Optical 90-degree hybrid

Abstract

An optical 90-degree mixer includes two splitters, two combiners, and four arm waveguides connecting the output ports of the splitters and the input ports of the combiners. Each of the splitters, arm waveguides, and combiners is part of an optical waveguide. The optical waveguides are configured such that phase errors generated in the splitters due to wavelength variations are suppressed by phase errors generated in the arm waveguides due to wavelength variations. The optical waveguides are also configured such that phase errors generated in the splitters due to deviations of structural parameters from specific values ​​(e.g., design values) are suppressed by phase errors generated in the arm waveguides due to such deviations.

Description

Technical Field

[0001] The implementation discussed in this article relates to a 90-degree optical mixer. Background Technology

[0002] An optical 90-degree mixer is an optical device that generates four interfering beams (i.e., beams generated by the interference of light) with a phase interval of 90° from a signal beam and a reference beam having a wavelength approximately the same as that of the signal beam (see, for example, Japanese Patent Application Laid-Open No. 2020-177109, US Patent No. 10731383, Japanese Patent Application Laid-Open No. 2011-18002, International Publication No. WO 2011 / 010469, and Japanese Patent Application Laid-Open No. 2021-148965). Optical 90-degree mixers are used, for example, in receivers in digital coherent optical communications, which enable high-speed and high-capacity communication. The interfering beams output from the optical 90-degree mixer are converted into two electrical signals by a balanced photodetector, with the phases of these two electrical signals differing by approximately 90° from each other. Two orthogonal transmission signals are demodulated from these electrical signals.

[0003] The optical 90-degree mixer splits each of the signal and reference beams into two, assigning a separate phase to each split reference (or signal) beam. Then, one of the split reference beams is combined with one of the split signal beams, and another of the split reference beams is combined with another of the split signal beams, resulting in four interfering beams with a phase spacing of approximately 90°.

[0004] A phase difference deviation of the interfering light relative to 90° degrades the orthogonality of the two electrical signals obtained from the interfering light, resulting in a degraded waveform of the demodulated signal. Therefore, it is desirable to minimize the phase difference deviation of the interfering light relative to 90°. In the following text, the phase difference deviation of the interfering light relative to 90° will be referred to as phase error.

[0005] Currently, when the wavelength of the signal light changes along with the wavelength of the reference light, the phase error of the interfering light also changes. Therefore, techniques have been proposed to maintain the phase error of the interfering light at approximately 0° even when the wavelength of the signal light changes along with the wavelength of the reference light (see, for example, Japanese Patent Application Publication No. 2011-18002, International Publication No. WO 2011 / 010469, and Japanese Patent Application Publication No. 2021-148965). This technique is important in wavelength multiplexing communications, especially in wavelength multiplexing communications using a wide wavelength range such as the C-band.

[0006] When the width of the optical waveguide included in the optical 90° mixer deviates from the design value, the phase error of the interfering light also changes. The increase in deviation from the design value (i.e., manufacturing error) leads to a larger phase error. Therefore, a technique has been proposed to maintain the phase error of the interfering light at about 0° even if the manufacturing error is large (see, for example, Japanese Patent Application Publication No. 2021-148965).

[0007] Currently, for example, many optical 90-degree mixers separate (or combine) signal and reference beams using multimode interference waveguides, etc. (e.g., see Lucas B. Sodano and Erik CM Pennings, “Optical Multi-Mode Interference Devices Based on Self-Imaging,” Journal of Optical Technology, April 1995, Vol. 13, No. 4, pp. 615-627). Various other types of elements besides multimode interference waveguides are being proposed as optical components for separating (or combining) light (e.g., see Weijie Chang et al., “Inverse design and demonstration of an ultracompact broadband dual-mode 3 dB power splitter,” Optical Express, 2018, Vol. 26, No. 18, pp. 24135-24144). Summary of the Invention

[0008] However, the problem with the prior art is that even if the increase in phase error caused by wavelength change (i.e., wavelength variation) can be suppressed, the phase error will still increase when manufacturing errors increase. Therefore, one aspect of the present invention aims to solve this problem.

[0009] According to one aspect of the embodiments, a 90-degree optical mixer is provided, comprising: a first splitter having a first output port and a second output port different from the first output port; a second splitter, different from the first splitter, having a third output port and a fourth output port different from the third output port; a first combiner having a first input port and a second input port different from the first input port; a second combiner, different from the first combiner, having a third input port and a fourth input port different from the third input port; a first arm waveguide connecting the first output port and the third input port; a second arm waveguide connecting the second output port and the second input port; a third arm waveguide connecting the third output port and the first input port; and a fourth arm waveguide connecting the fourth output port and the fourth input port, wherein the first splitter splits a first beam into a first split beam and a second split beam, outputs the first split beam from the first output port, and outputs the second split beam from the second output port. The second splitter outputs a second split beam, which splits the second beam into a third split beam and a fourth split beam. The third split beam is output from the third output port, and the fourth split beam is output from the fourth output port. The first combiner combines the second split beam entering it via the second arm waveguide and the third split beam entering it via the third arm waveguide to generate a first interference beam and a second interference beam that is out of phase with the first interference beam. The second combiner combines the fourth split beam entering it via the fourth arm waveguide and the first split beam entering it via the first arm waveguide to generate a third interference beam and a fourth interference beam that is out of phase with the third interference beam. Each of the first and second splitters, the first arm waveguide to the fourth arm waveguide, and the first and second combiners is part of an optical waveguide. The optical waveguide has a core and a cladding around the core. The optical waveguide is configured to satisfy the following expressions (1) to (7) when λ is a specific wavelength and X is zero, where X is the deviation of the parameter from the first value. The parameter is based on the size or shape of the cross-section of the core.

[0010] [Mathematical Expression 1]

[0011]

[0012] [Mathematical Expression 2]

[0013]

[0014] [Mathematical Expression 3]

[0015]

[0016] [Mathematical Expression 4]

[0017]

[0018] [Mathematical Expression 5]

[0019]

[0020] [Mathematical Expression 6]

[0021]

[0022] [Mathematical Expression 7]

[0023]

[0024] [Mathematical Expression 8]

[0025]

[0026] Where λ is the wavelength of the first and second rays, and the cross section is the cross section perpendicular to the direction of light propagation through the core. The difference is obtained by subtracting the second phase of the electric field of the second separated light from the first phase of the electric field of the first separated light, where the first phase is the phase at the first output port and the second phase is the phase at the second output port. The difference is obtained by subtracting the fourth phase of the electric field of the fourth split beam from the third phase of the electric field of the third split beam. The third phase is the phase at the third output port, and the fourth phase is the phase at the fourth output port. Φ is the phase given by expression (8). Φ1 is the phase given to the first split beam by the first arm waveguide, Φ2 is the phase given to the second split beam by the second arm waveguide, Φ3 is the phase given to the third split beam by the third arm waveguide, and Φ4 is the phase given to the fourth split beam by the fourth arm waveguide. m is an integer, k is +1 or -1, and the unit of phase is radians. Attached Figure Description

