Optical element

Abstract

An optical element 1 comprises an HOE 2 having a periodic refractive index distribution in which light having a specific wavelength undergoes Bragg reflection. When α1 represents the structural inclination angle and Λ1 represents the structural period of an array on a first surface 2A side of the HOE 2 through which the light enters, α2 represents the structural inclination angle and Λ2 represents the structural period of the array on a second surface 2B side opposite to the first surface 2A, Λ1 and α1 are respectively different from Λ2 and α2. When ni represents the external refractive index of the first surface 2A and θi represents the angle at which the light enters the first surface, formula (1) is satisfied. When n0 represents the external refractive index of the second surface 2B, formula (2) or (3) is satisfied.

Description

Optical elements

[0001] The present invention relates to an optical element that diffracts incident light, and more particularly to a transmissive diffractive optical element that diffracts incident light while transmitting it.

[0002] In recent years, diffractive optical elements using alignment patterning of liquid crystals have been attracting attention. For example, Non-Patent Document 1 discloses that a transmissive diffractive optical element can be realized by using nematic liquid crystals.

[0003] C. Oh and MJ Escuti, “Achromatic diffraction from polarization gratings with high efficiency”, Optics Letters, Vol. 33, Issue 20, pp. 2287-2289 (2008)

[0004] However, a transmissive diffractive optical element using nematic liquid crystal generally diffracts light of all wavelengths incident thereon, and therefore the diffraction angle varies with wavelength, resulting in chromatic aberration.

[0005] The present invention has been made in view of the above problems, and an object of the present invention is to provide a transmission type element that does not cause chromatic aberration.

[0006] In order to solve the above problems, the present invention includes the following aspects: Item 1. An optical element including a volume hologram element (HOE) having a periodic refractive index distribution that Bragg-reflects light of a specific wavelength, wherein the structural period of the arrangement on a first surface side of the HOE onto which the light is incident is set to Λ １ , the structural tilt angle is α １ and the structural period of the array on the second surface side opposite to the first surface is Λ ２ , the structural tilt angle is α ２ Then, Λ １ and α １ is Λ ２ and α ２ and the external refractive index of the first surface is n ｉ , the incident angle of the light to the first surface is θ ｉ Then, the following formula (1) is satisfied: The external refractive index of the second surface is n０ Then, the optical element is characterized in that the following formula (2) or formula (3) is satisfied: Item 2. An optical element comprising: a volume hologram element (HOE) having an arrangement of rod-shaped molecules that Bragg-reflect light of a specific wavelength; and a substrate formed on a first surface of the HOE onto which the light is incident, wherein the structural period of the arrangement on the first surface side of the HOE is Λ １ , the structural tilt angle is α １ and the structural period of the array on the second surface side opposite to the first surface is Λ ２ , the structural tilt angle is α ２ Then, Λ １ and α １ is Λ ２ and α ２ and the external refractive index of the first surface is n ｉ , the refractive index of the HOE relative to the substrate is n ｇ , the incident angle of the light to the first surface is θ ｉ Then, the following equation (4) is satisfied: The external refractive index of the second surface is n ０ Then, the following formula (2) or formula (3) is satisfied. Item 3. The optical element according to item 1 or 2, wherein α ２ is α １ If larger, Λ ２ is Λ １ Larger than α ２ is α １ If smaller, Λ ２ is Λ １ Item 4. The optical element according to item 1 or 2, wherein the refractive index of the first surface is n ｏ１ , the ordinary refractive index of the second surface is n ｏ２ Then, α ２ is α １ If greater than n ｏ２ Ga n ｏ１ Larger than α ２ is α １ If n is smaller than ｏ２ Ga n ｏ１Item 5. The optical element according to item 1 or 2, wherein the extraordinary refractive index of the first surface is n ｅ１ , the extraordinary refractive index of the second surface is n ｅ２ Then, α ２ is α １ If greater than n ｅ２ Ga n ｅ１ Larger than α ２ is α １ If n is smaller than ｅ２ Ga n ｅ１ Item 6. The optical element according to any one of Items 1 to 5, wherein the difference between the spatial frequency in the in-plane direction of the HOE resulting from the distribution of the structural tilt angles of the second surface and the spatial frequency in the in-plane direction of the HOE resulting from the distribution of the structural tilt angles of the first surface is designed by a computer-generated hologram algorithm. Item 7. The optical element according to Item 6, wherein the difference between the spatial frequency in the in-plane direction of the HOE resulting from the distribution of the structural tilt angles of the second surface and the spatial frequency in the in-plane direction of the HOE resulting from the distribution of the structural tilt angles of the first surface is constant. Item 8. The optical element according to Item 6, wherein the difference between the spatial frequency in the in-plane direction of the HOE resulting from the distribution of the structural tilt angles of the second surface and the spatial frequency in the in-plane direction of the HOE resulting from the distribution of the structural tilt angles of the first surface is distributed quadratically. Item 9. Item 6. The optical element according to item 6, wherein a difference between a spatial frequency in an in-plane direction of the HOE resulting from the distribution of the structural tilt angles of the second surface and a spatial frequency in an in-plane direction of the HOE resulting from the distribution of the structural tilt angles of the first surface has a spatial phase singularity. Item 10. The optical element according to any one of items 1 to 9, wherein the rod-like molecules are cholesteric liquid crystal molecules. Item 11. A composite optical element including a plurality of the optical elements according to any one of items 1 to 10, wherein the optical elements diffract light in different wavelength bands, and an optical resin having a refractive index that prevents total reflection from occurring in the space or at the interface between the optical elements is interposed between the optical elements.

[0007] The optical element according to the present invention exhibits high diffraction efficiency in a specific wavelength band, and the diffraction efficiency drops off sharply outside that band, making it possible to provide a transmission type element that does not produce chromatic aberration.

[0008] 1. An explanatory diagram of a cholesteric liquid crystal. A simplified diagram of the structure shown in FIG. 1. A cross-sectional view of a conventional reflective liquid crystal diffractive optical element. A cross-sectional view showing the configuration of an optical element according to embodiment 1. A cross-sectional view showing the configuration of an optical element according to embodiment 2. A cross-sectional view showing the configuration of an optical element according to a modified example. A diagram for explaining the diffraction behavior of light in the optical element shown in FIG. 6. A transmission spectrum of a general HOE. An explanatory diagram of a cholesteric liquid crystal. A cross-sectional view showing the configuration of a composite optical element according to embodiment 3. A schematic diagram of an optical system for forming an alignment pattern in Example 1. A schematic diagram of an alignment pattern formed on a substrate in Example 1. A cross-sectional view of the optical element according to Example 1. A transmission spectrum of the optical element according to Example 1. A schematic diagram of an optical system for forming an alignment pattern in Example 2. A cross-sectional view of the optical element according to Example 2. A transmission spectrum of the optical element according to Example 2. A photograph showing the light-collecting effect of the optical element according to Example 2 on 520 nm light. A photograph showing the light-collecting effect of the optical element according to Example 2 on 670 nm light. A schematic diagram showing a part of the manufacturing procedure of the optical element according to Example 3. 10 is a diagram for explaining modulation of the structural period by dropping a liquid crystal solution. It is a cross-sectional view of the optical element according to Example 3. It is a transmission spectrum of the optical element according to Example 3.

