater than twice the wavelength of the incident wave and the reflected wave, and the diffracted wave has an orbital angular momentum, It is a reflection type diffraction grating hologram formed with a plurality of convex and concave shapes and reflecting the incident wave, the position where the X-ray source is placed, the focal point where the diffracted wave converges, and the diffraction The incident wave on the incident surface of the grating hologram And the linear direction of travel, the radius of curvature in a plane including the Rowland circle include intersections circumference drawn by the straight line in the traveling direction of the diffracted wave is a system equal to the diameter of the Rowland circle.

  Therefore, X-rays with orbital angular momentum can be generated as diffracted waves, unnecessary zero-order light can be weakened or completely extinguished, and the direction of emission of diffracted waves can be easily changed, In addition, an X-ray condensing system including a reflective diffraction grating hologram that can be enlarged and can be easily produced can be provided.

  An embodiment of the X-ray condensing system of the present invention will be described below with reference to FIGS. 1 to 5C.

[1. Example of X-ray focusing system]
First, based on FIG.1 and FIG.2 (a) * FIG.2 (b), the structure of the X-ray condensing system 10 which is an example of an X-ray condensing system is demonstrated.

  As shown in FIG. 1, the X-ray condensing system 10 includes an X-ray source 1, a reflective diffraction grating hologram 2, and a condensing point 3. The X-ray source 1 is a source of X-rays arranged at point A, and is for irradiating the reflection diffraction grating hologram 2 with X-rays. The X-ray source 1 can be easily configured by using a normal divergent X-ray source. However, the X-ray source 1 is not limited to such a divergent type as long as it is a source of X-rays. It may be.

  The incident surface of the reflective diffraction grating hologram 2 is a reflective diffraction grating in which a plurality of convex portions and concave portions are alternately and regularly arranged on the incident surface side of the incident wave. In the reflection type diffraction grating hologram 2, when both of the plurality of convex portions and concave portions reflect incident waves (for example, when a lamina type diffraction grating or the like is used), the height between the concave portions and the convex portions. By appropriately adjusting the grating depth d (the same description is omitted hereinafter), which is the difference between the lowermost part of the concave part and the uppermost part of the convex part, the zero-order reflected wave is weakened or completely eliminated. Can be erased.

  The case where only a plurality of convex portions reflect incident waves, or the case where only a plurality of concave portions reflect incident waves (for example, when a blazed diffraction grating is used) is also included in the scope of the present invention. . Further, unlike the transmission type diffraction grating, the reflection type diffraction grating hologram 2 can change the direction of the zero-order light if the direction of the diffraction grating is changed, and diffracted waves having different orders of signs are emitted in the same direction. Can be made.

  Below, the case where the shape of the cross section of the concavo-convex portion of the reflective diffraction grating hologram 2 is a laminar diffraction grating having a grating period a and a grating depth d will be described. Further, the concave and convex portion on the incident surface side is formed such that the grating period a is considerably larger than the wavelength λ of the diffracted wave (the grating period a is larger than twice the wavelength λ). In this case, the diffracted wave can be reproduced by forming the diffracted wave so as to satisfy the diffraction condition that the integral multiple of the beat interval generated by the superposition of the incident wave and the diffracted wave is equal to the grating period. Therefore, the diffraction grating can be enlarged and can be easily created.

  As described above, the application range of the present invention is not limited to such a lamina type diffraction grating, but includes other reflection type diffraction gratings such as a blazed type. Here, the lamina type is a diffraction grating in which the cross-sectional shape of the plurality of convex portions in the concavo-convex direction is a rectangular shape as shown in the enlarged view of the cross section of the diffraction grating in FIG.

  In FIG. 1, the ratio of the unevenness in the lattice period a, which is the sum of the distance between the nearest convex parts and the distance between the concave parts, is shown as the same ratio, but these ratios are arbitrary. There may be. The unevenness ratio is preferably 1: 1. However, it may be in a range in which angular momentum light can be created, preferably 0.2 to 0.8: 0.8 to 0.2, more preferably 0.4 to 0.6: 0.6 to 0.00. 4.

  As another example of the shape of the concave and convex portions of the reflective diffraction grating hologram 2, the shape of the cross section of the convex and concave portions in the concave and convex direction is formed along a sine curve having the same period as the grating period a. Or a saw-tooth wave shape. If the cross-sectional shape is formed along a sine curve, the outgoing wave is analytically only the first-order wave, so that the zero-order diffracted wave (reflected wave), the second-order wave, etc. Other diffracted waves are suppressed, and a first-order diffracted wave can be obtained efficiently. In addition to the sine curve as described above, the sine curve may not be a strict sine curve, and the same effect can be exhibited when the sine curve is along a curve close to the sine curve.

