WO2011099550A1 - Optical element and optical system - Google Patents

Abstract

Disclosed is an optical element provided with an optical member having a grid interface on which a relief pattern is formed. A waveguide comprising an optical material having a higher refractive index than said optical member is formed on those faces constituting the aforementioned relief pattern which are vertical faces approximately parallel to the optical axis of the aforementioned optical element.

Description

Optical element and optical system

The present invention relates to an optical element and an optical system.
This application claims priority based on Japanese Patent Application No. 2010-030435 filed in Japan on February 15, 2010, the contents of which are incorporated herein by reference.

As an optical element, a diffraction element in which a relief pattern having a sawtooth cross-section is formed is widely used. In this type of diffractive element, optical performance deteriorates due to the flare light generated at the edge of the relief pattern, and therefore various contrivances have been made to suppress the generation of flare light and the adverse effects of flare light (for example, patents). Reference 1).

Japanese Patent No. 3717555

In the invention described in Patent Document 1, diffraction efficiency is increased by appropriately selecting an optical material of two layers having a relief pattern as an interface. However, an optimal one of two types of optical materials (low refractive index high dispersion material, high refractive index low dispersion material) has not yet been obtained. On the other hand, it is possible to increase the diffraction efficiency by forming a high relief pattern or increasing the grating interface. However, if the relief pattern is increased, flare is likely to occur, and manufacturing becomes difficult if the grating interface is increased. There was a problem of becoming.

The present invention has been made in view of the above-described problems of the prior art, and an object thereof is to provide an optical element with reduced flare light.

The optical element according to the first aspect of the present invention includes an optical member having a lattice interface on which a relief pattern is formed. A waveguide made of an optical material having a refractive index higher than that of the optical member is formed on a cliff surface substantially parallel to the optical axis of the optical element among the surfaces constituting the relief pattern.

The optical element according to the second aspect of the present invention is laminated with a first optical member having a lattice interface on which a relief pattern is formed, in close contact with or close to the lattice interface of the first optical member. And a second optical member. Of the surfaces constituting the relief pattern, a cliff surface substantially parallel to the optical axis of the optical element is made of an optical material having a higher refractive index than the first optical member and the second optical member. A waveguide is formed.

According to the first and second aspects of the present invention, an optical element with reduced flare light can be provided.

It is a fragmentary sectional view showing the optical element concerning a 1st embodiment of the present invention. It is a graph which shows the result of having performed the diffraction efficiency calculation of the optical element by RCWA method. It is a fragmentary sectional view showing an optical element concerning a 2nd embodiment of the present invention. It is a graph which shows the relationship between waveguide width and diffraction efficiency. It is a graph which shows the relationship between the wavelength of incident light, and diffraction efficiency. It is a graph which shows the relationship between a refractive index difference and diffraction efficiency. It is a graph which shows the relationship between the amount of phase shifts, and diffraction efficiency. It is a fragmentary sectional view showing the modification of a 2nd embodiment. It is a fragmentary sectional view showing other modifications of a 2nd embodiment. It is a fragmentary sectional view which shows the conventional optical element. It is a graph which shows the calculation result of the diffraction efficiency by RCWA method. It is a fragmentary sectional view which shows the conventional optical element.

Hereinafter, although each embodiment of the present invention will be described with reference to the drawings, the present invention is not limited to these.

(First embodiment)
FIG. 1 is a partial cross-sectional view showing an optical element 10 according to an embodiment of the first aspect of the present invention.
The optical element 10 is a single-layer diffractive optical element (single-layer DOE (Diffractive Optical Elements)). The optical element 10 includes an optical member 10A made of a transparent optical material, and one main surface (the upper surface in the drawing) of the optical member 10A is a lattice interface 11 on which a relief pattern having a sawtooth cross section is formed. .
The grating interface 11 is formed with a plurality of inclined surfaces 11a formed to be inclined with respect to the optical axis direction of the incident light L, and a plurality of ridges having a triangular cross section along with the inclined surfaces 11a. A plurality of cliff surfaces 11b formed as surfaces substantially parallel to the axial direction are formed. The relief pattern is formed by alternately arranging the inclined surface 11a and the cliff surface 11b.
In the optical element 10 of the present embodiment, the waveguide 12 having a uniform width (thickness) is formed on the cliff surface 11b at any position in the direction along the optical axis of the incident light L.

