Optical filter, method for manufacturing optical filter, method for designing optical filter, device for designing optical filter, and computer-readable storage medium

Abstract

The invention provides an optical filter capable of improving tolerance, a manufacturing method, a design method and a design device of the optical filter, and a computer readable storage medium. Provided is a method for manufacturing an optical filter provided with two or more waveguides having four or more sections, the modes of light propagating through the four or more sections being two or more. The manufacturing method has a step for designing the lengths of the four or more sections, and a step for forming the two or more waveguides on the basis of the lengths of the four or more sections. The step of designing includes a step of designing the lengths of the four or more sections on the basis of a differential of the propagation constant of the sections relating to the temperature and the width of the sections.

Description

Technical Field

[0001] The invention relates to an optical filter, a manufacturing method, a design method, a design device and a computer-readable storage medium of the optical filter. Background Art

[0002] Silicon photonics, which forms optical elements on silicon, is attracting attention. For example, a Mach-Zehnder interferometer is sometimes formed on the silicon layer of an SOI (Silicon on Insulator) substrate. The light is divided into TE0 mode and TE1 mode and propagates to multiple waveguides of the Mach-Zehnder interferometer. The temperature dependence of the spectrum is reduced by adjusting the length and width of the waveguide according to the mode (Non-Patent Document 1). A polarization rotation separator is set in the silicon waveguide to convert the mode of light (Non-Patent Document 2). Prior Art Literature Non-patent literature Non-patent document 1: “Broadband CMOS-compatible SOI temperature insensitive Mach-Zehnder interferometer” Peng Xing and Jaime Viegas OPTICS EXPRESS Vol. 23, No. 19 pp. 24098-24107 (2015) Non-patent document 2: “Polarization rotator-splitters in standard activesilicon photonics platforms” Wesley D. Sacher et al. OPTICS EXPRESS Vol. 22, No. 4 pp. 3777-3786 (2014) Summary of the invention Problems to be solved by the invention According to formula (9) of non-patent document 1, a waveguide can be designed so that the temperature dependence of the characteristic becomes small. For example, silicon is etched to form a waveguide. However, the width of the waveguide produces an error. The width of the waveguide changes, resulting in an increase in the temperature dependence of the characteristic. Therefore, the purpose of the present invention is to provide an optical filter capable of improving tolerance, a manufacturing method, a design method, a design device, and a computer-readable storage medium for an optical filter.

[0003] Means used to solve problems The manufacturing method of the optical filter involved in the present invention is a manufacturing method of the optical filter, wherein the optical filter has two or more waveguides, the two or more waveguides have four or more intervals, and the modes of light propagating in the four or more intervals are two or more. The manufacturing method includes a step of designing the lengths of the four or more intervals and a step of forming the two or more waveguides based on the lengths of the four or more intervals; the designing step includes a step of designing the lengths of the four or more intervals based on the differentials of the propagation constants of the intervals related to temperature and the widths of the intervals.

[0004] Effects of the Invention According to the present invention, it is possible to provide an optical filter capable of improving tolerance, a method for manufacturing the optical filter, a method for designing the optical filter, a designing device, and a computer-readable storage medium. BRIEF DESCRIPTION OF THE DRAWINGS

[0005] Figure 1 This is a schematic diagram illustrating the optical filter according to the first embodiment.

[0006] Figure 2 It is a cross-sectional view illustrating an optical filter.

[0007] Figure 3A This is a block diagram illustrating an optical filter design device.

[0008] Figure 3B This is a block diagram showing the hardware configuration of the control unit.

[0009] Figure 4A This is a flowchart illustrating a method for manufacturing an optical filter.

[0010] Figure 4B This is a flowchart illustrating a method for manufacturing an optical filter.

[0011] Figure 5A This is a cross-sectional view illustrating a method for manufacturing an optical filter.

[0012] Figure 5B This is a cross-sectional view illustrating a method for manufacturing an optical filter.

[0013] Figure 6 This is a schematic diagram illustrating an optical filter according to a comparative example.

[0014] Fig. 7A This is a diagram illustrating a spectrum in a comparative example.

[0015] Figure 7B This is a diagram illustrating a spectrum in a comparative example.

[0016] Figure 7CThis is a diagram illustrating a spectrum in a comparative example.

[0017] Fig.7D It is a graph showing the displacement amount in the comparative example.

[0018] Fig. 8A This is a diagram illustrating the spectrum in the first embodiment.

[0019] Figure 8B This is a diagram illustrating the spectrum in the first embodiment.

[0020] Figure 8C This is a diagram illustrating the spectrum in the first embodiment.

[0021] Fig.8D It is a diagram showing the displacement amount in the first embodiment.

[0022] Fig. 9A This is a diagram illustrating the spectrum in the first embodiment.

[0023] Fig. 9B This is a diagram illustrating the spectrum in the first embodiment.

