JP2010139602A - Optical module - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To perform optical multiplexing and demultiplexing for polarized waves using a birefringent crystal without a lens or the like. <P>SOLUTION: A waveguide substrate 10 where a λ/2 plate 13 is stuck to the end face 11b thereof is shaped so that an end face 11a includes an angle θa. As to the positional relationship between the waveguide substrate 10 and the birefringent crystal 14, the waveguide substrate 10 and the birefringent crystal 14 are positioned so that abnormal light emitted through the λ/2 plate 13 and normal light emitted from a waveguide 11 are multiplexed in the interior of the birefringent crystal 14 to emit the multiplexed light to the outside, and when signal light entering the birefringent crystal 14 from the outside are demultiplexed into normal light and abnormal light in the interior of the birefringent crystal 14, the abnormal light emitted from the birefringent crystal 14 becomes normal light and enters a waveguide 12 through the λ/2 plate 13, and the normal light emitted from the birefringent crystal 14 enters the waveguide 11. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to an optical module that performs polarization multiplexing / demultiplexing.

  In recent years, in an optical communication network, in order to increase the transmission capacity, two orthogonal polarizations of signal light are transmitted by being combined on the transmitting side and demultiplexed on the receiving side. Optical transmission systems that increase communication speed have been developed.

  In addition, an optical fiber amplifier for WDM (Wavelength Division Multiplexing) communication amplifies and transmits a plurality of channels of wavelength-multiplexed signal light to a high output. However, as the number of channels increases, the pumping light power required for amplification also increases. Therefore, a high-power excitation light source is required. In order to increase the output of the pumping light, a pumping light source module that increases the pumping light power by combining two orthogonal polarizations of the pumping light has been developed.

  Here, as the polarization multiplexing / demultiplexing element, a birefringent crystal such as PBS (Polarization Beam Splitter) or calcite is generally used. Birefringence is a phenomenon in which light incident on a crystal or other anisotropic substance is separated into two lights having vibration directions perpendicular to each other.

  For example, when light is incident on calcite, the light is refracted at two different angles and separated into two as it travels through and exits. Such a phenomenon showing two (or more) refraction angles is called birefringence.

  FIG. 5 shows PBS. The PBS 50 is a cube-shaped element configured by depositing a dielectric multilayer film 53 on the inclined surface of the right-angle prism 51 and bonding the inclined surfaces of the right-angle prisms 51 and 52 using an organic adhesive.

  When natural light (non-polarized light) is incident on the PBS 50, two orthogonally polarized waves are generated and emitted. Of the emitted light, light on the vibration plane parallel to the optical axis is called extraordinary ray, and light on the vibration plane perpendicular to the optical axis is called ordinary light. Normally, ordinary light is written as o and abnormal light is written as e.

  It is used as a polarization multiplexing element that performs multiplexing opposite to the above-described light flow, such that normal light and extraordinary light that are perpendicular to each other are incident and non-polarized light is generated and emitted. In this case, it is called a PBC (Polarization Beam Combiner).

  PBS50 is widely used for polarizers and spectroscopic devices because it is inexpensive, but the transmission wavelength band is generally narrow, and because it is bonded, it is not heat resistant, so high output light It has drawbacks such as reduced adhesive strength when incident.

  FIG. 6 shows a birefringent crystal. Ordinary light and extraordinary light are incident on the birefringent crystal 60 from the incident points p1 and p2, respectively. The ordinary light and extraordinary light come closer to each other as they travel through the birefringent crystal 60, and are combined at the emission point p3. The combined light is emitted.

  In general, a birefringent crystal is more expensive than PBS, but has a characteristic that it has a wide transmission wavelength band and is excellent in heat resistance depending on the type of crystal. In particular, among birefringent crystals, a rutile crystal having a large birefringence is widely used as a polarization multiplexing / demultiplexing element. The difference from the refractive index of light is large).