In the optical element 10 of the present embodiment, since the waveguide 12 is formed on the cliff surface 11b, the diffraction efficiency can be increased and diffracted light (flare light) other than the designed order can be reduced. Hereinafter, the optical element 10 of the present embodiment will be described in comparison with a conventional optical element.

FIG. 2 is a graph showing the result of calculating the diffraction efficiency of the optical element 10 shown in FIG. 1 by the RCWA (Rigorous Coupled Wave Analysis) method.
The calculation model is as follows: grating pitch P1 = 10 μm, grating height H1 = 1.1 μm, refractive index na = 1.5 of the optical member 10A, refractive index ng = 1.5 + Δn of the optical material constituting the waveguide 12, and Δn Was changed in the range of 0.02 to 0.2, and the width W1 of the waveguide 12 was changed in the range of 0 to 0.3 μm. The incident light L was a TE (Transverse Electric) plane wave having a wavelength of 0.55 μm.

In the present embodiment, the calculation is made on the assumption that the incident light L is emitted from the inside of the optical member 10A through the lattice interface 11 to the outside. In the actual calculation of the diffraction efficiency, it is necessary to consider the light incident on the optical member 10A from the air. However, the diffraction efficiency when the refractive index ng and the width W1 of the waveguide 12 are changed is completely compared. I left it out to simplify the calculation because it had no effect.

The horizontal axis of the graph shown in FIG. 2 corresponds to the width W1 of the waveguide 12, and the vertical axis corresponds to the first-order diffraction efficiency. FIG. 2 also shows 10 curves showing changes in diffraction efficiency with respect to the width W1 of the waveguide 12 when Δn is changed in increments of 0.02 in the range of 0.02 to 0.2. Yes. The first-order diffraction efficiency when the width W1 of the waveguide 12 is 0 (zero) corresponds to the first-order diffraction efficiency of an optical element having a conventional configuration that does not include the waveguide 12.

Here, FIG. 9 is a partial sectional view showing a conventional optical element. A conventional optical element 1000 shown in FIG. 9 is a single-layer DOE composed of an optical member 1000A having a lattice interface 11 formed on one surface.
The optical element 1000 is usually used only at a single wavelength with optimized diffraction efficiency. For example, the grating height H is set so that the diffraction efficiency of the primary light L1 is highest at a wavelength of 0.55 μm. Specifically, in the case of the optical element 1000 that does not include the waveguide 12, the grating height H (μm) for obtaining the optimum first-order diffraction efficiency at the wavelength λ (μm) is the refractive index of the optical member 1000A. When nb, it is set so that H = λ / (nb−1).

The first-order diffraction efficiency according to the scalar calculation of the above formula is 100%, but this is valid only when the grating period (grating pitch P shown in FIG. 9) is sufficiently large. Assuming the use in the visible light region, the deviation from the strict calculation with respect to the scalar calculation starts to be noticeable when the grating pitch P is in the range of 100 μm or less or 50 μm or less. In particular, when the grating pitch P is reduced to about 10 μm, the maximum diffraction efficiency is reduced to about 90%.

FIG. 10 is a graph showing a calculation result of diffraction efficiency by the RCWA method when the incident light L is 0.55 μm in wavelength, the grating pitch P is 10 μm, and the refractive index nb is 1.5. The horizontal axis of the graph shown in FIG. 10 corresponds to the grating height H, and the vertical axis corresponds to the first-order diffraction efficiency.
As shown in FIG. 10, the grating height H at which the optimum first-order diffraction efficiency is obtained under the above conditions is 1.1 μm, and the maximum diffraction efficiency at that time is about 91.3%. That is, the grating height H at which the first-order diffraction efficiency is maximized coincides with the grating height (0.55 / (1.5-1) = 1.1 (μm)) derived from the above equation. However, the first-order diffraction efficiency is not 100%. Further, when the grating height H deviates from the optimum value 1.1 μm, the first-order diffraction efficiency is greatly reduced.