[0027] Figure 1 This is a diagram used to describe the characteristics of the 90-degree optical mixer 2;

[0028] Figure 2 This is a diagram illustrating an example of a light 90-degree mixer 8 according to an embodiment;

[0029] Figure 3 This is a diagram used to describe the operation of the 90-degree optical mixer 8;

[0030] Figure 4 It is along Figure 2 A cross-sectional view taken from lines IV, XII-IV, XII in the diagram;

[0031] Figure 5 This is an example 1' + A diagram illustrating an example of the relationship between 2' and wavelength λ;

[0032] Figure 6 This is a plan view of a 2×2 MMI used for simulation;

[0033] Figure 7 This is a diagram used to describe the first arm waveguide to the fourth arm waveguide 14 having the phase shift section 32;

[0034] Figure 8 This is a plan view of the core 34 of the i-th phase shift section 32;

[0035] Figure 9 This is a diagram illustrating an example of the relationship between Φ and wavelength λ obtained from expression (16);

[0036] Figure 10 This is a diagram illustrating an example of the relationship between phase error Δθ and wavelength λ;

[0037] Figure 11 This is a diagram illustrating an example of the relationship between the phase error Δθ and wavelength λ of a 1×2 MMI optical 90-degree mixer, where the first separator 10a and the second separator 10b are 1×2 MMIs.

[0038] Figure 12 This is a diagram illustrating an example of a method for manufacturing a 90-degree light mixer 8 according to an embodiment; and

[0039] Figure 13 This is a plan view of a modified example 108 of the 90-degree light mixer 8. Detailed Implementation

[0040] As mentioned earlier, a technique has been proposed to maintain the phase error of the interference light at approximately 0° even when the wavelength of the signal light changes along with that of the reference light. However, the problem with the prior art is that even if the increase in phase error caused by wavelength change (i.e., wavelength variation) can be suppressed, the phase error will still increase when manufacturing errors increase.

[0041] According to one aspect of the implementation, while suppressing the increase in phase error caused by wavelength variation (more precisely, the increase in the absolute value of the phase error), it is also possible to suppress the increase in phase error caused by the increase in deviations of structural parameters (more precisely, the increase in the absolute value of the deviations). Here, an example of a deviation in structural parameters is manufacturing error.

[0042] In the following description, embodiments of the invention will be presented with reference to the accompanying drawings. However, it should be noted that the scope of the invention is not limited to the embodiments described below, but rather covers the contents described in the claims and their equivalents. Here, the same reference numerals are used for the same parts even in different drawings, and their descriptions are omitted.

[0043] (1) Description of the 90-degree optical mixer

[0044] Figure 1 This diagram illustrates the characteristics of a 90-degree light mixer 2. The 90-degree light mixer 2 is a device configured to, upon receiving two lights 4 and 6 of the same wavelength, mix the two lights 4 and 6 and output four interfering lights Ip, In, Qp, and Qn with a phase interval of approximately 90°. The absolute value of the phase difference between interfering lights Ip and In is approximately 180°. The absolute value of the phase difference between interfering lights Qp and Qn is approximately 180°. The absolute value of the phase difference between interfering lights Ip and Qp is approximately 90° (preferably not less than 85° and not greater than 95°). The absolute value of the phase difference between interfering lights In and Qn is approximately 90° (preferably not less than 85° and not greater than 95°). The phase difference between the interfering lights refers to the phase difference in the light intensity (i.e., power) of the interfering lights. The 90-degree light mixer according to the embodiment is a device having these characteristics.

[0045] (2) Structure and operation

[0046] Figure 2 This is a diagram illustrating an example of a light 90-degree mixer 8 according to an embodiment. Figure 3 This is a diagram used to describe the operation of the 90-degree optical mixer 8. Figure 4 It is along Figure 2 The cross-sectional view taken from lines IV, XII-IV, XII in the diagram.

[0047] The optical 90-degree mixer 8 includes a first splitter 10a having a first output port Pout1 and a second output port Pout2. The first splitter 10a is, for example, a 2×2 multimode interferometer. The term "2×2 multimode interferometer" will be abbreviated as "2×2 MMI" below. The second output port Pout2 is, for example, a first input light 16a described later (see [link to documentation]). Figure 3 The first output port Pout1 is, for example, a cross port relative to the input port PA (i.e., another output port separate from the pass-through port).

[0048] The optical 90-degree mixer 8 also includes a second splitter 10b having a third output port Pout3 and a fourth output port Pout4. The second splitter 10b is, for example, a 2×2 MMI. The fourth output port Pout4 is, for example, a through port (i.e., an output port facing the input port PB) into which the second input light 16b enters. The third output port Pout3 is, for example, a cross port relative to the input port PB.

[0049] The optical 90-degree mixer 8 also includes a first combiner 12a having a first input port Pin1 and a second input port Pin2. The first combiner 12a is, for example, a 2×2 MMI.

[0050] The optical 90-degree mixer 8 also includes a second combiner 12b having a third input port Pin3 and a fourth input port Pin4. The second combiner 12b is, for example, a 2×2 MMI.

[0051] The optical 90-degree mixer 8 also includes a first-arm waveguide 14a connecting the first output port Pout1 and the third input port Pin3. The optical 90-degree mixer 8 further includes a second-arm waveguide 14b connecting the second output port Pout2 and the second input port Pin2. The optical 90-degree mixer 8 also includes a third-arm waveguide 14c connecting the third output port Pout3 and the first input port Pin1. The optical 90-degree mixer 8 also includes a fourth-arm waveguide 14d connecting the fourth output port Pout4 and the fourth input port Pin4. The first-arm waveguides 14a to the fourth-arm waveguides 14d are, for example, channel waveguides.

[0052] First separator 10a (see...) Figure 3 The first light 16a (hereinafter referred to as the first input light) is split into a first split light 18a and a second split light 18b. The first split light 18a is output from the first output port Pout1, and the second split light 18b is output from the second output port Pout2. The first split light 18a and the second split light 18b are obtained by splitting the first input light 16a. The first input light 16a is, for example, the reference light LO.

[0053] The second splitter 10b splits the second light 16b (hereinafter referred to as the second input light) into a third split light 18c and a fourth split light 18d. The third split light 18c is output from the third output port Pout3, and the fourth split light 18d is output from the fourth output port Pout4. The third split light 18c and the fourth split light 18d are obtained by splitting the second input light 16b. The second input light 16b is, for example, the signal light S.

[0054] The first combiner 12a combines the second split beam 18b entering it via the second arm waveguide 14b and the third split beam 18c entering it via the third arm waveguide 14c to generate a first interference beam IF1 and a second interference beam IF2. The first combiner 12a outputs the generated first interference beam IF1 and the generated second interference beam IF2. The second interference beam IF2 is an interference beam with a phase opposite to the first interference beam IF1. The first interference beam IF1 and the second interference beam IF2 are generated by the interference between the second split beam 18b and the third split beam 18c. The first interference beam IF1 is a reference... Figure 1The interference beam In is described. The second interference beam IF2 is a reference. Figure 1 The interference light Ip is described.