  Next, the shape of the plurality of concavo-convex portions is a so-called fork shape, so that if a normal plane wave is incident on the reflective diffraction grating hologram 2, X-rays having orbital angular momentum are diffracted. It can be generated as a wave. The shapes of the plurality of convex portions and the concave portions of the fork-shaped diffraction grating are based on the wavefront (the wavefront of the Laguerre Gaussian beam) when the diffracted wave has an orbital angular momentum. Should be formed.

  Although details will be described later, the shape of a plurality of convex portions and concave portions is a wave when the wavelength of the diffracted wave is extended to a length equal to the product of the grating period and the sine of the exit angle of the diffracted wave. What is necessary is just to form along the locus | trajectory which the intersection of the half line extended along this wave front from the rotation center axis | shaft of this wave front and an entrance plane draws. If a normal plane wave is incident on this fork type diffraction grating, a diffraction wave having an orbital angular momentum can be generated.

  The incident surface of the reflective diffraction grating hologram 2 may form a so-called toroidal surface, may form a spherical surface, or may be a flat surface. Here, with reference to FIGS. 2A and 2B, the relationship between the Roland circle and the radius of curvature will be described first, and then the relationship between the spherical surface and the toroidal surface will be described.

As shown by the broken line in FIG. 2A, the Roland circle centered at the point O ₁ is the point A where the X-ray source 1 that is the light source of the incident wave is placed, and the incidence of the reflective diffraction grating hologram 2 Surrounded by a circle drawn including the intersection of the X-ray traveling direction line of the incident wave on the surface and the straight line of the traveling direction of the diffracted wave and the condensing point 3 located at the point B where the diffracted wave converges It is a circle.

  Further, in the X-ray focusing system 10, as shown in FIG. 2A, the curvature radius of the incident surface of the reflective diffraction grating hologram 2 in the plane including the Roland circle is equal to the diameter of the Roland circle. ing. In FIG. 2 (a), a semicircle having a radius (the radius of curvature) of the Roland circle is drawn.

  If the arrangement along the Roland circle as described above is adopted and the shape of the incident surface of the reflective diffraction grating hologram 2 is adjusted, X-rays within the solid angle range in which the incident surface of the diffraction grating is expected from the X-ray source 1. Therefore, the orbital angular momentum X-rays generated by diffracting by the reflection type diffraction grating hologram 2 can be efficiently condensed on the condensing point 3. It should be noted that any form of the diffraction grating hologram 2 described in the present embodiment can be used for the X-ray condensing system 10.

As the radius of curvature that determines the shape of the incident surface of the reflective diffraction grating hologram 2, a first radius of curvature in a plane including a Roland circle and a second radius of curvature in a plane orthogonal to the Roland circle can be considered. . Here, the second radius of curvature is called a vertical radius, and FIG. 2B shows the relationship between the center of curvature O ₂ and the vertical radius. The first radius of curvature is not shown here.

The first radius of curvature is always equal to twice the radius of the Roland circle, that is, the diameter of the Roland circle. Further, the second radius of curvature (vertical radius) does not necessarily have to be equal to the diameter of the Roland circle, and is determined by the positional relationship between the point A and the point B, but r ₁ and r ₂ shown in FIG. If α is equal to β, then r ₁ cos β.

  Here, the relationship between the spherical surface and the toroidal surface will be described. A spherical surface is when the first radius of curvature is equal to the diameter of the Roland circle and the second radius of curvature is equal to the diameter of the Roland circle. In this case, the first radius of curvature is equal to the second radius of curvature. When the shape of the incident surface of the reflection type diffraction grating hologram 2 is a spherical surface, the diffracted light can be efficiently converged on the condensing point 3, and since it is a spherical surface, processing is easy.

  On the other hand, a case where the first radius of curvature is equal to the diameter of the Roland circle and the second radius of curvature is different from the diameter of the Roland circle is a toroidal surface. In this case, even the divergent X-ray source 1 can be adjusted so that the light converges on the condensing point 3 in both the circumferential direction of the Roland circle and the direction perpendicular to the Roland circle. In comparison, the convergence efficiency is even better.

  Here, the case where the incident surface of the reflection type diffraction grating hologram 2 forms a toroidal surface will be described. However, the present invention is not limited to such an incident surface, and various shapes of the incident surface are adopted as necessary. It is possible. In addition, from the viewpoint of light collection efficiency, it is more preferable that the incident surface is formed as a spheroid.

  In addition, although the basics of condensing are as described above, it is also possible to condense in a different arrangement from the above by combining the reflection type diffraction grating hologram 10 of the present embodiment and another optical element. Such cases are also included in the scope of the present invention.