On the other hand, in the optical element 10 according to the present embodiment, as shown in FIG. 2, the optical element 10 according to the present embodiment is suitable for all conditions in which the refractive index of the waveguide 12 is changed by appropriately selecting the width W1 of the waveguide 12. 1st diffraction efficiency higher than the maximum diffraction efficiency (91.3%) of the optical element 1000 can be obtained. For example, when the refractive index difference Δn (= ng−na) is 0.1, the diffraction efficiency is about 93.5% when the width W1 of the waveguide 12 is about 0.2 μm.

As described above, according to the optical element 10 of the present embodiment, the refractive index difference Δn (that is, the refractive index ng, na) between the waveguide 12 and the optical member 10A and the width W1 of the waveguide 12 are appropriately selected. With this configuration, it is possible to obtain a diffraction efficiency that exceeds that of the conventional optical element 1000 that does not include the waveguide 12.

It is considered that the optical element 10 of the present embodiment can obtain a higher diffraction efficiency than the conventional optical element 1000 for the following reason.
The above results shown in FIGS. 2 and 10 are knowledge obtained only when the electromagnetic field is calculated by vector calculation (RCWA method in the present embodiment), and therefore it is difficult to explain based on geometrical differences. . However, it is probably related to the disturbance of the electromagnetic field at the cliff portion of the relief pattern, which is the cause of the diffraction efficiency falling below the scalar value.

格子 In diffraction efficiency calculation with scalar calculation, the grating height is not included in the parameters. This is because it is assumed that the phase is smoothly switched at the joint of each grating. However, there is actually a phase disturbance in this part. Therefore, only when the grating pitch is sufficiently large with respect to the wavelength, the scalar calculation of the diffraction efficiency is valid. As the lattice pitch decreases, the number of relief pattern cliffs per unit area increases, and the ratio of disturbance of the electromagnetic field by the cliffs increases. If the disturbance of the electromagnetic field becomes a magnitude that cannot be ignored, the diffraction efficiency will be less than 100%. The reason why the maximum value of the diffraction efficiency is about 90% when the grating pitch is as small as about 10 μm is considered to be largely due to the phase disturbance of the cliff portion of the relief pattern.

On the other hand, in the present embodiment, by providing the waveguide 12 at the cliff portion of the relief pattern where the electromagnetic field is disturbed, the light passing just outside the cliff surface 11b is confined in the waveguide 12. Then, the light confined in the waveguide 12 travels in substantially the same phase as the light traveling toward the inclined surface 11a in the convex portion of the relief pattern, and is output as a substantially spherical wave from the tip of the waveguide 12. . Thereby, in the edge part of a relief pattern, the phase on either side of this edge part can be connected smoothly. As a result, it is considered that the diffraction efficiency can be improved.

In addition, from the graph of FIG. 2, the higher the refractive index difference Δn, the higher the diffraction efficiency, while the peak width of the first-order diffraction efficiency is narrowed. The next diffraction efficiency changes greatly. In consideration of actual processing, it may be difficult to precisely control the width W1 of the waveguide 12. In such a case, the first-order diffraction efficiency can be prevented from changing (decreasing) rapidly even if an error occurs in the width W1 of the waveguide 12 by reducing the refractive index difference Δn. For example, as shown in FIG. 2, when the refractive index difference Δn is 0.1, the change in diffraction efficiency is within a range of −0.5% from the peak value compared to the case where the refractive index difference Δn is 0.2. The allowable range of the width W1 is about double. On the other hand, when the width W1 of the waveguide 12 can be controlled with sufficient accuracy, a very high diffraction efficiency can be obtained by increasing the refractive index difference Δn.