As a prior art, for example, Patent Document 1 has been proposed as an optical fiber amplifier that synthesizes signal light polarization using a birefringent crystal. For example, Patent Document 2 has been proposed as an excitation light source module that combines excitation light polarization using a birefringent crystal.
JP 2002-252420 A (paragraph numbers [0037] to [0044], FIG. 2) Japanese Patent Laid-Open No. 11-258453 (paragraph numbers [0051] to [0064], FIG. 1)

  In a birefringent crystal, the refractive index of ordinary light and the refractive index of extraordinary light are different from each other, so that when light enters the birefringent crystal, the path of ordinary light traveling in the crystal and the extraordinary light traveling in the crystal Since the optical path is separated, polarization demultiplexing is performed (polarization multiplexing can be performed if the traveling direction of light is considered in reverse).

  However, even if a crystal having a large birefringence such as a rutile crystal is selected as the birefringent crystal, it means that the birefringence is large among the types of crystals, and the refractive index of ordinary light and The refractive index of extraordinary light is generally very close to any birefringent crystal (the difference in refractive index is small).

  For this reason, in FIG. 6, for example, when considering the combination of polarized waves, the incident points p1 and p2 of the ordinary light and the extraordinary light with respect to the birefringent crystal 60 are in very close positions. In order to make normal light and extraordinary light accurately incident on the incident points p1 and p2 (in order to combine and emit the normal light and extraordinary light at the point p3 as the normal light and extraordinary light travel inside the birefringent crystal 60). In other words, an optical element such as a lens or a prism must be arranged in the previous stage of the birefringent crystal 60 to precisely adjust the positional relationship of light to be combined.

  FIG. 7 is a diagram showing a configuration of a conventional polarization multiplexing / demultiplexing module. This shows the state of multiplexing. The polarization multiplexing / demultiplexing module 6 includes a waveguide substrate 61, a λ / 2 plate 62, a correction lens 63, and a birefringent crystal 60.

  The λ / 2 plate 62 is a wavelength plate that is disposed between the waveguide substrate 61 and the correction lens 63 and does not absorb light, but rotates the polarization plane of the incident ordinary light by π and emits it as extraordinary light. Yes (or incident extraordinary light is rotated by π and emitted as ordinary light).

  Ordinary light propagates through the two waveguides 61 a and 61 b on the waveguide substrate 61 and is emitted from the waveguide substrate 61. Ordinary light emitted from the waveguide 61 a enters the correction lens 63. Further, ordinary light emitted from the waveguide 61 b becomes abnormal light by passing through the λ / 2 plate 62, and the abnormal light enters the correction lens 63.

  The correction lens 63 is a lens that performs optical path correction so that ordinary light and extraordinary light are incident on an appropriate position of the inner boundary surface 60-1 of the birefringent crystal 60. When ordinary light and extraordinary light pass through the correction lens 63, the directions of the optical paths of the ordinary light and extraordinary light are corrected, and are incident on appropriate points on the inner boundary surface 60-1 of the birefringent crystal 60. Thereby, light obtained by combining ordinary light and extraordinary light is emitted from the outer boundary surface 60-2 of the birefringent crystal 60.

  In this way, when performing multiplexing / demultiplexing using a birefringent crystal, it is necessary to precisely adjust the positional relationship of the light to be multiplexed / demultiplexed. The optical path was adjusted by inserting between the waveguide substrate 61 and the birefringent crystal 60.

  However, when a correction lens, prism, or the like is inserted, the number of optical elements increases, resulting in an increase in mounting space and cost. In addition, since such an optical element is arranged, the optical path length is extended, so that there is a problem that excessive loss also increases.

