JP6168642B2 - Diffraction grating and manufacturing method thereof, optical waveguide - Google Patents

Description

  The present invention relates to various optical measuring instruments, head-up displays such as automobile and aircraft instruments, three-dimensional video displays, high-efficiency diffraction gratings used for introducing external light into energy-saving offices and energy-saving houses, or polarized light The present invention relates to a diffraction grating having a separation function, and further to an active diffractive optical element used for optical information processing, optical computing, and the like.

[Transmission type VPH diffraction grating]
A thick diffraction grating manufactured by two-beam laser interference exposure and having a refractive index changing in a sinusoidal shape is called VPH (Volume Phase Holographic). Here, when the wavelength is λ, the thickness of the grating is t, the grating period is Λ, and the average refractive index is n = (nmax + nmin) / 2.
Q = 2πλt / (nΛ ² ) (1)
When the Q value of the diffraction grating defined by (1) is Q <1, the diffraction grating is classified as a thin diffraction grating, and when Q> 10, the diffraction grating is classified as a thick diffraction grating. Note that nmax and nmin are the maximum refractive index and the minimum refractive index of the diffraction grating, respectively.

As shown in FIG. 1, the transmissive VPH diffraction grating 1 is adjusted to S polarization (electric field vector) by adjusting the grating thickness t and refractive index modulation: Δn = (nmax−nmin) / 2 to satisfy the following Bragg diffraction conditions. It is possible to achieve a diffraction efficiency of up to 100% for either a polarization component that oscillates horizontally relative to the grating direction) or a P-polarized light (a polarization component whose electric field vector oscillates perpendicular to the grating direction). . Bragg's diffraction conditions are
mλ = 2nΛ sin (θ) (2)
Given by. Here, m is the diffraction order. Further, when the grating is perpendicular to the surface on which the light beam enters and exits the transmission type VPH diffraction grating 1, the Bragg angle θ = incidence angle = diffraction angle, and the grating is inclined at an angle α. Are incident angle = θ + α and diffraction angle = θ−α.

  A thick diffraction grating such as a VPH diffraction grating whose refractive index changes in a sinusoidal shape is obtained by using a two-wave coupling analysis method that handles only the combination of the 0th-order diffracted light and the 1st-order diffracted light. The relative value (the maximum value of S-polarized light and P-polarized light is always 100%) can be estimated. According to Non-Patent Document 1 and Non-Patent Document 2, when the light beam incident on the transmission type VPH diffraction grating 1 perpendicular to the surface on which the grating enters and the surface on which the light exits satisfies the Bragg diffraction condition, The Bragg angle θ is obtained by substituting the grating period Λ, wavelength λ, and average refractive index n into 2), and given the maximum refractive index nmax, minimum refractive index nmin, and grating thickness t, the S-polarized light of the first-order diffracted light The diffraction efficiency ηS for P and the diffraction efficiency ηP for P-polarized light are respectively

によって求めることができる。

Can be obtained.

  The transmissive VPH diffraction grating 1 is made of, for example, a hologram resin 20 made by Nippon Paint. Nippon Paint's hologram resin 20 is a resin monomer (RPM) that is highly refractive index polymerized by visible light and ultraviolet light, a monomer monomer (CPM: Cationically polymerized monomer) that is polymerized by UV light and a low refractive index. , A photoinitiator, a solvent, and the like, and a hologram resin 20 in which glass beads (not shown) or the like are mixed as a spacer for adjusting the thickness t between the substrate 30 and the substrate 40 as shown in FIG. When the RPM of the bright part of the interference fringe is overlapped by the interference exposure of the visible light laser, a CPM and RPM density gradient is generated between the bright part and the dark part. And the RPM moves from the dark part to the bright part. Thereafter, the remaining RPM and CPM are polymerized by performing uniform ultraviolet irradiation, and the refractive index modulation is fixed. That is, development and fixing of the hologram resin 20 are dry processes. In addition, dichromated gelatin or the like is used as a thick hologram recording material. Development and fixing (bleaching) of dichromated gelatin is a wet process.

  FIG. 2 shows the wavelength λ = 0.96, 1.02, 1.11 μm of the transmissive VPH diffraction grating 1 manufactured using the hologram resin 20 and having a grating period Λ = 0.984 μm and an average refractive index n = 1.53. That is, from equation (2), the Bragg angles are measured values of the wavelength characteristics of the polarization diffraction efficiency at θ = 18.6 °, 19.8 °, and 21.6 °, respectively. Since the thickness of the grating is t = 20 μm, a plausible refractive index modulation amount Δn that satisfies the expressions (3) and (4) from the polarization diffraction efficiency characteristics at the Bragg angles of three wavelengths in FIG. = (Nmax-nmin) /2=0.17 was obtained. FIG. 3 is a diagram showing numerical calculation of polarization diffraction efficiency with respect to the thickness of the transmission type VPH diffraction grating 1 of FIG. 2 at λ = 1.02 μm (θ = 19.8 °). As shown in FIG. 3, this transmission type VPH diffraction grating 1 has the maximum diffraction efficiency of S-polarized light at t = 23.8 μm from the equation (3), and P-polarized light at t = 31.4 μm from the equation (4). It can be seen that the diffraction efficiency is maximum, and the average of the diffraction efficiency of S polarization and that of P polarization is 96% of the maximum value at t = 26.6 μm.

  According to Non-Patent Document 3, when the Bragg angle inside the transmissive VPH diffraction grating 1 is θ = 30 °, the diffraction of P-polarized light as shown in FIG. 4 from the equations (3) and (4). It is shown that the polarization separation element is a condition (Dixon's condition 1) in which the diffraction efficiency of S-polarized light becomes 0% at the thickness where the efficiency is first maximized. The transmission type VPH diffraction grating 1 of FIG. 4 has a grating period: Λ = 0.4 μm, wavelength: λ = 0.6 μm, average refractive index: n = 1.5, refractive index modulation amount: Δn = 0.07, θ = 30 °. From Snell's refraction formula: n × sin θ = sin θ0, the Bragg angle in vacuum is θ0 = 48.6 °. In FIG. 4, the maximum of the average value of the diffraction efficiencies of S-polarized light and P-polarized light seen in the vicinity of the first maximum of S-polarized light is 79%. Further, in the case of θ = 35.3 °, from the equations (3) and (4), the diffraction efficiency of the S-polarized light is the second maximum when the diffraction efficiency of the P-polarized light is the first maximum thickness as shown in FIG. In order to maximize, it is shown that both S-polarized light and P-polarized light are conditions (Dixon condition 2) that can achieve a high diffraction efficiency of 100% at the maximum. However, since the wavelength bandwidth becomes narrower as the thickness of the transmission type VPH diffraction grating 1 increases, the wavelength bandwidth at the second maximum thickness of S-polarized light is the thickness of the first maximum of S-polarized light. 1/3 of the wavelength bandwidth. The transmission type VPH diffraction grating 1 in FIG. 5 has Λ = 0.346 μm, λ = 0.6 μm, n = 1.5, Δn = 0.07, and θ = 35.3 ° (θ0 = 60 °). In FIG. 5, the maximum of the average value of the diffraction efficiency of S-polarized light and P-polarized light seen in the vicinity of the first maximum of S-polarized light is 63.5%.

[Thick transmission type rectangular diffraction grating]
As shown in FIG. 6, the thick transmission type rectangular diffraction grating 2 has a rectangular or parallel four-sided cross section between an optically isotropic medium substrate 30 having a refractive index n1 and an optically isotropic medium substrate 40 having a refractive index n3. This is a thick phase type diffraction grating in which an optically isotropic medium 21 having a refractive index n2a and an optically isotropic medium 22 having a refractive index n2b (n2a ≠ n2b) are alternately arranged.

  In many cases, the thick transmission type rectangular diffraction grating 2 is formed of an optically isotropic medium layer formed on the optically isotropic medium substrate 30 or the substrate 30 itself by a photolithography technique or the like. A rectangular lattice of ridges: Ridge is formed, and a groove: Groove of the rectangular lattice is filled with the optical isotropic medium 22. In other words, the optical isotropic medium 21 may be the same material as the substrate 30. Furthermore, an optically isotropic medium substrate 40 may be provided on the grating. The substrate 40 of the optical isotropic medium may be the same material as the optical isotropic medium 22. Also, when the grooves of the rectangular grating and the substrate 40 are a gas such as air or a vacuum, it is also called a surface engraved diffraction grating.

  When calculating the diffraction efficiency of the thick transmissive rectangular diffraction grating 2, the numerical calculation by the two-wave coupling analysis is insufficient in accuracy, and in order to estimate the accurate polarization diffraction efficiency for the 0th-order diffracted light and the 1st-order diffracted light, According to Non-Patent Document 4, numerical calculation of, for example, about 8 waves from -3rd order diffracted light to 4th order diffracted light using a strictly coupled wave analysis (RCWA) or the like is necessary. However, the ratio of the grating period Λ to the width of the groove or groove (duty ratio) is 2: 1, that is, the thick transmission type rectangular diffraction grating 2 in which the optical isotropic medium 21 and the optical isotropic medium 22 are equal in width. The polarization diffraction efficiency characteristics of the transmissive VPH diffraction grating 1 are similar. As shown in FIGS. 3 to 5, the diffraction efficiency of the S-polarized light and the P-polarized light is periodically maximized and minimized with respect to the thickness. repeat. According to Non-Patent Document 5, the thick transmission type rectangular diffraction grating 2 is provided with a refractive index n2a of the optical isotropic medium 21 and a refractive index of the optical isotropic medium 22 when a use wavelength λ and a grating period Λ are given. By adjusting n2b and the grating thickness t to satisfy the Bragg diffraction conditions, it is possible to achieve a diffraction efficiency of up to 100% for either S-polarized light or P-polarized light. However, the transmission type VPH diffraction grating in which the period of diffraction efficiency with respect to the grating thickness t of the thick transmission type rectangular diffraction grating 2 having a duty ratio of 2: 1 and the operating wavelength λ, the grating period Λ, the maximum refractive index, and the minimum refractive index are equal. The period of the diffraction efficiency of 1 becomes more dissimilar as the Bragg angle θ increases.