  The diffraction condition of the reflective diffraction grating hologram 2 may be a condition that an integral multiple of the beat interval generated by the superposition of the incident wave and the diffracted wave is equal to the grating period a. Thereby, even when the grating period a is considerably larger than the wavelength of the diffracted wave, a desired diffracted wave can be reproduced.

  The diffraction condition may be a condition that the number of diffracted waves entering the grating period a is an integer greater than one. At this time, if the grating period a is set to a size that is easy to manufacture and the emission angle β is adjusted, a desired diffracted wave can be reproduced even if the number of waves entering the grating period is different from one. If either one of the above diffraction conditions is satisfied, the diffraction grating can be enlarged and can be easily created.

  The grating depth d (also referred to as the lamina depth in the case of the lamina type; hereinafter the same description is omitted) is the difference in height between the convex portion and the concave portion on the incident surface side (the lowermost portion of the concave portion and the convex portion). By adjusting the grating depth d, the zero-order reflected wave can be weakened or completely eliminated. For example, it is preferable to determine the grating depth d so that the phases of the reflected waves from the plurality of convex portions and the reflected waves from the plurality of concave portions are 180 degrees different from each other. At this time, if the two reflected waves interfere with each other, they cancel each other according to the principle of wave superposition, so that the zero-order reflected wave can be completely eliminated. Therefore, the ratio of ± 1st order diffracted light can be made larger than the ratio of 0th order diffracted light (reflected wave), and X-rays having angular momentum can be obtained efficiently.

  The condensing point 3 is a point where the diffracted wave by the reflection type diffraction grating hologram 2 is converged. In FIG. If a specific sample is placed at the condensing point 3, the sample can be irradiated with X-rays having angular momentum. As a method for analyzing physical properties such as magnetism and atomic arrangement of the sample by irradiating the sample with X-rays having angular momentum, a conventionally used method may be used.

  Here, based on Table 1 below, a specific example of parameters such as the grating period a in the case of creating the reflective diffraction grating hologram 2 using ultraviolet light will be described. In this example, a case where an AlKα X-ray (energy 1486.7 eV, wavelength 0.8340 nm) is used as the X-ray source 1 will be described. In addition, each parameter is not restricted to the numerical value of following Table 1, and can be suitably set according to the objective.

  When a reflection type diffraction grating hologram 2 of lamina type and toroidal type is used, an X-ray that diverges like an X-ray source in the laboratory is placed at point A, and the diffracted wave is focused on the sample at point B. Can be irradiated. The parameters are as shown in Table 1.

  Here, each of the parameters shown in Table 1 will be described. It is assumed that the X-ray source 1 and the reflection type diffraction grating hologram 2 have a sufficient distance. Then, the divergent X-ray can be considered as a plane wave in the vicinity of the center (the origin O) of the reflection type diffraction grating hologram 2. The traveling direction of this plane wave is aligned with the center of the reflective diffraction grating hologram 2.

First, consider a case where the distance r ₁ between the point A and the origin O is set to 235 mm and X-rays are incident on the incident surface of the reflective diffraction grating hologram 2 at an incident angle α. Further, it is assumed that the X-ray is diffracted at the exit angle β, and the X-ray having the angular momentum that is a diffracted wave converges at the focal point 3.

In Table 1, the distance _{r 2} between B and the origin point O is the position of the focal point 3 is set to 235 mm, it is equal to _{r 1.} However, the present invention is not limited to such a case, and r ₁ and r ₂ may be set to any value as long as the above Roland circle condition is satisfied.

  As shown in Table 1, when the incident angle α at which X-rays are incident is 70 degrees, the angular momentum is

  The emission angle β at which the X-rays are emitted as diffracted waves is 69.67 degrees. In addition,

Is a quantity represented by h / (2π) where Planck constant is h = 6.626176 × 10 ³⁴ (Js: J is a unit of energy and s is a unit of time). .

  On the other hand, the outgoing angle β at which the X-ray with an angular momentum of 1 is emitted as a diffracted wave is 70.34 degrees. Therefore, the opening angle between the X-ray with the angular momentum of 1 and the X-ray with −1 is 0.67 degrees.

  When the reflection type diffraction grating hologram 2 is formed using ultraviolet rays, the number of engraved lines is limited to 2400 per 1 mm. Therefore, the grating period when the number of engraved lines is set is 417 nm, which is on the order of several hundred nanometers. It is.