  The present invention has been made in view of the above points, and when performing polarization multiplexing / demultiplexing using a birefringent crystal, light to be multiplexed / demultiplexed without using an optical element such as a lens. It is an object of the present invention to provide an optical module that optimizes the positional relationship of

  In order to solve the above-described problems, an optical module that performs polarization multiplexing / demultiplexing is provided. The optical module is provided with a first waveguide and a second waveguide, and has a first end face having an end of the first waveguide and an end of the second waveguide. A waveguide substrate having a second end face, a wave plate attached to the second end face, for rotating the polarization plane of incident light, and birefringence for combining and splitting ordinary light and extraordinary light A crystal.

  Here, the waveguide substrate has a shape with an inclination angle on the first end face, and the positional relationship between the waveguide substrate and the birefringent crystal is such that the extraordinary light emitted through the wave plate and the first The ordinary light emitted from the waveguide is combined inside the birefringent crystal and the combined light is emitted to the outside, and the signal light incident on the birefringent crystal from the outside is inside the birefringent crystal. The extraordinary light emitted from the birefringent crystal when separated into ordinary light and extraordinary light becomes ordinary light via the wave plate, enters the second waveguide, and is emitted from the birefringent crystal. , The waveguide substrate and the birefringent crystal are positioned so as to be incident on the first waveguide.

  It is possible to perform polarization multiplexing / demultiplexing using a birefringent crystal without using an optical element for adjusting the optical path such as a lens, thereby reducing the mounting scale and excess loss. Become.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings. FIG. 1 is a diagram illustrating a configuration of an optical module. The optical module 1 includes a waveguide substrate 10, a wave plate (hereinafter referred to as λ / 2 plate) 13, and a birefringent crystal 14, and is a module that performs polarization multiplexing / demultiplexing.

  The waveguide substrate 10 is provided with a waveguide 11 (first waveguide) and a waveguide 12 (second waveguide) parallel to the waveguide 11, and an end surface 11 a (with an end portion of the waveguide 11). A first end face) and an end face 11b (second end face) on which the end of the waveguide 12 is provided.

  The λ / 2 plate 13 is directly attached to the end face 11b, does not absorb light, rotates the polarization plane of incident light by π, and emits abnormal light when normal light is incident. When incident, it is emitted as ordinary light. The birefringent crystal 14 performs multiplexing / demultiplexing of ordinary light and extraordinary light.

  Here, the waveguide substrate 10 has a shape with an inclination angle θa by polishing the end face 11a. The positional relationship between the waveguide substrate 10 and the birefringent crystal 14 is such that light emitted from the waveguides 11 and 12 is multiplexed by the birefringent crystal 14 and separated by the birefringent crystal 14. The waveguide substrate 10 and the birefringent crystal 14 are positioned so that the waved light enters the waveguides 11 and 12.

  That is, the extraordinary light emitted through the λ / 2 plate 13 and the ordinary light emitted from the waveguide 11 are combined inside the birefringent crystal 14 to be combined light (signal light s). ) When the signal light s entering the birefringent crystal 14 so as to be emitted to the outside is demultiplexed into ordinary light and extraordinary light inside the birefringent crystal 14, the birefringent crystal 14 The emitted extraordinary light becomes ordinary light through the λ / 2 plate 13 and enters the waveguide 12, and the ordinary light emitted from the birefringent crystal 14 enters the waveguide substrate 10 so that it enters the waveguide 11. A birefringent crystal 14 is located.

Although FIG. 1 shows the traveling direction of light during demultiplexing, the traveling direction of light is simply reversed at the time of multiplexing.
Next, the positional relationship between the waveguide substrate 10 and the birefringent crystal 14 will be described in detail. FIG. 2 is a diagram illustrating the positional relationship between the components of the optical module. In addition, since the angle regarding the advancing direction of normal light and extraordinary light can be shown with the same view, in FIG. 2, the angle regarding the advancing direction of normal light is mainly shown. In addition, since the demultiplexing and the multiplexing are merely in which the traveling directions of the light are opposite to each other, the following description will be made by paying attention to the progress of the ordinary light during the demultiplexing. Further, for the angle, an acute angle is selected.