[0009] Hereinafter, an embodiment of the present invention will be described with reference to the accompanying drawings.

[0010] (About HOE) A holographic optical element (HOE) is a type of diffractive optical element that operates by diffraction, and generally, a diffractive optical element that has a periodic refractive index distribution in the depth direction of the element is called an HOE. The HOE according to this embodiment uses cholesteric liquid crystal in which rod-shaped molecules are arranged in a helical structure to form a periodic refractive index distribution, but the constituent material of the HOE is not limited to this. For example, it may be a photopolymer that is optically isotropic and generates a refractive index distribution depending on the intensity of light during polymerization, thereby functioning as a volume hologram. Cholesteric liquid crystal is also called chiral nematic liquid crystal.

[0011] 1(a) to (c) are explanatory diagrams of a cholesteric liquid crystal and an HOE made of a cholesteric liquid crystal. The liquid crystal is composed of rod-like molecules collectively aligned in a specific direction, and the average alignment direction is called the director. The liquid crystal is optically a uniaxial anisotropic medium, and the refractive index along the direction parallel to the director is called the extraordinary refractive index n ｅ , the refractive index along the perpendicular direction is the ordinary refractive index n ｏ In other words, the direction of the liquid crystal director corresponds to the optic axis of a uniaxial anisotropic medium. In cholesteric liquid crystals, the director forms a helical structure, and the refractive index changes periodically. In Figure 1, a dot is placed on one side of the long axis of the elliptical director, but this is a guide to represent the helical structure; in actual standard liquid crystal materials, there is no distinction between the head and tail of the director.

[0012] Depending on the composition of the material, cholesteric liquid crystals exhibit a natural pitch length P (P is defined as the distance a molecule rotates 360°). When cholesteric liquid crystals exist on a substrate and the orientation of the molecules on the surface of the substrate is uniform, the equiphase plane exists approximately parallel to the substrate, and circularly polarized light with the same helical winding direction as the helix is ​​n ｏ P-n ｅ The light is reflected in the wavelength range of P.

[0013] It is known that when a periodic pattern of the molecular alignment restraining force direction of cholesteric liquid crystal is applied to a substrate, the equiphase plane of the periodic structure is tilted, as shown in Figure 1(b), and the HOE functions as a HOE. As will be described later, in this case, the diffraction angle of the HOE depends on the structural period Λ of the periodic structure and the tilt angle α. It is also possible that the molecular alignment direction in the bulk is raised from the substrate, but the tilt angle β affects the effective refractive index of the HOE and does not directly affect the diffraction angle at a certain wavelength.

[0014] In the following explanation, the structure shown in Fig. 1 is simplified as shown in Fig. 2. In Fig. 2, the area where the director's projected component onto the paper surface is larger than its projected component out of the plane is shown by a dark line, and the other area is shown by a light line.

[0015] Diffractive optical elements, which are made by patterning the molecular orientation of cholesteric liquid crystals on a substrate, modulate the wavefront of reflected light while barely affecting the wavefront of unreflected light. In other words, they have wavelength selectivity, where diffraction occurs in a wavelength range determined by the Bragg reflection wavelength of the cholesteric liquid crystal, and the diffraction efficiency drops off sharply outside that range.

[0016] (Diffraction of a Single-Layer Element) To explain the operating principle of the optical element according to the present invention, the operating principle of a reflective liquid crystal diffractive optical element will first be explained.

[0017] 3, the direction of the director (molecular long axis direction and optical axis) rotates within the film of the thin-film HOE 102, forming a periodic structure. In the following, it is assumed that the thin-film liquid crystal diffractive optical element exists on the xy plane, and that light waves enter the HOE 102 from the negative region.

[0018] The equiphase surface of the periodic structure is generally curved three-dimensionally within the HOE 102. The diffraction behavior at a certain position of the HOE 102 can be understood using the grating vector, which is the normal direction of the equiphase surface of the periodic structure at that position. In the following, the grating vector near the incident-side interface of the HOE 102 is assumed to exist in the xz plane, and its period is Λ １ The tilt angle of the periodic structure from the xy plane is α １Let us assume that:

[0019] In this case, the period of the structure along the x and z axes is Λ ｘ１、 Λ ｚ１ Let Λ １ The following relationship holds between

[0020] At the interface between the incident medium and the front side of the HOE 102, the following Snell's law (equation (C)) holds, and further, the light reflected by the periodic structure is refracted in the output optical path and emitted to the outside of the element (equation (D)).

[0021] In addition, n ｉ , n ｇ , n' １ are the refractive indices of the external medium, the substrate 103, and the effective refractive index of the HOE 102. ｉ , θ ｇ , θ ｉ１ θ′ represents the propagation angle of light in the external medium, the substrate 103, and the HOE 102. ｏｇ， θ ｏ represents the propagation angle (diffraction angle) of the diffracted light in the substrate 103 and the HOE 102.

[0022] The wavelength λ1 of light diffracted in the front region of the HOE 102 satisfies the following equation (E):

[0023] Substituting equation (E) into the left side of equation (D), the following equation (F) is obtained.

[0024] By transforming the left side of equation (D), the following relational expression is obtained. Substituting equation (C) into the above equation, the following relational expression is obtained. Therefore, the following relation is obtained:

[0025] Furthermore, rearranging the second term in the middle equation of equation (F) gives the following relational expression:

[0026] By rewriting equation (F) using the above equations, we obtain the following equation (G).

[0027] By rearranging the formula (G), the formula (H) for diffraction by the HOE 102 is obtained.

[0028] The diffraction angle at the substrate 103 between the HOE 102 and the external medium can be found by applying Snell's law to the exit angle in equation (H). Using the equations on the second and third sides from the left in equation (D), the following equation can be derived:

[0029] The above discussion has explained the operation of a reflective liquid crystal diffractive optical element based on ray-like considerations, but diffraction behavior can also be understood based on wave-like considerations. The fact that the wavefront of the light wave reflected by the thin-film element is emitted at an angle that satisfies the diffraction condition means that constructive interference occurs. Focusing on the two light paths reflected at the element surface, the difference in their optical paths (the difference in the distance between the bold lines in the diagram on the right) is an integer multiple of the wavelength. In other words, the wavefront of the light reflected at the equiphase plane of the periodic structure has a phase shift of an integer multiple of the wavelength (2π radians).

[0030] Therefore, by changing the position of the equiphase surface (i.e., by distributing the tilt angle) on the surface of a thin-film element, it is possible to modulate the wavefront of the reflected wave and realize a phase hologram element that can create any wavefront shape. Such phase hologram elements can be designed using computer-generated hologram algorithms such as the Gerchberg-Saxton method, and have been reported in, for example, J. Kobashi, H. Yoshida, and M. Ozaki, "Circularly-polarized, semitransparent, and double-sided holograms based on helical photonic structures," Sci. Rep. 7, 16470 (2017).