  Thick transmissive rectangular diffraction grating 2 in which the refractive index of the optical isotropic medium 21 is n2a = 1.7, the refractive index of the optical isotropic medium 22 is n2b = 1.5, and the duty ratio is 2: 1. Is equal to the grating period at which the diffraction efficiency of the first-order diffracted light is first maximized when the wavelength λ is equal to the grating period Λ, that is, when the Bragg angle in vacuum is θ0 = 30 °. When the thickness: t / Λ is obtained by the RCWA method, t / Λ = 1.80 for S-polarized light and t / Λ = 2.30 for P-polarized light. On the other hand, the transmissive VPH diffraction grating 1 having a maximum refractive index: nmax = 1.7 and a minimum refractive index: nmin = 1.5 (that is, the maximum refractive index of the transmissive rectangular diffraction grating 1 is transmissive rectangular diffraction). When θ0 = 30 ° with respect to the larger one of the refractive indexes of the optically isotropic media 21 and 22 of the grating 2 and the smaller one of the refractive indexes of the optically isotropic media 21 and 22, the formula ( When the diffraction efficiency of the first-order diffracted light is obtained by 3) and Equation (4), the S-polarized light is t / Λ = 2.38 and the P-polarized light is t / Λ = 2.95. Therefore, the ratio of the thicknesses of the thick transmissive rectangular diffraction grating 2 and the transmissive VPH diffraction grating 1 is 1: 1.32 and 1: 1.28 for S-polarized light and P-polarized light, respectively.

  According to Patent Document 1, by adjusting the duty ratio and the refractive index of the grating ridge for a thick surface-transmitted rectangular diffraction grating 2, the diffraction efficiency of one polarized light can be obtained for an arbitrary Bragg angle θ. The numerical calculation shows the condition that the diffraction efficiency of the other polarized light becomes 0% at the maximum thickness. Further, according to Non-Patent Document 6, by adjusting the duty ratio and the refractive index of the grating ridge in the surface-transmitted thick transmission rectangular diffraction grating 2, the S-polarized light can be obtained for any incident angle and diffraction angle. Numerical calculations show that high wavelength efficiency close to 100% can be achieved for S polarization and P polarization simultaneously, that is, natural polarization, circular polarization, 45 ° linear polarization, etc. ing. Thick transmissive rectangular diffraction grating 2 has a refractive index of optical isotropic medium 21: n2a = 1.4 and a refractive index of optical isotropic medium 22: n2b = 1.0. Regarding the rectangular diffraction grating 2, according to Non-Patent Document 6, when the operating wavelength λ is equal to the grating period Λ, that is, when the Bragg angle in vacuum is θ0 = 30 °, the duty ratio of (22) is It is estimated that a high diffraction efficiency of about 97% can be achieved with respect to natural polarized light or the like under the condition of approximately 10: 3 and t / Λ = 3.1. At this time, the aspect ratio of the thickness t and the width w2 of the optical isotropic medium 22 is 10.3: 1.

  According to Patent Document 2 and Patent Document 3, the polarization separating element uses an optically anisotropic medium instead of the optically isotropic medium 21 of the thick transmission type rectangular diffraction grating 2, so By making the refractive index of the P-polarized light coincide with the refractive index n2b of the optical isotropic material 22 filled in the grooves of the grating, and making the other polarized light different from the refractive index n2b of the optical isotropic medium 22, A diffractive optical element that uses only S-polarized light or P-polarized light for diffracted light other than the 0th order is described.

  According to Non-Patent Document 7, a groove of a thick rectangular diffraction grating as shown in FIG. 6 is filled with liquid crystal, and the refractive index n2a of the optical isotropic medium 21 and the optically anisotropic medium with respect to the incident light beam without an electric field. The refractive index of the liquid crystal is matched. Functional diffractive optics that switches from a transparent window to a diffraction grating by applying a voltage to the grating and changing the refractive index of the liquid crystal by means of transparent electrodes placed on the light incident and exit surfaces of a thick rectangular diffraction grating The device is described. However, there is no description about the refractive index and diffraction efficiency anisotropy for S-polarized light and P-polarized light even when no voltage is applied.

JP 2004-198641 A JP 2000-75130 A JP 2005-55773 A JP 2006-201388 A

H. Kogelnik, “Coupled Wave Theory for Thick Hologram Grating”, Bell System Technical Journal, 48, 2909-2946, 1969. I. K. Baldry, J. Bland-Hawthorn, J.G. Robertson, “Volume Phase Holographic gratings: Polarization properties and Diffraction Efficiency”, Publ. Astron. Soc. Pacific 116, 403-414, 2004. L. D. Dickson, R. D. Rallison, B. H. Yung, “Holographic polarization-separation elements”, Appl. Opt. 33, 5378-5385, 1994. N. Chateau, J. Hugonin, “Algorithm for the rigorous coupled-wave analysis of grating diffraction”, J. Opt. Soc. Am. A, 11,1321-1331, 1994. M. C. Gupta, S. T. Peng, “Diffraction characteristics of surface-relief gratings”, Appl. Opt., 32, 2911-2917, 1993. H. J. Gerritsen, M. L. Jepsen, “Rectangular Surface-Relief Transmission Gratings with a Very Large First-Order Diffraction Efficiency (95%) for Unpolarized Light”, Appl. Opt., 37, 5823-5829, 1998. M. L. Jepsen, H. J. Gerritsen, “Liquide-crystal-filled gratings with high diffraction efficiency”, Opt. L., 21, 1081-1083, 1996. N. Ebizuka, M. Iye, T. Sasaki, “Optically Anisotropic Crystalline Grisms or Astronomical Spectrographs”, Appl. Opt., 37, 1236-1242, 1998.

  The problem to be solved is that the diffractive efficiency characteristics of the S-polarized light and the P-polarized light deviate as the Bragg angle θ increases in the transmissive VPH diffraction grating 1. When the Bragg angle in vacuum of the transmission type VPH diffraction grating 1 is θ0 = 45 °, that is, when the optical axis is bent at a right angle, the average refractive index of the grating is n = 1.41. The diffraction efficiency with respect to natural polarized light or the like is about 79% at maximum because of the polarization diffraction efficiency characteristic of 1. Although the diffraction efficiency for natural polarized light and the like can be improved by increasing the average refractive index n of the grating, the average refractive index n of the currently available hologram recording material is about 1.55 at the maximum, so The problem is that the diffraction efficiency with respect to the maximum is about 85%. Further, the transmission type VPH diffraction grating 1 can achieve a high diffraction efficiency of up to 100% with respect to natural polarization or the like under the above-mentioned Dixon condition 2, but θ0 is limited by the average refractive index n. In addition, there is a problem that the full width at half maximum of the diffraction efficiency characteristic becomes narrow as the grating thickness t increases.

  The thick transmission type rectangular diffraction grating 2 adjusts the refractive index ratio and the width of the optical isotropic medium 21 and the optical isotropic medium 22 as described above, thereby bringing the diffraction efficiency characteristics of S-polarized light and P-polarized light closer to each other. Can do. However, according to the numerical calculation of RCWA, the smaller the ratio of the refractive index n2a of the optical isotropic medium 21 and the refractive index n2b of the optical isotropic medium 22, or the larger the Bragg angle θ, the lower the refractive index of the medium. Since the width becomes narrower and the grating thickness t becomes thicker, the aspect ratio between the width of the medium having a low refractive index and the thickness t becomes large, making it difficult to process a groove for injecting a medium having a low refractive index. Is a problem. According to Non-Patent Document 6, the refractive index of the optical isotropic medium 21 is n2a = 1.4, and the refractive index of the optical isotropic medium 22 is n2b = 1.0. In the diffraction grating 2, when the Bragg angle in vacuum is θ0 = 45 °, the duty ratio of the grating period Λ and the width w2 of the optical isotropic medium 22 is about Λ: w2 = 20: 3, and t / Λ = It is estimated that high diffraction efficiency of about 98% can be achieved with respect to natural polarized light or the like under the condition of 4.2. However, since the aspect ratio of the groove of the optical isotropic medium 22 is t: w2 = 28: 1, it is difficult to process the groove of the optical isotropic medium 22 by dry etching or the like.

The diffraction grating according to claim 1 is a transmission type VPH diffraction grating having a grating structure in which a refractive index is modulated in a sine wave shape, using an optically anisotropic medium, and having a desired wavelength and a desired Bragg angle. In contrast, the maximum refractive index for S-polarized light is nSmax, the minimum refractive index is nSmin, the maximum refractive index for P-polarized light is nPmax, and the minimum refractive index is nPmin.
nSmax, nSmin, nPmax, and nPmin are
(NSmax−nSmin) / cos θS and (nPmax−nPmin) * cos 2θP / cos θP are set so that the difference is within 10%, and thereby the thickness dependence of the diffraction efficiency of S-polarized light and the period in the characteristic, the difference between the period in the thickness dependence of the diffraction efficiency of the P-polarized light are matched to be within 10%, further, the thickness of the diffraction grating, the diffraction efficiency of the set S polarized light thickness dependent properties, and on the basis of the thickness dependence of the diffraction efficiency of the P-polarized light, the average of the diffraction efficiency and the diffraction efficiency of the P polarized light of S-polarized light is set to be 90% or more, characterized in that .
In the above equation, θS is the Bragg angle for S-polarized light, and θP is the Bragg angle for P-polarized light.
In other words, it is possible to arbitrarily control the difference between the maximum refractive index and the minimum refractive index for the S-polarized light of the optically anisotropic medium, the difference between the maximum refractive index and the minimum refractive index for the P-polarized light, and the thickness t of the grating. The main characteristic is that the diffraction efficiencies of the S-polarized light and the P-polarized light are controlled to the desired spectral characteristics at the wavelength λ and the arbitrary grating period Λ, that is, the arbitrary Bragg angle θ. In place of the above difference, the refractive index modulation amount for S-polarized light (one half of the difference between the maximum refractive index and the minimum refractive index), the refractive index modulation amount for P-polarized light, and the thickness t of the grating are controlled. The same applies to the above.