(Second Embodiment)
Next, an embodiment of an optical element according to the second aspect of the present invention will be described with reference to FIGS.
FIG. 3 is a cross-sectional view showing the optical element of the present embodiment.
The optical element 20 shown in FIG. 3 is a contact multilayer type DOE. The optical element 20 has an optical member 20A, which is a lattice interface 11 having a relief pattern with a sawtooth cross section on one main surface (illustrated upper surface), and a second optical element formed in close contact with the lattice interface 11 of the optical member 20A. And a member 20B. The grating interface 11 has a plurality of inclined surfaces 11a formed to be inclined with respect to the optical axis direction of the incident light L, and a plurality of ridges having a triangular cross section along with the inclined surfaces 11a. A plurality of cliff surfaces 11b formed as surfaces substantially parallel to the direction are formed. The relief pattern is formed by alternately arranging the inclined surface 11a and the cliff surface 11b. A waveguide 12 having a uniform width (thickness) is formed on the cliff surface 11b at any position in the direction along the optical axis of the incident light L.

Also in the contact multilayer DOE, when vector calculation using the RCWA method is performed, disturbance of the electromagnetic field is observed at the cliff portion of the relief pattern. Therefore, even if the refractive index n1 of the first optical member 20A and the refractive index n2 of the second optical member 20B are optimized, the first-order diffraction efficiency is 90 when the grating pitch is 20 μm and the grating height is 25 μm, for example. % Is the maximum.
In the scalar calculation, the diffraction efficiency when the wavelength is optimized is 100%. This is because the lattice height is not included in the parameters in the scalar calculation. However, if the disturbance of the electromagnetic field is reduced by reducing the grating height, the optical material constituting the first optical member 20A and the optical material constituting the second optical member 20B are extremely reduced in refractive index dispersion. A good combination is required. Further, when the grating height is reduced, the influence of height variation is increased, and there is a concern that the diffraction efficiency largely fluctuates due to manufacturing errors. On the other hand, the optical element 20 of the present embodiment can obtain a higher diffraction efficiency than the conventional optical element without excessively reducing the grating height H2 due to the action of the waveguide 12.

Hereinafter, the optical element 20 was verified with respect to the relationship between the configuration (width W2, refractive index ng) of the waveguide 12 and the diffraction efficiency when the optical element 20 was configured using a glass material.

The optical element 20 was composed of the materials shown in Table 1 below.

N-SF2 (trade name) shown in Table 1 is a low refractive index and high dispersion material, and N-BAF10 (trade name) is a high refractive index and low dispersion material. The refractive index of each wavelength for calculating the diffraction efficiency was calculated using the following Cermeier dispersion formula using the constants of the dispersion formula disclosed by Schott. The refractive index at a wavelength of 0.62 μm described in Table 1 was calculated by the following equation.
n ² (λ) -1 = {B ₁ λ ² / (λ ² -C ₁ )} + {B ₂ λ ² / (λ ² -C ₂ )} + {B ₃ λ ² / (λ ² -C ₃ )}

The grating pitch P2 of the optical element 20 was 20 μm.
The grating height H2 was optimized at a wavelength of 0.62 μm. That is, from the refractive index difference Δn _{620 at} a wavelength of 0.62 μm between the optical material (N-SF2) constituting the first optical member 20A and the optical material (N-BAF10) constituting the second optical member 20B, A height corresponding to the blaze condition at a wavelength of 0.62 μm was calculated and used. The calculation formula is shown below.
Δn ₆₂₀ = 1.66785-1.44481 = 0.02304
H2 = λ / Δn ₆₂₀ = 26.9095 (μm)
Note that the refractive index difference Δn between the optical material (N-LAK12) constituting the waveguide 12 and the optical material (N-BAF10) constituting the second optical member 20B is 1.667600-1.66785 = 0. [00815].

Here, FIG. 11 is a diagram showing a contact multilayer DOE in which the second optical member 2000B is formed in close contact with the lattice interface 11 of the first optical member 2000A.
For comparison, the same conditions were set for the conventional optical element 2000 shown in FIG. 11 except that the waveguide 12 was not provided. Specifically, the grating pitch is 20 μm, the grating height is 26.9095 μm, the optical material constituting the first optical member 20A is N-SF2 (refractive index 1.64481), and the optical material constituting the second optical member 20B is used. N-BAF10 (refractive index: 1.667785) was used.