The radius of curvature in the plane including the Roland circle (the radius of curvature in the Roland circle) is 687.1 mm, and the size of the X-ray focusing system 10 is a space of about r ₁ + r ₂ (470 mm). The X-ray focusing system 10 can be used in a normal laboratory. The vertical radius (Roland circular surface vertical curvature radius) is 80.37 mm, and the lamina depth d is 0.6096 nm.

  Here, since X-rays are transmitted through a normal substance, a device is required to improve the reflection efficiency. Here, a case where a multilayer film using Bragg reflection is used will be described. This multilayer film is formed by alternately stacking atoms having a large mass and atoms having a small mass. The interval between the multilayer films, which is the interval between the layer of atoms with a large mass and the layer of atoms with a small mass, may be set to an interval that satisfies the Bragg reflection condition. Thereby, X-rays can be reflected efficiently.

  The reflectivity is about 40% at the maximum although it depends on the combination of atoms. The result is a diffraction efficiency of 37% at an energy of 8 keV with a soft X-ray diffraction grating developed by Mr. Masato Koike of the Nuclear Research Institute, coated with a multilayer film in which tungsten atoms and carbon atoms are alternately stacked. (See Non-Patent Document 2). In this example, a laminate of silicon and tungsten is used. In addition, as an example of an atom, various atoms, such as a calcium atom and a tantalum atom, can be adopted. In the example of Table 1, the interval between the multilayer films is set to 1.219 nm.

  Next, an example different from Table 1 is shown in Table 2.

First, the distance r ₁ is set to 500 mm, and the distance r ₂ is set to 500 mm. As shown in Table 2, when the incident angle α is 80 degrees, the exit angle β from which X-rays having an angular momentum of −1 are emitted as diffracted waves is 79.52 degrees, and the angular momentum is 1. The exit angle β from which X-rays are emitted as diffracted waves is 80.50 degrees. Therefore, the opening angle between the X-ray with the angular momentum of 1 and the X-ray with −1 is 0.98 degrees.

  In the case of a conventional transmissive fork type diffraction grating, it is about 0.09 degrees if the grating period a is the same. Then, in the reflective diffraction grating hologram 2, it is easy to separate diffracted waves having different signs (diffracted waves having angular momentum of +1 and −1, etc.) as compared with a conventional transmissive diffraction grating. The number of engraved lines is 1200 per 1 mm, and the lattice period when the number of engraved lines is set is 833 nm.

  The radius of curvature in the plane including the Roland circle is 2879.4 mm, the vertical radius is 86.82 mm, and the lamina depth d is 1.785 nm. In the example of Table 2, the interval between the multilayer films is set to 3.57 nm.

  As described above, X-rays having orbital angular momentum can be generated as diffracted waves, unnecessary zero-order light can be weakened or completely extinguished, and the exit direction of diffracted waves can be easily changed, Furthermore, it is possible to provide the X-ray condensing system 10 including the reflection type diffraction grating hologram 2 and the reflection type diffraction grating hologram 2 which can be enlarged and can be easily produced.

[2. (Fork-type diffraction grating)
In the case of visible light, it is conventionally known that a diffracted wave having an orbital angular momentum can be obtained by using a fork type diffraction grating. Therefore, an outline of the structure of the fork-type diffraction grating will be described based on FIGS. 3 (a) to 3 (d). FIG. 3A to FIG. 3D are simulations of a pattern drawn by a fork-type diffraction grating using a computer. Details of this calculation method and the like will be described later.

FIG. 3A is a diagram showing the state of the engraving when the angular momentum of the first-order diffracted light is ± 1, and FIG. 3B is a diagram showing the angular momentum of the first-order diffracted light being ± 2. FIG. 3C is a diagram showing the state of the engraving when the angular momentum of the first-order diffracted light is ± 3, and FIG. It is a figure which shows the mode of the marking when the angular momentum of the 1st-order diffracted light is +/- 4. Here, for the sake of simplicity, the initial phase φ ₀ is set to 0 degrees.

  In a normal diffraction grating, a plurality of engraved lines are straight lines parallel to each other. In addition, since the plurality of concave and convex portions of the diffraction grating are formed along these score lines, they are in parallel with each other and arranged in the concave and convex direction.

  On the other hand, as shown in FIGS. 3 (a) to 3 (d), the curve drawn by the plurality of engraved lines of the fork-type diffraction grating is inflected near the center and approaches a parallel line as the distance from the center is increased. The pattern that goes is formed.

  As shown in FIGS. 3A to 3D, the fork-type diffraction grating engraving line has a plurality of curves such as a tangent curve arranged substantially symmetrically.