[0055] The second combiner 12b combines the fourth split beam 18d entering it via the fourth arm waveguide 14d and the first split beam 18a entering it via the first arm waveguide 14a to generate a third interference beam IF3 and a fourth interference beam IF4. The second combiner 12b outputs the generated third interference beam IF3 and the generated fourth interference beam IF4. The fourth interference beam IF4 is an interference beam with a phase opposite to that of the third interference beam IF3. The third interference beam IF3 and the fourth interference beam IF4 are generated by the interference between the fourth split beam 18d and the first split beam 18a. The third interference beam IF3 is a reference... Figure 1 The interference beam Qn is described. The fourth interference beam IF4 is a reference beam. Figure 1 The interference light Qp is described.

[0056] Each of the first splitter 10a and the second splitter 10b, the first arm waveguide 14a to the fourth arm waveguide 14d, and the first combiner 12a and the second combiner 12b is part of an optical waveguide 24 having a core 20 (see [link]). Figure 4 The core 20 and the cladding 22 surrounding the core 20. The cladding 22 is a component having a refractive index lower than that of the core 20.

[0057] Optical waveguide 24 is an optical element configured to satisfy the following expressions (1) to (7) when the wavelength λ is a specific wavelength and X is zero. Here, the variable X is the deviation of the structural parameter (e.g., the width W of the core 20) from a first value (e.g., the design value). This situation (i.e., the wavelength λ is a specific wavelength and X is zero) will be referred to as the “optimal condition” below.

[0058] [Mathematical Expression 9]

[0059]

[0060] [Mathematical Expression 10]

[0061]

[0062] [Mathematical Expression 11]

[0063]

[0064] [Mathematical Expression 12]

[0065]

[0066] [Mathematical Expression 13]

[0067]

[0068] [Mathematical Expression 14]

[0069]

[0070] [Mathematical Expression 15]

[0071]

[0072] [Mathematical Expression 16]

[0073]

[0074] However, note that λ is the wavelength of the first input light 16a and the second input light 16b (the same applies below). "Structural parameters" are parameters based on the dimensions or shape of the cross-section of the core 20. This "cross-section" is defined by the cross-section passing through the core 20 (see...). Figure 4 The cross section perpendicular to the direction (in other words, the path) of the propagating light.

[0075] Parameters based on the "dimensions of the core's cross-section" include, for example, the dimensions of the core 20 (e.g., the width W or thickness T of the core 20). Parameters based on the "shape of the cross-section" include, for example, the angle between the sidewalls and the bottom surface of the core 20 (i.e., the sidewall angle).

[0076] The width W of the core 20 is the dimension of the aforementioned "cross-section" (i.e., the cross-section perpendicular to the direction of light propagation through the core 20), and is the dimension in the direction H parallel to the substrate Sub on which the optical waveguide 24 is disposed. The thickness T of the core 20 is the dimension of the aforementioned "cross-section," and is the dimension in the direction V perpendicular to the substrate Sub on which the optical waveguide 24 is disposed.

[0077] As described above, the "first value" is, for example, the design value used to manufacture the light 90-degree mixer 8 (i.e., the target value of the structural parameters obtained as a result of the design of the light 90-degree mixer 8). The aforementioned "deviation" is, for example, a manufacturing error. A manufacturing error is, for example, the difference between the design value A of the width W (or thickness T) of the core 20 and the actual value B of the width W (or thickness T) of the core 20, where the difference is B minus A. In many cases, the manufacturing error is almost constant and independent of the position within the component.

[0078] The value of the structural parameter x is obtained by adding the deviation X to the aforementioned "first value" X0. In other words, the value of the structural parameter x can be expressed as x = X0 + X. Therefore, the actual value of the structural parameter of the optical waveguide 24 is obtained by adding a specific deviation (e.g., manufacturing error of 25 nm) to the first value X0 (e.g., design value of 1.136 μm) (e.g., 1.161 μm). This specific deviation can be of various values ​​(e.g., -25 nm, 0 nm, +25 nm, etc.).

[0079] The “first value” X0 changes along the respective paths of the first input light 16a, the second input light 16b, and the first splitting light 18a to the fourth splitting light 18d. For example, the first value X0 (e.g., the design value) of the core width of the first splitter 10a is greater than the first value X0 (e.g., the design value) of the core width of the first arm waveguide 14a. “Core width” refers to the width of the core.

[0080] 1 is the difference obtained by subtracting the second phase Ph2 of the electric field of the second separating beam 18b from the first phase Ph1 of the electric field of the first separating beam 18a (i.e., Ph1 minus Ph2). It should be noted that the first phase Ph1 is the phase at the first output port Pout1. The second phase Ph2 is the phase at the second output port Pout2.

[0081] 2 is the difference obtained by subtracting the fourth phase Ph4 of the electric field of the fourth separating beam 18d from the third phase Ph3 of the electric field of the third separating beam 18c (i.e., Ph3 minus Ph4). It should be noted that the third phase Ph3 is the phase at the third output port Pout3. The fourth phase Ph4 is the phase at the fourth output port Pout4.

[0082] Φ is the phase assigned by expression (8). Φ1 is the phase assigned to the first split beam 18a by the first arm waveguide 14a (i.e., the change in the phase of the first split beam 18a due to its passage through the first arm waveguide 14a, the same below). Φ2 is the phase assigned to the second split beam 18b by the second arm waveguide 14b. Φ3 is the phase assigned to the third split beam 18c by the third arm waveguide 14c. Φ4 is the phase assigned to the fourth split beam 18d by the fourth arm waveguide 14d. m is an integer. k is +1 or -1. Unless otherwise specified, the unit of phase is radians (the same below). It should be noted that the above "phase" does not include ωt (where ω is the angular frequency of the light and t is time).

[0083] 1 and 2. And Φ1 to Φ4 are functions of λ and X. Note that... 1 and 2. And Φ1 to Φ4 are functions obtained when the wavelengths of the first input light 16a and the second input light 16b are consistent with each other.

[0084] In the following description, the first combiner 12a and the second combiner 12b are assumed to be 2×2 MMIs with the same configuration. However, even if the first combiner 12a and the second combiner 12b are not 2×2 MMIs with the same configuration, the conclusions described below will not change. It should be noted that the first combiner 12a is an optical element configured to output a first interference beam IF1 and a second interference beam IF2 that is phase-opposite to the first interference beam IF1. In the same manner, the second combiner 12b is an optical element configured to output a third interference beam IF3 and a fourth interference beam IF4 that is phase-opposite to the third interference beam IF3.

[0085] Expression (9) gives the phase difference ΔP between the second interference light IF2 (i.e., interference light Ip) and the fourth interference light IF4 (i.e., interference light Qp).