Under the above conditions, the calculation was performed by the RCWA method with the incident light as the TE plane wave (wavelength 0.62 μm) and the wavelength range of the incident light as the visible light range (0.42 to 0.75 μm).
Also in the present embodiment, for the sake of simplicity, the second incident light L when the incident light L passes through the lattice interface 11 from the first optical member 20A (2000A) and enters the first optical member 20B (2000B). The diffraction efficiency inside the optical member 20B (2000B) was calculated. In the actual calculation of diffraction efficiency, the light incident on the first optical member 20A (2000A) from the outside of the first optical member 20A (2000A) and the light emitted from the second optical member 20B (2000B) to the outside. Although it is necessary to consider the light beam to be used, it is omitted here because it does not affect the comparison of diffraction efficiency when the configuration of the waveguide 12 is changed.

FIG. 4 is a graph showing the relationship between the width W2 of the waveguide 12 and the first-order diffraction efficiency obtained by calculation.
As shown in FIG. 4, in the range where the waveguide width W2 is less than 1.175 μm (intersection Q in the figure), the optical element 20 of the present embodiment has the first-order diffraction efficiency (waveguide width W2) of the conventional optical element 2000. = 0 μm position) can be obtained. In addition, the maximum diffraction efficiency (about 95.5%) is obtained when the waveguide width W2 = 0.07 μm.

Next, FIG. 5 is a graph showing the relationship between the wavelength of the incident light L and the first-order diffraction efficiency.
As shown in FIG. 5, when the waveguide width W2 is in the range of 0.2 μm to 0.8 μm, the diffraction efficiency of the conventional optical element 2000 in all the calculated wavelength ranges (condition of W2 = 0 μm indicated by the dotted line in the figure) A diffraction efficiency exceeding 1 is obtained. In particular, when the waveguide width W2 is in the range of 0.6 μm to 0.8 μm, it stably exceeds the diffraction efficiency of the conventional optical element 2000 in all wavelength regions.

Next, FIG. 6 shows 1 when the waveguide width W2 is fixed to 0.8 μm and the refractive index difference Δn between the waveguide 12 and the second optical member 20B is changed in the range of 0 to 0.1. It is a graph which shows the result of having calculated the change of the next diffraction efficiency by RCWA method about TE plane wave.
As shown in FIG. 6, when the waveguide width W2 is fixed at 0.8 μm and the refractive index of the waveguide 12 is gradually increased from the refractive index of the second optical member 20B, first, the refractive index difference Δn is 0. The first-order diffraction efficiency has a maximum value at a position M1 near .008. Further, when the refractive index of the waveguide 12 is increased, the first-order diffraction efficiency rapidly decreases. This is because the phase of the light traveling inside the waveguide 12 is shifted from the phase of the light traveling outside the waveguide 12, so that disturbance of the electromagnetic field occurs at the tip of the waveguide 12 (the edge portion of the relief pattern). It is believed that there is. However, when the refractive index difference Δn is further increased, the first-order diffraction efficiency starts to increase around the refractive index difference Δn exceeding 0.025, and takes the local maximum again at the position M2 where Δn is near 0.04. . The first-order diffraction efficiency at the position M2 is also higher than the diffraction efficiency of the conventional optical element 2000. This is because the phase of the light traveling in the waveguide 12 and the phase of the light traveling outside the waveguide 12 are aligned because the phase is shifted by 2π from the first maximum position M1.

Here, FIG. 7 is a graph in which the calculation result shown in FIG. 6 is plotted with the horizontal axis converted into a phase shift amount. The amount of phase shift means a phase difference generated between light traveling in the waveguide 12 and light traveling in the second optical member 20B. The position where the phase shift amount is 0 is a case where the effective refractive index of the waveguide 12 matches the refractive index of the second optical member 20B, and the fundamental mode of the slab waveguide is established. It corresponds to a point. Since the peak of the first-order diffraction efficiency shown in FIG. 7 is shifted by 2π, it can be understood that the condition of the waveguide 12 is allowed even if the phase is shifted by 2π × N (N: natural number). . Further, the phase shift amount from the position where the diffraction efficiency takes the maximum value is allowed to be about ± 0.25π to ± 0.4π.