  As the birefringent crystal, a wedge-shaped birefringent crystal (V-shape that is thick at one end and gradually narrows toward the other end) is used (referred to as birefringent crystal 14a). A λ / 2 plate 13 is affixed to the end face 11 b of the waveguide substrate 10, and a birefringent crystal 14 a with a wedge portion facing downward is disposed in the vicinity of the λ / 2 plate 13.

  Here, the angle formed by the vertical line h1 drawn to the apex P of the wedge portion and the boundary surface 14-1 of the birefringent crystal 14a on which the signal light s enters is θ1, and the vertical line h1 and the signal light s An angle formed by the boundary surface 14-2 of the birefringent crystal 14a from which the demultiplexed light is emitted is defined as θt.

  When the signal light s is incident on the boundary surface 14-1 of the birefringent crystal 14a, the signal light s is demultiplexed into ordinary light and abnormal light, but the signal light s is relative to the vertical line h2 of the boundary surface 14-1. Is incident at an angle of θ1, the angle formed by the vertical line h2 and ordinary light traveling in the crystal (referred to as ordinary light o1) is θ2o, the refractive index in air is n1, and the ordinary light o1 in the birefringent crystal 14a is If n2o is the refractive index with respect to, Equation (1a) is established from Snell's law, and θ2o is obtained from Equation (1a-1).

n2o · sin θ2o = n1 · sin θ1 (1a)
θ2o = sin ⁻¹ ((n1 / n2o) sin θ1) (1a-1)
The angle formed by the vertical line h3 drawn on the boundary surface 14-2 and the parallel line pa parallel to the vertical line h2 and drawn on the boundary surface 14-2 is equal to the wedge angle θv (= θt + θ1), The angle formed by the ordinary light o1 and the parallel line pa is θ2o (relation between complex angles).

Accordingly, when the ordinary light o1 in the crystal travels and is emitted to the outside via the boundary surface 14-2, θ3o can be obtained by Expression (2a), where θ3o is an angle formed by the vertical line h3 and the ordinary light o1.
θ3o = θv−θ2o = θ1 + θt−θ2o (2a)
Further, assuming that the angle formed between the normal light (referred to as normal light o2) emitted from the birefringent crystal 14a and the vertical line h3 is θ4o, the equation (3a) is established from Snell's law, and θ4o is expressed as 3a-1).

n1 · sin θ4o = n2o · sin θ3o (3a)
θ4o = sin ⁻¹ ((n2o / n1) sin θ3o) (3a-1)
Furthermore, if the angle formed by the ordinary light o2 and the x axis (in the case of FIG. 2, the x axis and the optical axis of the signal light s are parallel) is θ5o, the angle formed by the x axis and the vertical line h3 is θt. Therefore, Expression (4a) is established.

θ5o = θ4o−θt (4a)
On the other hand, the ordinary light o2 emitted through the boundary surface 14-2 of the birefringent crystal 14a enters the waveguide 11 having an end on the end surface 11a of the waveguide substrate 10. Assuming that the angle formed between the vertical line h4 with respect to the end face 11a and the ordinary light o2 is θ6o, and the angle formed between the end face 11a and the x axis is θo, the ordinary light o2, the end face 11a and the x axis are as shown in FIG. Since a simple triangle abc is created, equation (5a) is established, and θ6o is obtained from equation (5a-1).

π = θo + θ5o + θ6o + π / 2 (5a)
θ6o = −θo−θ5o + π / 2 (5a-1)
Further, the angle formed between ordinary light (referred to as ordinary light o3-1) that is incident on the waveguide 11 and propagates through the waveguide 11, and the vertical line h4 with respect to the end face 11a, that is, the angle formed between the waveguide 11 and the vertical line h4. Is θ7o, and the refractive index of the waveguide 11 is n3 (the refractive index of the waveguide 12 is also n3), Equation (6a) is established from Snell's law, and θ7o is obtained by Equation (6a-1).

n3 · sin θ7o = n1 · sin θ6o (6a)
θ7o = sin ⁻¹ ((n1 / n3) sin θ6o) (6a-1)
If the angle between the ordinary light o3-1 and the x-axis, that is, the angle between the waveguide 11 and the x-axis is θ8o, since there is a relationship of the equation (7a) (see FIG. 3), θ8o 7a-1).