That is, the diffraction grating of the present invention is the diffraction grating according to claim 1, wherein the maximum refractive index for S-polarized light is nSmax, the minimum refractive index is nSmin, the maximum refractive index for P-polarized light is nPmax, and the minimum refractive index is nPmin. nSmax, nSmin, nPmax, and nPmin are
(NSmax−nSmin) / cos θS = (nPmax−nPmin) * cos 2θP / cos θP
By satisfying the above condition, the average of the diffraction efficiency of S-polarized light and the diffraction efficiency of P-polarized light is set to 90% or more at a desired wavelength and incident angle. Further, it can be 95% or more, or 99% or more.
In the above equation, θS is the Bragg angle for S-polarized light, and θP is the Bragg angle for P-polarized light.

The diffraction grating of the present invention is a diffraction grating different from that of claim 1, wherein the maximum refractive index for S-polarized light is nSmax, the minimum refractive index is nSmin, the maximum refractive index for P-polarized light is nPmax, and the minimum refractive index is nPmin. , NSmax, nSmin, nPmax, and nPmin are
(NSmax−nSmin) / cos θS = 2 (nPmax−nPmin) * cos 2θP / cos θP
Or
2 (nSmax−nSmin) / cos θS = (nPmax−nPmin) * cos 2θP / cos θP
By setting the value to satisfy the above, one of the diffraction efficiencies of S-polarized light and P-polarized light is set to 90% or more and the other is set to 1% or less. One diffraction efficiency can be 95% or more, or 99% or more.
In the above equation, θS is the Bragg angle for S-polarized light, and θP is the Bragg angle for P-polarized light.

Moreover, the diffraction grating of Claim 1 can be set as the following structures.
One is a resin in which uniaxial or biaxial optically anisotropic liquid crystal oriented in a predetermined direction is mixed with an optically isotropic resin, and the refractive index is sinusoidal depending on the concentration of the liquid crystal in the resin. The difference between the maximum refractive index and the minimum refractive index for the S-polarized light and the difference between the maximum refractive index and the minimum refractive index for the P-polarized light are different from each other according to the concentration of the liquid crystal and the orientation direction of the liquid crystal molecules. This is a diffraction grating characterized by the above.
The other is that a biaxial optically anisotropic liquid crystal, a liquid crystal alignment film that contacts the liquid crystal with the liquid crystal sandwiched therebetween, and aligns the liquid crystal in a predetermined direction, and a pair of electrodes that sandwich the liquid crystal periodically And controlling the orientation direction of the liquid crystal molecules by applying a voltage to the electrode portion, thereby modulating the refractive index of the liquid crystal in a sine wave shape, and the maximum refractive index for S-polarized light By making the difference between the minimum refractive index and the difference between the maximum refractive index and the minimum refractive index for P-polarized light different from each other and changing the voltage applied to the electrode section, the diffraction efficiency of S-polarized light and the diffraction of P-polarized light are changed. The diffraction grating is characterized in that the efficiency is variable.

  In the diffraction grating according to claim 1, when an optical anisotropic medium such as liquid crystal is used in the transmission type VPH diffraction grating, the optical anisotropic medium has a maximum refractive index of nSmax and a minimum refractive index of S-polarized light. Assuming that the maximum refractive index for nSmin and P-polarized light is nPmax, the minimum refractive index is nPmin, and the Bragg angles for S-polarized light and P-polarized light are θS and θP, respectively, by adjusting nSmax, nSmin, nPmax, and nPmin,

From Snell's equation of refraction
(nSmax + nSmin) sinθS = (nPmax + nPmin) sinθP
Because

Since θS and θP satisfying the above conditions, the equations (3) and (4) are equal, so that the diffraction efficiency characteristics of the first-order diffracted light of S-polarized light and P-polarized light coincide as shown in FIG. The diffraction efficiency is 90% or more at the matched maximum value. That is, in (a desired grating period lambda, the wavelength λ in other words) the desired Bragg angle, the maximum refractive index and the minimum difference between the maximum refractive index and the minimum refractive index for S-polarized light, and for P-polarized light so as to satisfy the equation (5) If the difference from the refractive index is controlled, the characteristics of the diffraction efficiency of S-polarized light and the characteristics of diffraction efficiency of P-polarized light are matched, and the average of the diffraction efficiency of S-polarized light and P-polarized light is 90% or more at the matched maximum value. It can be. The reason why the left side and the right side of Equation (5) are connected by an approximate equal sign is that in many cases, the left side and the right side can be used without any problem even if they are not exactly equal. If the difference between the left side and the right side is within 10%, there is no practical problem.

Apart from the invention, another diffraction grating is a transmissive VPH diffraction grating, and when an optical anisotropic medium such as liquid crystal is used, the optical anisotropic medium has a maximum refractive index of nSmax and a minimum refractive index of S-polarized light. Assuming that the maximum refractive index for nSmin and P-polarized light is nPmax, the minimum refractive index is nPmin, and the Bragg angles for S-polarized light and P-polarized light are θS and θP, respectively, by adjusting nSmax, nSmin, nPmax and nPmin,

あるいは、

Or

For any θS and θP that satisfy the above, the period for the grating thickness t in equation (3) is twice or ½ the period for the grating thickness t in equation (4). As shown in the above-mentioned Dixon condition 1, the efficiency of the first-order diffracted light of P-polarized light or S-polarized light becomes 0% at the grating thickness t at which the efficiency of the first-order diffracted light of S-polarized light or P-polarized light reaches the first maximum. It becomes polarization characteristics. That is, at a desired Bragg angle, the difference between the maximum refractive index and the minimum refractive index for S-polarized light and the difference between the maximum refractive index and the minimum refractive index for P-polarized light are controlled so as to satisfy Expression (6) or Expression (7). If so, one of the S-polarized light and the P-polarized light can have a diffraction efficiency of 90% or more, and the other can have a diffraction efficiency of 1% or less, and can function as a polarization separation element. The reason why the left side and the right side of the equations (6) and (7) are connected by the approximate equal sign is that even if the left side and the right side are not exactly equal, in many cases, they can be used without any practical problem.
From the above, if the difference between the maximum refractive index and the minimum refractive index for S-polarized light and the difference between the maximum refractive index and the minimum refractive index for P-polarized light at the desired Bragg angle is controlled, It can be seen that the diffraction efficiency of P-polarized light can be set to a desired characteristic.

The diffraction grating according to claim 4 is a transmission type diffraction grating having a rectangular grating structure in which two kinds of materials having different refractive indexes are alternately and periodically arranged, and one of the two kinds of materials is optical. An anisotropic medium, the other is an optical isotropic medium, and the maximum refractive index for S-polarized light of the optical anisotropic medium is n2cS and the maximum refractive index for P-polarized light is n2cP for a desired wavelength and a desired Bragg angle. And the refractive index of the optically isotropic medium is n2a,
n2a, n2cS, and n2cP are
In the case of n2cP>n2cS> n2a or n2cP <n2cS <n2a, A1 * (n2cS−n2a) / cosθS and B1 * (n2cP−n2a) * cos2θP / cosθP
When n2cP>n2a> n2cS or n2cP <n2a <n2cS, A2 * (n2cS−n2a) / cosθS and −B2 * (n2cP−n2a) * cos2θP / cosθP should be within 10%. a is the values are set, thereby matching as the difference between the period in the thickness dependence of the diffraction efficiency of the S polarized light, and the period in the thickness dependence of the diffraction efficiency of the P polarized light is within 10% Let
Further, the thickness of the diffraction grating is determined based on the above-described thickness dependency characteristic of the diffraction efficiency of S-polarized light and the thickness dependency characteristic of the diffraction efficiency of P-polarized light. The average is set to be 90% or more.
In the above equation, θS is the Bragg angle for S-polarized light, and θP is the Bragg angle for P-polarized light. A1 and A2 are the wave numbers (1 / periods) in the thickness dependence of the diffraction efficiency of the S-polarized light of the diffraction grating obtained by the RCWA method, and the S-polarized light of the transmission-type VPH diffraction grating obtained by the two-wave coupling analysis method. It is a value divided by the wave number (1 / period) in the thickness dependence characteristic of the diffraction efficiency. Further, B1 and B2 are diffractions of P-polarized light of a transmission type VPH diffraction grating obtained by a two-wave coupling analysis method in which the wave number (1 / period) in the thickness dependence characteristic of the diffraction efficiency of P-polarized light of the diffraction grating obtained by the RCWA method is obtained. It is a value divided by the wave number (1 / period) in the thickness dependence characteristic of efficiency. The transmission type VPH diffraction grating described above has a maximum refractive index for S-polarized light of n2cS and n2a, a minimum refractive index of n2cS and n2a, and a maximum refractive index for P-polarized light of n2cP and n2a. Is a transmission type VPH diffraction grating having a larger one of n2cP and a smaller refractive index of n2a.
Further, it can be 95% or more, or 99% or more.
The diffraction grating of the present invention is a diffraction grating different from that of claim 4 , wherein the maximum refractive index for the S-polarized light of the optically anisotropic medium is n2cS and the maximum refractive index for the P-polarized light is n2cP. The refractive index of the other material is n2a, and n2a, n2cS, and n2cP are
In the case of n2cP>n2cS> n2a or n2cP <n2cS <n2a, 2A1 * (n2cS−n2a) / cosθS = B1 * (n2cP−n2a) * cos2θP / cosθP or A1 * (n2cS−n2a) / cosθS = 2B1 * (n2cP-n2a) * cos2θP / cosθP
In the case of n2cP>n2a> n2cS or n2cP <n2a <n2cS, 2A2 * (n2cS−n2a) / cos θS = −B2 * (n2cP−n2a) * cos 2θP / cos θP or A2 * (n2cS−n2a) / cos θS = −2B2 * (n2cP−n2a) * cos2θP / cosθP is set to a value satisfying one of the diffraction efficiencies of S-polarized light and P-polarized light, and one is set to 90% or more and the other is set to 1% or less. . One diffraction efficiency can be 95% or more, or 99% or more.
Note that θS, θP, A1, A2, B1, and B2 in the above formula are the same as described above.
The diffraction grating according to claim 4 is a transmissive diffraction grating having a grating structure in which two types of materials having different refractive indexes are alternately and periodically arranged. If the refractive index of the optically anisotropic medium for S-polarized light is n2cS, the refractive index for P-polarized light is n2cP, and the Bragg angles for S-polarized light and P-polarized light are θS and θP, respectively, n2a, n2cS, and By choosing n2cP

