JP2011039383A - Polarization independent type optical wavelength filter, optical multiplexing/demultiplexing element and mach-zehnder interferometer - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a polarization independent type optical wavelength filter which uses a multi-mode interference optical waveguide, is made of Si and is easy to create, and then an optical multiplexing/demultiplexing element and a Mach-Zehnder interferometer using the polarization independent type optical wavelength filter. <P>SOLUTION: The polarization independent type optical wavelength filter is formed by embedding, in a clad 14, the multi-mode interference optical waveguide 16, which is made of single crystal Si, is a rectangular parallelepiped surrounded by first and second side faces 16<SB>1</SB>and 16<SB>2</SB>facing each other, third and fourth side faces 16<SB>3</SB>and 16<SB>4</SB>facing each other and an upper surface and a lower surface 16<SB>u</SB>and 16<SB>d</SB>facing each other, and wavelength-separates the mixed light of first and second lights of different wavelengths 1.2-1.6 μm independent of polarization, a first optical waveguide 18 which is connected to the first side face and to which the mixed light is input, and second and third optical waveguides 20 and 22, which are connected to the second side face and output the wavelength-separated first and second lights respectively. The refractive index n of the clad is the value of 1-1.6, the thickness t of the multi-mode interference optical waveguide is the value of 0.2-0.4 μm, the width W of the multi-mode interference optical waveguide is the value of 1.0-3.7 μm, and the relation that the width increases as the refractive index of the clad increases and the width increases as the thickness increases is provided. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to a polarization-independent optical wavelength filter that separates light of different wavelengths, and an optical multiplexing / demultiplexing element and a Mach-Zehnder interferometer using the optical wavelength filter.

  In an optical subscriber system, it is necessary to perform optical transmission (uplink communication) from the subscriber side to the station side and optical transmission from the station side to the subscriber side (downlink communication) using a single optical fiber. Uplink communication and downlink communication are performed using light of different wavelengths. For this reason, an optical wavelength filter that separates light of different wavelengths is required on both the station side and the subscriber side. In general, in an optical subscriber system, this optical wavelength filter, a light emitting element, and a light receiving element are used as an optical multiplexing / demultiplexing element by spatially optically aligning and assembling. An optical multiplexing / demultiplexing element used on the subscriber side is called a subscriber-side terminal unit (ONU: Optical Network Unit) (for example, Patent Documents 1 to 5).

  In recent years, optical waveguide type optical wavelength filters that do not require optical axis alignment have been studied as optical wavelength filters. As this type of optical wavelength filter, a filter using a Mach-Zehnder interferometer, a filter using a directional coupler, a filter using a multimode interference optical waveguide, and the like are known.

  An optical wavelength filter using a Mach-Zehnder interferometer has an advantage that wavelength characteristics can be designed using circuit theory. However, a Si Mach-Zehnder type optical wavelength filter used for the ONU is difficult to design because the wavelength dependency of the equivalent refractive index and coupling coefficient is large.

  In addition, since the transmittance of the optical wavelength filter using the directional coupler has wavelength dependency, the transmittance changes due to the wavelength shift of the light output from the light source.

  As an optical wavelength filter using a multimode interference optical waveguide, an optical element (for example, see Non-Patent Document 1) that can separate light having a wavelength of 1.3 μm and light having a wavelength of 1.5 μm is known. Yes.

  Although different from the wavelength filter, as a technique related to the present invention, an optical element that makes the output light distribution ratio independent of polarization in a specific wavelength band (for example, see Non-Patent Document 2) is known. .

US Pat. No. 4,860,294 U.S. Pat. No. 5,764,826 US Pat. No. 5,960,135 U.S. Pat. No. 7,072,541 JP-A-8-163028

Baojun Li et al. “1 × 2 optical waveguide filters based on multimode interface for 1.3-and 1.55-μm operation”, Optical Engineering, vol. 41, no. 3, pp 723-727 (March, 2002) Daoxin Dai and Sailing He, “Optimization of ultracompact polarization insensitive multimode interferers based on Sinoheve Wave Elevation. 18, no. 19, pp. 2017-2019 (Oct, 2006)

  However, the optical wavelength filter described in Non-Patent Document 1 has a large polarization dependency, and only one of the TE component and the TM component can be used.

  Moreover, since the material which comprises the optical wavelength filter described in the nonpatent literature 1 is SiGe, preparation was difficult compared with the element made from Si.

  Furthermore, the optical element described in Non-Patent Document 2 does not separate wavelengths of light having different wavelengths without depending on polarization.

  As a result of intensive studies, the inventor has come up with the idea that by optimizing the width and thickness of the multimode interference optical waveguide with respect to the refractive index of the cladding, light of different wavelengths can be wavelength-independently separated. The invention has been completed.

  The present invention has been made in view of such problems. Accordingly, an object of the present invention is to provide a polarization-independent optical wavelength filter made of Si and using a multimode interference optical waveguide, which is easy to produce.

  Another object of the present invention is to provide an optical multiplexing / demultiplexing device and a Mach-Zehnder interferometer using a polarization-independent optical wavelength filter.

  In order to achieve the above object, the polarization-independent optical wavelength filter of the present invention includes a multimode interference optical waveguide, a first optical waveguide, a second optical waveguide, and a third optical waveguide. The main surface is embedded (embedded) in the cladding.

  The multimode interference optical waveguide is formed using single crystal Si, and includes first and second side surfaces facing in parallel to each other, third and fourth side surfaces facing in parallel to each other, and top surfaces facing to each other in parallel. And a rectangular parallelepiped surrounded by the lower surface, and the first and second mixed lights having different wavelengths selected from the wavelength range of 1.2 to 1.6 μm are wavelength-separated without depending on the polarization. .

  The first optical waveguide is optically connected to the first side surface and receives mixed light.

  The second and third optical waveguides are optically connected to the second side surface, and the first and second lights separated from the second and third optical waveguides are output.

  The clad refractive index n is in the range of 1 to 1.6, and the thickness t, which is the distance between the upper and lower surfaces of the multimode interference optical waveguide, is in the range of 0.2 to 0.4 μm. Yes, and the width W, which is the distance between the third and fourth side surfaces of the multimode interference optical waveguide, is a value in the range of 1.0 to 3.7 μm. Further, the refractive index n, the width W, and the thickness t are in a relationship in which the refractive index n increases and the width W increases, and the thickness t increases and the width W increases.

  According to a preferred embodiment of the polarization-independent optical wavelength filter described above, the width of the first to third optical waveguides measured in a direction perpendicular to the light propagation direction and parallel to the first main surface of the substrate is It is preferable that the distance increases linearly from the side away from the multimode interference optical waveguide toward the connection portion with the multimode interference optical waveguide.

  According to another preferred embodiment of the polarization-independent optical wavelength filter described above, the multimode interference optical waveguide passes through a rectangular center point in a plane parallel to the first main surface of the substrate and extends in the width direction. When the extending straight line is the first axis, the second optical waveguide is provided at a position symmetrical with the first optical waveguide with the first axis as the symmetry axis, and the third optical waveguide is at the center point. It is preferable to be provided at a point-symmetrical position with respect to the first optical waveguide with respect to the center of symmetry.

According to another preferred embodiment of the polarization-independent optical wavelength filter described above, the cladding material may be SiO ₂ .

According to yet another preferred embodiment of the polarization-independent optical wavelength filters as described above, the overall length is the distance between the first and second side of the multimode interference optical waveguide (i) and L _a, first the propagation constant difference of the zero-order mode light and first-order mode light in the TE component of the first light and [Delta] [beta] _1, and the interference order after propagation of the multimode interference optical waveguide TE component of the first light m _{1 (provided} that m ₁ is a positive integer)
(Ii) the propagation constant difference of the zero-order mode light and first-order mode light in the TM component of the first light and [Delta] [beta] _2, and the interference order after propagation of the multimode interference optical waveguide of the TM component of the first light m ₂ (where m ₂ is a positive integer)
(Iii) the propagation constant difference of the zero-order mode light and first-order mode light in the TE component of the second light and [Delta] [beta] _3, and the interference order after propagation of the multimode interference optical waveguide TE component of the second light m ₃ (where m ₃ is a positive integer)
(Iv) the propagation constant difference of the zero-order mode light and first-order mode light in the TM component of the second light and [Delta] [beta] _4, and the interference order after propagation of the multimode interference optical waveguide of the TM component of the second light m ₄ (where m ₄ is a positive integer)
The following equations (A) to (D) that give the interference conditions in the multimode interference optical waveguide are established, and m ₁ = m ₂ and m ₃ = m ₄ and the difference between m ₁ and m ₃ is odd. Is good.
_{Δβ 1 L a = m 1 π} ··· (A)
_{Δβ 2 L a = m 2 π} ··· (B)
_{Δβ 3 L a = m 3 π} ··· (C)
_{Δβ 4 L a = m 4 π} ··· (D)

According to still another preferred embodiment of the polarization-independent optical wavelength filter described above, when the wavelength of the first light is 1.31 μm and the wavelength of the second light is 1.49 μm, It is preferable that the thickness t and the width W of the multimode interference optical waveguide satisfy the following expressions (E) and (F).
When t ≧ 0.25 μm: W = 42 (t−0.25) ^1.48 + 1.15 (E)
When t <0.25 μm: 1.1 <W <1.15 (F)

  The optical multiplexing / demultiplexing device of the present invention uses the above-described polarization-independent wavelength filter, and the first light is input from the second optical waveguide and output from the first optical waveguide through the multimode interference optical waveguide. The second light is input from the first optical waveguide and output from the third optical waveguide via the multimode interference optical waveguide.