[0086] [Mathematical Expression 17]

[0087]

[0088] As can be understood from expression (7), when the wavelength λ is the aforementioned “specific wavelength” and the above structural parameters are consistent with the first value, the phase difference ΔP will be -k × π / 2 - 2mπ (where k is 1 or -1, and m is an integer). However, when the structural parameters deviate from the first value or the wavelength λ deviates from the “specific wavelength”, the phase difference ΔP will change and become -k × π / 2 - 2mπ - Δθ. Δθ will be referred to as the “phase error” below. Thus, this yields expression (10).

[0089] [Mathematical Expression 18]

[0090]

[0091] Now, with k = -1 and m = 0, the phase error Δθ can be expressed as in expression (11).

[0092] [Mathematical Expression 19]

[0093]

[0094] Even if k = -1 and m = 0, the conclusions described below will remain unchanged. Φ is a function expressed by expression (8).

[0095] Expression (12) represents the total derivative δ(Δθ) of the phase error Δθ.

[0096] [Mathematical Expression 20]

[0097]

[0098] It should be noted that δλ is the change in λ (i.e., the amount of change). δX is the change in X.

[0099] The coefficients of δλ in expression (12) are the partial derivatives of Φ with respect to λ and 1 2. The sum of partial derivatives of Φ with respect to λ. When λ is a specific wavelength and the deviation X is zero (i.e., the aforementioned "optimal condition"), the sum of partial derivatives of Φ with respect to λ. 1 2. The partial derivatives with respect to λ have opposite signs, as can be understood from expressions (1) to (3). Therefore, when λ is the “specific wavelength” mentioned above and the deviation X is zero, the coefficient of δλ in expression (12) becomes smaller. The same applies to the coefficient of δX in expression (12).

[0100] Therefore, according to this embodiment, the increase in phase error Δθ caused by the increase in deviation X (e.g., manufacturing error) (more precisely, the increase in the absolute value of deviation X) can be suppressed, while the change in phase error Δθ caused by the change in wavelength λ (i.e., the wavelength dependence of phase error) can also be suppressed. It should be noted that when λ is the aforementioned “specific wavelength” and deviation X is zero, the coefficients of δλ and δX can be easily made zero (see “(4) Arm Waveguide”).

[0101] (3) Separator

[0102] First separator 10a and second separator 10b (see...) Figure 3 The first separator 10a and the second separator 10b, implemented by the 2×2 MMI, are implemented by the 2×2 MMI, as illustrated in “(2) Structure and Operation”. Therefore, the first separator 10a and the second separator 10b, implemented by the 2×2 MMI, will be described here to satisfy expressions (1), (2), (4) and (5).

[0103] The first separator 10a is implemented by 2×2 MMI 1 is approximately -π / 2. The second separator 10b is implemented by another 2×2 MMI. 2 is also approximately -π / 2. Therefore, 1 Deviation relative to -π / 2 1' and 2 relative to -π / 2 2' can be used to rewrite expression (11) as follows.

[0104] [Mathematical Expression 21]

[0105]

[0106] It should be noted that 1' and 2' is satisfied 1 = -π / 2 + 1' and 2 = -π / 2 + The variable is 2'.

[0107] Figure 5 This is an example in 1' + A diagram illustrating an example of the relationship between 2' and wavelength λ (i.e., the wavelengths of both the first input light 16a and the second input light 16b). Figure 5 This is a graph calculated through simulation. In this simulation, it is assumed that the first separator 10a and the second separator 10b are 2×2 MMIs with identical structures. The vertical axis is... 1' + 2'. The horizontal axis is the wavelength λ. The range of the horizontal axis includes the C-band (for...). Figures 9 to 11 The same applies to a wide range (1.525 μm to 1.57 μm). 1' + 2' is a portion of the phase error Δθ, which appears in the separator 10 (i.e., the first separator 10a and the second separator 10b).

[0108] Figure 6 This is a planar diagram of the 2×2 MMIs used for simulation. These 2×2 MMIs are channel waveguides, each with a core made of silicon (Si) and a cladding made of silicon dioxide (SiO2). The core 20 has a thickness of 220 nm. The modes of both the first input light 16a and the second input light 16b are assumed to be TE0. Figure 6 The dimensions of the various parts of the core 20 are shown.

[0109] Figure 5 The solid line 26 in the graph represents a curve obtained when the deviation X (e.g., manufacturing error) of the width W of the core 20 is 0 nm. This curve indicates... 1' + The relationship between 2' and wavelength λ (the same applies below). The dashed line 28 is a graph obtained when the deviation X of the width W of the core 20 is 25 nm. The dotted line 30 is a graph obtained when the deviation X of the width W of the core 20 is -25 nm.

[0110] With a deviation X of 0 nm, as indicated by solid line 26, at wavelength λ0 near the center wavelength of 1.5475 μm on the horizontal axis, 1' + 2' is 0°. Furthermore, in the case of λ = λ0 and X = 0, 1' + The partial derivative of 2' with respect to wavelength λ is positive, as shown by solid line 26.

[0111] The 2×2 MMI implementing the first separator 10a and the 2×2 MMI implementing the second separator 10b have the same structure (as described earlier), and therefore 1' and 2' are consistent with each other. Therefore, when λ = λ0 and X = 0, The partial derivative of 1' with respect to wavelength λ is positive. This is for... The partial derivative of 2' with respect to wavelength λ also holds true.

[0112] Now, The partial derivatives of 1' and The partial derivatives of 1 are consistent with each other, according to The definition of 1' is clear. This is for The partial derivative of 2' also holds. Therefore, when λ = λ0 and X = 0, the first separator 10a and the second separator 10b satisfy the following condition regarding... The expression for the partial derivative of 1 (1) and about The expression for the partial derivative of 2 is (2).

[0113] also, 1' + The sign of the partial derivative of 2' with respect to the deviation X is negative, as is clear from the dashed line 28 and the dotted line 30. Therefore, in the case of λ = λ0 and X = 0, the first separator 10a and the second separator 10b satisfy expressions (4) and (5).

[0114] In other words, when λ is a specific wavelength λ0 and the deviation X is 0, a 2×2 MMI can realize a separator 10 (i.e., a first separator 10a and a second separator 10b) that satisfies expressions (1), (2), (4), and (5).

[0115] In addition, Figure 5 In the example shown, expressions (1), (2), (4), and (5) are satisfied over a wide range of λ from 1.525 nm to 1.57 nm and deviation X from -25 nm to 25 nm.

[0116] 1' and 2' wavelength dependence

[0117] In a 2×2 MMI, when the wavelength of the input light ( Figure 5 λ in the value deviates from the optimal wavelength ( Figure 5 In the example shown, when λ0), the center of the electric field distribution formed at each output port of the 2×2 MMI is shifted relative to the center of each output port. As a result, the phase difference... 1 and The phase difference λ changes, where each phase difference is the phase difference between the waveguide modes (i.e., the output light) emitted from the two output ports of the MMI. In other words, when the wavelength λ of the input light changes, the phase difference of the output light changes. 1 and Changes in 2 1' and 2' changes from zero to a non-zero value. Here, the "input light" mentioned above is the light input into the MMI, while the "output light" mentioned above is the light output from the MMI.