  The engraved line pattern in FIG. 3A corresponds to the case where the orbital angular momentum is ± 1, and is characterized in that the difference in the number of engraved lines on the upper and lower sides is one. When the orbital angular momentum is ± m (m is an integer), the difference in the number is m. For example, when the angular momentum is ± 2, the difference between the number of engraved lines on the upper and lower sides is two, which is a pattern as shown in FIG. Similarly, when the angular momentum is ± 3 and ± 4, the difference in the number of upper and lower engraved lines is 3 and 4, respectively, and the patterns are as shown in FIGS. 3 (c) and 3 (d). . Since the pattern drawn by these engraved lines is similar to a fork, the diffraction gratings in FIGS. 3A to 3D are called fork type diffraction gratings. Moreover, what is necessary is just to form the shape of the some recessed part and convex part of the reflection type diffraction grating hologram 2 so that said several engraving line may be followed.

[3. (Theoretical calculation of the curve drawn by the fork type grating)
Next, the curve drawn by the engraving line of the fork type diffraction grating is derived by theoretical calculation. First, based on FIG. 4 (a) and FIG. 4 (b), the characteristics of the wavefront of a diffracted wave having an orbital angular momentum of ± 1 and ± 2 (hereinafter sometimes referred to as “angular momentum light”). explain. Although the incident light is not shown, it is incident from above the Z axis at an incident angle of 0 degree, and the phase is equal and 0 degree on the xy plane.

  The angular momentum light with an angular momentum of m is a wave that travels while rotating in a phase like a spiral staircase as shown in FIG. 4C, and is traveling upward from the xy plane at an emission angle β. The figure shows the case where m = 2. A wave that travels while rotating in phase like this spiral staircase is called an LG beam (Laguerre Gaussian beam) or a vortex wave, and is a light wave represented by a function such as the following equation (1).

... (1)
here,

  Is a wave vector indicating the traveling direction of the wave, and is given by k = 2π / λ where k is the magnitude and λ is the wavelength of the angular momentum light.

(2)
Is a displacement vector and indicates a point on the wavefront.

Furthermore, φ is the size of the corner of PQ measured from a line parallel to the y-axis in FIG. 4C, and point Q is a point on the central axis of the vortex wave. It should be noted that, here, is the initial phase and φ _0. The point R is a point on the x-axis and satisfies the angle OQR = 90 degrees. Furthermore, the point P is a point where the half line and the xy plane intersect when a half line is drawn along the wavefront from the point Q which is a point on the axis of the vortex wave. Draw a fork-shaped diffraction grating.

Next, what kind of curve the engraved line of the fork type diffraction grating draws will be described. Consider the relationship between x and y at point P (x, y). The expression (1) takes the maximum value 1 when n is an arbitrary integer and the value in the parenthesis is 2nπ. The φ at that time and φ _M, seek the relationship between the φ _M and r.

                      (4)

... (5)
Here, β is the angle of emission of angular momentum light.

When r is considered constant cross-section, (3) the value of phi _M taking the maximum value 1 is can be seen that the m. For example, when r = 0

.... (6)
It can be seen that there are m in 2π. with r change of the maximum value phi _M is rotated as shown in FIG. 4 (c). When these are connected, it becomes an m-fold spiral. The case of m = 2 and φ ₀ = 0 is shown in FIG. Given the interval of x when the same φ _M.

  From equation (4)

... (7)
If the nth x is _xn and the difference from _xn-1 is Δx, this interval Δx corresponds to the wave period.

(8)
In other words, when φ _M is the same, the interval of x is

(9)
It is. Since β is close to 90 °, the interval between the engraving lines is almost the length of the wavelength. Line extending from the point Q to the phi _M direction to seek relationship of x and y of the point P intersecting the xy plane (x, y).

First, n and x are determined, φ _M is obtained from the equation (5), and is expressed as φ _M = 2π + φ ′. If x is positive, there is an intersection if π <φ ′ <2π, and if x is negative, 0 <φ ′ <π. From FIG. 4, when x is negative, it is expressed by the following equation.

(10)
When x is positive, it is expressed by the following equation.

(11)
That is, the same expression can be used for both positive and negative x. After all, it becomes as follows.

  here,

(12)
It is.

The way to draw a curve is summarized as follows. First, n and x are obtained. Next, it expressed as (5) seek phi _M from equation it φ _M = 2π + φ '. Further, if x is positive and π <φ ′ <2π, and x is negative, 0 <φ ′ <π, and y is obtained using equation (12). The points (x, y) obtained in this way are connected.

  The accuracy that can be produced by the direct drawing method using an electron beam is several tens of nanometers, and those with an interval of 100 nm are easy to produce. Since λ is on the order of 1 nm in the soft X-ray wavelength region, the incident light is normal incident (incident angle 90 degrees), and the emitted light satisfies the diffraction conditions if β is about 0.5 degrees.