  The Mach-Zehnder interferometer of the present invention uses the polarization-independent optical wavelength filter described above, and includes a polarization-independent optical wavelength filter, an optical coupler, a polarization-independent optical wavelength filter, and an optical coupler. First and second arm optical waveguides that are optically connected are provided.

  The optical coupler is configured by further providing a fourth optical waveguide at a position line-symmetric with the third optical waveguide with the first axis in the polarization-independent optical wavelength filter as the axis of symmetry.

  The first arm optical waveguide connects the second optical waveguide of the polarization-independent optical wavelength filter and the first optical waveguide of the optical coupler.

  The second arm optical waveguide connects the third optical waveguide of the polarization-independent optical wavelength filter and the fourth optical waveguide of the optical coupler.

  And the cross-sectional shape orthogonal to the light propagation direction of the first and second arm optical waveguides is square, and the optical path lengths of the first and second arm optical waveguides are different.

  According to the preferred embodiment of the Mach-Zehnder interferometer described above, the interference order of the first light and the second light after propagating through the multimode interference optical waveguide is determined in both the polarization-independent optical wavelength filter and the optical coupler. The total length of the polarization-independent optical wavelength filter and the optical coupler is preferably determined so that one is a half integer and the other is an even number.

  According to another preferred embodiment of the Mach-Zehnder interferometer described above, the interference between the first light and the second light after propagating through the multimode interference optical waveguide in both the polarization-independent optical wavelength filter and the optical coupler. It is preferable that the total length of the optical coupler is determined so that both orders are half integers.

  The present invention has the structural features as described above. As a result, a polarization-independent optical wavelength filter made of Si and using a multimode interference optical waveguide can be obtained. Furthermore, an optical multiplexing / demultiplexing device and a Mach-Zehnder interferometer using this polarization-independent optical wavelength filter can be obtained.

1 is a perspective view schematically showing a configuration of a polarization-independent optical wavelength filter according to Embodiment 1. FIG. 2 is a plan view schematically showing a configuration of a polarization-independent optical wavelength filter according to Embodiment 1. FIG. In the polarization-independent optical wavelength filter of the first embodiment, when SiO ₂ is used as the cladding, the wavelength of the first light is 1.31 μm, and the wavelength of the second light is 1.49 μm, multimode interference It is a characteristic view for demonstrating the relationship between the width | variety and thickness which make an optical waveguide polarization independent. In the optical wavelength filter of Embodiment 1, it is the schematic diagram which showed typically an example of the propagation path of the mixed light in a multimode interference optical waveguide. In the optical wavelength filter of Embodiment 1, it is a characteristic view for demonstrating the relationship between the full length of a multimode interference optical waveguide and the interference order calculated | required by numerical calculation. FIG. 3 is a characteristic diagram for explaining wavelength separation characteristics of the optical wavelength filter according to the first embodiment. It is a top view which shows the structure of an optical multiplexing / demultiplexing device roughly. It is a top view which shows roughly the structure of the Mach-Zehnder interferometer of Embodiment 2. FIG. 10 is a characteristic diagram for explaining the relationship between the total length of the optical wavelength filter and the optical coupler and the interference order obtained by numerical calculation when the optical wavelength filter and the optical coupler are applied to the Mach-Zehnder interferometer of Embodiment 2. It is a characteristic view with which it uses for description of the wavelength separation characteristic of the Mach-Zehnder interferometer of Embodiment 2. (A) is a top view which shows roughly the structure of the 1st optical element of a 1st modification, and (B) is a top view which shows the structure of the 2nd optical element of a 2nd modification schematically. It is. It is a characteristic view with which it uses for description of operation | movement of the 1st optical element of a 1st modification.

  Embodiments of the present invention will be described below with reference to the drawings. Each drawing schematically shows the shape, size, and arrangement relationship of each component to the extent that the present invention can be understood. Moreover, although the preferable structural example of this invention is demonstrated hereafter, the material of each component, a numerical condition, etc. are only a suitable example. Therefore, the present invention is not limited to the following embodiments. Moreover, in each figure, the same code | symbol is attached | subjected to a common component and the description may be abbreviate | omitted.

(Embodiment 1)
The polarization-independent optical wavelength filter (hereinafter simply referred to as “optical wavelength filter”) according to the first embodiment will be described below with reference to FIGS.

(Construction)
FIG. 1 is a perspective view schematically showing the configuration of the optical wavelength filter of this embodiment. FIG. 2 is a plan view schematically showing the configuration of the optical wavelength filter of this embodiment. In FIGS. 1 and 2, the optical wavelength filter 10 is embedded in the clad 14 and cannot be directly observed, but is drawn with a solid line to emphasize its presence.

  Referring to FIGS. 1 and 2, the optical wavelength filter 10 is formed by being embedded (embedded) in the clad 14 on the first main surface 12a side of the substrate 12, and includes a multimode interference optical waveguide 16, One optical waveguide 18, a second optical waveguide 20, and a third optical waveguide 22 are provided.

  The substrate 12 is a parallel plate formed using single crystal Si as a material.

The clad 14 is a substantially parallel plate-like layered body formed by embedding the optical wavelength filter 10 on the first main surface 12 a of the substrate 12. The clad 14 is formed of a material having a refractive index n in the range of 1 to 1.6. In the case of this embodiment, the clad 14 is preferably made of, for example, SiO ₂ having a refractive index n of 1.46. The thickness of the cladding 14 interposed between the lower surface 16 _d of the first main surface 12a and the multimode interference optical waveguide 16 of the substrate 12 is preferably, for example, about 1μm or more in size. This is to prevent loss due to radiation of light propagating through the multimode interference optical waveguide 16 to the substrate 12.

Multimode interference optical waveguide 16 (hereinafter, simply referred to as "multi-mode waveguide 16".) Is, it is formed using a single crystal Si, first and second side surfaces 16 ₁ and 16 in parallel to oppose to each other ₂ When, the third and fourth side surfaces 16 ₃ and 16 ₄ in parallel to oppose to each other, it is formed surrounded by rectangular parallelepiped with the upper surface 16 _u and the lower surface 16 _d parallel to oppose to each other, the plan view of FIG. 2 As shown, the planar shape of the multimode waveguide 16 is rectangular.

  As will be described in detail later, the multimode waveguide 16 does not polarize the mixed light LM of the first light L1 and the second light L2 having different wavelengths selected from the wavelength range of 1.2 to 1.6 μm. It has a function of wavelength separation depending on the dependence.

In this embodiment, the wavelength of the first light L1 is preferably set to, for example, a wavelength of 1.31 μm used for subscriber side → station side communication in the optical subscriber communication field. The TE component and TM component of the first light L1 are represented as L1 _TE and L1 _TM , respectively.

Further, the wavelength of the second light L2 is preferably set to a wavelength of 1.49 μm, for example, used for communication from the station side to the subscriber side in the optical subscriber communication field. The TE component and TM component of the second light L2 are represented as L2 _TE and L2 _TM , respectively.

Here, the multi-mode waveguide 16, the length along the light propagation direction to be described later, i.e., the distance between the first and second side surfaces 16 ₁ and 16 ₂ and the total length L _a. Further, the direction along this entire length L _a is referred to as "lengthwise direction" or "direction of light propagation."

Similarly, the multimode waveguide 16, parallel to the direction of the distance to the first main surface 12a of the perpendicular to the light propagation direction and the substrate 12, that is, the width of the distance between the third and fourth side surfaces 16 ₃ and 16 ₄ W. A direction along the width W is referred to as a “width direction”.

Further, the multimode waveguide 16, the distance measured in the direction perpendicular to the first main surface 12a, that is, the distance between the upper surface 16 _u and the lower surface 16 _d and thickness t. A direction along the thickness t is referred to as a “thickness direction”.

Further, the center axis C0 and the midpoint of the first side surface 16 ₁ in the width direction, a straight line passing through the midpoint of the second side surface 16 ₂ in the width direction. Further, the third side surface 16 ₃ of the midpoint in the longitudinal direction, the first axis C1 of the line passing through the midpoint of the fourth side 16 ₄ in the longitudinal direction. Further, an intersection of two diagonal lines on the upper surface 16 _u , that is, an intersection of the central axis C0 and the first axis C1 is defined as a central point P (see FIG. 2).

  As will be described in detail later, the multimode waveguide 16 has a thickness t and a width W with respect to the refractive index n of the cladding 14 in order to separate the wavelength of the first light L1 and the second light L2 without depending on the polarization. Optimized.

  More specifically, the thickness t is preferably selected from a value in the range of about 0.2 to 0.4 μm, for example, according to the design. In the case of this embodiment, the thickness t is preferably about 0.3 μm.

  Similarly, for the width W, it is preferable to select a suitable value from the range of, for example, about 1.0 to 3.7 μm according to the design. In the case of this embodiment, the width W is about 1.65 μm.

  By setting the thickness t and the width W of the multimode waveguide 16 to values within the above-described range, when the refractive index n of the clad 14 is 1 to 1.6, the multimode waveguide 16 has the first light and the first light. The two lights L1 and L2 can be propagated without depending on the polarization.

  In the multimode waveguide 16, between the refractive index n, the width W, and the thickness t of the clad 14, the refractive index n increases, the width W increases, and the thickness t increases. The relationship that the width W increases is established. This reason will be described in detail in the section of (Design conditions).