π / 2 = θ7o + θ8o + θo (7a)
θ8o = −θo−θ7o + π / 2 (7a-1)
Although the calculation formula of the angle with respect to the ordinary light has been described above, the same formula holds for the abnormal light. Since the concept is the same, only the formula for calculating the angle related to abnormal light is shown below. However, the refractive index of extraordinary light in the birefringent crystal 14a is n2e, and the angle between the end face 11b and the x-axis is θe.

θ2e = sin ⁻¹ ((n1 / n2e) sin θ1) (1b-1)
θ3e = θv−θ2e = θ1 + θt−θ2e (2b)
θ4e = sin ⁻¹ ((n2e / n1) sin θ3e) (3b-1)
θ5e = θ4e−θt (4b)
θ6e = −θe−θ5e + π / 2 (5b−1)
θ7e = sin ⁻¹ ((n1 / n3) sin θ6e) (6b−1)
θ8e = −θe−θ7e + π / 2 (7b-1)
Next, the above formula will be described using specific numerical values. FIG. 4 is a table showing angle values. The unit of angle is “°”. The refractive index n1 of light in the air is 1, the refractive index n2o of ordinary light in the birefringent crystal 14a is 2.451, the refractive index n2e of extraordinary light in the birefringent crystal 14a is 2.709, the waveguide 11, The refractive index n3 of 12 is 2.14.

  Further, when θ1 = θt = 8 °, θo = 47.9815 °, θe = 52.203 °, θa = 52.203−47.9815 = 4.2215 °, the angle calculation is performed based on the above formula. The values shown in the table of FIG. 4 are obtained, and θ8o = θ8e = 34.037 ° is finally obtained.

  The fact that θ8o and θ8e have the same value means that when the signal light s is demultiplexed into ordinary light and extraordinary light by the birefringent crystal 14a, the ordinary light enters the waveguide 11 and the extraordinary light is λ / It means that the light enters the waveguide 12 through the two plates 13 as ordinary light, that is, without using an optical element such as a lens, only the configuration of the waveguide substrate 10 and the birefringent crystal 14a. This means that polarization splitting is performed.

  In addition, since the light is simply transmitted in the opposite direction, if the light is incident on the waveguides 11 and 12 from the outside with respect to the optical module 1 having the positional relationship layout shown in FIG. The combined light is emitted from the refractive crystal 14a, and polarization can be combined only by the configuration of the waveguide substrate 10 and the birefringent crystal 14a without using an optical element such as a lens. It becomes possible.

  Next, a summary of the angular relationship in arranging the components of the optical module 1 will be described. The birefringent crystal is a wedge-shaped birefringent crystal 14a, and divides the wedge angle θv from the inner boundary surface 14-2 that is a boundary surface of the birefringent crystal 14 on which ordinary light and extraordinary light enter or exit. The angle formed with the first vertical line (vertical line h1) drawn in such a manner is θt.

The waveguide substrate 10 has an angle formed between the end surface 11b and the x axis as θe, an inclination angle as θa, and an angle formed between the end surface 11a and the x axis as θo obtained by subtracting θa from θe.
An angle formed between the second vertical line (vertical line h4) with respect to the end face 11a and the ordinary light o3-1 propagating through the waveguide 11 is θ7o, and a third vertical line (vertical line h5) with respect to the end face 11b, When the angle formed by the ordinary light o3-2 propagating through the waveguide 12 is θ7e, the waveguide 11 and the waveguide 12 are parallel to each other on the waveguide substrate 10 so as to satisfy the following formula (8). (Formula (8) is set to θ8o = θ8e with respect to formulas (7a-1) and (7b-1)).