Also in the optical element of the second embodiment described above, it is considered that the high diffraction efficiency is obtained with respect to the conventional multi-layer DOE because of the same reason as in the first embodiment. That is, light in the vicinity of the cliff portion is confined by the waveguide 12 formed on the cliff portion of the relief pattern, and the phase is smoothly connected at the edge portion of the relief pattern by emitting the light as a substantially spherical wave from the tip of the waveguide 12. be able to. As a result, it is considered that the diffraction efficiency can be improved.

[Modification]
8A and 8B are diagrams showing a modification of the optical element 20 of the present embodiment. 8A corresponds to the first modification, and FIG. 8B corresponds to the second modification.
Each of the optical element 201 and the optical element 202 shown in FIGS. 8A and 8B has a high refractive index layer 121 formed so as to cover the lattice interface 11 of the first optical member 20A. The high refractive index layer 121 is formed using an optical material having a higher refractive index than either of the first optical member 20A and the second optical member 20B, similarly to the waveguide 12 in the optical element 20 of the above embodiment. ing.

The difference between the optical element 201 and the optical element 202 is only the configuration of the lattice interface 11, and the optical element 201 is used for the light L incident perpendicularly to the optical element 201, whereas the optical element 201 is optical. The element 202 is used for light L incident on the optical element 202 from an oblique direction. Therefore, in the optical element 202, the cliff surface 11b of the lattice interface 11 is formed as an inclined surface that intersects the normal direction (vertical direction in the figure) of the horizontal plane 202a in the optical element 202. However, the relationship between the incident light L and the cliff 11b in the optical element 202 is the same as that of the optical element 201, and the cliff 11b is formed substantially parallel to the optical axis of the incident light L.

Also in the optical elements 201 and 202 according to the modified example, the high refractive index layer 121 is formed on the cliff surface 11b, so that the effect of increasing the diffraction efficiency and reducing the flare light as in the previous embodiment. Obtainable. In the optical elements 201 and 202 according to the modified example, not only the cliff surface 11b but also the entire lattice interface 11 is covered with the high refractive index layer 121. Of the high refractive index layer 121, on the inclined surface 11a. The portion formed in does not affect the optical characteristics of the optical elements 201 and 202. This is because this portion only gives a uniform phase difference to the light transmitted through the high refractive index layer 121, so that it is the same as no change when viewed from the whole optical element.

In the optical elements 201 and 202, an element in which the optical member 20B is an air layer can be configured. In this case, the refractive index difference between the high refractive index layer 121 and the air layer is between the optical member 20A and the air layer. Therefore, the reflection loss may increase due to the formation of the high refractive index layer 121 on the inclined surface 11a. In order to reduce such reflection loss, an appropriate antireflection film may be provided in consideration of the refractive index and film thickness of the high refractive index layer 121 on the inclined surface 11a. Further, instead of providing the antireflection film, the film thickness t of the high refractive index layer 121 on the inclined surface 11a satisfies the antireflection condition, that is, t = Mλ / 2ng (M = 1, 2,...). You may form as follows.

Further, in the above embodiment, the case where the base material is a glass material has been described. However, the configuration of the above embodiment and the modified example includes two types as disclosed in International Publication No. WO2006 / 068137. The present invention can also be applied to a contact multilayer DOE made of a resin.

Also, the operation effect and the conditions of the waveguide by forming the waveguide can be theoretically explained as will be described in detail below.

In the optical element 20 shown in FIG. 3, the wavelength λ, the refractive index n ₁ of the incident side medium (medium 1; first optical member 20A) of the blazed grating, and the exit side medium (medium 2; second optical member 20B) refractive index _{n 2} of the grating depth H (height Gakemen 11b). The refractive index ng and the width of the high refractive index member (waveguide 12) added to the side surface of the grating are Wg. In an ideal blazed grating, wavefronts separated by the grating after passing through the grating are well joined, so that energy is concentrated and diffracted in a specific direction. As is well known, this condition is represented by the following formula (1).