[0031] (Embodiment 1) Fig. 4 is a cross-sectional view showing the configuration of an optical element 1 according to embodiment 1. The optical element 1 comprises a HOE 2 and a substrate 3 formed on a first surface 2A onto which light from the HOE 2 is incident. The HOE 2 has an arrangement of cholesteric liquid crystals that Bragg-reflects light of a specific wavelength. It is conceivable that the HOE 2 has a substrate outside the first surface 2A, outside the second surface 2B, or outside both the first surface 2A and the second surface 2B. However, as will be explained below, in this embodiment, the refractive index outside the substrate (hereinafter referred to as "external refractive index") is important, and therefore the explanation will be given assuming that the substrate exists only outside the first surface 2A. The refractive index of the substrate is n ｇ Let's say.

[0032] The wavelength of light diffracted by the optical element 1 is defined as λ. In the optical element 1, the structural period of the arrangement on the first surface 2A side of the HOE 2 is defined as Λ. １ , the structural tilt angle is α １ and the structural period of the arrangement on the second surface 2B side opposite to the first surface 2A is Λ ２ , the structural tilt angle is α ２ Then, Λ １ and α １ is Λ ２ and α ２ and the external refractive index of the first surface 2A is n ｉ , the incident angle of light to the first surface 2A is θ ｉ Then, the following formula (1) is satisfied, and the external refractive index of the second surface 2B is n ｏ Then, the following formula (2) or formula (3) is satisfied.

[0033] As a result, the light diffracted on the first surface 2A side of the HOE2 is totally reflected between the substrate 3 and the external medium, and the totally reflected light reaches the interface on the second surface 2B side of the HOE2, where it is totally reflected again at the interface between the second surface 2B and the external medium, and enters the second surface 2B side of the HOE2, and the light diffracted on the second surface 2B side is emitted into the external air.

[0034] First, the process of deriving formula (1) will be described. In order for the light diffracted at the first surface 2A side of the HOE 2 to be totally reflected between the substrate 3 and the external medium, the diffraction angle given by formula (H) must exceed the critical angle, and therefore the following formulas (J) and (K) must be satisfied. In the configuration of FIG. 4, n in formula (H) ｏ = n ｉ This becomes:

[0035] Therefore, equation (1) is derived.

[0036] Next, the process of deriving equations (2) and (3) will be explained. The light totally reflected at the interface between the first surface 2A and the substrate 3 reaches the interface on the second surface 2B side of the HOE 2, is totally reflected again at the interface between the second surface 2B and the external medium, enters the second surface 2B side of the HOE 2, and is diffracted at the second surface 2B side. As will be described later, the exit angle θo of the light from the HOE 2 at this time is calculated by multiplying the incident angle θ of the light onto the HOE 2 by the angle of incidence of the light. ｉ and is given by the following equation (L):

[0037] In order for the light diffracted by the HOE 2 to be emitted to the outside (not satisfying the total reflection condition), the following condition must be satisfied.

[0038] Therefore, the following formula (M) must be satisfied:

[0039] Equations (2) and (3) are derived from equation (M).

[0040] 5 is a cross-sectional view showing the configuration of an optical element 1′ according to embodiment 2. The structure of the optical element 1′ is the same as that of the optical element 1 shown in FIG. 4 except for the structural period and structural tilt angle of the cholesteric liquid crystal arrangement in the HOE 2.

[0041] In the optical element 1′, the structural period of the arrangement on the first surface side of the HOE is Λ １ , the structural tilt angle is α １ and the structural period of the array on the second surface side opposite to the first surface is Λ ２ , the structural tilt angle is α ２ Then, Λ１ and α １ is Λ ２ and α ２ The external refractive index of the first surface 2A is n ｉ , the refractive index of the HOE 2 with respect to the substrate 3 is n ｇ , the incident angle of light to the first surface 2A is θ ｉ Then, the following formula (4) is satisfied, and the external refractive index of the second surface 2B is n ０ Then, the following formula (2) or formula (3) is satisfied.

[0042] As a result, the light diffracted on the first surface 2A side of the HOE2 is totally reflected between the first surface 2A and the substrate 3, the totally reflected light reaches the interface on the second surface 2B side of the HOE2, the light is totally reflected again at the interface between the second surface 2B and the external medium, and enters the second surface 2B side of the HOE2, and the light diffracted on the second surface 2B side is emitted into the external medium.

[0043] The process for deriving equations (2) and (3) is the same as in the first embodiment, so the process for deriving equation (4) will be described below. In order for the light diffracted at the first surface 2A side of the HOE 2 to be totally reflected between the first surface 2A and the substrate 3, θog in equation (I) must be 90° or greater, and therefore the following equations (N) and (O) must be satisfied.

[0044] Therefore, equation (4) is derived.

[0045] 4 and 5 has a single-layer structure, it may have a structure consisting of two layers or multiple HOEs, as in the optical element 1A' shown in Fig. 6. In the optical element 1A', the HOE 2 includes a first HOE 21 and a second HOE 22, with the surface of the first HOE 21 facing the substrate 3 forming a first surface 2A of the HOE 2 and the surface of the second HOE 22 facing the external medium forming a second surface 2B of the HOE 2.

[0046] The optical path in the optical element 1A' is such that light diffracted by the first HOE 21 is totally reflected at the interface between the first surface 2A and the substrate 3 or the external medium, and the totally reflected light is refracted inside the HOE 2 until it reaches the interface near the second surface 2B, where it is totally reflected at the second surface 2B, and then enters the second HOE 22 and is diffracted.

[0047] The structural period of the arrangement of the first HOE 21 is Λ １ , the structural tilt angle is α １ and the structural period of the arrangement of the second HOE 22 is Λ ２ , the structural tilt angle is α ２ The refractive index of the external air (external medium) and the substrate 3 is n ｉ , n ｇ The effective refractive index of the first HOE 21 and the second HOE 22 is n'. １ , n' ２ The propagation angle of light in the external air (external medium), the substrate 3, the first HOE 21, and the second HOE 22 is defined as θ ｉ , θ ｇ , θ' １ , θ' ２ Let's say.

[0048] The light diffracted by the first HOE 21 is totally reflected at the interface between the first HOE 21 and the substrate 3 or the interface between the first HOE 21 and the external medium, and is emitted toward the second HOE 22. Because the propagation angle of the light in the second HOE 22 is equal to the diffraction angle of the light diffracted by the first HOE 21, the following relational expression (P) holds true.

[0049] Considering the diffracted light from the second HOE 22 after total reflection at the interface between the second surface 2B and the external medium, the following Snell's law (Q) holds true.

[0050] The wavelength λ of light diffracted by the second HOE 22 ２ The operating condition of this element is as follows: ２ must match the wavelength λ of light diffracted on the front side of the first HOE 21. Furthermore, as will be described later, it is desirable that the bands of light wavelengths diffracted by the first HOE 21 and the second HOE 22 (operating wavelength bands) match.