θ7o + θo = θ7e + θe (8)
Further, regarding the positional relationship between the birefringent crystal 14a and the waveguide substrate 10, the angle formed by the fourth vertical line (vertical line h3) with respect to the inner boundary surface 14-2 and the ordinary light o2 in the outside air is θ4o. When the angle formed between the second vertical line (vertical line h4) with respect to the end face 11a and the ordinary light o2 in the outside air is θ6o, the following expression (9a) is satisfied (expression (4a) and expression (5a− Equation (9a)) is obtained by eliminating θ5o from 1).

θ6o + θ4o = θt−θo + π / 2 (9a)
Further, an angle formed by the fourth vertical line (vertical line h3) with respect to the inner boundary surface 14-2 and the abnormal light e2 in the outside air is θ4e (not shown), and the third vertical line (vertical) with respect to the end surface 11b. When the angle formed between the line h5) and the abnormal light e2 in the outside air is θ6e (not shown), the following equation (9b) is satisfied (from equation (4b) and equation (5b-1), θ5e is What is erased is equation (9b)).

θ6e + θ4e = θt−θe + π / 2 (9b)
The birefringent crystal 14a and the waveguide substrate 10 are positioned at an angle satisfying the expressions (9a) and (9b).

  On the other hand, the angle between the outer boundary surface 14-1 that is the boundary surface of the birefringent crystal 14a through which the signal light s is incident or the combined light is emitted and the first vertical line (vertical line h1) is θ1. When the signal light s is incident on the outer boundary surface 14-1, the angle formed by the fifth vertical line (vertical line h2) with respect to the outer boundary surface 14-1 and the signal light s is θ1. Is incident on. Similarly, when the combined light is emitted from the outer boundary surface 14-1, the angle is emitted at θ1 with respect to the fifth vertical line (vertical line h2) with respect to the outer boundary surface 14-1.

  The wedge angle θv of the birefringent crystal 14a is θ2o, which is an angle formed between the fifth vertical line (vertical line h2) and the ordinary light o1 traveling inside the birefringent crystal 14a, and the inner boundary surface 14-2. When the angle formed by the fourth vertical line (vertical line h3) with respect to and the ordinary light o1 traveling through the birefringent crystal 14a is θ3o, the relationship satisfies the expression (2a).

That is, the relation (2a) holds for the relationship between the refraction angle of the ordinary light in the birefringent crystal 14a with respect to the outer boundary surface 14-1, the refraction angle with respect to the inner boundary surface 14-2, and the wedge angle.
Furthermore, an angle formed by the fifth vertical line (vertical line h2) and the extraordinary light e1 traveling through the birefringent crystal 14a is θ2e (not shown), and the fourth vertical line (vertical line h3) When the angle formed by the extraordinary light e1 traveling inside the birefringent crystal 14a is θ3e (not shown), the relationship satisfies the expression (2b).

That is, the relationship between the refraction angle of the extraordinary light in the birefringent crystal 14a with respect to the outer boundary surface 14-1, the refraction angle with respect to the inner boundary surface 14-2, and the wedge angle is established.
As described above, according to the optical module 1, an optical element such as a lens or a prism used for conventional optical path adjustment is not inserted between the waveguide substrate 10 and the birefringent crystal 14. Since waves can be generated, the number of optical elements can be reduced, and it is possible to reduce the mounting space and cost, and to reduce excess loss by shortening the optical path length.