[0024] Fig. 9C This is a diagram illustrating the spectrum in the first embodiment.

[0025] Fig.9D It is a diagram showing the shift amount.

[0026] Fig.10 It is a plan view illustrating an optical filter according to the second embodiment.

[0027] Fig.11 It is a plan view illustrating an optical filter according to the third embodiment.

[0028] Description of Reference Numerals 1: injection port; 2: injection port; 10, 12: substrate; 14, 14a: buried oxide layer; 16: waveguide core; 16a: silicon layer; 20, 22, 24, 26, 28, 29, 40, 42, 44, 46: waveguide; 24a, 24b, 26a, 26b, 54, 57, 62, 68, 74: interval; 30, 32: coupler; 50, 52, 56, 58, 60, 61, 63, 64, 66, 67 7, 69, 70, 72, 73, 75, 76: parts; 80, 81, 82, 83: directional couplers; 100, 101, 200, 300: optical filters; 110: design device; 111: control unit; 112: design unit; 113: first calculation unit; 114: second calculation unit; 115: third calculation unit; 116: CPU; 117: RAM; 118: ROM; 119: storage device; 120: interface. DETAILED DESCRIPTION

[0029] [Description of Embodiments of the Invention] First, the contents of the embodiments of the present invention will be listed and described.

[0030] One embodiment of the present invention is (1) a method for manufacturing an optical filter, wherein the optical filter includes two or more waveguides, the two or more waveguides have four or more sections, and the light propagating in the four or more sections has two or more modes, the manufacturing method includes a step of designing the lengths of the four or more sections, and a step of forming the two or more waveguides based on the lengths of the four or more sections, the designing step includes a step of designing the lengths of the four or more sections based on the differential of the propagation constant of the section with respect to temperature and the width of the section. By making the section length an appropriate size, tolerance can be improved.

[0031] (2) In the above (1), the step of designing the lengths of the four or more sections may include the step of designing the lengths of the four or more sections based on Mathematical Formula 1. By setting the section lengths to appropriate sizes, tolerance can be improved.

[0032] [Formula 1]

[0033] L1 to Ln: length of the interval β1 to βn: propagation constant for each interval T: Temperature λ: wavelength k: wave number FSR: The interval between the peaks of the spectrum w: The width of the interval.

[0034] (3) In the above (1) or (2), the four or more intervals include a first interval, a second interval, a third interval, and a fourth interval, and the step of designing the lengths of the four or more intervals may be a step of designing the length of the first interval, the length of the second interval, the length of the third interval, and the length of the fourth interval. By making the lengths of the four intervals appropriate, the tolerance can be improved.

[0035] (4) A method for designing an optical filter, wherein the optical filter comprises two or more waveguides, the two or more waveguides have four or more sections, the four or more sections have two or more modes of light propagating, and the lengths of the four or more sections are designed based on the differentials of the propagation constants of the sections with respect to temperature and the widths of the sections. By making the section lengths appropriate, tolerance can be improved.

[0036] (5) In the above (4), designing the lengths of the four or more sections may include designing the lengths of the four or more sections based on Mathematical Formula 1. By setting the section lengths to appropriate sizes, tolerance can be improved.

[0037] [Formula 1]

[0038] L1 to Ln: length of the interval β1 to βn: propagation constant for each interval T: Temperature λ: wavelength k: wave number FSR: The interval between the peaks of the spectrum w: The width of the interval.

[0039] (6) Based on the above (4) or (5), the four or more intervals include a first interval, a second interval, a third interval, and a fourth interval, and the lengths of the four or more intervals may be designed to be the length of the first interval, the length of the second interval, the length of the third interval, and the length of the fourth interval. By making the lengths of the four intervals appropriate, the tolerance can be improved.

[0040] (7) An optical filter design device, wherein the optical filter includes two or more waveguides, the two or more waveguides have four or more sections, the four or more sections have two or more modes of light propagating, and the design device is an optical filter design device including a design unit for designing the lengths of the four or more sections based on differentials of propagation constants of the sections with respect to temperature and widths of the sections. By making the section lengths appropriate, tolerance can be improved.

[0041] (8) In the above (7), designing the lengths of the four or more sections may include designing the lengths of the four or more sections based on Mathematical Formula 1. By setting the section lengths to appropriate sizes, tolerance can be improved.

[0042] [Formula 1]

[0043] L1 to Ln: length of the interval β1 to βn: propagation constant for each interval T: Temperature λ: wavelength k: wave number FSR: The interval between the peaks of the spectrum w: The width of the interval.

[0044] (9) Based on the above (7) or (8), the four or more intervals include a first interval, a second interval, a third interval, and a fourth interval, and the lengths of the four or more intervals may be designed to be the length of the first interval, the length of the second interval, the length of the third interval, and the length of the fourth interval. By making the lengths of the four intervals appropriate, the tolerance can be improved.