[4. Relationship between diffraction conditions and grating period)
Next, based on the (a) part of FIG. 5 to the (c) part of FIG. 5, the relationship between the diffraction conditions of the reflective diffraction grating and the grating period will be described. In addition, the pattern of the shape of the concavo-convex portion of the diffraction grating that generates angular momentum light as a reflection type diffraction grating is along the engraving lines of the patterns shown in FIGS. 3 (a) to 3 (d). However, the engraving interval (lattice period) is created at about 400 nm, which is easy to create by ultraviolet exposure.

  The direction in which the diffracted wave appears is determined by the diffraction conditions of the diffraction grating, and a is the grating period. Further, α is an incident angle of the incident wave, β is an exit angle of the diffracted wave, and λ is the wavelength of the incident wave and the diffracted wave. N is an arbitrary integer value. Then

・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ (13)
It is represented by

  The value of the depth d of the lamina is obtained under the following condition that the specular reflection light (0th order light) is weakened (it becomes zero in the calculation).

When n = 0, d = λ / (4 cos α).
In the case of soft X-rays, α and β are almost equal, so the value of a is about 500 times larger than the wavelength, and there are several hundreds of wave peaks in the grooves that form the engraving lines of the diffraction grating. In addition, it cannot be understood by ordinary interpretation of wavefront reproduction. In the following, in the case of a reflection type diffraction grating, it is proved that if the diffraction condition is satisfied, the condition for wavefront reproduction of the diffracted wave is also satisfied.

  Note that the above diffraction condition is a grating which is the sum of an integral multiple of the beat interval generated by superposition of the incident wave and the diffracted wave, and the interval between the nearest convex portions and the interval between the concave portions on the incident surface side. The condition may be that the period is equal.

  From another point of view, the condition may be that the number of diffracted waves entering the grating period is an integer greater than one.

Let us consider a case in which the light wave Ψ ¹ is incident at an incident angle α and the light wave Ψ ² is reflected at an emission angle β as shown in FIG. The wavelength of each light wave is assumed to be λ.

FIG. 5C shows a case where the reflection type diffraction grating hologram 2 is a lamina type diffraction grating. The grating period of the reflection type diffraction grating hologram 2 is a. When the x-axis and the z-axis are taken as shown in FIG. 5A to FIG. 5C, the concave portion of the reflective diffraction grating hologram 2 extends in the y direction. The wave vector of the light wave Ψ ¹ is

  And is decomposed into an x component and a z component as follows.

(14)
Considering the plane of z = 0, it becomes as follows.

... (15)
Here, α is an incident angle, and the fact that k _x = k sin α is satisfied with k being the magnitude of the wave vector is used. This function is represented by a curve indicated by a broken line in part (a) of FIG. Similarly, the light wave Ψ ² is as follows in the plane of z = 0.

・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ (16)
This function is represented by a curve indicated by a solid line in part (a) of FIG. Next, it is proved that the wave represented by the function of Ψ ^{2 in} the equation (16) is reproduced only by irradiating the diffraction grating with the light wave Ψ ¹ .

  In this diffraction grating, the convex portion (from y = −a / 4 + ma to y = a / 4 + ma, where m is an integer) has no phase shift between the incident wave and the reflected wave when reflected, but the concave portion (y = a / 4 + ma to y = 3a / 4 + ma, where m is an integer), it is assumed that there is a phase shift of π (180 degrees) between the incident wave and the reflected wave when reflected.

  Such a diffraction grating can be formed by selecting a material and a thickness of a reflection type using a multilayer film or the like and a transmission type.

  The above-described configuration is for reproducing the phase of the first-order diffracted wave reflecting the convex part and the concave part as accurately as possible, and simultaneously canceling the zero-order diffracted wave (reflected wave), This is to prevent a 0th-order reflected wave from appearing in the calculation result. In the case of a lamina type diffraction grating, the depth d of the grating shown in part (c) of FIG. 5 may be adjusted so that the phase difference of the light wave reflected from the convex part and the concave part is 180 degrees.

  Then, the function of the diffracted wave Ψ can be approximated as follows.

                        ... (17)

  The term (1) is obtained by approximating a function of a rectangular line, which is a cross-sectional shape of the lamina-type diffraction grating shown in part (c) of FIG. 5, with a sine curve indicated by a thick solid line.

  Equation (17) is transformed using the formula of the triangle function,

... (18)
Here, the equation (13) is transformed and

・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ (19)
From equation (18),

(20)
Note that sin β _{n = −1} indicates sin β when n = −1 (hereinafter, the same description is omitted).
Thus, it was proved that the wavefronts of the + 1st order and −1st order diffracted waves were reproduced.