[0051] Substituting formula (R) into formula (Q) gives the following relational expression:

[0052] By modifying equation (Q), the following relational expression is obtained. Therefore, the following relation is obtained:

[0053] By rearranging the second term of the middle equation of equation (S), we obtain the following relational expression.

[0054] By rewriting equation (S) using the above equations, the following equation is obtained:

[0055] Substituting equation (P) into equation (T) and rearranging, the following equation (T) is obtained.

[0056] From formula (U), formula (L) is derived.

[0057] Comparing with equation (H), it can be seen that in optical element 1A', light is diffracted twice, by the first HOE 21 and the second HOE 22, before being emitted, and the diffraction angle is determined by the difference between the reciprocals of the periods of the two HOEs in the direction parallel to the plane (the left side of equation (U)).

[0058] When the diffraction behavior is understood based on wave-like considerations, in this structure in which light is confined by diffraction at the first HOE 21 and emitted to the outside by diffraction at the second HOE 22, it can be understood that the wavefront is shifted by one wavelength at positions separated by the reciprocal difference between the periods of the two HOEs in the direction parallel to the plane (the left side of equation (U)).

[0059] Therefore, when the difference in the reciprocal of the period in the direction parallel to the in-plane has a phase distribution given by a computer-generated hologram algorithm, that is, when the difference between the spatial frequency in the in-plane direction of HOE2 resulting from the distribution of the structural tilt angle of second surface 2B and the spatial frequency in the in-plane direction of HOE2 resulting from the distribution of the structural tilt angle of first surface 2A is designed by a computer-generated hologram algorithm, a transmission-type phase hologram element can be realized. Note that, more precisely, the "in-plane direction" means "the direction along the incident-side interface between the HOE and the external medium when light is incident from outside the HOE."

[0060] For example, if the difference between the in-plane spatial frequency of the HOE2 resulting from the distribution of the structural tilt angles of the second surface 2B and the in-plane spatial frequency of the HOE2 resulting from the distribution of the structural tilt angles of the first surface 2A is constant, an optical element that functions as a transmissive polarizing element that changes the direction of light in a constant direction can be realized. If the difference between the in-plane spatial frequency of the HOE2 resulting from the distribution of the structural tilt angles of the second surface 2B and the in-plane spatial frequency of the HOE2 resulting from the distribution of the structural tilt angles of the first surface 2A is distributed quadratically, an optical element that functions as a transmissive lens can be realized. If the difference between the in-plane spatial frequency of the HOE2 resulting from the distribution of the structural tilt angles of the second surface 2B and the in-plane spatial frequency of the HOE2 resulting from the distribution of the structural tilt angles of the first surface 2A has a spatial phase singularity, an optical element that functions as a wavefront of a laser beam can be realized.

[0061] LD Sio et al., "Beam shaping diffractive wave plates," Appl. Opt. 57, A118-A121 (2018) discloses a transmission-type phase hologram element using pattern-oriented nematic liquid crystal (liquid crystal without a helical twist structure), but it does not provide the sharp wavelength selectivity of Examples 1 to 4 described below.

[0062] (Explanation Using Grating Vectors) The diffraction behavior of light in the optical element 1A' will be explained below with reference to FIG.

[0063] To generalize the diffraction behavior of a reflective liquid crystal diffractive optical element, the equiphase surface of the periodic structure is generally three-dimensionally curved. The diffraction behavior at any position (x, y) on the thin film is expressed as the grating vector G of the periodic structure at that position. １ This can be understood using

[0064] In the optical element 1A′ shown in FIG. 7, the direction of the grating vector changes along the film thickness direction of the element. １ , and in the vicinity of the interface of the second HOE 22, the grating vector G ２ It shall have the following.

[0065] In the considered xyz-coordinate system, the periodic structure is ｘ , i ｙ , i ｚ along the period Λ ｊｘ ,Λ ｊｙ ,Λ ｊｚ (j=1, 2). In this case, the grating vector G １ , G ２ is expressed as the following formula (V).

[0066] where i ｐ is the period (G ｊｘ i ｘ +G ｊｙ i ｙ ) is a unit vector in the direction The structural period is Λ ｊ = 2π / |G ｊ |, the inclination angle is tan α ｊ = G ｊｐ / G ｊｚ is defined as:

[0067] The wave vector of the incident wave is k ｉ = k ｉｘ i ｘ +k ｉｙ i ｙ +k ｉｚ i ｚ Here, if the wavelength of light is λ, then When the incident wave enters the HOE2, it is refracted according to Snell's law, and inside the HOE2, the following wave vector k１ｉ It has.

[0068] The wave vector of the diffracted wave inside the HOE2 is k １ｏ Then, the light wave in HOE2 is G = k １ｉ -k １ｏ Change the direction of travel so that This becomes:

[0069] The diffracted light is refracted according to Snell's law and emitted to the outside. That is, the wave vector k of the emitted wave ｏ１ becomes:

[0070] In the optical element 1A', the wave vector of the diffracted wave is given by the following: As described above, the light diffracted by the first HOE 21 is diffracted by the second HOE 22. Considering the traveling direction of the light, the wave vector k of the emitted wave is given by ｏ is given by the following formula (X):

[0071] Comparing the formula (W) and the formula (X), in the optical element 1A′, the difference component (G １ｘ -G ２ｘ ), (G １ｙ -G ２ｙ ) determines the diffraction behavior. １ｘ -G ２ｘ ), (G １ｙ -G ２ｙ If the optical element 1A' is designed so that the diffractive index θ has an arbitrary spatial distribution, the optical element 1A' can be manufactured with arbitrary diffraction characteristics.

[0072] (Discussion on operating wavelength band) In the optical element 1A', the structural angles of the first HOE 21 and the second HOE 22 are different. On the other hand, it is known that the diffractive operating wavelength of the HOE 2 varies depending on the structural period and the structural tilt angle. Therefore, it is desirable to change the values ​​of the structural periods of the first HOE 21 and the second HOE 22 of the HOEs.

[0073] As shown in Figure 8, HOEs generally have an operating wavelength band of about several tens of nanometers centered on a certain wavelength. On the other hand, when a HOE is realized using cholesteric liquid crystals, the diffracted wavelength is approximately given by the product of the minimum and maximum refractive indices and the periodic length that light can perceive in the structure (R. Ozaki et al., "Geometrical optics analysis of diffraction in patterned cholesteric liquid crystals", ACS Appl. Opt. Mater. 2, 1338-1346 (2024)).

[0074] As shown in FIG. 9, an incident angle θ ｉ In order to realize a HOE using cholesteric liquid crystal, the tilt angle of the molecules in the bulk is assumed to be β. The refractive index of the external medium of the HOE is assumed to be n ｉ Then, the propagation angle θ' of the light incident from outside in the medium is ｉ is given by the refraction at the interface as follows: In addition, n ｉ ' is the effective refractive index of the first HOE 21 at the interface between the external medium and the first HOE 21 .