[0118] therefore, The partial derivative of 1' with respect to wavelength λ becomes a non-zero value. The same applies to the partial derivative of 2' with respect to the wavelength λ. That is, 1' and 2' exhibits wavelength dependence. Furthermore, 1' and 2' increases with wavelength λ, such as Figure 5 As shown. Therefore, 1' and 2' satisfies expressions (1) and (2).

[0119] 1' and 2' Manufacturing error (deviation X) dependence

[0120] Expression (14) is the element length L that indicates the minimum loss of the MMI (see [reference]). Figure 6 The mathematical expression of ).

[0121] [Mathematical Expression 22]

[0122]

[0123] It should be noted that n r This is the effective refractive index of the MMI. W eΛ is the effective core width of the MMI, and Λ is the wavelength of the light input into the MMI. In Lucas. B. Sodano and Erik CM Pennings, “Optical Multi-Mode Interference Devices Based on Self-Imaging”, Journal of Optical Technology, April 1995, Vol. 13, No. 4, pp. 615-627, expression (14) can be readily obtained from expressions (6) and (19). Here, in order to obtain the above expression (14), the constant p in expression (19) is set to 1.

[0124] When the element length L of the MMI satisfies expression (14), the loss becomes minimal, and the phase difference between the waveguide modes emitted from the output port also becomes almost exactly -π / 2. That is, 1' and 2' is almost entirely zero. Therefore, Λ (hereinafter referred to as the "zero phase difference wavelength") that satisfies expression (14) is 1' and 2' is a wavelength that is almost exactly zero.

[0125] Many MMIs have a sufficiently large core width W (see...) Figure 6 Therefore, the effective core width We and the actual width W of the MMI are approximately the same. When a positive deviation X occurs in the width W, the zero phase difference wavelength Λ shifts to the longer wavelength side, which can be clearly understood from expression (14). Therefore, when a positive manufacturing error occurs, Figure 5 The solid line 26 in the middle is shifted towards the longer wavelength side (see...) Figure 5 (Dash line 28 in the diagram). Conversely, when a negative deviation X occurs in the width W, the zero-phase-difference wavelength Λ shifts to the shorter wavelength side. Therefore, when a negative manufacturing error occurs, Figure 5 The solid line 26 in the middle shifts towards the shorter wavelength side (see...) Figure 5 (30) in the dotted line.

[0126] 1' and The partial derivative of 2' with respect to manufacturing error (i.e., the example of deviation X) is therefore negative. That is, 2×2 MMI satisfies the expressions (4) and (5) with respect to deviation X.

[0127] The deviation X described above refers to the deviation of the core width W. However, the same conclusion can be drawn for other deviations X (e.g., manufacturing errors in the core thickness T or manufacturing errors in the sidewall corners of the core).

[0128] Furthermore, the TE0 mode has an electric field parallel to the width direction of the core, and is therefore susceptible to manufacturing errors in the width direction of the core. Conversely, the TM0 mode has an electric field parallel to the thickness direction of the core, and is therefore susceptible to manufacturing errors in the thickness direction of the core. Therefore, when the TM0 mode is used for the first input light 16a and the second input light 16b, the deviation X relative to the thickness T of the core 20 preferably satisfies expressions (4) and (5) (see...). Figure 4 ).

[0129] (4) Arm waveguide

[0130] First arm waveguide to fourth arm waveguide 14 (see...) Figure 3 For example, it can be implemented by a channel waveguide with a phase shift section (see Japanese Patent Application Publication No. 2021-148965). Here, we will describe how the first arm waveguide to the fourth arm waveguide 14 implemented by the channel waveguide with a phase shift section satisfies expressions (3) and (6).

[0131] Figure 7 This diagram illustrates the first to fourth arm waveguides 14, each with a phase-shifting portion 32. Each phase-shifting portion 32 is part of an arm waveguide (e.g., the first arm waveguide 14a) and is assigned a different optical path length than the other arm waveguide 14 (e.g., the second arm waveguide 14b). The other portions of the arm waveguide 14 (i.e., portions other than the phase-shifting portions) will be referred to hereinafter as "non-phase-shifting portions." The non-phase-shifting portions of a particular arm waveguide 14 (e.g., the first arm waveguide 14a) have the same optical path length as the non-phase-shifting portions of all the other waveguides 14 (e.g., the second to fourth arm waveguides 14d).

[0132] In the following description, the phase shift section of the first arm waveguide 14a (see...) Figure 7 This will be referred to as "first phase shifter 32a". The same applies to the phase shifters of the other arm waveguides 14. Figure 8 This is a plan view of the core 34 of the i-th phase shifter 32 (where i is an integer from 1 to 4, the same below). The i-th phase shifter 32 is, for example, a channel waveguide with a width Wi and a length Li, such as... Figure 8 As illustrated. Core 34 is a reference. Figure 4 A portion of the core 20 of the described optical waveguide 24.

[0133] Expression (15) is an expression that exemplifies the phase Φi assigned to the i-th split beam (e.g., the first split beam 18a) by the i-th arm waveguide (e.g., the first arm waveguide 14a).

[0134] [Mathematical Expression 23]

[0135]

[0136] It should be noted that Φ0 is the phase imparted by the non-phase-shifted portion of each arm waveguide 14 (e.g., the first arm waveguide 14a) to the separated light (e.g., the first separated light 18a) propagating through that arm waveguide. eff (λ, W i ) is the effective refractive index of the separated light propagating through the i-th phase shift section 32. N is... eff (λ, W i () represents the wavelength λ and the width W of the core 34. i The function.

[0137] For example, N eff (λ, W i N can be calculated using the finite element method. eff (λ, W i The value is calculated based on the dimensions (e.g., width or thickness) and shape (e.g., sidewall angle) of the cross-section of the core 34, the refractive index of the material of the core 34, and the refractive index of the material of the cladding surrounding the core 34.

[0138] Substituting Φ1 to Φ4 given by expression (15) into expression (8) produces expression (16). However, it should be noted that Φ1 = Φ3 and Φ2 = Φ4 have been set for simplification.

[0139] [Mathematical Expression 24]

[0140]

[0141] Figure 9 This is a diagram illustrating an example of the relationship between Φ and wavelength λ obtained from expression (16). Figure 9 This is a graph calculated through simulation. The vertical axis is Φ - π / 2. The horizontal axis is the wavelength λ. Φ - π / 2 is a portion of the phase error Δθ, and this portion is generated from the first arm waveguide 14a to the fourth arm waveguide 14d.

[0142] Used for Figure 9 The simulated arm waveguide 14 is a channel waveguide with a core made of Si and a cladding made of SiO2. The core of these arm waveguides 14 has the characteristics used in... Figure 5 The simulated 2×2 MMI has the same core thickness (i.e., 220 nm). It is assumed that the mode of light propagating through arm waveguide 14 is... Figure 5 The mode used in the simulation (i.e., TE0). Several expressions (17) indicate the size of the phase shifter 32 used in the simulation.