Next, the relationship between the diffraction grating and the hologram will be described. The part (b) of FIG. 5 is obtained by superposing the light wave Ψ ¹ and the light wave Ψ ² which are the two waves of part (a) of FIG. It can be seen that waves with slightly different wavelengths interfere with each other. For the sake of convenience, in the swaying of the portion (b) in FIG. 5, there are seven waves with small amplitudes in the swaying vibrations. The case where it exists is assumed.

  The period of turning is a / 2. Since the hologram records the waveform of a wave with a small amplitude in this distortion, it needs to be processed with an accuracy of 1 nm or less when the soft X-ray has a short wavelength, which is impossible with the current technology. .

  In part (b) of FIG. 5, it can be seen that the phase of the wave having a small amplitude in the beat is inverted in the adjacent beat. This turning function is obtained by multiplying a sine curve having a large frequency (thin solid line curve) in FIG. 5C and a sine curve having a low frequency (thick solid line curve).

  This result is the same as the approximate expression (17). That is, by using a phase-inverted diffraction grating, it is possible to substantially create a hologram with a grating period on the order of a sine curve period with a small frequency in part (c) of FIG. Yes. Then, since the interval of the diffraction grating can be set to the order of μm, it can be created with ordinary ultraviolet light, and can be created with a conventional technique.

  The pattern of the reflective diffraction grating for creating angular momentum light is the same as that shown in FIGS. 3A to 3D, and the grating period is about 500 times larger. The deviation of the score line from the straight line in the positive region and the negative region is also about 500 times larger than the wavelength.

  In order to reproduce the wavefront of angular momentum light, the wavefront shift may change in phase from about −π / 2 to about π / 2, and the value of x from about −1/4 to ¼ of the wavelength. This change is necessary and is a change that is about 1/500 smaller than the change of the grating period.

  It is shown that such a small phase change is possible even with a pattern having a concave and convex shape of a diffraction grating having a grating period as large as 500 times the wavelength.

  The deviation of the engraving line is expressed as a phase deviation φ when the grating period is 2π. In other words, if the deviation of the score line is Δ,

・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ (21)
When the function of the reflected wave is calculated by writing the parenthesized cosine on the right side of the equation (17) as follows:

                            .... (22)

(23)
From equation (19), equation (23) is

... (24)
Thus, it has been proved that the wavefronts of the + 1st order and the −1st order are shifted by the phase φ. That is, it was proved that it is possible to give a change smaller by about 1/500 than the change of the grating period.

  As described above, the wavefront of the angular momentum light can be reproduced by the reflective diffraction grating, and the angular momentum light that efficiently converges on the sample even with the divergent X-ray emitted from the normal X-ray tube. It was shown that can be created.

  The present invention is not limited to the above-described example of the X-ray focusing system, and various modifications are possible within the scope of the technical means described in the section of the best mode for carrying out the present invention. Embodiments obtained by appropriately combining the respective technical means are also included in the technical scope of the present invention.

  The present invention relates to the field of structural analysis for analyzing the structure of a substance by irradiating the substance with X-rays having orbital angular momentum and obtaining a solid state of a magnetic state or atomic arrangement that cannot be obtained by ordinary X-rays, and a substance In addition to the field of physical property analysis for analyzing the magnetic state and the like, the present invention can be widely applied in any field as long as it is a technical field that can use X-rays having orbital angular momentum.

It is a schematic diagram showing one embodiment of an X-ray condensing system in the present invention. (A) is a schematic diagram for demonstrating the Roland circle and curvature radius regarding the reflection type diffraction grating hologram of this invention, (b) is a schematic diagram for demonstrating a toroidal surface. (A) is a figure which shows the mode of the marking when the angular momentum of the primary diffraction light in the reflection type diffraction grating hologram of this invention is ± 1, (b) is the angle of the primary diffraction light It is a figure which shows the mode of engraving when momentum is +/- 2, (c) is a figure which shows the state of engraving when angular momentum of the 1st-order diffracted light is +/- 3, (d) FIG. 6 is a diagram showing a state of engraving when the angular momentum of the first-order diffracted light is ± 4. (A) is a figure which shows the mode of the wavefront of the diffracted wave whose angular momentum is 1, (b) is a figure which shows the mode of the wavefront of the diffracted wave whose angular momentum is 2. (C) is a figure which shows a mode that the score line of a diffraction grating is drawn based on the wavefront of the diffracted wave whose angular momentum is 2. FIG. It is a figure for demonstrating the relationship between the grating period of the said reflection type diffraction grating hologram, and diffraction conditions. It is a schematic diagram for demonstrating the outline | summary of the conventional transmission type diffraction grating.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 X-ray source 2 Reflection type diffraction grating hologram 3 Focusing point 10 X-ray focusing system a Grating period d Grating depth α Incident angle β Emission angle λ Wavelength