[0075] A characteristic of periodic structures such as HOEs is that the effective refractive index changes depending on the diffracted wavelength. Specifically, the effective refractive index of the medium increases as the diffracted wavelength band transitions from the short wavelength side to the long wavelength side. When a periodic structure is formed by rotating the orientation of the director with birefringence, such as in cholesteric liquid crystals, the minimum effective refractive index is given by the ordinary light refractive index, and the maximum effective refractive index is given by the value averaged over one period, taking into account the angle of the director with respect to the direction of travel of the light ray. From equation (Y), it can be seen that as the effective refractive index changes, the propagation angle θ' of light within the medium ｉ The angle is the propagation angle θ corresponding to the minimum effective refractive index. o The propagation angle θ corresponding to the maximum effective refractive index e It changes up to.

[0076] The director of the rod-shaped liquid crystal constituting the cholesteric liquid crystal has an extraordinary refractive index nｅ , the ordinary refractive index n ｏ Then, the effective refractive index n ｉ The value of the short wavelength side of ', that is, the minimum effective refractive index value is n ｏ The value on the long wavelength side, i.e., the maximum effective refractive index, is given by is given by

[0077] In addition, when considering the effective refractive index n' related to diffraction within the HOE film, this is the average value of the effective refractive indexes of the light propagating through the HOE film in Figure 9 before and after Bragg reflection by the periodic structure of the HOE. Therefore, the effective refractive index n' on the short wavelength side is n ｏ and the effective refractive index n' on the long wavelength side is given by is given by

[0078] however, is the average extraordinary refractive index taking into account the helical structure, is.

[0079] For the reflection wavelength bands of the optical elements 1, 1', and 1A' shown in FIGS. 4 to 6, the structural period, structural tilt angle, extraordinary refractive index, and ordinary refractive index of the first surface 2A are Λ １ , α １ , n ｅ１ and n ｏ１ and the structural period, structural tilt angle, extraordinary refractive index, and ordinary refractive index of the second surface 2B are Λ ２ , α ２ , n ｅ２ and n ｏ２ and the propagation angle corresponding to the minimum and maximum effective refractive index on the first surface 2A is θ ｏ1 , θ ｅ1 , and the propagation angle corresponding to the minimum and maximum effective refractive index on the second surface 2B is θ ｏ２ , θ ｅ２ Therefore, the reflection wavelength band is λ ｏ１ From λ ｅ１ and λ on the second surface 2B side. ｏ２ From λ ｅ２ Specifically, the short wavelength end λ of the reflection wavelength band on the first surface 2A side ｏ１ and the long wavelength end λ ｅ１teeth, and the short wavelength end λ of the reflection wavelength band on the second surface 2B side ｏ２ and the long wavelength end λ ｅ２ teeth, This becomes:

[0080] The greater the overlap range between the reflection wavelength band on the first surface 2A side shown in formulas (Z) and (AA) and the reflection wavelength band on the second surface 2B side shown in formulas (AB) and (AC), the larger the operating wavelength band. ２ is α １ If larger, Λ ２ is Λ １ Larger than α ２ is α １ If smaller, Λ ２ is Λ １ It is preferable to adjust the refractive index of ordinary light so that it is smaller than α ２ is α １ If greater than n ｏ２ Ga n ｏ１ Larger than α ２ is α １ If n is smaller than ｏ２ Ga n ｏ１ It is preferable to adjust the refractive index of extraordinary light so that it is smaller than α. ２ is α １ If greater than n ｅ２ Ga n ｅ１ Larger than α ２ is α １ If n is smaller than ｅ２ Ga n ｅ１ It is preferable to adjust it to be smaller.

[0081] It has been reported that the structural period or refractive index of an HOE can be locally modulated by applying a different liquid crystal material dissolved in a solvent to the HOE film and allowing it to penetrate (K. Igeta et al., "Tuning the Reflection Bandwidth of Polarization Volume Gratings by Guest Material Penetration", ACS Appl. Opt. Mater. vol.2, pp.1314-1320, (2024)).

[0082] (Element Design) The element design of the optical elements 1, 1', and 1A' (hereinafter referred to as the proposed elements) shown in FIGS. 4 to 6 will be described.

[0083] First, the element design based on the concept of light rays will be explained.

[0084] Consider the required light emission direction at each position of the element, and define this as θ ｔ (Target).

[0085] Outgoing ray angle θ ｏ is given by the following equation by modifying equation (U).

[0086] θ ｏ = θ ｔ By doing so, the structural period Λ required at each position is ２ and the tilt angle α ２ The relationship between

[0087] Furthermore, since the design operating wavelength is given by the following equations (AB) and (AC), the structural period Λ is set to satisfy the design conditions. ２ and the tilt angle α ２ Just decide.

[0088] structural period Λ ２ and the tilt angle α ２The HOE designed as described above can be fabricated by several methods, such as etching after photolithography or interference exposure. It can also be fabricated by applying an alignment film to the surface of a substrate, forming an orientation distribution of the alignment control force, and then forming a film of cholesteric liquid crystal. When realizing an HOE using cholesteric liquid crystal, the orientation of the alignment control force on the substrate is set to φ ０ Then, the rate of change of the orientation (dφ ０ / dx), the tilt angle α, and the structural period Λ have the following relationship: Therefore, spatially (dφ ０ / dx) can be changed to change the tilt angle.

[0089] When a certain structural period Λ is given, the azimuth distribution of the orientation control force required to obtain a desired tilt angle distribution can be calculated as follows.

[0090] As already mentioned, since the operating wavelength band of the HOE depends on the structural period Λ and the tilt angle α, it is desirable to spatially distribute the structural period in order to reflect at a desired wavelength. In this case, equation (AE) can be calculated assuming that the structural period also depends on space.

[0091] Next, element design based on wave optics will be described.

[0092] Consider a hologram element that can provide any two-dimensional or three-dimensional light intensity distribution using the proposed element. When a plane wave is generally incident on a hologram element, the exit wavefront is shaped depending on the position within the element, thereby achieving its function. Since a wavefront generally corresponds to the normal plane of a wave vector, shaping the exit wavefront depending on the position within the element is equivalent to obtaining the spatial distribution of the exit wave vector of equation (X), assuming that the plane of the optical element exists on the xy plane.

[0093] As mentioned above, in the proposed element, the wave vector of the output wave is the difference between the components parallel to the film surface of the front and rear grating vectors (G １ｘ -G ２ｘ ) and (G １ｙ -G ２ｙ) Therefore, by designing the element so that the difference between the grating vectors of the first surface 2A and the second surface 2B at the emission position at any position (x, y) within the element is a desired value, it is possible to obtain any wave vector distribution and realize a hologram element that provides any two-dimensional or three-dimensional light intensity distribution.

[0094] An example of the design of a reflective HOE that functions as a hologram element and provides a two-dimensional light intensity distribution using cholesteric liquid crystals is reported in J. Kobashi, H. Yoshida, and M. Ozaki, "Circularly-polarized, semitransparent, and double-sided holograms based on helical photonic structures," Sci. Rep. 7, 16470 (2017). In this report, the orientation pattern on the HOE substrate is designed two-dimensionally using the Gerchberg-Saxton algorithm, a type of computer-generated algorithm. In other words, assuming that the plane of the optical element exists on the x-y plane, the orientation pattern φ on the substrate to realize the desired hologram element is calculated using a computer-generated hologram algorithm. ０ '(x, y) can be obtained.