[0143] [Mathematical Expression 25]

[0144]

[0145] In expression (17), Wi and Li are values ​​obtained through a genetic algorithm to minimize the worst (i.e., the maximum) value of |Δθ|. Δθ is based on expressions (11), (16), and Figure 5 illustrative 1' + It is calculated based on the relationship between 2' and wavelength λ.

[0146] However, it should be noted that Wi and Li are chosen to minimize the worst-case scenario such that Φ - π / 2 becomes zero when the deviation X is zero and λ = λ0. λ0 is the wavelength described in "(3) Separator". The range for minimizing the worst-case scenario is the range that satisfies 1.525 μm ≤ λ ≤ 1.57 μm and -25 nm ≤ X ≤ 25 nm.

[0147] Figure 9 The solid line 36 in the figure represents the width Wi of each phase shift section (see [reference]). Figure 8 The graph is obtained when the deviation X (e.g., manufacturing error) of the width Wi of each phase shift section is 0 nm. The dashed line 38 is the graph obtained when the deviation X of the width Wi of each phase shift section is 25 nm. The dotted line 40 is the graph obtained when the deviation X of the width Wi of each phase shift section is -25 nm.

[0148] With a deviation X of 0 nm, Φ - π / 2 is 0° at wavelength λ0, which is approximately 1.5475 μm from the center wavelength of the horizontal axis, as shown by solid line 36. Furthermore, with λ = λ0 and X = 0, the partial derivative of Φ with respect to wavelength λ is negative, as shown by solid line 36.

[0149] Furthermore, when λ = λ0 and X = 0, the partial derivative of Φ with respect to the deviation X is positive, which can be clearly understood from the dashed line 38 and the dotted line 40. Therefore, when the wavelength λ = λ0 and the deviation X = 0, the arm waveguide 14 satisfies expressions (3) and (6).

[0150] That is, the arm waveguide 14 that satisfies expressions (3) and (6) when λ is a specific wavelength λ0 and the deviation X is 0 can be realized by a channel waveguide with a phase shift section, where the deviation X is the manufacturing error of the core width. Additionally, in Figure 9 In the example shown, expressions (3) and (6) are satisfied over a wide range of λ from 1.525 nm to 1.57 nm and deviation X from -25 nm to 25 nm.

[0151] Wavelength dependence of Φ

[0152] Expression (3) indicates the wavelength dependence that Φ satisfies. The reason why the arm waveguide 14 with phase shift section 32 can satisfy expression (3) will be described. First, the partial derivative of λ is performed on the rightmost expression in expression (16) to obtain the partial derivative of Φ with respect to λ (i.e., the left side of expression (3)). Expression (18) is obtained by this partial derivative.

[0153] [Mathematical Expression 26]

[0154]

[0155] It is well known that the greater the increase in wavelength λ, the greater the leakage of the electric field into the cladding. This "electric field" refers to the electric field of light propagating through the core (the same applies below).

[0156] Therefore, the greater the increase in wavelength λ, the stronger the influence of the cladding material's refractive index on the effective refractive index of the core. The cladding material's refractive index is lower than that of the core material. Therefore, the greater the increase in wavelength λ, the greater the decrease in the core's effective refractive index. Thus, the effective refractive index N... eff The partial derivative of (λ, W1) with respect to wavelength λ is negative. Similarly, the effective refractive index N... eff The partial derivative of (λ, W2) with respect to wavelength λ is also negative.

[0157] The larger the cross-sectional area of ​​the core, the more concentrated the electric field is in the core. Therefore, the larger the cross-sectional area of ​​the core, the smaller the decrease in effective refractive index due to the increase in wavelength λ. Therefore, when the phase shift section 32 satisfies W1 < W2, expression (19) holds.

[0158] [Mathematical Expression 27]

[0159]

[0160] If the phase shifter 32 further satisfies L2 / L1 ≤ 1, the partial derivative of Φ with respect to λ is always negative, which can be clearly understood from expressions (18) and (19). That is, expression (3) holds. However, it should be noted that there are cases where expression (3) holds even if L2 / L1 ≤ 1 is not present.

[0161] Dependence of manufacturing error (deviation X) on Φ

[0162] Expression (6) indicates the dependence of Φ on manufacturing error (i.e., deviation X). The reason why the arm waveguide 14 with phase shift section 32 can satisfy expression (6) will be described.

[0163] First, perform a partial derivative of the rightmost expression in expression (16) with respect to the deviation w of the core width W to obtain the partial derivative of Φ with respect to w. Expression (20) is the expression obtained through this partial derivative.

[0164] The deviation w is of the form of the deviation X. The deviation of the core width W will be expressed by “w” in the description of expression (20) to avoid confusion.

[0165] [Mathematical Expression 28]

[0166]

[0167] It is well known that the larger the cross-sectional area of ​​the core, the stronger the electric field's constraint on the core. Therefore, the larger the cross-sectional area of ​​the core, the stronger the influence of the core's material refractive index on the effective refractive index. The core's material refractive index is higher than that of the cladding material, and therefore, the greater the increase in deviation w (i.e., the change in width W), the greater the increase in the core's effective refractive index. Therefore, the effective refractive index N... eff The partial derivative of (λ, W1) with respect to the deviation w is positive. Similarly, the effective refractive index N... eff The partial derivative of (λ, W2) with respect to the deviation w is positive.

[0168] The larger the cross-sectional area of ​​the core (hereinafter referred to as the core cross-sectional area), the more concentrated the electric field is in the core. Therefore, the larger the core cross-sectional area, the less electric field leaks out of the core. Therefore, the larger the core cross-sectional area, the smaller the increase in effective refractive index due to the increase in core cross-sectional area. Therefore, when the phase shift section 32 satisfies W1 < W2, expression (21) holds.

[0169] [Mathematical Expression 29]

[0170]

[0171] If the phase shifter 32 further satisfies L2 / L1 ≤ 1, the partial derivative of Φ with respect to w (i.e., the left side of expression (20)) is always positive, which can be clearly understood from expressions (20) and (21). The deviation w is in the form of the deviation X of the structural parameter, and therefore, expression (6) holds when L2 / L1 ≤ 1 holds. However, it should be noted that there are cases where expression (6) holds even if L2 / L1 ≤ 1 does not hold.

[0172] W1 < W2 and L2 / L1 ≤ 1 are the same conditions that hold for expression (3) (see “Wavelength dependence of Φ”).

[0173] (5) Phase error Δθ

[0174] The phase error Δθ in an optical 90-degree mixer having a splitter 10 (see “(3) Splitter”) implemented by a 2×2 MMI and an arm waveguide 14 (see “(4) Arm Waveguide”) implemented by a channel waveguide with a phase shift section will be described. Figure 10 This is a graph illustrating an example of the relationship between phase error Δθ (see expression (13)) and wavelength λ. The vertical axis is the phase error Δθ. The horizontal axis is the wavelength λ. Figure 10 It is a curve calculated through simulation.