More specifically, as in this embodiment, SiO ₂ having a refractive index n of 1.46 is used as the clad 14, the wavelength of the first light L1 is 1.31 μm, and the wavelength of the second light L2 is 1. When the thickness is 49 μm, the thickness t and the width W of the multimode waveguide 16 are designed to satisfy the following expressions (1) and (2). FIG. 3 is a characteristic diagram showing the relationship between the thickness t and the width W. Although details will be described later in (Design Conditions), FIG. 3 shows the equivalent refractive index felt by each of the components L1 _TE , L1 _TM , L2 _TE and L2 _TM propagating through the multimode waveguide 16 by the finite element method. It was obtained by calculating using Equations (1) and (2) were derived by fitting an approximate curve to FIG.

When t ≧ 0.25 μm: W = 42 (t−0.25) ^1.48 + 1.15 (1)
When t <0.25 μm: 1.1 <W <1.15 (2)
Expressions (1) and (2) will be described later.

In this way, by using SiO ₂ having a refractive index n of 1.46 as the clad 14 and setting the thickness t and the width W to values satisfying the expressions (1) and (2), the multimode waveguide 16 is The first light L1 and the second L2 light can be propagated without depending on the polarization.

Further, by setting the thickness t and the width W to values satisfying the expressions (1) and (2), the TE component L1 _TE and the TM component L1 _{TM of} the first light L1, and the TE component L2 of the second light L2 _{With TE} and TM component L2 _TM , only the 0th-order mode light and the 1st-order mode light are excited in the multimode waveguide 16. As a result, there is no need to consider the interference condition of the second- or higher-order mode light, per the determination of the overall length L _a, can apply the expression (3) to (6) described later.

Overall length L _a of the multimode waveguide 16 in the case of this embodiment, preferably, it is for example to about 23.5. Although details will be described later, the total length L _a of the multimode waveguide 16 are engaged with the first light L1 and the second light L2 in the ability to wavelength separation, using later-described equation (3) to formula (6) To decide.

The first optical waveguide 18 is tapered planar optical waveguides, one end of the wide side, are connected together at a connection 18a to the first side 16 ₁ of the multimode waveguide 16, and the narrow side the other end is integrally connected to the first input-output optical waveguide 24 _1.

More specifically, as shown in the plan view of FIG. 2, the planar shape of the first optical waveguide 18 is an isosceles triangle. Accordingly, the first optical waveguide 18 has a width measured in a direction perpendicular to the light propagation direction and parallel to the first main surface 12a of the substrate 12 from the side away from the multimode waveguide 16. As it goes to the connecting part 18a, the connecting part 18a is linearly enlarged with the bottom side. That is, the planar shape of the first optical waveguide 18, the other end connected first to the input and output optical waveguide 24 ₁ as short as the upper base, the connected connection part 18a to the first side 16 ₁ elongated It is an isosceles trapezoid shape which makes a bottom bottom (refer FIG. 2).

The first optical waveguide 18 is from the central axis C0 is connected to a position shifted to the side of the fourth side surface 16 _4. Further, the thickness of the first optical waveguide 18 is t as in the multimode waveguide 16. The total length L _{io in} the length direction of the first optical waveguide 18 is preferably 5 μm or more in order to prevent loss due to mode conversion of propagating light. In this embodiment, the total length L _io of the first optical waveguide 18 is preferably about 5 μm, for example.

  The maximum width of the first optical waveguide 18, that is, the width at the connection portion 18 a is selected from a value less than ½ of the width W of the multimode waveguide 16 according to the design.

Details will be described later, the first optical waveguide 18 is input mixed light LM propagated the optical waveguide 24 ₁ for the first input, propagates toward the inside first optical waveguide 18 to the multimode waveguide 16 .

The first input-output optical waveguide 24 ₁ connected to the first optical waveguide 18 is a single mode optical waveguide for inputting and outputting light to the light wavelength filter 10, the cross-sectional shape perpendicular to the light propagation direction Is, for example, a square having a width of 0.3 μm and a thickness of 0.3 μm.

The second optical waveguide 20, wide end, connection portion 20a is integrally connected to the second side surface 16 ₂ of the multimode waveguide 16 in, and the width and the other end of the narrow is the second input-output optical waveguide 24 ₂ is a tapered planar optical waveguide that is integrally connected to ₂ . The shape of the second optical waveguide 20 is the same as that of the first optical waveguide 18 except for its maximum width.

  The second optical waveguide 20 is provided at a position line-symmetric with the first optical waveguide 18 with the first axis C1 as the axis of symmetry, with the multimode waveguide 16 interposed therebetween.

The maximum width of the second optical waveguide 20, that is, the width at the connection portion 20 a is selected from a value less than ½ of the width W of the multimode waveguide 16 according to the design. By maximize the maximum width within the range described above, the collection efficiency of the first light L1 that has reached the ₂ second side 16 is increased.

Details will be described later, the second optical waveguide 20 first light L1 whose wavelength is separated by the multi-mode waveguide 16 is input to propagate toward the second output optical waveguide 24 _2.

Note that the second output optical waveguide 24 ₂ connected to the second optical waveguide 20 is a single mode optical waveguide for inputting and outputting light to the light wavelength filter 10, first input-output optical waveguide 24 ₁ It has the same cross-sectional shape.

Third optical waveguide 22 is wide at one end, at the connecting portion 22a is connected to the second side surface 16 ₂ of the multimode waveguide 16 optically, and the width and the other end of the narrow is the third input-output optical waveguide 24 ₃ is connected to tapered planar optical waveguides together. The shape of the third optical waveguide 22 is the same as that of the second optical waveguide 20.

  The third optical waveguide 22 is provided at a point-symmetrical position with respect to the first optical waveguide 18 with the multimode waveguide 16 sandwiched between the center point P and the center of symmetry. In other words, the third optical waveguide 22 is provided at a position symmetrical to the second optical waveguide 20 with the central axis C0 as the axis of symmetry.

For the maximum width of the third optical waveguide 22, that is, the width at the connection portion 22a, a suitable value is selected from values less than ½ of the width W of the multimode waveguide 16 according to the design. By as large as possible within the scope of this maximum width above, the collection efficiency of the second light L2 which has reached the ₂ second side 16 is increased.

Although this will be described in detail later, the third optical waveguide 22, the second light L2 is input which is wavelength-separated by the multimode waveguide 16 and propagates toward the third input-output optical waveguide 24 _3.

The third input-output optical waveguide 24 ₃ connected to the third optical waveguide 22 is a single mode optical waveguide for inputting and outputting light to the light wavelength filter 10, first input-output optical waveguide 24 ₁ It has the same cross-sectional shape.

Here, the gap G between the second and third optical waveguides 20 and 22 will be described. A gap G exists between the connection portion 20 a of the second optical waveguide 20 and the connection portion 22 a of the third optical waveguide 22. This gap G is inevitably formed in the production of the optical wavelength filter 10. From the gap G, the first light L 1 and the second light L ₂ that have reached the second side surface 162 leak out of the optical wavelength filter 10. Therefore, it is necessary to make the width of the gap G as small as possible. In the case of this embodiment, the width of the gap G is preferably set to 0.3 μm, which is a manufacturing limit dimension in a semiconductor manufacturing process, for example.

(Operation)
Next, the operation of the optical wavelength filter 10 will be described with reference to FIG.

  FIG. 4 is a diagram schematically illustrating an example of the propagation path of the mixed light LM in the multimode waveguide 16. In FIG. 4, the substrate 12 and the clad 14 are not shown in order to avoid complication of the drawing. In FIG. 4, a curved line I indicated by a one-dot broken line indicates a propagation path of the first light L1, and a curved line II indicated by a solid line indicates a propagation path of the second light L2.

The mixed light LM obtained by mixing the first light L1 and the second light L2, more specifically, the two components L1 _TE and L1 _{TM of} the first light L1 and the two components L2 _TE and L2 _{TM of} the second light L2, Input from the first optical waveguide 18 to the multimode waveguide 16. In the process of propagating through the multimode waveguide 16, the 0th-order mode light and the first-order mode light are excited for each of the components L1 _TE , L1 _TM , L2 _TE and L2 _TM of the mixed light LM.

By the way, the width W and the thickness t of the multimode waveguide 16 are optimized with respect to the refractive index n of the clad 14, and as a result, the multimode waveguide 16 has the first light L1 and the second light. It is independent of polarization with respect to L2. Therefore, in the multimode waveguide 16, the two polarization components L1 _TE and L1 _TM of the first light L1 propagate through the same propagation path. Similarly, in the multimode waveguide 16, the two polarization components L2 _TE and L2 _TM of the second light L2 propagate through the same propagation path different from the first light L1. Therefore, in the following description, unless specifically required, the propagation path for each of the components L1 _TE , L1 _TM , L2 _TE and L2 _TM does not matter, and the propagation path for each of the first light L1 and the second light L2 explain.

The 0-order mode light and first-order mode light excited in the multimode waveguide 16, while interfere with each other, the internal multimode waveguide 16 and propagates toward the second side surface 16 _2. As shown in FIG. 4, as a result of the interference between the 0th-order mode light and the 1st-order mode light, the first light L1 and the second light L2 propagate through paths that meander through the multimode waveguide 16, respectively.

  In the example illustrated in FIG. 4, the first light L <b> 1 indicated by the curve I is output to the second optical waveguide 20 while changing the propagation direction six times in the multimode waveguide 16. In addition, the second light L2 indicated by the curve II is output to the third optical waveguide 22 with the propagation direction changed seven times in the multimode waveguide 16.

  The reason why the number of changes in the propagation direction differs for each of the first light L1 and the second light L2 is that the state of interference in the multimode waveguide 16 differs between the first light L1 and the second light L2. This is because the equivalent refractive indexes of the multimode waveguide 16 felt by the first light L1 and the second light L2 are different from each other.