[0095] When a transmission type hologram element is realized by the proposed element, the pattern φ obtained by the above-mentioned method is ０ '(x, y) is modulated as follows, and the pattern φ ０ In the element of the present invention, the grating vector G １ exists uniformly in the xz plane, and the second HOE 22 has a grating vector G ２ (x, y) exists. The structural period of the first HOE 21 is Λ １ , the structural tilt angle is α １ and it is assumed that equation (1) or (4) is satisfied.

[0096] The orientation pattern φ on the substrate before modulation obtained by the computer-generated hologram algorithm. ０ '(x, y) is the distribution of grating vectors G ２ When such a hologram element exists as a single layer, the diffracted wave is expressed by the grating vector G in equation (W). ２ It functions as a reflective HOE that is modulated only by '.

[0097] In the element of the present invention, the grating vector G of the first HOE 21 １ The light diffracted by the second HOE 22 is incident on the grating vector G ２ (x, y) and the output wave transmitted through the element is ２ From equation (X), the following relationship holds:

[0098] G １ By considering each component of G, the above equation can be transformed into ２ The components of (x, y) are found as follows:

[0099] From the above equation, the grating vector of the second HOE 22 is the desired grating vector G ２ It can be seen that all that is needed is to add a component to ' that cancels out the diffraction of the first HOE 21. When the first HOE 21 forms a uniform periodic structure in the x-z plane, as in the present example, this is equivalent to tilting the entire structure by an angle α1 while maintaining the relative tilt angle distribution between each (x, y) position. In other words, since the grating vector is given as the normal plane of the periodic structure, in order to tilt the grating vector in the x-axis direction, it is necessary to tilt the periodic structure in the x-z plane.

[0100] Using equation (AD), the pattern of the second HOE 22 after modulation can be determined as follows:

[0101] Third Embodiment By stacking a plurality of optical elements that diffract light in different wavelength bands, the operating wavelength band can be made wider than that of a single optical element.

[0102] 10 is a cross-sectional view showing the configuration of a composite optical element 10 according to this embodiment. The composite optical element 10 includes three optical elements 1-1, 1-2, and 1-3. The optical elements 1-1, 1-2, and 1-3 have the same basic structure as the optical element 1 shown in FIG. 4, but have different operating wavelength bands. Specifically, the operating wavelength band of the optical element 1-1 is a band that includes blue light, the operating wavelength band of the optical element 1-2 is a band that includes green light, and the operating wavelength band of the optical element 1-3 is a band that includes red light.

[0103] Furthermore, a member (optical resin or the like) having a refractive index that causes total reflection at the interface between each of the optical elements 1-1, 1-2, and 1-3 is interposed between the optical elements 1-1, 1-2, and 1-3 or the space D. This enables the composite optical element 10 to operate in all of the operating wavelength bands of the optical elements 1-1, 1-2, and 1-3.

[0104] [Method of Manufacturing Optical Element] Next, a method of manufacturing the proposed element using cholesteric liquid crystal will be specifically described.

[0105] (Method 1: Cell fabrication method) In the cell fabrication method, two alignment-treated substrates are bonded together with a gap between them, and cholesteric liquid crystal (which has fluidity) is sealed between them to create an element. Specifically, the fabrication process involves steps 1 to 5 below: 1. Prepare two substrates, and coat each with an alignment agent to form a film (spin coating, bar coating, slit coating, printing, etc.). 2. Align the substrates (interference exposure, etc.). 3. Bond the two substrates together with a specified gap between them. 4. Seal the cholesteric liquid crystal material. 5. Operate as a diffractive optical element that follows the alignment pattern.

[0106] (Method 2: Coating film formation method) In the coating film formation method, a precursor solution containing polymerizable cholesteric liquid crystal is applied to a substrate, and after drying, it is polymerized by stimulation such as light irradiation to obtain a solid film. Specifically, it is produced by the following steps 1 to 6. 1. An alignment agent is applied to the substrate to form a film (spin coating, bar coating, slit coating, printing, etc.). 2. An alignment treatment is performed on the substrate. 3. A precursor solution containing polymerizable cholesteric liquid crystal is applied to the substrate to form a film (spin coating, bar coating, slit coating, etc.). 4. The liquid crystal solution is vacuum dried and baked to obtain a homogeneous film with uniform alignment. 5. A film with a fixed liquid crystal structure is obtained by light irradiation. 6. It acts as a diffractive optical element that follows the alignment pattern.

[0107] (Method for producing composite optical elements) A composite optical element can be produced by layering the optical element (film) produced by the method described above using the following steps 1 to 4. 1. A heat- or light-peeling film is attached to the polymerized liquid crystal film (such as Nitto Denko's Rivalpha). 2. The liquid crystal film with the attached peelable film is peeled off from the substrate. 3. The transfer process is completed by transferring it to another substrate and peeling off the peelable film by heating or irradiating it with light. 4. The liquid crystal film can be layered by performing the transfer process on another substrate to which the liquid crystal film has already been transferred.

[0108] Examples of the present invention will be described below, but the present invention is not limited to the following examples.

[0109] [Example 1] (Summary) In Example 1, a wavelength-selective transmissive diffraction element was fabricated by sandwiching two substrates that had been subjected to different alignment treatments to achieve different tilt angles on both sides of the HOE. This fabrication method is similar to that described in J. Kobashi, H. Yoshida, and M. Ozaki, "Circularly-polarized, semitransparent, and double-sided holograms based on helical photonic structures," Sci. Rep. 7, 16470 (2017).