    (When n2cP> n2cS> n2a or n2cP <n2cS <n2a),

(When n2cP>n2a> n2cS or n2cP <n2a <n2cS)
In any θS and θP that satisfy any of the above, since the equations (3) and (4) are equal, the diffraction efficiency characteristics of the first-order diffracted light of S-polarized light and P-polarized light are coincident as shown in FIG. To do. The diffraction efficiency is 90% or more at the matched maximum value. That is, at the desired Bragg angle (in other words, the desired grating period Λ, wavelength λ), the refractive index of the optically anisotropic medium with respect to the S-polarized light and the refractive index of other materials so as to satisfy the expressions (8) and (9) And the difference between the refractive index of the optically anisotropic medium for the P-polarized light and the refractive index of the other material, the characteristics of the diffraction efficiency of the S-polarized light and the characteristics of the diffraction efficiency of the P-polarized light can be controlled. By matching, the average of the diffraction efficiencies of S-polarized light and P-polarized light can be 90% or more at the thickness of the grating having the matched maximum value. Here, A1 and A2 are the wave number (1 / period) PRS in the dependence characteristic of the diffraction efficiency of S-polarized light of the thick transmission rectangular diffraction grating obtained by the RCWA method with respect to the thickness t of the grating, and the PRS is obtained by the two-wave coupling analysis method. The wave number (1 / period) in the dependence of the diffraction efficiency of S-polarized light on the thickness t of the thick transmission type VPH diffraction grating, divided by P2S. B1 and B2 are the wave number (1 / period) PRP in the dependence characteristic of the grating thickness t of the P-polarized diffraction efficiency of the thick transmission rectangular diffraction grating obtained by the RCWA method, and the two-wave coupling analysis method. Further, the wave number (1 / period) in the dependence characteristic of the diffraction efficiency of P-polarized light of the transmission type VPH diffraction grating 1 regarding the thickness t of the grating is a value divided by P2P. Note that the reason why the left and right sides of Equations (8) and (9) are connected by an approximate equal sign is that they can be used without practical problems in many cases even if the left and right sides are not exactly equal. is there.

または、

あるいは、ｎ２ｃＰ＞ｎ２ｃＳ＞ｎ２ａまたはｎ２ｃＰ＜ｎ２ｃＳ＜ｎ２ａの場合に、

または、

のように、所望のブラッグ角において、式（８）、（９）の右辺または左辺の一方を２倍とした等式を満たすよう一方の材料である光学異方性媒質のＳ偏光に対する屈折率と他の材料の屈折率との差、および光学異方性媒質のＰ偏光に対する屈折率と他の材料の屈折率との差、および格子の厚さtの３つを制御すれば、Ｓ偏光とＰ偏光のうち、一方を９０％以上の回折効率とし、他方を１％以下の回折効率とすることができ、偏光分離素子として機能させることができる。なお、式（１０）〜（１３）の左辺と右辺が近似等号によって結ばれているのは、左辺と右辺が厳密に等しくなくても、多くの場合に実用上問題なく利用できるからである。
以上のことから、所望のブラッグ角において、一方の材料である光学異方性媒質のＳ偏光に対する屈折率と他の材料の屈折率との差、および光学異方性媒質のＰ偏光に対する屈折率と他の材料の屈折率との差、および格子の厚さtを制御すれば、Ｓ偏光の回折効率と、Ｐ偏光の回折効率を所望の特性とすることができることがわかる。 On the other hand, n2a is satisfied by selecting n2a, n2cS, and n2cP in the same manner as in Expression (6) and Expression (7), that is, satisfying the equality in which one of the right side or the left side of Expressions (8) and (9) is doubled. And n2cS and n2cP, the period with respect to the grating thickness t in equation (3) becomes twice or ½ the period with respect to the grating thickness t in equation (4) at any θS and θP. 4, the efficiency of the first-order diffracted light of P-polarized light or S-polarized light at the thickness t of the grating where the efficiency of the first-order diffracted light of S-polarized light or P-polarized light reaches the first maximum, as in the Dixon condition 1 shown in FIG. A polarization characteristic of 0% can be realized. That is, when n2cP>n2cS> n2a or n2cP <n2cS <n2a,

Or

Alternatively, if n2cP>n2cS> n2a or n2cP <n2cS <n2a,

Or

As shown, the refractive index with respect to the S-polarized light of the optically anisotropic medium, which is one of the materials, satisfies the equation where one of the right side or the left side of the formulas (8) and (9) is doubled at the desired Bragg angle. S-polarized light can be controlled by controlling the difference between the refractive index of the other material and the refractive index of the optically anisotropic medium, the difference between the refractive index of the optically anisotropic medium and the refractive index of the other material, and the thickness t of the grating. And P-polarized light, one can have a diffraction efficiency of 90% or more and the other can have a diffraction efficiency of 1% or less, and can function as a polarization separation element. The reason why the left side and the right side of the equations (10) to (13) are connected by an approximate equal sign is that even if the left side and the right side are not exactly equal, they can be used without any practical problems in many cases. .
From the above, at the desired Bragg angle, the difference between the refractive index of the optically anisotropic medium, which is one material, with respect to S-polarized light and the refractive index of the other material, and the refractive index of the optically anisotropic medium with respect to P-polarized light. It can be seen that the diffraction efficiency of S-polarized light and the efficiency of diffraction of P-polarized light can be made to have desired characteristics by controlling the difference between the refractive index of the other material and the refractive index of other materials and the thickness t of the grating.

As the optically anisotropic medium of the diffraction grating of the present invention, liquid crystal, photo-alignment resin, stretched resin, uniaxial crystal, biaxial crystal, photonic crystal, metamaterial, and the like can be used.
The diffraction grating of the present invention may be a linear or curved shape extending in the grating period direction and embedded with a core material and a clad material to form a planar optical waveguide. In the optical waveguide, the S-polarized light in this specification may be read by replacing it with the TE wave and the P-polarized light with the TM wave.

The diffraction gratings according to claims 1 and 4 can achieve desired characteristics of diffraction efficiency for S-polarized light and diffraction efficiency for P-polarized light at an arbitrary Bragg angle θ.
In particular, in the diffraction grating according to claim 1, the refractive index of the optical anisotropic medium is adjusted so as to satisfy the expression (5), and in the diffraction grating according to claim 4, the expression (8) or the expression (9) ) To adjust the refractive index of the optically anisotropic medium and the thickness t of the grating so that the S-polarized light and the P-polarized light are simultaneously 90% or more, and a high diffraction efficiency and a wide band reaching a maximum of 100%. There is an advantage that the width can be achieved.

Further, a diffraction grating different from that of the first aspect can be obtained by adjusting the refractive index of the optically anisotropic medium so as to satisfy the formula (6) or the formula (7) at an arbitrary Bragg angle θ. It is possible to realize a diffraction grating with a polarization separation function with a high diffraction efficiency so that the polarization diffraction efficiency reaches 1% or less ( minimum 0%) and the polarization efficiency of the other polarization reaches 90% or more (maximum 100%). There are advantages. Similarly, a diffraction grating different from claim 4 adjusts the refractive index of the optically anisotropic medium, which is one material, and the refractive index of the other material at an arbitrary Bragg angle θ, and sets the thickness t of the grating. By adjusting the diffraction grating, the polarization separation function is added so that the diffraction efficiency of one polarization reaches 1% or less ( minimum 0%) and the diffraction efficiency of the other polarization reaches 90% or more (maximum 100%). There is an advantage that high diffraction efficiency can be realized.

  The diffraction grating according to claim 4 can also be applied to higher-order diffracted light.

The conventional thick transmission type VPH diffraction grating 1 and thick transmission type rectangular diffraction grating 2 are polarized light orthogonal to the diffraction order grating when the diffraction light of the order satisfying the Bragg condition and the incident light are orthogonal within the diffraction grating. Therefore, the diffraction efficiency of P-polarized light is significantly reduced. The diffraction grating according to claim 1 is characterized in that the diffraction order is adjusted by adjusting an average refractive index of P-polarized light of an optically anisotropic material and an alignment direction of liquid crystal so that incident light of P-polarized light and diffracted light are not orthogonal to each other. It is possible to prevent or reduce the decrease in diffraction efficiency of P-polarized light. In the diffraction grating according to claim 4 , the diffraction order is selected by selecting the orientation direction of the liquid crystal or the like and the combination of the refractive indices of the P-polarized light of the two materials so that the incident light and the diffracted light are not orthogonal in the P-polarized light. It is possible to prevent or reduce the decrease in diffraction efficiency of P-polarized light.

  The diffraction grating according to claim 1 or the diffraction grating according to claim 4 uses a curable liquid crystal material as an optically anisotropic medium, and polarization diffraction in a manufacturing process by controlling an orientation direction of liquid crystal by an electric field or the like. Adjustment of efficiency characteristics is facilitated.

The diffraction grating according to claim 1 and the diffraction grating according to claim 4 use a liquid crystal material as an optically anisotropic medium and dispose an electrode or a transparent electrode, thereby enabling diffraction efficiency for S-polarized light and P-polarized light. It is possible to realize an active diffractive optical element capable of varying the above.
The same advantages as described above can also be obtained for the optical waveguide according to claim 10 using the diffraction grating of the present invention.