Hereinafter referred to as "meander" that propagation direction of the first light L1 and the second light L2 is changed greatly in the third and fourth side surfaces 16 ₃ and 16 ₄ of the multimode waveguide 16. The number of changes in the propagation direction described above is referred to as “meander number of times”.

  In this way, by propagating through the multimode waveguide 16, polarization-independent wavelength separation of the first light (wavelength: 1.31 μm) and the second light (wavelength: 1.49 μm) is performed. The design conditions for the optical wavelength filter 10 will be described in the next section.

(Design condition)
Next, design conditions for the optical wavelength filter 10, particularly the multimode waveguide 16, will be described with reference to FIGS. 3, 5, and 6.

  First, the design conditions for the width W and the thickness t of the multimode waveguide 16 will be described with reference to FIG.

FIG. 3 shows that the multimode waveguide 16 is independent of polarization when SiO ₂ is used as the clad 14, the wavelength of the first light L1 is 1.31 μm, and the wavelength of the second light L2 is 1.49 μm. It is a characteristic view showing the relation between width W and thickness t. In FIG. 3, the vertical axis represents the width W (μm) of the multimode waveguide 16, and the horizontal axis represents the thickness t (μm) of the multimode waveguide 16. FIG. 3 is obtained by calculating the equivalent refractive index felt by each component L1 _TE , L1 _TM , L2 _TE and L2 _TM propagating through the multimode waveguide 16 using the finite element method.

  According to the curve I depicted in FIG. 3, the multimode waveguide 16 has a relationship in which the width W increases as the thickness t increases.

  It should be noted that the formulas (1) and (2) already described have two horizontal axis sections (section 1) 0.2 to 0.25 μm (section 2) with respect to the curve I drawn in FIG. This is obtained by applying approximate curves to 0.25 to 0.4 μm.

  Although not shown, between the refractive index n of the cladding 14 and the width W of the multimode waveguide 16, the width W of the multimode waveguide 16 increases linearly as the refractive index n of the cladding 14 increases. This relationship holds. This is because the effective refractive index of the multimode waveguide 16 decreases as the refractive index n of the cladding 14 increases. In order to suppress the decrease in the effective refractive index, if the refractive index n of the clad 14 increases, it is necessary to linearly increase the size (width W and thickness t) of the multimode waveguide 16 accordingly. is there.

  As described above, the width W and the thickness t of the multimode waveguide 16 are set so as to follow the above-described equations (1) and (2), and the size of the multimode waveguide 16 is set to the refractive index n of the clad 14. Accordingly, the first light L1 and the second light L2 propagate through the multimode waveguide 16 without depending on the polarization.

The following describes the design condition of the total length L _a of the multimode waveguide 16.

Overall length L _a of the multimode waveguide 16, (state of meandering) the propagation path of the first light L1 and the second light L2 in the multimode waveguide 16, i.e. it is necessary to determine in consideration of interference conditions.

Here, the propagation constant difference of the zero-order mode light and first-order mode light in the TE component _{L1 TE} of the first light L1 and [Delta] [beta] _1, and, in the multimode waveguide 16 in the TE component _{L1 TE} of the first light L1 propagates The subsequent interference order is m ₁ (where m ₁ is a positive integer).

Similarly, the 0-order mode light and the propagation constant difference of the first-order mode light in the TM component _{L1 TM} of the first light L1 and [Delta] [beta] _2, and, in the multimode waveguide 16 in the TM component _{L1 TM} of the first light L1 propagates The subsequent interference order is m ₂ (where m ₂ is a positive integer).

Further, the propagation constant difference of the zero-order mode light and first-order mode light in the TE component _{L2 TE} of the second light L2 is [Delta] [beta] _3, and, after propagation of the multimode waveguide 16 in the TE component _{L2 TE} of the second light L2 Is the interference order of m ₃ (where m ₃ is a positive integer).

Furthermore, the propagation constant difference of the zero-order mode light and first-order mode light in the TM component _{L2 TM} of the second light L2 is [Delta] [beta] _4, and, after propagation of the multimode waveguide 16 in the TM component _{L2 TM} of the second light L2 Let m _{4 be} an interference order (where m ₄ is a positive integer).

Here, the "multi-interference order after propagation mode waveguide 16", at the time the first light L1 and the second light L2 reaches the ₂ second side 16 propagates through the multimode waveguide 16 Indicates the order of interference.

Then, the interference conditions of the first light L1 and the second light L2 are expressed by the following formulas (3) to (6) obtained by adapting a conventionally known mode propagation equation to the optical wavelength filter 10 of this embodiment. expressed.
_{Δβ 1 L a = m 1 π} ··· (3)
_{Δβ 2 L a = m 2 π} ··· (4)
_{Δβ 3 L a = m 3 π} ··· (5)
_{Δβ 4 L a = m 4 π} ··· (6)

In this case, the total length _{L a} of the multimode waveguide 16, (Condition ₁₎ m 1 = _{m 2} and _m 3 = _{m 4,} and (condition 2) the difference between _{m 1} and _{m 3} is an odd number, that It is necessary to determine so as to satisfy two conditions.

Hereinafter, the meaning of these conditions will be described. It is known that the interference orders m _{1 to} m ₄ indicate the number of meanders in the multimode waveguide 16 of each of the components L1 _TE , L1 _TM , L2 _TE and L2 _TM of the first light L1 and the second light L2. . In addition, if m _{1 to} m ₄ are integers, the components L1 _TE , L1 _TM , L2 _TE and L2 _TM of the first light L1 and the second light L2 are the second values according to the values of m _{1 to} m ₄ . It is known that the signal is output to one of the third optical waveguides 20 and 22.

Therefore, the condition that m ₁ = m ₂ and m ₃ = m ₄ is that the number of meanders in the multimode waveguide 16 of each component L1 _TE and L1 _TM of the first light L1 is equal, and each of the second light L2 The numbers of meanders in the multimode waveguide 16 of the components L2 _TE and L2 _TM are equal.

_The difference condition that is an odd number of _m 1 (= m ₂₎ and _m 3 (= _{m 4) is, m} 1 (= m ₂₎ and _m 3 either the (= _{m 4)} is an odd number Yes, and the other is an even number. As described above, m _{1 to} m ₄ represent the number of meanders of the first light L 1 and the second light L 2 in the multimode waveguide 16, and therefore, by satisfying this condition, the first light L 1 (L 1 _TE And L1 _TM ) meander an odd number of times, the second light L2 (L2 _TE and L2 _TM ) meanders an even number of times. Conversely, when the first light L1 (L1 _TE and L1 _TM ) meanders an even number of times, the second light L2 (L2 _TE and L2 _TM ) meanders an odd number of times.

  As a result, one of the first light L1 and the second light L2 is output to the third optical waveguide 22 when one is output to the second optical waveguide 20, and the other is output to the third optical waveguide 22. When output, the other is output to the second optical waveguide 20.

More specifically, when m ₁ (= m ₂ ) is an even number and m ₃ (= m ₄ ) is an odd number, the first light L1 meanders through the multimode waveguide 16 an even number of times. The second light L2 is output to the optical waveguide 20 and output to the third optical waveguide 22 by meandering the multimode waveguide 16 an odd number of times. When m ₁ (= m ₂ ) is an odd number and m ₃ (= m ₄ ) is an even number, the first light L1 meanders the multimode waveguide 16 an odd number of times and is output to the third optical waveguide 22. In addition, the second light L <b> 2 meanders the multimode waveguide 16 an even number of times and is output to the second optical waveguide 20.

Next, referring to FIG. 5, the design condition of the total length L _a of the multimode waveguide 16 will be described more specifically.

FIG. 5 is a characteristic diagram obtained by numerically calculating the above formulas (3) to (6) by the finite element method. FIG. 5A shows the calculation results for the multimode waveguide 16 (width W: 1.65 μm and thickness t: 0.3 μm) of this embodiment. FIG. 5B shows the calculation result when the width W of the multimode waveguide is 1.15 μm and the thickness t is 0.22 μm. In common with FIGS. 5A and 5B, the vertical axis indicates the interference order m (dimensionless), and the horizontal axis indicates the total length L _a (μm).

In FIG. 5A, four straight lines are drawn. The straight line I shows the behavior of the TE component L2 _TE of the second light L2. The straight line II shows the behavior of the TM component L2 _TM of the second light L2. A straight line III indicates the behavior of the TE component L1 _TE of the first light L1. A straight line IV indicates the behavior of the TM component L1 _TM of the first light L1.

Referring to FIG. 5 (A), and the straight line I and the straight line II, _{L a} is the order of interference in the range of 10~30μm indicates a very good match. Further, the straight line III and the straight line IV also, _{L a} indicates the order of interference is good agreement in the range of 10 to 30 [mu] m. For these reasons, the first light L1 (straight line III and straight line IV) and the second light L2 (straight line I and straight line II) propagate in the multimode waveguide 16 almost independent of polarization. I understand that.

FIG The _{5 (A), m 1 ~m} 4 is an integer, _{and, m} 1 (= m ₂₎ and _m 3 (= _{m 4)} the difference between the is odd satisfies _{L a} arrow A -C. That is, the multi-mode waveguide 16 indicates the total length L _a of the first light L1 and the second light L2 can be wavelength separation in polarization independent.

This condition is satisfied _{L a} is present three points in _{L a} range of 10 to 30 [mu] m. That is, in terms of _{L a} ≒ 20 [mu] m indicated by the arrow A, a point _{L a} ≒ 27 [mu] m indicated by points and an arrow C in _{L a} ≒ 23.5 indicated by the arrow B.