By the way, in an actual blazed grating, the wavefront is disturbed during wavefront propagation because the refractive index differs between the left and right sides of the grating side surface. This can be interpreted as it is scattered on the grating side surface and the wavefront spreads. As a result, the wavefront does not succeed after the grating is transmitted, and the diffraction efficiency is lower than the value predicted from an ideal blazed grating. By adding a high refractive index member to the side surface of the blazed grating and confining light by this waveguide structure, it becomes possible to suppress wavefront disturbance due to scattering and to suppress a decrease in diffraction efficiency. Consider the light confinement conditions necessary for this. Regarding a general asymmetric slab waveguide, the conditions for confining light in the waveguide are the following conditional expressions (2) and (3) for the TE mode, and the following conditional expressions (4) and (5) for the TM mode: (See the following document).
(Reference) A. Yariv Quantum Electronics, 2nd ed. P512

Here, n _eff corresponds to the effective refractive index of the high refractive index member (waveguide) on the side surface of the grating. If the waveguide width Wg is made wider than W in this equation, light can be confined. That is, the waveguide width Wg according to the aspect of the present invention is expressed by Expression (6) and Expression (7) for each of the TE wave and the TM wave.

For general light including partially polarized light, the intensity ratio of the TE component of the polarization component is α, the intensity ratio of the TM component is β, and the intensity ratio of the non-polarization component is 1−α−β (where α + β ≦ 1), and the waveguide thickness Wg may be obtained by the following equations (8) and (9). In Equation (8), the contribution of the TE component to Wg is αW _TE , the contribution of the TM component is βW _TM , and the contribution of the non-polarization component is {(W _TE + W _TM ) / 2} × (1−α−β). Derived from being.

In addition, since the high refractive index member does not have a blaze effect, the larger the waveguide width Wg, the higher the efficiency loss. Therefore, from the viewpoint of efficiency, Wg should be as small as possible within the range satisfying the confinement conditions. In the conditions where Wg is the smallest in the equations (6), (7), and (9), that is, in the conditions where the equal sign is established in each equation. Efficiency is highest.

Next, a condition in which the wavefronts of the waveguide and the wavefronts transmitted through the medium 1 and the medium 2 are substantially in phase, so-called phase matching conditions, will be examined.
The conditions for aligning the phases of the TE wave are to use the effective refractive index n _{eff, TE} obtained by solving equations (2) and (3) simultaneously, where H is the grating height, and n is large in n ₁ and n ₂ . Can be expressed by the following formula (10). Similarly, the phase matching condition for the TM wave is expressed by Expression (11).

In practice, if phase matching is performed within the range of 2πN ± 0.2π, an effect of improving efficiency is recognized. Therefore, the phase matching conditions of the aspect of the present invention relating to the TE wave and TM wave are expressed by the following formula (12), respectively. It is represented by (13).

On the other hand, the phase matching condition of the aspect of the present invention relating to general light including partially polarized light is expressed by the equation (14) similarly to the equation (8) based on the above discussion.

Each of the above equations is verified by the graphs of FIGS. The peaks M1, M2, M3, etc. shown in FIG. 6 are out of phase by N periods as shown in equation (9). N = 0, that is, n _eff −n = 0, is a state in which only the waveguide fundamental mode is established. At this time, the light traveling through the waveguide and the light traveling through the member having the refractive index n have the least phase disturbance. It becomes. Therefore, the peak M1 shows the highest first-order diffraction efficiency.

Also, each peak is not pinpoint but has a width. In FIG. 6, the default efficiency value (efficiency value when no highly refractive member is not provided) is exceeded by a width of about ± 1/8 period centering on the time of the horizontal axis 0, 2 (N = 0, 1). Yes. Therefore, when N = 0 and 1, it is more preferable to perform phase matching within a range of 2π (N ± 0.125).

According to each embodiment described above, it is possible to provide an optical element in which the phase disturbance of transmitted light at the edge portion can be suppressed and flare light is reduced.
The optical elements described in each embodiment are used for an optical system of a projection apparatus (stepper, liquid crystal projector, etc.), an optical system of a photographing apparatus (camera, etc.), and an optical system of an observation apparatus (microscope, binoculars, etc.). In any optical system, the effect of reducing flare light can be obtained.