FIG. 1 is a conceptual diagram of the polarization direction and amplitude of two beams and the polarization direction and amplitude of interference fringes and a VPH diffraction grating of a two-beam interferometer for holographic diffraction grating exposure. FIG. 2 is a diagram showing measured values of the spectral characteristics of the diffraction efficiency of the VPH diffraction grating. FIG. 3 is a diagram showing the results of numerical calculation of diffraction efficiency with respect to the thickness of the VPH diffraction grating of FIG. FIG. 4 is a diagram showing a calculated value of the diffraction efficiency with respect to the thickness under the condition (Dickson's condition 1) in which the efficiency of the S-polarized light becomes minimum at the first maximum thickness of the P-polarized light of the VPH diffraction grating. . FIG. 5 shows a condition (Dixon) in which the diffraction efficiency of any polarization reaches a maximum of 100% by adjusting the efficiency of the S polarization at the first maximum thickness of the P polarization of the VPH diffraction grating. It is the figure which showed the calculated value of the diffraction efficiency with respect to the thickness in condition 2). FIG. 6 is a conceptual diagram of a thick transmissive rectangular diffraction grating. FIG. 7 is a diagram showing a calculated value of the diffraction efficiency with respect to the thickness when the characteristics of the S-polarized light and the P-polarized light are matched by the diffraction grating 3. FIG. 8 is a diagram illustrating a configuration of the diffraction grating 3 according to the first embodiment. FIG. 9 is a diagram illustrating the configuration of the optical waveguide 4 according to the second embodiment. FIG. 10 is a diagram illustrating a configuration of the diffraction grating 5 according to the third embodiment. FIG. 11 is a diagram illustrating the configuration of the optical waveguide 6 according to the fifth embodiment. FIG. 12 is a diagram illustrating the configuration of the diffraction grating 7 according to the sixth embodiment. FIG. 13 shows the refractive indexes of incident azimuths of polarized light (solid line) whose electric field oscillates parallel to the coordinate surface (polarized line) and polarized light (broken line) oscillates perpendicularly to the light beam propagating in the coordinate plane of the biaxially anisotropic liquid crystal. FIG. FIG. 14 is a conceptual diagram of the optical waveguide 8 of the seventh embodiment. FIG. 15 is a conceptual diagram of the diffraction grating 9 according to the eighth embodiment. FIG. 16 is a conceptual diagram of the optical waveguide 10 of the ninth embodiment.

A manufacturing method of the diffraction grating 3 as shown in the front view (AA cross-sectional view in the side view) and the side view (cross-sectional view in the incident surface) of FIG. 8 will be described. The following materials are used in place of the hologram resin that has been conventionally used for manufacturing the VPH diffraction grating. The material is composed of an optically anisotropic liquid crystalline organic material 210 that selectively dimerizes when two adjacent photofunctional groups are parallel to the direction of electric field vibration of polarized light by irradiation with linearly polarized light, and refraction. An optically anisotropic hologram resin 230 mainly composed of a thermosetting resin material 220 having an isotropic rate. A hologram dry plate is produced by sandwiching the hologram resin 230 in which a spacer (not shown) such as glass beads is mixed between a substrate 200 and a substrate 240, which are two pieces of glass, resin, crystal, or the like. Alternatively, the hologram resin 230 may be applied to a substrate 200 such as glass, resin, or crystal.
Next, as indicated by the arrows shown in the upper part of FIG. 8, the long axis in the direction of the electric field oscillation of the polarized light in the bright part of the interference fringes is obtained by laser interference exposure of two light beams polarized in the direction of the diffraction grating period. The photosensitive group of the liquid crystal organic material 210 in which is placed selectively undergoes a crosslinking reaction to dimerize. Around the dimerized liquid crystal organic material 210, the monomer liquid crystal organic material 210 is aligned in the same direction as the dimerized liquid crystal organic material 210, and during the laser interference exposure, the adjacent monomer liquid crystal organic material 210 is aligned. Dimerizes with the liquid crystalline organic material 210. As a result, since the concentration of the monomer liquid crystalline organic material 210 decreases in the bright part of the interference fringes, the monomer liquid crystalline organic material 210 moves from the dark part of the interference fringes to the bright part, The thermosetting resin 220 moves from the bright part to the dark part, and the liquid crystalline organic material 210 of the monomer that has moved to the bright part is aligned in the same direction as the dimerized liquid crystalline organic material 210 and is close to the monomer. Dimerize with liquid crystalline organic materials.
After the laser interference exposure, the hologram dry plate is heated to the curing temperature of the thermosetting resin 220 and cooled to room temperature, whereby a liquid crystalline organic material is formed in the periodic direction of the diffraction grating as shown in the front view or side view of FIG. The diffraction grating 3 of the present invention in which 210 is oriented can be realized.
The diffraction grating 3 is a VPH in which the refractive index of the hologram resin 230 changes in a sine wave shape due to the difference in concentration of the liquid crystalline organic material 210. Further, the refractive index for S-polarized light and the refractive index for P-polarized light of the liquid-crystalline organic material 210 are different depending on the orientation of the liquid-crystalline organic material 210.
In the diffraction grating 3 of Example 1, as shown in the side view of FIG. 8, the concentration of the liquid crystalline organic material 210 is set in the thickness direction of the hologram resin 230 (direction perpendicular to the light incident surface). The content of the change in the refractive index is uniform, but the refractive index in the thickness direction is inclined at an angle α by changing the concentration of the liquid crystal organic material 210 in the thickness direction as shown in the top view of FIG. You may make it have.
The diffraction grating 3 of Example 1 is different from the maximum refractive index nSmax and the minimum refractive index nSmin for the S-polarized light of the hologram resin 230: nSmax−nSmin, and the maximum refractive index nPmax and the minimum refractive index nPmin for the P-polarized light. Difference: By controlling nPmax-nPmin to a predetermined value satisfying the equation (5), the diffraction efficiency characteristics of the first-order diffracted light of S-polarized light and P-polarized light (dependence of diffraction efficiency on the grating thickness t) are matched. By adjusting the thickness t of the grating, the average value of the diffraction efficiencies of S-polarized light and P-polarized light can be 90% or more with respect to a desired incident angle to the diffraction grating 3. Of course, it is controlled by a half of the difference, that is, the refractive index modulation amount for S-polarized light: ΔnS = (nSmax−nSmin) / 2 and the refractive index modulation amount for P-polarized light: ΔnP = (nPmax−nPmin) / 2. May be.
Further, the difference between the maximum refractive index nSmax and the minimum refractive index nSmin with respect to the S-polarized light of the hologram resin 230 and the difference between the maximum refractive index nPmax and the minimum refractive index nPmin with respect to the P-polarized light are expressed by Equation (6) or Equation (7). By controlling to a predetermined value to satisfy, the diffraction efficiency characteristic of the first-order diffracted light of P-polarized light becomes the minimum when the diffraction efficiency characteristic of the first-order diffracted light of S-polarization becomes maximum, or vice versa. When the diffraction efficiency characteristic of the first-order diffracted light is minimized, the diffraction efficiency characteristic of the P-polarized first-order diffracted light can be maximized. Therefore, with respect to the desired incident angle to the diffraction grating 3, the diffraction efficiency of S-polarized light is 90% or more and the diffraction efficiency of P-polarized light is 1% or less, or the diffraction efficiency of S-polarized light is 1% or less and The efficiency can be 90% or more, and the diffraction grating 3 can be a polarization separation element.

  The polarizing alignment liquid crystalline organic material 210 is a uniaxial liquid crystal, the ordinary ray refractive index is no = 1.5, the extraordinary ray refractive index is ne = 1.7, and the refractive index of the thermosetting resin 220 is 1. .5, the diffraction grating 3 has nSmax = 1.59, nSmin = 1.5, nPmax = 1.7, and nPmin = 1.59. Equation (5) and Snell's equation (2) Therefore, when the Bragg angle for S-polarized light is θS = 18.6 ° and the Bragg angle for P-polarized light is θP = 17.4 ° (Bragg angle in vacuum: θ0 = 29.4 °), S-polarized light and P-polarized light The characteristics match. FIG. 7 is a diagram showing a calculated value of diffraction efficiency with respect to thickness when the characteristics of S-polarized light and P-polarized light are matched by the diffraction grating 3 of Example 1 at a wavelength: λ = 0.6 μm. In FIG. 7, in order to make it easier to see the characteristics of S-polarized light and P-polarized light, the grating period is set so that the Bragg angle is slightly smaller than the condition in which Equation (5) becomes an equation. Λ = 0.646 μm, the Bragg angle for S-polarized light is θS = 17.5 °, the Bragg angle for P-polarized light is θP = 16.4 ° (the Bragg angles in vacuum are both θ0 = 27.7 °). The average value of the diffraction efficiency of S-polarized light and P-polarized light is 99.9% at the thickness t = 3.1 of the hologram resin 230.

As a manufacturing method of the optical waveguide 4 of the second embodiment shown in FIG. 9, the hologram resin 230 of the diffraction grating 3 manufactured by the method as in the first embodiment is cut in a direction perpendicular to the grating or in an arbitrary direction in the grating periodic direction. An optical waveguide 4 that is a planar optical waveguide can be realized by processing into an extending linear or curved shape and embedding it in the core layer 310 and the cladding layer 300.
This optical waveguide 4 can control the diffraction efficiency characteristics of TE wave and TM wave to desired characteristics by controlling the refractive index of the hologram resin 230 of the diffraction grating 3 as shown in the first embodiment. It is.

As a method for manufacturing the diffraction grating 5 of Example 3 shown in FIG. 10, an optically anisotropic crystal cut out in an arbitrary orientation or an optically anisotropic medium substrate 400 such as a resin having optical anisotropy caused by stretching is used. Striped grooves 410 are formed by photolithography and etching techniques to form a deep rectangular lattice 420, filled with an optical isotropic medium 450 such as a resin having an arbitrary refractive index, and a substrate 430 is disposed thereon. Then, the diffraction grating 5 can be realized by sealing. As shown in FIG. 10, the optical axis of the substrate 400, which is an optically anisotropic medium, is the same direction as the stripe direction of the groove 410.
Conversely, the diffraction grating 5 may be formed by forming a striped groove having a rectangular cross section on an optically isotropic substrate and filling the groove with an optically anisotropic medium. In this case, the optically anisotropic medium can be a liquid crystal that is cured while being aligned in a predetermined direction by irradiation of an electric field or light distribution.
Further, a diffraction grating is formed by forming an optically anisotropic film on an optically isotropic substrate, etching the film to form a striped groove having a rectangular cross section, and filling the groove with an optically isotropic medium. 5 may be formed. For the optically anisotropic film, a stretched resin, a liquid crystal cured in an aligned state, or the like can be used.