[0175] Separator 10 for simulation (see Figure 3 ) is used for Figure 5 The simulated 2×2 MMI. Arm waveguide 14 used for the simulation (see...) Figure 7 ) is used for Figure 9 The simulated channel waveguide.

[0176] Figure 10 The solid line 42 in the graph represents the graph obtained when the deviation X (e.g., manufacturing error) of the core width of each splitter 10 and each arm waveguide 14 is 0 nm. The dashed line 44 represents the graph obtained when the deviation X is 25 nm. The dotted line 46 represents the graph obtained when the deviation X is -25 nm.

[0177] With a deviation X of 0 nm, the phase error Δθ is approximately zero over a wide wavelength range (1.525 μm to 1.57 μm) on the horizontal axis, as shown by solid line 42. Furthermore, even with a core width deviation X of ±25 nm, the phase error Δθ over the wavelength range represented by the horizontal axis is at most ±0.72°, as shown by dashed line 44 and dotted line 46. This value is significantly smaller than the allowable variation range of the phase error Δθ for a 90-degree optical mixer, which is ±5°.

[0178] Therefore, according to the implementation method, the increase in phase error Δθ caused by the increase in deviation X of structural parameters (more precisely, the increase in the absolute value of deviation X) can be suppressed, while the increase in phase error Δθ caused by the change in wavelength can also be suppressed. Here, an example of deviation X is manufacturing error.

[0179] Figure 11 This is a diagram illustrating an example of the relationship between the phase error Δθ and wavelength λ of a 1×2 mm1 optical 90-degree mixer, where the first separator 10a and the second separator 10b are illustrative. The vertical axis represents the phase error Δθ. The horizontal axis represents the wavelength λ.

[0180] Figure 11The solid line 48 in the graph represents the curve obtained when the core width deviation X is 0 nm. The dashed line 50 represents the curve obtained when the core width deviation X is 25 nm. The dotted line 52 represents the curve obtained when the core width deviation X is -25 nm.

[0181] When the core width deviation X is 0 nm, the phase error Δθ is approximately zero over a wide wavelength range (1.525 μm to 1.57 μm) on the horizontal axis, as shown by solid line 48. However, when the core width deviation X (e.g., manufacturing error) is 25 nm, a phase error Δθ of -2.7° occurs, as shown by dashed line 50. Furthermore, when the core width deviation X is -25 nm, a phase error Δθ of 2.8° occurs, as shown by dotted line 52. The reason is that the first separator 10a and the second separator 10b formed by 1×2 MMIs do not satisfy expressions (4) and (5).

[0182] (6) How to use

[0183] The optical 90-degree mixer 8 according to the embodiment is used, for example, in a quadrature phase shift keying (QPSK) receiver. Specifically, the reference light LO is input to the first splitter 10a (see...). Figure 3 The phase-modulated signal light S is input to the second splitter 10b. The reference light LO is light with approximately the same wavelength as the signal light S. The phase of the signal light S is modulated with four values ​​spaced at 90° intervals (i.e., 0°, 90°, 180°, and 270°).

[0184] The first splitter 10a separates the reference light LO and inputs the separated reference light LO into the first combiner 12a and the second combiner 12b via the first arm waveguide 14a and the second arm waveguide 14b. Similarly, the second splitter 10b separates the signal light S and inputs the separated signal light S into the first combiner 12a and the second combiner 12b via the third arm waveguide 14c and the fourth arm waveguide 14d. The first combiner 12a and the second combiner 12b each mix the separated reference light LO and the separated signal light S, and output four interference beams In, Ip, Qn, and Qp with a 90° phase interval.

[0185] Interference beams In and Ip are input to a balanced photodetector (omitted in the figure) and converted into a first electrical signal. Interference beams Qn and Qp are input to different balanced photodetectors (omitted in the figure) and converted into a second electrical signal. Two orthogonal transmission signals are demodulated from the first and second electrical signals.

[0186] In the example above, the reference light LO is input to the first splitter 10a, and the signal light S is input to the second splitter 10b. However, it is also possible to input the signal light S to the first splitter 10a and the reference light LO to the second splitter 10b.

[0187] (7) Manufacturing method

[0188] Figure 12 This is a diagram illustrating an example of a method for manufacturing a light 90-degree mixer 8 according to an embodiment. Figure 12 It is along Figure 2 The cross-sectional view taken from lines IV, XII-IV, XII. See reference... Figure 4 The light 90-degree mixer 8 has a core 20 and a covering 22 surrounding the core. The covering 22 has, for example, a lower covering 54 and an upper covering 56.

[0189] First, the upper Si layer of the silicon-on-insulator (SOI) wafer is partially etched to form a core 20. Then, a SiO2 film is deposited on the SOI wafer with the formed core 20 to form an overlay layer 56. The optical 90-degree mixer 8 is formed using the above process. The underlay layer 54 is the buried oxide (BOX) layer of the SOI wafer.

[0190] (8) Modified Example

[0191] Figure 13 This is a plan view of a modified example 108 of the 90-degree light mixer 8. The structure of modified example 108 is similar to that of the reference example. Figure 2 and Figure 3 The structure of the light 90-degree mixer 8 is described. Therefore, the description of the parts common to the light 90-degree mixer 8 will be omitted or simplified.

[0192] Reference Figure 2 and Figure 3 The described optical 90-degree mixer 8 has a first arm waveguide 14a and a third arm waveguide 14c that intersect each other (see...). Figure 3 Conversely, Modified Example 108 has four arm waveguides 114 that bend 90° at its middle portion. In Modified Example 108, the separated light from the first input light 16a and the separated light from the second input light 16b are input to the first combiner 12a and the second combiner 12b through these four arm waveguides 114.

[0193] According to Modification 108, the arm waveguides 114 do not cross each other, and therefore, cross-loss (i.e., loss occurring at the cross-section of the optical waveguides) can be avoided. Furthermore, according to Modification 108, crosstalk at the cross-section of the arm waveguides can be avoided.

[0194] The core of the arm waveguide 114 is formed of Si (or SiN), and the cladding is formed of SiO2, which creates a large relative refractive index difference between the cladding and the core. Therefore, the radius of curvature of the curved portion of the arm waveguide 114 can be smaller. Because this structure is beneficial to reducing the size of the arm waveguide 114, it can further suppress the propagation loss at the arm waveguide 114.

[0195] According to this embodiment, the optical 90-degree mixer 8 is configured such that the phase error appearing at the separator 10 ( 1' + 2') is canceled out by the phase error (Φ - π / 2) that occurs at the arm waveguide, as shown in reference. Figures 2 to 10 As described. Therefore, according to the implementation, the increase in phase error Δθ caused by the increase in deviation of structural parameters (more precisely, the increase in the absolute value of the deviation) can be suppressed, while the increase in phase error Δθ caused by wavelength variation (more precisely, the increase in the absolute value of Δθ) can also be suppressed.