According to the present invention, an optical element with reduced flare light can be provided.

10, 20 Optical element 10A Optical member 11 Lattice interface 11a Inclined surface 11b Cliff surface 12 Waveguide 20A First optical member 20B Second optical member

Claims (7)

1. An optical element including an optical member having a lattice interface on which a relief pattern is formed,
   A waveguide made of an optical material having a refractive index higher than that of the optical member is formed on a cliff surface substantially parallel to the optical axis of the optical element among the surfaces constituting the relief pattern. Optical element.
2. An optical element comprising: a first optical member having a lattice interface on which a relief pattern is formed; and a second optical member laminated in close contact with or close to the lattice interface of the first optical member. And
   A waveguide made of an optical material having a higher refractive index than the first optical member and the second optical member, on a cliff surface substantially parallel to the optical axis of the optical element among the surfaces constituting the relief pattern. An optical element is formed.
3. 3. The optical element according to claim 1, wherein a high refractive index layer made of an optical material constituting the waveguide is formed so as to cover the lattice interface.
4. The optical element according to claim 1, wherein a width Wg of the waveguide satisfies Wg ≧ W.
   However, W is a value defined by the following formula (E1).
   Here, W _TE and W _TM are as follows when the refractive index of the medium constituting the lattice interface is n ₁ and n ₂ , the refractive index of the optical material constituting the waveguide is ng, and the wavelength used is λ. These are values defined by the equations (E2) to (E5), and n _{eff, TE} and n _{eff, TM} in the equations (E3) and (E5) are effective refractive indexes relating to the TE component and TM component of the waveguide. Where α and β are the intensity ratios of the TE component and the TM component of the light having the wavelength λ (where α + β ≦ 1), respectively.
   

   

   

   
5. An optical system comprising the optical element according to claim 1 or 2,
   The wavelength of light incident on the optical element is λ, the intensity ratio of the TE component and TM component of the light is α and β (where α + β ≦ 1),
   An optical system characterized in that a waveguide width Wg of the optical element satisfies Wg ≧ W.
   However, W is a value defined by the following formula (E1).
   Here, W _TE and W _TM are the following formulas (E2) to (E2), where n ₁ and n ₂ are the refractive indexes of the medium constituting the lattice interface, and ng is the refractive index of the optical material constituting the waveguide. (E5) is a value defined by (E5), and n _{eff, TE} and n _{eff, TM} in the equations (E3) and (E5) are effective refractive indexes related to the TE component and TM component of the waveguide.
   

   

   

   
6. The optical element according to claim 1 or 2,
   When the width of the waveguide is Wg, the refractive index of the medium constituting the lattice interface is n ₁ and n ₂ , the refractive index of the optical material constituting the waveguide is ng, and the wavelength used is λ, the following formula ( An optical element satisfying E6).
   

   

   Here, H is the height of the cliff face, n is the larger value of the refractive indexes n ₁ and n ₂ , and α and β are the intensity ratios of the TE component and TM component of the light of the wavelength λ, respectively (however, α + β ≦ 1), and n _{eff, TE} and n _{eff, TM} are effective refractive indexes for the TE component and the TM component defined by the following equations (E2) to (E5), respectively, and the equations (E2) to (E5 ) W _TE = W _TM = Wg.
   

   

   
7. An optical system comprising the optical element according to claim 1 or 2,
   The wavelength of light incident on the optical element is λ, the intensity ratios of the TE component and TM component of the light are α and β (where α + β ≦ 1), respectively, and the width of the waveguide is Wg,
   An optical system characterized by satisfying the following formula (E6).
   

   

   Here, H is the height of the cliff face, n is the larger value of the refractive indexes n ₁ and n ₂ , and α and β are the intensity ratios of the TE component and TM component of the light of the wavelength λ, respectively (however, α + β ≦ 1), and n _{eff, TE} and n _{eff, TM} are effective refractive indexes for the TE component and the TM component defined by the following equations (E2) to (E5), respectively, and the equations (E2) to (E5 ) W _TE = W _TM = Wg.
   

   

   

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