Examples of optically anisotropic crystal materials include yttrium fluoride-lithium (YLiF4: YLF), β-barium metaborate (β-BaB2O4: β-BBO), and lithium niobate (LiNbO3). The average refractive index of the resin in visible light is about 1.35 to 1.74. Of these, β-BBO has a large difference in refractive index between ordinary light and extraordinary light, ordinary light refractive index: no = 1.669, extraordinary light refractive index: ne = 1.551, and refractive index: n2a = 1.35. A wavelength band with a wide diffraction efficiency can be realized by combining with a resin having a value of about 1.5 or n2a = 1.6 or n2a = 1.7 to 1.74. According to Non-Patent Document 8, when the substrate other than the grating has optical anisotropy and can be regarded as a plane parallel plate, it is emitted into the optically isotropic medium 450 to be placed later. Since the diffraction angles of S-polarized light and P-polarized light are equal without being affected by the optical anisotropy (birefringence) of the plane-parallel plate portion, the groove 410 may not penetrate to the substrate 400.
The diffraction grating 5 has a refractive index n2a of the optical isotropic medium 450 and a refractive index n2cS for the S-polarized light and a refractive index n2cP for the P-polarized light of the substrate 400, which is an optically anisotropic medium. By controlling to a predetermined value that satisfies (9), the diffraction efficiency characteristics of the first-order diffracted light of S-polarized light and P-polarized light can be matched as shown in FIG. Thus, the average value of the diffraction efficiencies of S-polarized light and P-polarized light can be 90% or more.
Further, the refractive index n2a of the optically isotropic medium 450 and the refractive index n2cS for the S-polarized light and the refractive index n2cP for the P-polarized light of the substrate 400, which is an optically anisotropic medium, are represented by the left side of the equations (8) and (9) or Diffraction of S-polarized first-order diffracted light by controlling to a predetermined value satisfying any one of the equations in which one of the right-hand sides is doubled, that is, equations (10), (11), (12), and (13) When the efficiency characteristic is maximized, the diffraction efficiency characteristic of the P-polarized first-order diffracted light is minimized, or conversely, when the diffraction efficiency characteristic of the S-polarized first-order diffracted light is minimized, 1 of the P-polarized light The diffraction efficiency characteristic of the next diffracted light can be maximized. Therefore, with respect to a desired incident angle to the diffraction grating 5, the diffraction efficiency of S-polarized light is 90% or more and the diffraction efficiency of P-polarized light is 1% or less, or the diffraction efficiency of S-polarized light is 1% or less. The efficiency can be 90% or more, and the diffraction grating 5 can be a polarization separation element.
In the diffraction grating 5 of Example 3, the groove 410 is perpendicular to the light incident surface. However, as shown in the top view of FIG. 11, the groove 410 is oriented in a direction perpendicular to the light incident surface. Alternatively, the structure may be configured such that the optically anisotropic medium and the optically isotropic medium are alternately inclined and arranged at an angle α.

  As a method of manufacturing the diffraction grating of Example 4, a deep rectangular grating is formed by forming a stripe-shaped groove on the first transparent substrate or a transparent medium film applied to the first transparent substrate by photolithography or etching technique. The liquid crystal alignment film that aligns the liquid crystal in an arbitrary orientation and pretilt angle is placed at the bottom of the groove, the groove is filled with a curable liquid crystal, the liquid crystal is sealed with a second transparent substrate, and cured by ultraviolet rays or the like By doing so, it is possible to realize the diffraction grating of the fourth embodiment that has substantially the same configuration as the diffraction grating 5 of the third embodiment. Note that a liquid crystal alignment film that aligns the liquid crystal in substantially the same direction as the bottom of the groove may be disposed on the surface of the second transparent substrate that contacts the liquid crystal.

  As a method of manufacturing the optical waveguide 6 of Example 5 shown in FIG. 11, the diffraction grating 5 manufactured by the method of Example 3 or Example 4 is cut perpendicularly to the grating or in an arbitrary direction so as to be in the grating period direction. An optical waveguide 6 that is a planar optical waveguide can be realized by processing into an extending linear or curved shape and embedding it in the core layer 510 and the cladding layer 500. As shown in FIG. 11, the diffraction grating portion in which the optical waveguide 6 is embedded has a structure in which the optical anisotropic medium 530 and the optical isotropic medium 520 are alternately arranged in an inclined manner.

A method for manufacturing the diffraction grating 7 of Example 6 shown in FIG. 12 will be described below. The lower substrate 700 and the upper substrate 730 are arranged to face each other with a gap having an arbitrary thickness, and the opposing surfaces of the lower substrate 700 and the upper substrate 730 have the same upper and lower lattice periods and an arbitrary duty ratio. A grid of transparent electrodes 710 is arranged. At this time, the transparent electrode 710 provided on the lower substrate 700 side and the transparent electrode 710 provided on the upper substrate 730 side are arranged to face each other. In addition, a liquid crystal alignment film 720 is disposed on the opposite surface (the surface in contact with the liquid crystal) of the lower substrate 700 and the upper substrate 730 and the surface in which the transparent electrode 710 is in contact with the liquid crystal. Next, a liquid crystal 740 is filled in a gap between the lower substrate 700 and the upper substrate 730. Since the liquid crystal 740 is ferroelectric, it exhibits biaxial optical anisotropy due to spontaneous chirality (Chirality: a property in which a three-dimensional figure or object cannot be superimposed on its mirror image. Palmarity). It is a liquid crystal (banana-type liquid crystal, disk-type liquid crystal, etc.) and is oriented in an arbitrary direction and parallel to the lower substrate 700 and the upper substrate 730 or at an arbitrary pretilt angle. In addition, as shown in the side view of FIG. 12, the major axis of the molecule 750 of the liquid crystal 740 is inclined in the upper and lower electrode directions (direction parallel to the lines of electric force), the chirality disappears, and the molecule 750 of the liquid crystal 740 becomes uniaxial optical. As the distance from the molecules 750 of the liquid crystal 740 located between the transparent electrodes 710 increases, the lower substrate 700 and the upper substrate gradually move from the inclination of the molecules 750 of the liquid crystals 740 located between the upper and lower transparent electrodes 710. The inclination of the liquid crystal 740 changes parallel to the substrate 730 or at a pretilt angle so that it behaves as a biaxial optical isomer due to chirality. In this way, the diffraction grating 7 of Example 6 can be realized.
In the diffraction grating 7 of Example 6, the refractive index changes sinusoidally depending on the orientation of the liquid crystal 740 having biaxial optical anisotropy, and the refractive index is variable depending on the voltage applied to the transparent electrode 710. A transmissive VPH diffraction grating capable of satisfying the above has been realized. That is, the characteristics of the diffraction efficiency for S-polarized light and P-polarized light can be controlled by controlling the voltage applied to the transparent electrode 710.

FIG. 13 shows the refractive indices of incident azimuths of polarized light (solid line) whose electric field oscillates parallel to the coordinate plane (broken line) and polarized light (broken line) oscillates perpendicularly to the light beam propagating in the coordinate plane of the liquid crystal having biaxial anisotropy. It was. In the xy plane in the left diagram of FIG. 13, the light beam incident along the x-axis has a refractive index n1 of polarized light whose electric field oscillates in the z-axis direction and a refractive index n2 of polarized light whose electric field oscillates in the y-axis direction. It can be seen that the light beam incident along the y-axis has a refractive index n1 of polarized light whose electric field oscillates in the z-axis direction and a refractive index n3 of polarized light whose electric field oscillates in the x-axis direction. From the center or right figure, the light beam incident along the z-axis has a refractive index n3 of polarized light whose electric field oscillates in the x-axis direction and n2 of polarized light whose electric field oscillates in the y-axis direction. I understand.
For example, when the major axis of the molecule 750 of the liquid crystal 740 having the biaxial optical anisotropy is the z axis, and n1 = 1.7, n2 = 1.66, and n3 = 1.5, the liquid crystal alignment film 720 If the major axis of the molecules 750 of the liquid crystal 740 is aligned perpendicular to the lattice and parallel to the upper and lower substrates, and the y-axis is aligned parallel to the lattice, the refractive index of S-polarized light is 1.66 and the refractive index of P-polarized light is 1. .7. On the other hand, the molecules 750 of the liquid crystal 740 between the transparent electrodes 710 are such that when a voltage is applied to the transparent electrode 710, the major axis (z-axis) faces the direction of the transparent electrode 710 and the x-axis and y-axis of each molecule 750 of the liquid crystal 740. Is oriented in any direction with the z axis as the rotation center, the refractive index of S-polarized light and P-polarized light is the average value of n2 and n3 of 1.58. That is, nSmax = 1.66, nSmin = 1.58, nPmax = 1.7, and nPmin = 1.58. From Equation (5) and Snell's Equation (2), the Bragg angle for S-polarized light is θS = 23.8 ° and the Bragg angle for P-polarized light is θP = 24.1 ° (both Bragg angles in vacuum are θ0 = 40.8). )), The characteristics of S-polarized light and P-polarized light coincide as shown in FIG.