It is a figure which shows the structure of an optical module. It is a figure which shows the positional relationship of each structure part of an optical module. It is a figure for demonstrating an angle. It is a table which shows the value of an angle. It is a figure which shows PBS. It is a figure which shows a birefringent crystal. It is a figure which shows the structure of the conventional polarization multiplexing / demultiplexing module.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Optical module 10 Waveguide board | substrate 11, 12 Waveguide 11a, 11b End surface 13 (lambda) / 2 board 14 Birefringent crystal (theta) a Inclination angle s Signal light

Claims (3)

In an optical module that performs polarization multiplexing and demultiplexing,
A first end face provided with a first waveguide and a second waveguide, the first end face having an end of the first waveguide, and the second end face having an end of the second waveguide; A waveguide substrate having
A wave plate attached to the second end face and rotating a polarization plane of incident light;
A birefringent crystal for combining and splitting ordinary light and extraordinary light;
With
The waveguide substrate has a shape with an inclination angle on the first end face;
The positional relationship between the waveguide substrate and the birefringent crystal is:
The extraordinary light emitted through the wave plate and the ordinary light emitted from the first waveguide are combined inside the birefringent crystal so that the combined light is emitted to the outside, and the outside from the outside When the signal light incident on the birefringent crystal is demultiplexed into ordinary light and extraordinary light inside the birefringent crystal, the extraordinary light emitted from the birefringent crystal is ordinary light through the wave plate. Thus, the waveguide substrate and the birefringent crystal are positioned so that the ordinary light incident on the second waveguide and emitted from the birefringent crystal enters the first waveguide. ,
An optical module characterized by that. The birefringent crystal is
An angle formed by an inner boundary surface, which is a boundary surface of the birefringent crystal, on which ordinary light and extraordinary light enter or exit, and a first vertical line drawn so as to divide the wedge angle. Is θt,
The waveguide substrate is
The angle formed between the second end surface and the x axis is θe, the tilt angle is defined as θa, and the angle formed between the first end surface and the x axis is defined as θo obtained by subtracting θa from θe,
An angle formed by the second vertical line with respect to the first end face and the ordinary light propagating through the first waveguide is θ7o,
When the angle formed by the third vertical line with respect to the second end face and the ordinary light propagating through the second waveguide is θ7e,
θ7o + θo = θ7e + θe
The first waveguide and the second waveguide are provided on the waveguide substrate in parallel so as to satisfy
The positional relationship between the birefringent crystal and the waveguide substrate is as follows:
The angle formed by the fourth vertical line with respect to the inner boundary surface and ordinary light in the outside air is θ4o, and the angle formed by the second vertical line with respect to the first end surface and ordinary light in the outside air is θ6o. In case,
θ6o + θ4o = θt−θo + π / 2
The filling,
An angle formed by the fourth vertical line with respect to the inner boundary surface and extraordinary light in the outside air is defined as θ4e, and an angle formed by the third vertical line with respect to the second end surface and extraordinary light in the outer air is defined. When θ6e is assumed,
θ6e + θ4e = θt−θe + π / 2
The birefringent crystal and the waveguide substrate are positioned so as to satisfy
The optical module according to claim 1. An angle formed between an outer boundary surface, which is a boundary surface of the birefringent crystal from which the signal light is incident or the combined light is emitted, and the first vertical line is θ1,
When the signal light is incident on the outer boundary surface, the signal light is incident so that an angle formed by the fifth vertical line with respect to the outer boundary surface and the signal light is θ1,
When the combined light is emitted from the outer boundary surface, the angle of the outer boundary surface with respect to the fifth vertical line is emitted at θ1,
The wedge angle of the birefringent crystal is
An angle formed by the fifth vertical line and ordinary light traveling inside the birefringent crystal is θ2o, the fourth vertical line with respect to the inner boundary surface, and ordinary light traveling inside the birefringent crystal; If the angle formed by is θ3o,
θ3o + θ2o = θ1 + θt
The filling,
The angle formed between the fifth vertical line and the extraordinary light traveling inside the birefringent crystal is θ2e, and the angle formed between the fourth vertical line and the extraordinary light traveling inside the birefringent crystal. Is θ3e,
θ3e + θ2e = θ1 + θt
The optical module according to claim 2, wherein:

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