[0110] (Fabrication Procedure) The specific fabrication procedure is as follows. 1. (Substrate Cleaning) Two glass substrates A and B were ultrasonically cleaned for 5 minutes using an alkaline cleaning solution (Furuuchi Chemical, Semicoclean 56), and then cleaned using a UV ozone cleaner. 2. (Application of Alignment Film) A photo-alignment film was spread on substrates A and B using a bar coater, and then spin-coated at 750 rpm for 5 seconds and 2000 rpm for 20 seconds to form a coating film on substrates A and B, followed by heat treatment at 60°C for 2 minutes. 3. (Alignment Treatment of Substrate A) As shown in Figure 11, left and right circularly polarized light were interfered on substrate A using two-beam interference with a laser light source LS with a wavelength of 405 nm, forming an alignment pattern in which the direction of the alignment restraint force on substrate A changed linearly with a period of approximately 340 nm. Specifically, the laser beam was expanded by a combination of a concave lens L1 and a convex lens L2, then split into two beams via a beam splitter PBS. The polarization of each beam path was adjusted to become right- and left-handed circularly polarized light at the position of substrate A, and then irradiated onto substrate A. Specifically, a polarizer P was placed in each optical path to convert the beam into linear polarization, and then a λ / 4 wavelength plate Q was inserted. Taking into account the polarization reversal caused by a mirror M in the optical path, the angle of the optical axis of the λ / 4 wavelength plate Q relative to the linear polarization was adjusted so that each beam was irradiated as right- and left-handed circularly polarized light at substrate A. As a result, an alignment pattern was formed in which the direction of the alignment restraining force on substrate A changed linearly with a period of approximately 340 nm, as shown in Figure 12(a). After exposure, the alignment pattern was fixed through a baking process at 120°C for 15 minutes and then at 230°C for 15 minutes. (Alignment treatment of substrate B) As in step 3 above, left- and right-handed circularly polarized light was interfered on substrate B using two-beam interference with a laser light source LS with a wavelength of 405 nm, forming an alignment pattern in which the direction of the alignment restraint force on substrate B changes linearly with a period of approximately 390 nm, as shown in Figure 12(b). After exposure, the alignment restraint force was fixed through a baking process at 120°C for 15 minutes and at 230°C for 15 minutes. 5. (Fabrication of sandwich cell) Two alignment-treated substrates A and B were bonded together with a gap of approximately 5 μm. 6. (Encapsulation of liquid crystal) A cholesteric liquid crystal that spontaneously forms a right-handed helical structure with a structural period of approximately 180 nm was enclosed in the sandwich cell. As a result, as shown in Figure 13, the tilt angle α on the substrate A side was increased. １is about 31°, and the inclination angle α ２ An optical element (hereinafter referred to as a sample) having a .times. ...

[0111] (Evaluation) First, the diffraction wavelength of the sample was evaluated from the transmission spectrum. The transmission spectrum when right-handed circularly polarized light was incident on the sample is shown in FIG.

[0112] The band where the transmittance drops sharply (approximately 478-532 nm, where the transmittance is half the maximum-minimum value) is the operating wavelength band for diffraction by cholesteric liquid crystals. The gradual decrease in transmittance toward shorter wavelengths is due to the light absorption of the alignment agent used in the experiment; in actual applications, this can be avoided by using an alignment agent that does not absorb light in the same wavelength band.

[0113] Next, light with a wavelength of 510 nm, included in the reflection band, was incident perpendicularly on the sample, and the diffracted light from the sample was collected with a lens and observed to evaluate the diffraction angle. The structural parameters and diffraction wavelength in this example satisfied equations (1), (2), and (3), respectively. The observed diffraction angle was approximately 11°. This value is the theoretically predicted diffraction angle. It matched.

[0114] When light of wavelengths of 450 nm and 580 nm, which are outside the operating wavelength band, was incident on the sample, it was not diffracted but was transmitted, confirming that wavelength-selective diffraction occurred.

[0115] [Example 2] (Summary) In Example 2, an optical element that functions as a transmissive diffractive lens was fabricated by forming a structure with a uniform tilt angle on the first surface side of the HOE and forming a structure with a distributed tilt angle on the second surface side of the HOE.

[0116] (Fabrication Procedure) The specific fabrication procedure is as follows. 1. (Substrate Cleaning) A 50 mm square glass substrate was ultrasonically cleaned with an alkaline cleaning solution (Furuuchi Chemical, Semicoclean 56), then plasma-treated, and a photo-alignment film was applied to the substrate. 2. (Application of Alignment Film) The photo-alignment film was spread using a bar coater and then spin-coated to form a coating film on the substrate. 3. (Alignment Treatment of Substrate A) As in Example 2, as shown in Figure 11, left and right circularly polarized light were interfered on the substrate using two-beam interference with a laser light source LS with a wavelength of 405 nm, forming an alignment pattern in which the direction of the alignment restraining force on Substrate A changes linearly with a period of approximately 400 nm, and the pattern was fixed through a baking process at 120°C for 15 minutes and 230°C for 15 minutes. At this time, Substrate A was positioned so that it faced one beam. 4. (Formation of a liquid crystal film on an alignment-treated substrate A) A polymerizable cholesteric liquid crystal solution with a helical pitch (the period of 360° rotation of molecular orientation) of approximately 315 nm was spread on substrate A using a bar coater, followed by spin coating at 1000 rpm for 30 seconds. The solution was then vacuum dried for 2 minutes and heat-treated at 120°C for 3 minutes to promote alignment, after which a solid film was obtained by irradiating with ultraviolet light (360 nm). This resulted in an HOE (first HOE 21) with a structural period of approximately 155 nm and a tilt angle of approximately 24°. 5. (Attachment of a protective film) An optical adhesive was dropped onto the solid film, and a 0.3 mm glass substrate was attached as a protective film. 6. (Alignment treatment of substrate B) Substrate B was prepared, and as shown in Figure 15, left- and right-handed circularly polarized light was applied to substrate B using a two-beam interference method using a laser light source LS with a wavelength of 405 nm. At this time, a plano-convex lens L3 with a focal length of approximately 150 mm was placed in the optical path perpendicular to substrate B, forming an alignment pattern in which the carrier component was modulated by the convex lens L2 at a period of 400 nm. The alignment pattern was fixed through a baking process at 120°C for 15 minutes and then at 230°C for 15 minutes. 7. (Formation of a liquid crystal film on alignment-treated substrate B) A polymerizable cholesteric liquid crystal solution with a helical pitch (the period of 360° rotation of molecular alignment) of approximately 315 nm was spread on substrate B using a bar coater, then spin-coated at 1000 rpm for 30 seconds. The alignment was promoted through vacuum drying for 2 minutes and heat treatment at 120°C for 3 minutes, and a solid film was obtained by irradiating with ultraviolet light (360 nm).This resulted in a HOE (second HOE 22) in which the tilt angle was spatially distributed with parabolic dependence from approximately 21° to 26°. 8. (Attachment of protective film) An optical adhesive was dropped onto the solid film, and a 0.3 mm glass substrate was attached as protective film C. 9. (Stacking of two substrates) Two substrates A and B were attached together via an optical resin, completing an optical element (hereinafter referred to as a sample) that functions as a transmission type diffractive lens, as shown in Figure 16.

[0117] (Evaluation) The reflection wavelength band of the sample was evaluated. Specifically, white light was incident perpendicularly onto the sample, and the transmission spectrum was measured.

[0118] As a result, as shown in Figure 17(a), diffraction was confirmed at wavelengths of approximately 485-545 nm at the center of the sample. Meanwhile, when the transmission spectrum was measured at both ends of a sample approximately 30 mm long, a difference in the diffraction wavelength band was observed between the left and right ends, as shown in Figure 17(b). This is due to the fact that the structural tilt angle differs depending on the position on the sample, causing a change in the diffraction wavelength band. Therefore, the operating wavelength band of this optical element was approximately 490-535 nm, where diffraction was observed across the entire surface.

[0119] Next, right-handed circularly polarized laser beams with wavelengths of 520 nm and 670 nm were incident on the sample. The position dependence of the intensity distribution of the emitted light was measured by measuring the profile of the emitted light at different distances from the sample (49 mm, 65 mm, 81 mm, and 97 mm from the sample) using a beam profiler.