More specifically, when L _a ≈20 μm of the arrow A, m ₁ (= m ₂ ) ≈5 and m ₃ (= m ₄ ) ≈6. Further, when L _a ≈23.5 μm of the arrow B, m ₁ (= m ₂ ) ≈6 and m ₃ (= m ₄ ) ≈7. Further, when L _a ≈27 μm of the arrow C, m ₁ (= m ₂ ) ≈7 and m ₃ (= m ₄ ) ≈8.

Thus, in the multimode waveguide 16 of this embodiment, by setting the overall length _{L a L a} ≒ _20μm, either of the values of _{L a} ≒ 23.5 and _{L a} ≒ 27 [mu] m, and the first light L1 The second light L2 can be wavelength-separated without depending on the polarization.

  Next, FIG. 5B will be described.

From the already described formulas (1) and (2), the multimode waveguide in which the width W of the multimode waveguide 16 is 1.15 μm and the thickness t is 0.22 μm is also applied to the multimode of this embodiment. As with the waveguide 16, it has become clear that the first light L1 and the second light L2 can propagate independently of the polarization. Therefore, for the multimode waveguide of this dimension, I tried to calculate the total length L _a multimode waveguide the first light L1 and the second light L2 can be wavelength separation in polarization independent. The calculation in FIG. 5B was performed using the finite element method as in the case of FIG.

In FIG. 5B, four straight lines are drawn. The straight line I shows the behavior of the TE component L2 _TE of the second light L2. The straight line II shows the behavior of the TM component L2 _TM of the second light L2. A straight line III indicates the behavior of the TE component L1 _TE of the first light L1. A straight line IV indicates the behavior of the TM component L1 _TM of the first light L1.

Referring to FIG. 5 (B), and the straight line I and the straight line II, _{L a} indicates very good match in the range of 20 to 70 m. Further, the straight line III and the straight line IV also indicate a good match when La is in the range of 20 to 90 μm. Therefore, the first light L1 (straight line III and straight line IV) and the second light L2 (straight line I and straight line II) propagate within the multimode waveguide almost without depending on the polarization. I understand.

Figure. 5 _(B), m 1 ~m ₄ is is an integer, _{and, m} 1 (= m ₂₎ and _m 3 (= _{m 4)} the difference between the is odd satisfies _{L a} the arrow D -F.

This condition is satisfied La is present three points in _{L a} range of 20～90Myuemu. That is, in terms of _{L a} ≒ 46 [mu] m indicated by the arrow D, a point _{L a} ≒ 60 [mu] m indicated by points and an arrow F of _{L a} ≒ 52 .mu.m indicated by the arrow E.

More specifically, when L _a ≈46 μm of the arrow D, m ₁ (= m ₂ ) ≈5 and m ₃ (= m ₄ ) ≈6. Further, when L _a ≈52 μm of the arrow E, m ₁ (= m ₂ ) ≈6 and m ₃ (= m ₄ ) ≈7. Further, when L _a ≈60 μm of the arrow F, m ₁ (= m ₂ ) ≈7 and m ₃ (= m ₄ ) ≈8.

(effect)
Hereinafter, the effect of the optical wavelength filter 10 of this embodiment will be described with reference to FIG.

  FIG. 6 is a characteristic diagram for explaining the wavelength separation characteristics of the optical wavelength filter 10. In FIG. 6, the vertical axis indicates the light intensity (arbitrary unit) of the first light L1 and the second light L2 output from the second and third optical waveguides 20 and 22, and the horizontal axis indicates the wavelength (μm). ing.

FIG. 6 shows the input of the mixed light LM of the first light L1 and the second light L2, that is, the polarization components L1 _TE , L1 _TM , L2 _TE and L2 _TM from the first optical waveguide 18, and the second and third optical waveguides. The intensity of the light detected in each of 20 and 22 is calculated while changing the wavelength. In the calculation, a three-dimensional FDTD (Finite Difference Time Domain) method was used. The refractive index of single crystal Si constituting the wavelength filter 10 is 3.5. Further, the width W of the multimode waveguide 16 and 1.15 .mu.m, and the thickness t and 0.25 [mu] m, and the total length _{L a} to a 24 [mu] m.

In FIG. 6, four curves I to IV are drawn. A curve I indicates the light intensity of the TE component L1 _TE of the first light L1 output from the second optical waveguide 20. A curve II indicates the light intensity of the TM component L1 _TM of the first light L1 output from the second optical waveguide 20. A curve III indicates the light intensity of the TE component L2 _TE of the second light L2 output from the third optical waveguide 22. A curve IV indicates the light intensity of the TM component L2 _TM of the second light L2 output from the third optical waveguide 22.

Referring to FIG. 6, both polarization components L1 _TE and L1 _TM of the first light L1 (wavelength 1.31 μm) have a peak at a wavelength around 1.3 μm and a bottom at a wavelength around 1.47 μm. Have. The light intensities of both polarization components L1 _TE and L1 _{TM in} the vicinity of about 1.3 μm are substantially the same.

Further, both polarization components L2 _TE and L2 _TM of the second light L2 have a bottom at a wavelength near about 1.32 μm and have a peak at about 1.45 μm. The light intensities of both polarization components L2 _TE and L2 _{TM in} the vicinity of about 1.45 μm are substantially the same.

  As is apparent from these facts, the optical wavelength filter 10 can wavelength-separate the first light L1 and the second light L2 independent of polarization.

In the optical wavelength filter 10 of this embodiment, the clad 14 is made of SiO ₂ and the remaining components are made of Si. Therefore, it can be easily created by using a semiconductor manufacturing process using an easily available SOI (Silicon on Insulator) substrate.

(Modification)
Hereinafter, modified examples of the optical wavelength filter 10 will be described.

  In this embodiment, the case where the second and third optical waveguides 20 and 22 have the same shape has been described. However, the second and third optical waveguides 20 and 22 need not have the same shape. The apex angle of the isosceles triangle, that is, the taper angle may be set to be different from each other in the second and third optical waveguides 20 and 22. By doing in this way, it can prevent that the 2nd and 3rd optical waveguides 20 and 22 act as a directional coupler, and can improve the crosstalk of the 1st light L1 and the 2nd light L2. .

(Optical multiplexing / demultiplexing device)
Next, an optical multiplexing / demultiplexing device as an application example of the optical wavelength filter 10 will be described with reference to FIG. FIG. 7 is a plan view schematically showing the configuration of the optical multiplexing / demultiplexing element.

  The optical wavelength filter 10 of this embodiment can be used as an optical multiplexing / demultiplexing element used in an ONU of an optical subscriber communication system.

  The optical multiplexing / demultiplexing device 30 includes the optical wavelength filter 10 of this embodiment, an LD (Laser Diode) 32, and a PD (Photo Diode) 34.

LD32 is the second input-output optical waveguide 24 _{and second} optical wavelength filter 10 is optically connected, the second towards the output optical waveguide 24 _2, outputs a first light L1 having a wavelength 1.31μm To do.

PD34 is the third input-output optical waveguide 24 ₃ of the optical wavelength filter 10 is optically connected, the second light L2 of the third coming propagates the input optical waveguide 24 ₃ Wavelength 1.49μm Receive light.

The first input-output optical waveguide 24 ₁ of the optical wavelength filter 10 is connected to an optical fiber (not shown) leading to the station side.

In the optical multiplexing / demultiplexing element 30, the second light L2 (wavelength: 1.49 μm) as the downstream signal transmitted from the station side to the subscriber side is the first input / output optical waveguide 24 ₁ → first light. The signal is input to the multimode waveguide 16 through the waveguide 18. Second light L2 inputted to the multimode waveguide 16 are already through the propagation path as described, are outputted to the third optical waveguide 22, it is received by the third PD 34 via the input-output optical waveguide 24 ₃ The

On the other hand, the first light L1 (wavelength: 1.31 μm) as an upstream signal transmitted from the subscriber side to the station side is output from the LD 32, and the second input / output optical waveguide 24 ₂ → the second optical waveguide 20 Then, the signal is input to the multimode waveguide 16. By the way, since it is known that the reverse process is generally established in the propagation of light, the first light L1 input from the second optical waveguide 20 to the multimode waveguide 16 is opposite to the propagation path already described. through the propagation path, is output to the first optical waveguide 18, is transmitted to the first station side through the input-output optical waveguide 24 _1.

  As described above, the optical wavelength filter 10 of this embodiment can be used as the optical multiplexing / demultiplexing element 30 suitable as an ONU of an optical subscriber system without changing the configuration.

(Embodiment 2)
Next, the Mach-Zehnder interferometer of this embodiment will be described with reference to FIGS. FIG. 8 is a plan view schematically showing the structure of the Mach-Zehnder interferometer. In FIG. 8, the optical wavelength filter 35, an optical coupler 42, and first and second arm optical waveguides 44 ₁ and 44 ₂ is covered with a clad 14, can not be directly visually thereof In order to emphasize the presence of the component, it is represented by a solid line. In FIG. 8, the same components as those in FIGS. 1 and 2 are denoted by the same reference numerals, and the description thereof is omitted as appropriate.

(Construction)
Referring to FIG. 8, the Mach-Zehnder interferometer 40 includes an optical wavelength filter 35, an optical coupler 42, and the first and second arm optical waveguides 44 ₁ and 44 _2. Mach-Zehnder interferometer 40, the first light L1 is outputted from the second optical waveguide 46 ₂ to be described later, and the second light L2 and equally distributed from the second and third optical waveguide 46 ₂ and 46 ₃ will be described later and outputs It functions as a so-called 3 dB coupler.