Claims (9)

A plurality of convex portions and concave portions are alternately and regularly arranged on the incident surface side of the incident wave,
The grating period a which is the sum of the distance between the nearest convex portions and the distance between the concave portions on the incident surface side is larger than twice the wavelength of the incident wave and the reflected wave ,
A diffracted wave is emitted from the origin O in the XYZ orthogonal coordinate system in which the incident surface is the XY plane, in the traveling direction on the XZ plane, with an initial phase φ0, an emission angle β, and a wave number k (= 2π / asinβ). Assuming that
The shape of the plurality of convex portions and concave portions is a locus drawn by the intersection of a half line extending along the wavefront from the rotation center axis of the wavefront of the wave when the wavelength of the diffracted wave is extended to asin β and the incident surface. And formed along
The trajectory is expressed by the following formula (1) where m (m ≠ 0) and n are integers.
... (1)
Is a locus drawn by a point P (x, y) that satisfies
A reflective diffraction grating hologram, wherein the incident wave is reflected . 2. The reflection type diffraction grating hologram according to claim 1, wherein the plurality of convex portions are of a lamina type in which the cross-sectional shape in the concave-convex direction is a rectangular shape . The depth of the grating, which is the difference in height between the convex portions and the concave portions, is determined so that the phases of the reflected waves from the plural convex portions and the reflected waves from the plural concave portions are 180 degrees different from each other. The reflection type diffraction grating hologram according to claim 2 . According to claim 1, wherein the incident wave at the reflection satisfies intervals Bragg, multilayer film and a small atom of high atomic mass of the mass are alternately laminated, characterized in that it is formed on the incident surface side Reflective diffraction grating hologram. A Roland circle in which a circumference is drawn including the position where the light source of the incident wave is placed, the condensing point where the diffracted wave converges, and the intersection of the straight line in the traveling direction of the incident wave and the straight line in the traveling direction of the diffracted wave A radius of curvature in the plane containing,
2. The reflection diffraction grating hologram according to claim 1 , wherein an incident surface is formed as a spherical surface having a radius of curvature in a plane orthogonal to the Rowland circle equal to the diameter of the Rowland circle . Roland circle in which the circumference is drawn including the position where the light source of the incident wave is placed, the condensing point where the diffracted wave converges, and the intersection of the straight line in the traveling direction of the incident wave and the straight line in the traveling direction of the diffracted wave A radius of curvature in a plane including the same as the diameter of the Roland circle,
2. The reflection type diffraction grating hologram according to claim 1 , wherein an incident surface is formed as a toroidal surface having a radius of curvature in a plane orthogonal to the Rowland circle different from the diameter of the Rowland circle . Roland circle in which the circumference is drawn including the position where the light source of the incident wave is placed, the condensing point where the diffracted wave converges, and the intersection of the straight line in the traveling direction of the incident wave and the straight line in the traveling direction of the diffracted wave A radius of curvature in a plane including the same as the diameter of the Roland circle,
2. The reflection type diffraction grating hologram according to claim 1 , wherein an incident surface is formed as a spheroid having a radius of curvature in a plane orthogonal to the Rowland circle different from the diameter of the Rowland circle . Claims, characterized in that the number of waves of the diffracted wave enters into the grating period which is the sum of the distance between spacing and recesses between the projections of the nearest in the incident side is an integer greater than 1 8. The reflection type diffraction grating hologram according to any one of 1 to 7 . An X-ray condensing system comprising: an X-ray source that generates X-rays as an incident wave light source; and a diffraction grating hologram for generating a diffracted wave upon incidence of the incident wave,
In the diffraction grating hologram, a plurality of convex portions and concave portions are alternately and regularly arranged on the incident surface side of the incident wave,
The grating period, which is the sum of the distance between the nearest convex portions and the distance between the concave portions on the incident surface side, is larger than twice the wavelength of the incident wave and the reflected wave, and the diffracted wave has an orbital angular momentum. Based on the wavefront of the case, the shape of the plurality of protrusions and recesses is formed,
A reflection type diffraction grating hologram for reflecting the incident wave;
The position where the X-ray source is placed, the condensing point where the diffracted wave converges, and the intersection of the straight line in the traveling direction of the incident wave and the straight line in the traveling direction of the diffracted wave on the incident surface of the diffraction grating hologram An X-ray condensing system , wherein a radius of curvature in a plane including a Roland circle including a circumference is equal to a diameter of the Roland circle .