[0196] Although embodiments of the invention have been described above, these embodiments are exemplary and not limiting. For example, the first splitter 10a and the second splitter 10b can be optical elements other than a 2×2 MMI. The first splitter 10a and the second splitter 10b can be, for example, the splitter disclosed in Weijie Chang et al., “Inverse design and demonstration of an ultracompact broadband dual-mode 3 dB power splitter,” Optical Express, 2018, Vol. 26, No. 18, pp. 24135-24144 (which discloses a wavelength-dependent splitter that can control loss by providing multiple holes in the core). This splitter also enables control of the phase between the output ports.

[0197] According to this embodiment, each phase shifter in phase shifter 32 is a linear waveguide with a core of constant width. However, each phase shifter in phase shifter 32 can be an optical waveguide other than a linear waveguide. For example, each phase shifter in phase shifter 32 can be a tapered optical waveguide with a core whose width gradually increases or decreases.

[0198] The optical waveguide 24 according to this embodiment is a silicon photonics-based optical waveguide. However, the optical waveguide 24 can be an optical waveguide based on technologies other than silicon photonics. For example, the optical waveguide 24 can be an optical waveguide based on a planar optical circuit (PLC) in which both the core 20 and the cladding layer 22 are formed of SiO2. Alternatively, the optical waveguide 24 can be an indium phosphide (InP) waveguide or a gallium arsenide (GaAs) waveguide. Alternatively, the optical waveguide 24 can be an optical waveguide in which the core 20 is made of SiN. In this case, the lower cladding layer 54 is made of SiO2, for example, while the upper cladding layer 56 is made of SiO2 or air. Alternatively, the optical waveguide 24 can be an optical waveguide based on a reference... Figure 12 The optical waveguide of the overlay 56 is omitted in the description (i.e., the optical waveguide in which the overlay 56 is formed of air).

[0199] According to this embodiment, the optical waveguide 24 is a channel waveguide. However, the optical waveguide 24 can be an optical waveguide other than a channel waveguide. For example, the optical waveguide 24 can be any of a ribbed waveguide, a high-mesh waveguide, and a ridged waveguide.

[0200] In a channel waveguide, the light is strongly confined to the core, and therefore the radius of curvature of the curved portion of the arm waveguide 114 can be made very small. A portion of the light propagating through the core leaks from the thick rib portion of the ribbed waveguide to the thin planar portion, and is therefore less affected by the sidewall roughness of the core. Thus, the ribbed waveguide can reduce losses at the arm waveguide 14.

[0201] According to reference Figure 2 In the described embodiment, the arm waveguide 14 crosses at one location. However, the arm waveguide 14 can cross at multiple locations. This configuration allows the arm waveguide 14 to be manufactured shorter, and therefore, losses at the arm waveguide 14 can be reduced.

[0202] Deviation X is a manufacturing error in the implementation. However, deviation X is not necessarily a manufacturing error. For example, when the structural parameters are taken at their designed values ​​and λ is a specific wavelength λ0, the arm waveguide 14, etc., can be designed such that the phase error Δθ is a value other than zero (e.g., 0.05°). In such a case, deviation X is not a manufacturing error, but a deviation from the structural parameter value (i.e., the value of the structural parameter), relative to which the phase error Δθ becomes zero at the specific wavelength λ0.

Claims

1. A 90-degree light mixer, the 90-degree light mixer comprising: A first separator, the first separator having a first output port and a second output port different from the first output port; A second separator, which is different from the first separator, has a third output port and a fourth output port that is different from the third output port; A first combiner, the first combiner having a first input port and a second input port different from the first input port; A second combiner, which is different from the first combiner, has a third input port and a fourth input port that is different from the third input port; A first arm waveguide connects the first output port and the third input port; The second waveguide connects the second output port and the second input port. A third waveguide is provided, wherein the third waveguide connects the third output port and the first input port; as well as The fourth waveguide connects the fourth output port and the fourth input port. in, The first splitter splits the first light into a first split beam and a second split beam, outputting the first split beam from the first output port and the second split beam from the second output port. The second splitter splits the second light into a third split light and a fourth split light, outputting the third split light from the third output port and the fourth split light from the fourth output port. The first combiner combines the second split beam entering the first combiner via the second arm waveguide and the third split beam entering the first combiner via the third arm waveguide to generate a first interference beam and a second interference beam that is out of phase with the first interference beam. The second combiner combines the fourth split beam entering the second combiner via the fourth arm waveguide and the first split beam entering the second combiner via the first arm waveguide to generate a third interference beam and a fourth interference beam that is out of phase with the third interference beam. Each of the first and second splitters, the first waveguide to the fourth waveguide, and the first and second combiners is part of an optical waveguide having a core and a cladding surrounding the core. The optical waveguide satisfies the following expressions (1) to (7) when λ is a specific wavelength and X is zero, where X is the deviation of the parameter from a first value, and the parameter is based on the dimensions of the cross-section of the core. [Mathematical Expression 1] [Mathematical Expression 2] [Mathematical Expression 3] [Mathematical Expression 4] [Mathematical Expression 5] [Mathematical Expression 6] [Mathematical Expression 7] [Mathematical Expression 8] Where λ is the wavelength of the first light and the second light, the cross section is a cross section perpendicular to the direction of light propagating through the core, and the parameter is the width or the thickness of the core. The difference is obtained by subtracting the second phase of the electric field of the second separated light from the first phase of the electric field of the first separated light, where the first phase is the phase at the first output port and the second phase is the phase at the second output port. The difference is obtained by subtracting the fourth phase of the electric field of the fourth splitting light from the third phase of the electric field of the third splitting light, where the third phase is the phase at the third output port and the fourth phase is the phase at the fourth output port. Φ is the phase assigned by expression (8), where Φ1 is the phase assigned to the first splitting light by the first arm waveguide, Φ2 is the phase assigned to the second splitting light by the second arm waveguide, Φ3 is the phase assigned to the third splitting light by the third arm waveguide, and Φ4 is the phase assigned to the fourth splitting light by the fourth arm waveguide. m is an integer, k is +1 or -1, and the unit of phase is radians.

2. The optical 90-degree mixer according to claim 1, wherein, The actual value of the parameter of the optical waveguide is obtained by adding a specific value of the deviation to the first value.

3. The optical 90-degree mixer according to claim 1 or 2, wherein, The first value changes along each path from the first light, the second light, and the first split light to the fourth split light.

4. The optical 90-degree mixer according to claim 1 or 2, wherein, Each of the first separator and the second separator is a 2×2 multimode interferometer, and Each of the first combiner and the second combiner is a 2×2 multimode interferometer.

5. The optical 90-degree mixer according to claim 1 or 2, wherein, The and stated And Φ1 to Φ4 are functions obtained when the wavelengths of the first light and the second light are consistent with each other.

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