Optical wavelength filter 35, except that different total length L _a, and is configured similarly to the optical wavelength filter 10 described in the first embodiment. In this Mach-Zehnder interferometer 40, the total length _{L a} of the optical wavelength filter 35 is preferably, for example, about 15.5. This is because the Mach-Zehnder interferometer 40 functions as a 3 dB coupler. This point will be described later. Further, the width W and the thickness t of the optical wavelength filter 35 are configured in the same manner as the wavelength filter 10 of the first embodiment.

The optical coupler 42, except that the fourth optical waveguide 46 ₄ are provided, and is configured similarly to the optical wavelength filter 35. The optical coupler 42 is, as it were, is constructed by adding a fourth optical waveguide 46 ₄ to light wavelength filter 35. More specifically, the optical coupler 42, the third optical waveguide ₄₆₃ and the line fourth optical waveguide 46 ₄ at symmetrical positions is constructed is further provided a first axis C1 'as a symmetrical axis (see FIG. 2 ). In other words, the fourth optical waveguide 46 _4, the central axis C0 'may be that provided in the first optical waveguide 46 ₁ axisymmetrical positions as a symmetrical axis.

The fourth optical waveguide 46 _4, the first side 16 ₁ of the multimode waveguide 16, and is connected integrally with the multimode waveguide 16. The fourth optical waveguide 46 ₄ are formed on the first optical waveguide 46 ₁ and the same shape.

In the following description, in order to distinguish the first to third optical waveguides 18, 20 and 22 of the optical wavelength filter 35 from the first to fourth optical waveguides of the optical coupler 42, the first of the optical coupler 42 is used. ~ denoted by the reference numerals ₄₆ 1 to 46 ₄ in the fourth optical waveguide.

The first arm optical waveguide 44 _1, a second optical waveguide 20 of the optical wavelength filter 10 is the channel optical waveguides of the polarization-independent connecting the first optical waveguide 46 ₁ of the optical coupler 42 optically . The shape of cross section orthogonal to the first optical propagation direction of the arm optical waveguide 44 ₁ is preferably, for example, the width 0.3μm and thickness 0.3μm square shaped. By the first arm optical waveguide 44 ₁ of the cross-sectional shape of the square, the first arm optical waveguide 44 ₁ is capable of propagating light without depending on the polarization.

The second arm optical waveguide 44 _2, a third optical waveguide 22 of the optical wavelength filter 10 is the channel optical waveguides of the polarization-independent for connecting the fourth optical waveguide 46 ₄ of the optical coupler 42 optically . Cross-sectional shape perpendicular to the second light propagation direction of the arm optical waveguide 44 _2, and similar to the first arm optical waveguide 44 _1.

₂ the first and second arm optical waveguides 44 ₁ and 44, in order to function Mach-Zehnder interferometer 40 as a coupler, the optical path length is different. In the example shown in this embodiment, toward the first arm optical waveguide 44 ₁ the optical path length than the second arm optical waveguide 44 ₂ is set longer.

More specifically, the optical path length difference between the first and second arm optical waveguides 44 ₁ and 44 _2, the phase difference with respect to the second light L2 having a wavelength of 1.49μm is 0 (zero), and the and wavelength 1.31μm The first light L1 is set so that the phase difference becomes a value near π. In this embodiment, the optical path length difference is preferably about 1.3433 μm, for example.

(Design condition)
Subsequently, with reference to FIG. 9, the design conditions for the functioning of the Mach-Zehnder interferometer 40 as 3dB couplers, particularly the design conditions of the total length L _a of the optical wavelength filter 35 and the optical coupler 42 will be described.

Overall length L _a of the optical wavelength filter 35 and the optical coupler 42, in both of the optical wavelength filter 35 and the optical coupler 42, the interference order of the first light L1 and the second light L2 after propagating a multi-mode waveguide 16 one Is a half integer and the other is an even number.

  Hereinafter, this point will be described in detail with reference to FIG.

FIG. 9 is a characteristic diagram obtained by applying the equations (3) to (6) already described to the optical wavelength filter 35 and the optical coupler 42 and performing numerical calculation by the finite element method. In FIG. 9, the vertical axis indicates the interference order (dimensionalless), and the horizontal axis indicates the total length L _a (μm) of the optical wavelength filter 35 and the optical coupler 42.

In FIG. 9, four straight lines are drawn. The straight line I shows the behavior of the TE component L2 _TE of the second light L2. The straight line II shows the behavior of the TM component L2 _TM of the second light L2. A straight line III indicates the behavior of the TE component L1 _TE of the first light L1. A straight line IV indicates the behavior of the TM component L1 _TM of the first light L1.

  In order for the Mach-Zehnder interferometer 40 to function as a 3 dB coupler for the second light L2 having a wavelength of 1.49 μm, the interference order m of the second light L2 after propagating through the multimode waveguide 16 is set to a half integer. It is generally known that this is necessary (Condition 1).

  Furthermore, in order to output the first light L1 having a wavelength of 1.31 μm from the second optical waveguide 20, the interference order m of the first light L1 after propagating through the multimode waveguide 16 is set to an even number as described above. (Condition 2).

Referring to FIG. 9, it can be seen that these two conditions are satisfied by two points indicated by arrows G and H in the drawing. That is, the point of L _a ≈15.5 μm indicated by the arrow G and the point of L _a = 31.5 μm indicated by the arrow H. More specifically, at L _a ≈15.5 μm of the arrow G, the interference order of the first light L1 is about 4, and the interference order of the second light L2 is about 4.5. In addition, when L _a = 31.5 μm of the arrow G, the interference order of the first light L1 is about 8, and the interference order of the second light L2 is about 9.5.

Therefore, by setting the overall length _{L a} of the optical wavelength filter 35 and the optical coupler 42 to about 15.5μm or about 31.5Myuemu, Mach-Zehnder interferometer 40 functions as a 3dB coupler with respect to the second light L2, and, The first light L1 can be output from the second optical waveguide 20.

Referring to FIG. 9, for example, at L _a ≈25 μm indicated by an arrow J, the interference order of the first light L1 is about 6.5, and the interference order of the second light L2 is about 7.5. . Thus, it is possible to order of interference m in the first light L1 and the second light L2 both to the half-integer, to determine the total length L _a of the optical wavelength filter 35 and the optical coupler 42.

By setting the overall length L _a of the optical wavelength filter 35 and the optical coupler 42 so that the half-integer order of interference m in the first light L1 and the second light L2 Both, 3 dB for both the light L1 and L2 A Mach-Zehnder interferometer 40 that operates as a coupler is obtained.

(Operation and effect)
Next, operations and effects of the Mach-Zehnder interferometer will be described with reference to FIG.

FIG. 10 is a characteristic diagram for explaining wavelength separation characteristics of the Mach-Zehnder interferometer 40. 10, the vertical axis represents the light intensity of the first light L1 and the second light L2 outputted from the second and third optical waveguide 46 ₂ and 46 ₃ (arbitrary unit) and the horizontal axis represents wavelength ([mu] m) Is shown.

10, from the first optical waveguide 18 and enter the mixed light LM of the first light L1 and the second light L2, the intensity of light detected in each of the second and third optical waveguide 46 ₂ and 46 _3, This is calculated while changing the wavelength. In the calculation, a three-dimensional FDTD method was used. The refractive index of single crystal Si constituting the Mach-Zehnder interferometer 40 is 3.5. Further, the width W of the optical wavelength filter 35 and the optical coupler 42 and 1.15 .mu.m, and the thickness t and 0.25 [mu] m, and was, respectively of the total length _{L a} and 15.5.

In FIG. 10, two curves are drawn. Curve I indicates the light intensity of the first light L1 output from the second optical waveguide 46 _2. Curve II shows the light intensity of the second light L2 output from the third optical waveguide 46 _3.

  Referring to FIG. 10, the first light L1 (wavelength 1.31 μm) shown in the curve I has a peak at a wavelength around 1.3 μm and a bottom at a wavelength around 1.51 μm. The second light L2 (wavelength 1.49 μm) indicated by the curve II has a bottom at a wavelength near about 1.32 μm and a peak at about 1.51 μm. The peak intensity of the second light L2 is about ½ of the peak intensity of the first light L1.

  From these facts, it is clear that the Mach-Zehnder interferometer 40 functions as a polarization-independent 3 dB coupler for the first light L1 and the second light L2.

(Modification)
Next, a modified example of the Mach-Zehnder interferometer 40 will be described with reference to FIGS. 11A and 11B and FIG.

  FIG. 11A is a plan view schematically showing the structure of the first optical element of the first modification. FIG. 11B is a plan view schematically showing the structure of the second optical element of the second modified example. FIG. 12 is a characteristic diagram for explaining the operation of the first optical element. In FIGS. 11A and 11B, the substrate 12 and the clad 14 are not shown for easy understanding. In FIGS. 11A and 11B, the same components as those in FIG. 8 are denoted by the same reference numerals, and the description thereof is omitted as appropriate.

Referring to FIG. 11 (A), the first optical element 50, so to speak, have a structure connected in series to Mach-Zehnder interferometer 40 described above in the third and fourth arm waveguides 56 ₃ and 56 ₄ 2-stage through In addition, like the Mach-Zehnder interferometer 40 of the second embodiment, it is used as a 3 dB coupler.