[0120] As a result, a light-collecting effect was observed for light of 520 nm within the reflection wavelength band, as shown in Figure 18. On the other hand, no light-collecting effect was observed for light of 670 nm outside the reflection wavelength band, as shown in Figure 19. This confirmed that a wavelength-selective transmission lens function was produced.

[0121] [Example 3] (Summary) In Example 3, an optical element was fabricated in which the diffraction wavelengths coincide at the front surface of the element by modulating not only the structural tilt angle but also the structural period on the first and second surface sides of the HOE. That is, in Example 3, the structural period was changed by infiltrating a portion of the optical element in Example 2 with a liquid crystal solution (guest molecules), thereby making the analysis wavelengths coincide at the front surface of the element.

[0122] (Fabrication Procedure) The specific fabrication procedure is as follows. 1. An optical element functioning as a transmissive diffractive lens, as shown in FIG. 16, was fabricated using the same method as in Example 2 (steps 1 to 9). 2. A liquid crystal solution was locally dispensed onto substrate B to modulate the structural period. Specifically, low-molecular-weight liquid crystal (LCC, 5CT) was dissolved in a solvent (cyclohexanone) at a concentration of 10 mg / ml, and the solution was dispensed onto a portion of substrate B using a micropipette, as shown in FIG. 20. This allows the low-molecular-weight liquid crystal molecules to penetrate into the HOE film, locally extending the structural period Λ. It should be noted that the low-molecular-weight liquid crystal solution can be dispensed using a micropipette or inkjet printing. When the liquid crystal solution is dispensed onto the orientation pattern with a structural period Λ shown in FIG. 21(a), the liquid crystal molecules enter between the orientation patterns, changing the structural period to Λ', as shown in FIG. 21(b). 3. By varying the amount of liquid crystal permeated at different locations on the substrate A, an optical element (hereinafter referred to as a sample) was fabricated in which the second HOE 22 had an in-plane distribution of structural period and tilt angle, as shown in Figure 22. １ is constant at about 155 nm, whereas the structural period Λ of the second HOE 22 is ２ It should be noted that in order to match the operating diffraction wavelengths of the first HOE 21 and the second HOE 22, Λ ２ / sinα ２ Λ so that is constant ２ Depending on the change in α ２ was adjusted.

[0123] (Evaluation) As in Example 2, the reflection wavelength band of the sample was evaluated. FIG. 23 shows the diffraction wavelength spectra at the left and right ends of the sample. Compared to FIG. 17(b) of Example 2, the difference between the diffraction wavelength bands at the left and right ends is smaller. That is, it was confirmed that the overlapping region of the diffraction wavelength bands, which was approximately 495-535 nm in Example 2, had expanded to approximately 490-545 nm. This indicated that the operating wavelength band of the sample had expanded.

[0124] REFERENCE SIGNS LIST 1 optical element 1' optical element 1A optical element 1A' optical element 1-1 optical element 1-2 optical element 1-3 optical element 2 HOE (volume hologram element) 3 substrate 10 composite optical element 21 first HOE 22 second HOE A substrate B substrate C protective film S space

Claims

1. An optical element having a volume hologram element (HOE) with a periodic refractive index distribution that Bragg-reflects light of a specific wavelength, wherein the structural period of the arrangement on the first surface side of the HOE onto which the light is incident is Λ １ , the structural tilt angle is α １ and the structural period of the array on the second surface side opposite to the first surface is Λ ２ , the structural tilt angle is α ２ Then, Λ １ and α １ is Λ ２ and α ２ and the external refractive index of the first surface is n ｉ , the incident angle of the light to the first surface is θ ｉ Then, the following formula (1) is satisfied: The external refractive index of the second surface is n ０ Then, the optical element is characterized in that the following formula (2) or formula (3) is satisfied:

2. An optical element comprising: a volume hologram element (HOE) having a periodic refractive index distribution that Bragg-reflects light of a specific wavelength; and a substrate formed on a first surface of the HOE onto which the light is incident, wherein the structural period of the arrangement on the first surface side of the HOE is Λ １ , the structural tilt angle is α １ and the structural period of the array on the second surface side opposite to the first surface is Λ ２ , the structural tilt angle is α ２ Then, Λ １ and α １ is Λ ２ and α ２ and the external refractive index of the first surface is n ｉ , the refractive index of the HOE relative to the substrate is n ｇ , the incident angle of the light to the first surface is θ ｉ Then, the following equation (4) is satisfied: The external refractive index of the second surface is n ０ Then, the following formula (2) or formula (3) is satisfied.

3. The optical element according to claim 1 or 2, wherein α ２ is α １ If larger, Λ ２ is Λ １ Larger than α ２ is α １ If smaller, Λ ２ is Λ １ Smaller optics.

4. An optical element according to claim 1 or 2, wherein the ordinary refractive index of the first surface is n ｏ１ , the ordinary refractive index of the second surface is n ｏ２ Then, α ２ is α １ If greater than n ｏ２ Ga n ｏ１ Larger than α ２ is α １ If n is smaller than ｏ２ Ga n ｏ１ Smaller optics.

5. An optical element according to claim 1 or 2, wherein the extraordinary refractive index of the first surface is n ｅ１ , the extraordinary refractive index of the second surface is n ｅ２ Then, α ２ is α １ If greater than n ｅ２ Ga n ｅ１ Larger than α ２ is α １ If n is smaller than ｅ２ Ga n ｅ１ Smaller optics.

6. An optical element according to claim 1 or 2, wherein the difference between the spatial frequency in the in-plane direction of the HOE resulting from the distribution of the structural tilt angles of the second surface and the spatial frequency in the in-plane direction of the HOE resulting from the distribution of the structural tilt angles of the first surface is designed by a computer-generated hologram algorithm.

7. An optical element according to claim 6, wherein the difference between the spatial frequency in the in-plane direction of the HOE resulting from the distribution of the structural tilt angles of the second surface and the spatial frequency in the in-plane direction of the HOE resulting from the distribution of the structural tilt angles of the first surface is constant.

8. An optical element according to claim 6, wherein the difference between the spatial frequency in the in-plane direction of the HOE resulting from the distribution of the structural tilt angle of the second surface and the spatial frequency in the in-plane direction of the HOE resulting from the distribution of the structural tilt angle of the first surface is distributed in the form of a quadratic function.

9. An optical element according to claim 6, wherein the difference between the spatial frequency in the in-plane direction of the HOE resulting from the distribution of the structural tilt angles of the second surface and the spatial frequency in the in-plane direction of the HOE resulting from the distribution of the structural tilt angles of the first surface has a spatial phase singularity.

10. An optical element according to claim 1 or 2, wherein the periodic refractive index distribution is formed by a helical periodic structure of rod-like molecules contained in a cholesteric liquid crystal.

11. A composite optical element comprising a plurality of optical elements according to claim 1 or 2, wherein each optical element diffracts light in a different wavelength band, and a member having a refractive index that causes total reflection in the space or at the interface between each optical element is interposed between each optical element.

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