A method for manufacturing the optical waveguide 8 of Example 7 shown in FIG. 14 will be described. Part of the core layer 810 of the planar optical waveguide sandwiched between the upper and lower sides of the core layer 810 by the clad layer 800 is removed in a strip shape that draws a straight line or an arbitrary curve. The gratings of the electrodes 830 having the same upper and lower grating periods and an arbitrary duty ratio are arranged on the upper and lower clad layers 800 of the removed core layer 810 in substantially the same phase perpendicular to the straight line or curve or at an arbitrary angle. . In addition, since the liquid crystal 840 that exhibits biaxial optical anisotropy due to spontaneous chirality due to its ferroelectricity is aligned in an arbitrary direction and parallel to the upper and lower cladding layers 800 or in an arbitrary pretilt angle, A liquid crystal alignment film 820 is disposed on the surface where the upper and lower cladding layers 800 and the electrode 830 are in contact with the liquid crystal 840. Next, liquid crystal 840 is filled in the removed core layer 810 portion. As described above, the planar optical waveguide 8 of Example 7 is manufactured.
In this optical waveguide 8, by applying an arbitrary voltage to the upper and lower electrodes 830, the liquid crystal 840 between the upper and lower electrodes 830 is tilted in the upper and lower electrode directions as shown in the front view of FIG. The liquid crystal 840 behaves as a uniaxial optical isomer, and gradually becomes parallel to the cladding layer 800 or pretilt angle from the inclination of the liquid crystal 840 positioned between the electrodes 830 as the distance from the liquid crystal 840 positioned between the electrodes 830 increases. The tilt of the orientation of the liquid crystal 840 changes, and it behaves as a biaxial optical isomer due to chirality. Thereby, the refractive index is modulated in a sine wave shape. That is, the optical waveguide has a planar structure in which the diffraction grating 7 of Example 6 is embedded with a core material and a cladding material, and the diffraction efficiency characteristics of the TE wave and the TM wave can be controlled by the voltage applied to the electrode 830. ing.

A method for manufacturing the diffraction grating 9 of Example 8 shown in FIG. 15 will be described. A transparent electrode 910 is disposed on a transparent substrate 900. A layer of an optically isotropic medium such as resin or glass is formed thereon by a photolithography technique or the like, and then a stripe-shaped groove 940 having a rectangular cross section is formed to form a deep rectangular lattice 930. The width of the groove 940 is w1, and the width of the rectangular lattice 930 is w2. A liquid crystal alignment film 920 that aligns liquid crystal in an arbitrary orientation and parallel to the transparent substrate 900 or in an arbitrary pretilt angle is disposed at the bottom of the groove 940. Then, the liquid crystal 960 is sealed by filling the groove 940 with the liquid crystal 960 and disposing the transparent substrate 950 on which the transparent electrode 910 is disposed with the transparent electrode 910 side facing the liquid crystal 960. Thus, the diffraction grating 9 of Example 8 can be manufactured.
This diffraction grating 9 uses the liquid crystal as the optically anisotropic medium in the diffraction grating 5 of the third embodiment, and controls the orientation of the liquid crystal molecules by applying a voltage, thereby improving the diffraction efficiency characteristics of S-polarized light and P-polarized light. It is variable. For example, when the liquid crystal 960 is a uniaxial liquid crystal, the ordinary ray refractive index is made to coincide with the refractive index of the optical isotropic medium, and the refractive index satisfying the formula (8) or the formula (9) in the absence of an electric field. In the case where the liquid crystal is aligned in a desired direction and a voltage is applied to the transparent electrode 910, the long axes of the molecules of the liquid crystal 960 are aligned in the direction of the transparent electrode 910, as shown in FIG. In addition, it is possible to switch from a diffraction grating that achieves diffraction efficiency up to 100% for both S-polarized light and P-polarized light to a plain window.

A method for manufacturing the optical waveguide 10 of Example 9 shown in FIG. 16 will be described. First, the electrode 1030 is formed on the cladding layer 1000, and the core layer 1010 is further formed on the electrode 1030. Next, a shallow strip-shaped groove 1040 arranged in a strip shape drawing a straight line or an arbitrary curve is formed on a part of the core layer 1010, and a rectangular lattice 1050 is formed. Next, a liquid crystal alignment film 1020 is disposed at the bottom of the groove 1040 so that the liquid crystal is aligned in an arbitrary orientation and parallel to the cladding layer or in an arbitrary pretilt angle. Then, the liquid crystal 1060 is filled in the groove 1040, and the cladding layer 1010 on which the electrode 1030 and the liquid crystal alignment film 1020 are formed is brought into contact with the core layer 1010 with the liquid crystal alignment film 1020 side facing the liquid crystal 1060, thereby sealing the liquid crystal 1060. Stop. Thus, the optical waveguide 10 of Example 9 can be manufactured.
In the optical waveguide 10 of the ninth embodiment, by applying a voltage to the electrode 1030, the liquid crystal 1060 tilts at an arbitrary angle in the upper and lower electrode directions, so that the refractive index can be changed. The characteristics of TM wave diffraction efficiency can be controlled.

  The diffraction grating 3, the optical waveguide 4, the diffraction grating 7, and the optical waveguide 8 according to the present invention should have a deviation of approximately ± 10% from the condition that the equation (5) or the equations (6) and (7) are equal. In many cases, it can be used without any practical problem.

  The diffraction grating 5, the optical waveguide 6, the diffraction grating 9, and the optical waveguide 10 according to the present invention have the formula (8), the formula (9), the formula (10), the formula (11), the formula (12), and the formula (13). If the deviation is approximately ± 10% from the condition that is an equation, it can be used practically without problems.

  The diffraction grating 5, the optical waveguide 6, the diffraction grating 9, and the optical waveguide 10 according to the present invention are different from the optically isotropic medium used in these elements, and the optical anisotropic medium used in these elements is A rectangular grating combining optically anisotropic media having different characteristics may be used.

  The diffraction grating 5, the optical waveguide 6, the diffraction grating 9, and the optical waveguide 10 of the present invention have the effect of adjusting the polarization diffraction efficiency characteristics by adjusting the refractive index of S-polarized light (TE wave) and the refractive index of P-polarized light (TM wave). And the effect of adjusting the polarization diffraction efficiency characteristics of S-polarized light (TE wave) and P-polarized light (TM wave) by adjusting the duty ratio as in Non-Patent Document 6 may be combined.

  As mentioned above, although the Example of this invention was described in detail, these are only illustrations and do not limit a claim. The technology described in the claims includes various modifications and changes of the specific examples illustrated above.

  The technical elements described in this specification or the drawings exhibit technical usefulness alone or in various combinations, and are not limited to the combinations described in the claims at the time of filing. In addition, the technology exemplified in this specification or the drawings can achieve a plurality of objects at the same time, and has technical usefulness by achieving one of the objects.

  The diffraction grating and optical waveguide of the present invention can simultaneously realize high diffraction efficiency, large wavelength dispersion, and a wide wavelength band, compared to conventional surface-stitched diffraction gratings, VPH diffraction gratings, and thick transmission rectangular diffraction gratings. In addition, it can be used in various optical measuring instruments such as Raman scattering, Thomson scattering, fluorescence of living organisms, and faint light spectroscopic measurement devices such as astronomical observation, etc., which can improve the measurement limit and greatly shorten the measurement time. become.

  By adopting a curable liquid crystal as the optically anisotropic medium of the diffraction grating 3 and the diffraction grating 5 of the present invention, a diffractive optical element of a metric class size can be manufactured at a low cost by the same manufacturing process as a liquid crystal flat display or the like. Can be produced. If a meter-class large-area diffraction grating is put to practical use, it will be possible to apply large head-up displays, large-sized displays for 3D images, energy-saving windows that guide outside light to the ceiling or the back of the room and use it as lighting. .

  The diffraction grating 7 and the diffraction grating 9 of the present invention employ a liquid crystal as an optically anisotropic medium, and arrange transparent electrodes on both sides of the grating, thereby switching from an arbitrary polarization diffraction efficiency characteristic to an arbitrary polarization diffraction efficiency characteristic. It is possible to realize an active diffractive optical element with high efficiency. Such an optical element can be used for an optical measuring device such as a polarization spectroscopic measuring device, optical information processing, optical computing, and the like. In addition, dimming is possible when used for the large head-up display, the large display for 3D video, and the external light introduction window.

  The optical waveguide 8 and the optical waveguide 10 of the present invention are filled with a liquid crystal oriented in an arbitrary direction as an optically anisotropic medium having a rectangular lattice, and electrodes are arranged above and below the planar optical waveguide, An active diffractive optical element with high efficiency that can be switched from an arbitrary polarization diffraction efficiency characteristic to an arbitrary polarization diffraction efficiency characteristic can be realized. Such an optical element can be used for optical communication, optical information processing, optical computing, and the like.

DESCRIPTION OF SYMBOLS 1 Transmission type VPH diffraction grating 2 Thick transmission type rectangular diffraction grating 3, 5, 7, 9 Diffraction gratings 4, 6, 8, 10 Optical waveguide 20, 230 Hologram resin 21, 22, 450, 520 Optical isotropic medium 30, 40, 200, 240, 400, 430, 900, 950 Substrate 700 Lower substrate 730 Upper substrate 210 Liquid crystalline organic material 220 Thermosetting resin material 300, 500, 800, 1000 Clad layer 310, 510, 810, 1010 Core layer 410 , 940, 1040 Groove 420, 930, 1050 Rectangular grating 530 Optical anisotropic medium 710, 910 Transparent electrode 720, 820, 920, 1020 Liquid crystal alignment film 740, 840, 960, 1060 Liquid crystal 750 Liquid crystal molecule 830, 1030 Electrode

Claims (12)