More specifically, the first optical element 50 connects the Mach-Zehnder interferometer 40, the second optical coupler 52, the third optical coupler 54, and the optical coupler 42 and the second optical coupler 52 of the Mach-Zehnder interferometer 40. and third and fourth arm waveguides 56 ₃ and 56 _4, and a fifth and sixth arm optical waveguides 56 ₅ and 56 ₆ for connecting the second optical coupler 52 and the third optical coupler 54.

Mach-Zehnder interferometer 40 has an overall length L _a of the optical wavelength filter 35 and the optical coupler 42, except that it is optimized for using the first optical element 50 as a 3dB coupler, similar to the Mach-Zehnder interferometer of the second embodiment It is configured.

The second optical coupler 52 is configured in the same manner as the optical coupler 42 of the second embodiment already described. That is, the second optical coupler 52 is provided with a multi-mode optical waveguide 16 already described, and first to fourth optical waveguides ₅₂ 1 to 52 _4. Note that the total length L _a of the second optical coupler 52 is optimized to use the first optical element 50 as a 3dB coupler.

The third optical coupler 54 is configured in the same manner as the optical coupler 42 of the second embodiment already described. That is, the third optical coupler 54 is provided with a multi-mode optical waveguide 16 already described, and first to fourth optical waveguide ₅₄ 1-54 _4. Note that the total length L _a of the third optical coupler 54 is optimized to use the first optical element 50 as a 3dB coupler. And, of the each of the second and third optical waveguide 54 ₂ and 54 _{3, 2} the first and second output optical waveguides 58 ₁ and 58 are connected.

Third and fourth arm waveguides 56 ₃ and 56 ₄ are connected to the optical coupler 42 and the second optical coupler 52 optically, a channel type optical waveguide of the polarization independent single mode. Shape and dimensions of the cross section perpendicular to the third and fourth light propagation direction of the arm optical waveguides 56 ₃ and 56 ₄ are already the same as the first and second arm optical waveguides 44 ₁ and 44 ₂ as described.

More specifically, the third arm waveguide 56 _3, a second optical waveguide 46 _{and second} optical coupler 42, and the first optical waveguide 52 ₁ of the second optical coupler 52 optically connected. Fourth arm waveguide 56 _4, a third optical waveguide 46 ₃ of the optical coupler 42, and a fourth optical waveguide 52 ₄ of the second optical coupler 52 optically connected. Third and fourth arm waveguides 56 ₃ and 56 _4, the light propagating through the optical waveguides 56 ₃ and 56 ₄ are arranged at a distance of just do not interfere. The third and fourth arm waveguides 56 ₃ and 56 _4, the optical path length is equal to one another form.

Fifth and sixth arm optical waveguides 56 ₅ and 56 _6, a second optical coupler 52 and the third optical coupler 54 optically connecting a channel optical waveguide of the polarization independent single mode. Shape and dimensions of the cross section perpendicular to the light propagation direction of the fifth and sixth arm optical waveguides 56 ₅ and 56 _6, already the same as the first and second arm optical waveguides 44 ₁ and 44 ₂ as described.

More specifically, the fifth arm optical waveguide 56 _5, a second optical waveguide 52 ₂ of the second optical coupler 52, and the first optical waveguide 54 ₁ of the third optical coupler 54 optically connected. Sixth arm optical waveguide 56 _6, a third optical waveguide 52 ₃ of the second optical coupler 52, and connects the fourth optical waveguide 54 ₄ of the third optical coupler 54 optically.

Fifth and sixth arm optical waveguides 56 ₅ and 56 ₆ are optical path lengths are different. This point will be described in detail below.

The first and second arm optical waveguides 44 ₁ and 44 ₂ of the optical path length difference [Delta] L (= first arm optical waveguide 44 ₁ of the optical path length in the Mach-Zehnder interferometer 40 - second optical path length of the arm optical waveguide 44 ₂ ). At this time, the fifth and sixth arm optical waveguides 56 ₅ and 56 _6, and "optical path length of the first arm optical waveguide 44 ₁ of the optical path length = 6 arm optical waveguide 56 _6" the relationship, "second arm the optical path length of the optical waveguide 44 ₂ = is the fifth optical path length of the arm optical waveguide 56 ₅ "the relationship and is made up. That is, the optical path length difference between the fifth and sixth arm optical waveguides 56 ₅ and 56 _6, the value sign is reversed from that of the first and second arm optical waveguides 44 ₁ and 44 _2, i.e. -Delta L (= a 5 the optical path length of the arm optical waveguide 56 ₅ - the optical path length) of the sixth arm optical waveguide 56 _6.

The reason for reversing the polarity of the fifth and sixth arm optical waveguides 56 ₅ and 56 ₆ and the first and second arm optical waveguides 44 ₁ and 44 ₂ of the optical path length difference, the wavelength of the first optical element 50 This is to improve the separation characteristics.

Next, the operation of the first optical element 50 will be described with reference to FIG. FIG. 12 is a characteristic diagram for explaining the wavelength separation characteristic of the first optical element 50. 12, the vertical axis represents the light intensity of the first light L1 and the second light L2 output from the first and second output optical waveguides 58 ₁ and 58 ₂ (arbitrary units), the horizontal axis represents wavelength ( μm).

12, the first optical waveguide 18 and enter the mixed light LM of the first light L1 and the second light L2, the intensity of light detected in the first and second respective output optical waveguide 58 ₁ and 58 ₂ Is calculated while changing the wavelength. In the calculation, a three-dimensional FDTD method was used. Further, 3.5 was adopted as the refractive index of the single crystal Si constituting the first optical element 50. The wavelength filter 35, an optical coupler 42, the width W of the second optical coupler 52 and the third optical coupler 54 and 1.15 .mu.m, and the thickness t and 0.25 [mu] m, and was, respectively of the total length _{L a} and 15.5μm .

In FIG. 12, two curves are drawn. Curve III shows the light intensity of the first light L1 output from the first output optical waveguide 58 _1. Curve IV shows the light intensity of the second light L2 outputted from the second output optical waveguide 58 _2.

  Referring to FIG. 12, the first light L1 (wavelength 1.31 μm) shown in the curve III has a broad peak at a wavelength of about 1.3 to 1.4 μm and a bottom at a wavelength near about 1.51 μm. have. The second light L2 (wavelength 1.49 μm) indicated by the curve IV has a bottom at a wavelength near about 1.35 μm and a broad peak at a wavelength of about 1.5 to 1.6 μm.

  Comparing FIG. 12 with FIG. 10 showing the operating characteristics of the Mach-Zehnder interferometer 40, in the first optical element 50 (FIG. 12), the peaks (curves III and IV) of the first light L1 and the second light L2 are as follows. , Wider than the curves I and II in FIG. This means that the wavelength separation band in the first optical element 50 of the modification is widened and crosstalk is reduced.

  As described above, the first optical element 50 according to the first modification operates as a 3 dB coupler that exhibits a wavelength separation characteristic superior to that of the Mach-Zehnder interferometer 40 according to the second embodiment.

  Next, the second optical element of the second modification will be described with reference to FIG.

Referring to FIG. 11 (B), the second optical element 70 is, as it were, an optical coupler 42 of the first optical element 50 and the second optical coupler 52, the third and fourth arm waveguides 56 ₃ and 56 ₄ It is configured by joining directly without intervention.

More specifically, the second optical element 70 connects the optical wavelength filter 35, the fourth optical coupler 72, the fifth optical coupler 74, the optical wavelength filter 35, and the fourth optical coupler 72 described in the second embodiment. the 7 and eighth arm optical waveguide 76 ₇ and 76 _8, and a ninth and tenth arm optical waveguide 76 ₉ and _{76 10} for connecting the fourth optical coupler 72 and the fifth optical coupler 74.

Optical wavelength filter 35, the total length L _a of the optical wavelength filter 35, except that it is optimized for use with second optical element 70 as a 3dB coupler, is configured similarly to the second embodiment.

The fourth optical coupler 72 is configured in the same manner as the optical coupler 42 described above, except that the total length La is twice that of the optical coupler 42 of the second embodiment. That is, the fourth optical coupler 72 is provided with a multi-mode optical waveguide 78, and first to fourth optical waveguide ₇₂ 1-72 _4. Note that the total length L _a of the fourth optical coupler 72 is for use with the second optical element 70 as a 3dB coupler, and is about twice the size of the optical coupler 42 of Embodiment 2.

The fifth optical coupler 74 is configured in the same manner as the optical coupler 42 of the second embodiment already described. That is, the fifth optical coupler 74 is provided with a multi-mode optical waveguide 16 already described, and first to fourth optical waveguide _{72d 4.} Note that the total length L _a of the fifth optical coupler 74 is optimized to use the second optical element 70 as a 3dB coupler. And, of the each of the second and third optical waveguide 74 ₂ and 74 _{3, 2} the first and second output optical waveguides 58 ₁ and 58 are connected.

Seventh and eighth arm optical waveguide 76 ₇ and 76 _8, the optical wavelength filter 35 and the fourth optical coupler 72 optically connecting a channel optical waveguide of the polarization independent single mode. Shape and dimensions of the cross section perpendicular to the light propagation direction of the seventh and eighth arm optical waveguide 76 ₇ and 76 _8, already the same as the first and second arm optical waveguides 44 ₁ and 44 ₂ as described.

More specifically, the seventh arm optical waveguide 76 _7, a second optical waveguide 20 of the optical wavelength filter 35, and connects the first optical waveguide 72 ₁ of the fourth optical coupler 72 optically. Eighth arm optical waveguide 76 _8, a third optical waveguide 22 of the optical wavelength filter 35, and connects the fourth optical waveguide 72 ₄ of the fourth optical coupler 72 optically. Optical path length difference between the seventh and eighth arm optical waveguide 76 ₇ and 76 _8, [Delta] L - and (= optical path length of the seventh arm optical waveguide 76 ₇ optical path length of the 8-arm optical waveguide 76 _8).

The ninth and tenth arm optical waveguides 76 ₉ and 76 ₁₀ are polarization-independent single-mode channel optical waveguides that optically connect the fourth optical coupler 72 and the fifth optical coupler 74. Shape and dimensions of the cross section perpendicular to the light propagation direction of the ninth and tenth arm optical waveguide 76 ₉ and 76 _10, already the same as the first and second arm optical waveguides 44 ₁ and 44 ₂ as described.

More particularly, the ninth arm optical waveguide 76 _9, a second optical waveguide 72 ₂ of the fourth optical coupler 72, and the first optical waveguide 74 ₁ of the fifth optical coupler 74 optically connected. Tenth arm optical waveguide _{76 10,} a third optical waveguide 72 ₃ of the fourth optical coupler 72, and connects the fourth optical waveguide 74 ₄ fifth optical coupler 74 optically.

For the same reason as in the case of the first modification, the optical path length difference between the ninth and tenth arm optical waveguide 76 ₉ and 76 _10, when the sign of the seventh and eighth arm optical waveguide 76 ₇ and 76 ₈ are reversed is doing. That is, the optical path length difference between the ninth and tenth arm optical waveguide 76 ₉ and _{76 10} (= optical path length of the ninth arm optical waveguide 76 ₉ - optical path length of the 10 arm optical waveguide _{76 10),} and -Delta L.

  Similar to the first optical element 50 of the first modification, the second optical element 70 of the second modification operates as a 3 dB coupler that exhibits a wavelength separation characteristic superior to that of the Mach-Zehnder interferometer 40 of the second embodiment. Furthermore, since the second optical element 70 can make the entire length of the entire element shorter than that of the second optical element 50, the element can be miniaturized.

10, 35 Polarization-independent optical wavelength filter 12 Substrate 12a First main surface 14 Cladding 16, 78 Multimode interference optical waveguide (multimode waveguide)
16 ₁ first side 16 ₂ second side 16 ₃ third side 16 ₄ fourth side 16 _u top 16 _d underside 18, 46 _{1, 52 1,} 54 _1, 72 1, 74 ₁ the first optical waveguide 18a, 20a, 22a connecting portions 20, 46 _{2, 52 2,} 54 _2, 72 2, 74 ₂ second optical waveguide 22, 46 _{3, 52 3,} 54 _3, 72 3, 74 ₃ third optical waveguide 24 ₁ first input-output Optical waveguide 24 ₂ Second input / output optical waveguide 24 ₃ Third input / output optical waveguide 30 Optical multiplexing / demultiplexing element 32 LD
34 PD
40 Mach-Zehnder Interferor 42 Optical Coupler 44 ₁ First Arm Optical Waveguide 44 ₂ Second Arm Optical Waveguide 46 ₄ , 52 ₄ , 54 ₄ , 72 ₄ , 74 ₄ Fourth Optical Waveguide 50 First Optical Element 52 Second Optical Coupler 54 3rd optical coupler 56 ₃ 3rd arm optical waveguide 56 ₄ 4th arm optical waveguide 56 ₅ 5th arm optical waveguide 56 ₆ 6th arm optical waveguide 58 ₁ 1st output optical waveguide 58 ₂ 2nd output optical waveguide 70 1st 2 Optical element 72 4th optical coupler 74 5th optical coupler 76 ₇ 7th arm optical waveguide 76 ₈ 8th arm optical waveguide 76 ₉ 9th arm optical waveguide 76 ₁₀ 10th arm optical waveguide

Claims (10)

It is formed using single crystal Si, and is surrounded by first and second side surfaces facing each other in parallel, third and fourth side surfaces facing each other in parallel, and upper and lower surfaces facing each other in parallel. A multi-mode interference optical waveguide that is a rectangular parallelepiped and separates the mixed light of the first and second lights having different wavelengths selected from the wavelength range of 1.2 to 1.6 μm without depending on the polarization;
A first optical waveguide optically connected to the first side surface and receiving the mixed light;
The second and third optical waveguides that are optically connected to the second side surface and output the first and second light beams separated from each other are buried in the cladding on the first main surface side of the substrate. (Embedded)
The cladding has a refractive index n in the range of 1 to 1.6;
The thickness t, which is the distance between the upper surface and the lower surface of the multimode interference optical waveguide, is a value in the range of 0.2 to 0.4 μm, and the third and fourth side surfaces of the multimode interference optical waveguide The width W, which is the distance between, is a value in the range of 1.0 to 3.7 μm,
The refractive index n, the width W, and the thickness t have a relationship that the refractive index n increases and the width W increases, and that the thickness t increases and the width W increases. Features a polarization-independent optical wavelength filter.   The width of the first to third optical waveguides measured in a direction perpendicular to the light propagation direction and parallel to the first main surface of the substrate is the multimode interference light guide from the side away from the multimode interference optical waveguide. The polarization-independent optical wavelength filter according to claim 1, wherein the polarization-independent optical wavelength filter is linearly expanded toward a connection portion with the waveguide. When the first axis is a straight line passing through the center point of the rectangle formed by the multimode interference optical waveguide in a plane parallel to the first main surface of the substrate and extending in the width direction,
The second optical waveguide is provided at a position symmetrical to the first optical waveguide with the first axis as a symmetry axis, and
3. The polarization-independent optical wavelength according to claim 1, wherein the third optical waveguide is provided at a point-symmetrical position with respect to the first optical waveguide with the center point as a symmetric center. 4. filter. Polarization-independent optical wavelength filter according to claim 1, characterized in that the material of the cladding and SiO _2. The overall length is the distance between the first and second side of the multimode interference optical waveguide and L _a,
The propagation constant difference of the zero-order mode light and first-order mode light in the TE component of the first light and [Delta] [beta] _1, and the interference order after propagation of the multimode interference optical waveguide of the TE component of the first light m ₁ (where m ₁ is a positive integer)
The propagation constant difference of the zero-order mode light and first-order mode light in the TM component of the first light and [Delta] [beta] _2, and the interference order after propagation of the multimode interference optical waveguide of the TM component of the first light m ₂ (where m ₂ is a positive integer)
The propagation constant difference of the zero-order mode light and first-order mode light in the TE component of the second light and [Delta] [beta] _3, and the interference order after propagation of the multimode interference optical waveguide of the TE component of the second light m ₃ (where m ₃ is a positive integer)
The propagation constant difference of the zero-order mode light and first-order mode light in the TM component of the second light and [Delta] [beta] _4, and the interference order after propagation of the multimode interference optical waveguide of the TM component of the second light m ₄ (where m ₄ is a positive integer)
The following formulas (1) to (4) that give interference conditions in the multimode interference optical waveguide are established,
The polarization-independent light according to any one of claims 1 to 4, wherein m ₁ = m ₂ and m ₃ = m ₄ , and the difference between m ₁ and m ₃ is an odd number. Wavelength filter.
_{Δβ 1 L a = m 1 π} ··· (1)
Δβ ₂ L _a = m ₂ π (2)
_{Δβ 3 L a = m 3 π} ··· (3)
_{Δβ 4 L a = m 4 π} ··· (4) When the wavelength of the first light is 1.31 μm and the wavelength of the second light is 1.49 μm, the thickness t and the width W of the multimode interference optical waveguide are expressed by the following formulas (5) and (5) 6. The polarization-independent optical wavelength filter according to claim 4 or 5, characterized in that 6) is satisfied.
When t ≧ 0.25 μm: W = 42 (t−0.25) ^1.48 + 1.15 (5)
When t <0.25 μm: 1.1 <W <1.15 (6) An optical multiplexing / demultiplexing device using the polarization-independent wavelength filter according to claim 6,
The first light is input from the second optical waveguide, is output from the first optical waveguide through the multimode interference optical waveguide,
The optical multiplexing / demultiplexing device, wherein the second light is input from the first optical waveguide and output from the third optical waveguide through the multimode interference optical waveguide. A Mach-Zehnder interferometer using the polarization-independent optical wavelength filter according to claim 3 or 4,
The polarization-independent optical wavelength filter, an optical coupler, and first and second arm optical waveguides that optically connect the polarization-independent optical wavelength filter and the optical coupler;
The optical coupler is configured such that a fourth optical waveguide is further provided at a position symmetrical to the third optical waveguide with the first axis in the polarization-independent optical wavelength filter as an axis of symmetry,
The first arm optical waveguide connects the second optical waveguide of the polarization-independent optical wavelength filter and the first optical waveguide of the optical coupler,
The second arm optical waveguide connects the third optical waveguide of the polarization-independent optical wavelength filter and the fourth optical waveguide of the optical coupler,
A Mach-Zehnder interferometer, characterized in that the cross-sectional shape orthogonal to the light propagation direction of the first and second arm optical waveguides is a square shape, and the optical path lengths of the first and second arm optical waveguides are different. .   In both the polarization-independent optical wavelength filter and the optical coupler, one of the interference orders of the first light and the second light after propagating through the multimode interference optical waveguide is a half integer and the other is an even number. The Mach-Zehnder interferometer according to claim 8, wherein total lengths of the polarization-independent optical wavelength filter and the optical coupler are determined.   In both the polarization-independent optical wavelength filter and the optical coupler, the light is set so that the interference orders of the first light and the second light after propagating through the multimode interference optical waveguide are both half integers. 9. The Mach-Zehnder interferometer according to claim 8, wherein a total length of the coupler is determined.

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