A transmissive VPH diffraction grating having a grating structure with a refractive index modulated in a sinusoidal shape,
Using an optically anisotropic medium, for a desired wavelength and a desired Bragg angle,
The maximum refractive index for S-polarized light is nSmax, the minimum refractive index is nSmin, the maximum refractive index for P-polarized light is nPmax, and the minimum refractive index is nPmin.
nSmax, nSmin, nPmax, and nPmin are
(NSmax−nSmin) / cos θS and (nPmax−nPmin) * cos 2θP / cos θP are set so that the difference is within 10%, and thereby the thickness dependence of the diffraction efficiency of S-polarized light and the period of the characteristic, match as a difference between the period in the thickness dependence of the diffraction efficiency of the P polarized light is within 10%,
Further, the thickness of the diffraction grating, the thickness dependence of the diffraction efficiency of the set S-polarized light, and on the basis of the thickness dependence of the diffraction efficiency of the P-polarized light, the diffraction of the S-polarized light of the diffraction efficiency and P-polarized light The average efficiency is set to be 90% or more,
A diffraction grating characterized by that.
In the above equation, θS is the Bragg angle for S-polarized light, and θP is the Bragg angle for P-polarized light. The diffraction grating is a resin in which an optically isotropic resin is mixed with an optically anisotropic liquid crystal oriented in a predetermined direction,
The refractive index is modulated in a sinusoidal shape by the concentration of the liquid crystal in the resin,
The difference between the maximum refractive index and the minimum refractive index for S-polarized light and the difference between the maximum refractive index and the minimum refractive index for P-polarized light are set to different predetermined values depending on the concentration of liquid crystal and the orientation direction of liquid crystal molecules. The diffraction grating according to claim 1, wherein: The diffraction grating is
A biaxial optically anisotropic liquid crystal;
A liquid crystal alignment film in contact with the liquid crystal with the liquid crystal sandwiched therebetween, and aligning the liquid crystal in a predetermined direction;
An electrode portion in which a pair of electrodes sandwiching the liquid crystal is periodically arranged;
Have
By controlling the orientation direction of the liquid crystal molecules by applying a voltage to the electrode portion, the refractive index of the liquid crystal is modulated in a sinusoidal shape, and the difference between the maximum refractive index and the minimum refractive index for S-polarized light, The difference between the maximum refractive index and the minimum refractive index for P-polarized light is set to a different predetermined value.
The diffraction grating according to claim 1, wherein the diffraction efficiency of S-polarized light and the diffraction efficiency of P-polarized light are made variable by changing a voltage value applied to the electrode section. A transmission type diffraction grating having a rectangular grating structure in which two kinds of materials having different refractive indexes are alternately and periodically arranged,
One of the two types of materials is an optically anisotropic medium and the other is an optically isotropic medium. For a desired wavelength and a desired Bragg angle,
The maximum refractive index for the S-polarized light of the optically anisotropic medium is n2cS, the maximum refractive index for the P-polarized light is n2cP, and the refractive index of the optical isotropic medium is n2a, and n2a, n2cS, and n2cP are:
In the case of n2cP>n2cS> n2a or n2cP <n2cS <n2a, A1 * (n2cS−n2a) / cosθS and B1 * (n2cP−n2a) * cos2θP / cosθP
When n2cP>n2a> n2cS or n2cP <n2a <n2cS, A2 * (n2cS−n2a) / cosθS and −B2 * (n2cP−n2a) * cos2θP / cosθP should be within 10%. a is the values are set, thereby matching as the difference between the period in the thickness dependence of the diffraction efficiency of the S polarized light, and the period in the thickness dependence of the diffraction efficiency of the P polarized light is within 10% Let
Further, the thickness of the diffraction grating, the thickness dependence of the diffraction efficiency of the set S-polarized light, and on the basis of the thickness dependence of the diffraction efficiency of the P-polarized light, the diffraction of the S-polarized light of the diffraction efficiency and P-polarized light The average efficiency is set to be 90% or more,
A diffraction grating characterized by that.
In the above equation, θS is the Bragg angle for S-polarized light, and θP is the Bragg angle for P-polarized light. Further, A1 and A2 are the wave numbers (1 / periods) in the thickness- dependent characteristics of the diffraction efficiency of the S-polarized light of the diffraction grating obtained by the RCWA method, and the S of the transmission type VPH diffraction grating obtained by the two-wave coupling analysis method. it is divided by the wave number (1 / period) in the thickness dependence of the diffraction efficiency of the polarization. Also, B1, B2 is P-polarized light transmission VPH grating determined by the two-wave coupling analysis the wave number (1 / period) in the thickness dependence of the diffraction efficiency of the P polarized light of the diffraction grating obtained by RCWA method the diffraction efficiency of which is divided by the wave number (1 / period) in thickness dependent properties. The transmission type VPH diffraction grating described above has a maximum refractive index for S-polarized light of n2cS and n2a, a minimum refractive index of n2cS and n2a, and a maximum refractive index for P-polarized light of n2cP and n2a. Is a transmission type VPH diffraction grating having a larger one of n2cP and a smaller refractive index of n2a.   5. The diffraction grating according to claim 4, comprising a substrate made of an optically anisotropic material provided with a grating-like groove, and an optically isotropic material filling the groove of the substrate. .   The substrate is a crystal or stretched resin or orientation of β-barium metaborate (β-BaB2O4: β-BBO), yttrium fluoride-lithium (YLiF4: YLF), or lithium niobate (LiNbO3). The diffraction grating according to claim 5, wherein the diffraction grating is a liquid crystal cured in a finished state.   5. The substrate according to claim 4, wherein the substrate is made of an optically isotropic material provided with a lattice-shaped groove, and a liquid crystal is cured in a state of being oriented in a predetermined direction filling the groove. The diffraction grating described. A first substrate made of an optically isotropic material provided with a lattice-shaped groove;
A liquid crystal filled in the groove of the first substrate;
A second substrate provided on the first substrate and provided with a liquid crystal alignment film that contacts the liquid crystal and aligns the liquid crystal in a predetermined direction;
An electrode portion provided on a bottom surface of each groove of the first substrate and a position on the first substrate side surface of the second substrate facing the groove;
Have
By controlling the orientation direction of the molecules of the liquid crystal by applying a voltage to the electrode unit, the refractive index for S-polarized light and the refractive index for P-polarized light are different from each other, and
5. The diffraction grating according to claim 4, wherein the diffraction efficiency of S-polarized light and the diffraction efficiency of P-polarized light are made variable by changing a voltage value applied to the electrode section. The thickness of the diffraction grating, the thickness dependence of the diffraction efficiency of the set S-polarized light or of the maximum value of the thickness dependence of the diffraction efficiency of the P-polarized light, the thickness take the first local maximum near The diffraction grating according to claim 1, wherein the diffraction grating is set.   The diffraction grating according to any one of claims 1 to 9, wherein the diffraction grating has a linear or curved shape extending in a grating period direction, and the diffraction grating is embedded in a core material and a cladding material. An optical waveguide. A method of designing a transmissive VPH diffraction grating having a grating structure with a refractive index modulated in a sinusoidal shape,
Using an optically anisotropic medium, for a desired wavelength and a desired Bragg angle,
The maximum refractive index for S-polarized light is nSmax, the minimum refractive index is nSmin, the maximum refractive index for P-polarized light is nPmax, and the minimum refractive index is nPmin.
nSmax, nSmin, nPmax, and nPmin,
These values are set so that (nSmax−nSmin) / cos θS and (nPmax−nPmin) * cos 2θP / cos θP are within 10%, and thus the thickness dependence of the diffraction efficiency of S-polarized light The period in the characteristic and the period in the thickness-dependent characteristic of the diffraction efficiency of P-polarized light are matched so as to be within 10%,
Further, the thickness of the diffraction grating, the thickness dependence of the diffraction efficiency of the set S-polarized light, and on the basis of the thickness dependence of the diffraction efficiency of the P-polarized light, the diffraction of the S-polarized light of the diffraction efficiency and P-polarized light Set the average efficiency to be 90% or more,
A method for designing a diffraction grating.
In the above equation, θS is the Bragg angle for S-polarized light, and θP is the Bragg angle for P-polarized light. A method of designing a transmission type diffraction grating having a rectangular grating structure in which two kinds of materials having different refractive indexes are alternately and periodically arranged,
One of the two types of materials is an optically anisotropic medium and the other is an optically isotropic medium. For a desired wavelength and a desired Bragg angle,
The maximum refractive index for the S-polarized light of the optically anisotropic medium is n2cS, the maximum refractive index for the P-polarized light is n2cP, the refractive index of the optically isotropic medium is n2a, and n2a, n2cS, and n2cP are
If n2cP>n2cS> n2a or n2cP <n2cS <of n2a is, A1 * and (n2cS-n2a) / cosθS, B1 * and the (n2cP-n2a) * cos2θP / cosθP,
When n2cP>n2a> n2cS or n2cP <n2a <n2cS, A2 * (n2cS−n2a) / cosθS and −B2 * (n2cP−n2a) * cos2θP / cosθP should be within 10%. to, and set their values, thereby matching as the difference between the period in the thickness dependence of the diffraction efficiency of the S polarized light, and the period in the thickness dependence of the diffraction efficiency of the P polarized light is within 10% Let
Further, the thickness of the diffraction grating, the thickness dependence of the diffraction efficiency of the set S-polarized light, and on the basis of the thickness dependence of the diffraction efficiency of the P-polarized light, the diffraction of the S-polarized light of the diffraction efficiency and P-polarized light Set the average efficiency to be 90% or more,
A method for designing a diffraction grating.
In the above equation, θS is the Bragg angle for S-polarized light, and θP is the Bragg angle for P-polarized light. Further, A1 and A2 are the wave numbers (1 / periods) in the thickness-dependent characteristics of the diffraction efficiency of the S-polarized light of the diffraction grating obtained by the RCWA method, and the S of the transmission type VPH diffraction grating obtained by the two-wave coupling analysis method. It is a value obtained by dividing the diffraction efficiency of polarized light by the wave number (1 / period) in the thickness-dependent characteristic . B1 and B2 are the P-polarized light of the transmission type VPH diffraction grating obtained by the two-wave coupling analysis method of the wave number (1 / period) in the thickness-dependent characteristic of the diffraction efficiency of the P-polarized light of the diffraction grating obtained by the RCWA method. It is a value obtained by dividing the diffraction efficiency by the wave number (1 / period) in the thickness-dependent characteristic . The transmission type VPH diffraction grating described above has a maximum refractive index for S-polarized light of n2cS and n2a, a minimum refractive index of n2cS and n2a, and a maximum refractive index for P-polarized light of n2cP and n2a. Is a transmission type VPH diffraction grating having a larger one of n2cP and a smaller refractive index of n2a.

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