[0045] (10) A computer-readable storage medium storing a design program for an optical filter, wherein the optical filter includes two or more waveguides, the two or more waveguides have four or more sections, and the four or more sections have two or more modes of light propagating, and a computer functions as a design unit that designs the lengths of the four or more sections based on the differentials of the propagation constants of the sections with respect to temperature and the widths of the sections. By making the section lengths appropriate, tolerance can be improved.

[0046] (11) In the above (10), designing the lengths of the four or more sections may include designing the lengths of the four or more sections based on Mathematical Formula 1. By setting the section lengths to appropriate sizes, tolerance can be improved.

[0047] [Formula 1]

[0048] L1 to Ln: length of the interval β1 to βn: propagation constant for each interval T: Temperature λ: wavelength k: wave number FSR: The interval between the peaks of the spectrum w: The width of the interval.

[0049] (12) Based on the above (10) or (11), the four or more intervals include a first interval, a second interval, a third interval, and a fourth interval, and the lengths of the four or more intervals may be designed to be the length of the first interval, the length of the second interval, the length of the third interval, and the length of the fourth interval. By making the lengths of the four intervals appropriate, the tolerance can be improved.

[0050] (13) An optical filter comprising two or more waveguides and four or more sections provided in the two or more waveguides, wherein at least two or more modes propagate through the four or more sections. By setting the section length to an appropriate size, tolerance can be improved.

[0051] [Details of Embodiments of the Invention] The following is a description of specific examples of the optical filter, the manufacturing method, the design method, the design device, and the computer-readable storage medium according to the embodiments of the present invention with reference to the accompanying drawings. It should be noted that the present invention is not limited to these examples, but is represented by the claims, and is intended to include all changes within the meaning and scope equivalent to the claims.

[0052] <First embodiment> Figure 1 1 is a schematic diagram illustrating an optical filter 100 according to the first embodiment. The optical filter 100 is a Mach-Zehnder interferometer filter formed on a substrate 10. The substrate 10 is, for example, an SOI (Silicon on Insulator) substrate. Two edges of the substrate 10 are parallel in the X-axis direction. The other two edges are parallel in the Y-axis direction. The upper surface of the substrate 10 is parallel to the XY plane. The Z-axis direction is the normal direction of the substrate 10. The X-axis direction, the Y-axis direction, and the Z-axis direction are orthogonal to each other.

[0053] The optical filter 100 includes a waveguide 20 , a waveguide 22 , a waveguide 24 , a waveguide 26 , a waveguide 28 , a waveguide 29 , a coupler 30 , and a coupler 32 . The waveguides and the couplers are provided on a substrate 10 .

[0054] The coupler 30 and the coupler 32 are 3 dB couplers with two inputs and two outputs, and are directional couplers or the like.

[0055] The waveguide 20 has an injection port 1. The waveguide 28 has an emission port 2. The injection port 1 is located at one end of the substrate 10. The emission port 2 is located at the other end of the substrate 10. Figure 1The arrows in represent the light propagating in the optical filter 100. The light incident to the input port 1 is split, propagated, and combined in a plurality of waveguides and then emitted from the output port 2. In the waveguide, the front section refers to the portion close to the input port 1, and the rear section refers to the portion closer to the output port 2 than the front section.

[0056] The waveguides 20 and 22 extend parallel to the X-axis from one end of the substrate 10. The waveguides 20 and 22 are optically coupled to the input end of the coupler 30. The waveguides 24 and 26 are provided between the coupler 30 and the coupler 32, optically coupled to the output end of the coupler 30, and optically coupled to the input end of the coupler 32. The waveguides 28 and 29 are optically coupled to the output end of the coupler 32, and extend to the end of the substrate 10.

[0057] The optical filter 100 has four sections. The waveguide 24 has a section 24a and a section 24b. Between the coupler 30 and the coupler 32, the section 24a and the section 24b are arranged in sequence. The section 24a is coupled to the coupler 30. The section 24b is coupled to the coupler 32. The waveguide 26 has a section 26a and a section 26b. Between the coupler 30 and the coupler 32, the section 26a and the section 26b are arranged in sequence. The section 26a is coupled to the coupler 30. The section 26b is coupled to the coupler 32. One waveguide may include a plurality of sections. One waveguide may also function as one section.

[0058] The length of the interval 24a is L1. The length of the interval 24b is L2. The length of the interval 26a is L3. The length of the interval 26b is L4. In the design described later, the length of the interval is designed.

[0059] Figure 2 This is a cross-sectional view illustrating an optical filter 100, illustrating a cross section including a waveguide. The substrate 10 has a substrate 12, a buried oxide layer 14, and a waveguide core 16. The substrate 12 and the waveguide core 16 are formed of silicon (Si). The buried oxide layer 14 is formed of an insulator such as silicon oxide (SiO2). The buried oxide layer 14 is stacked on one surface of the substrate 12. The waveguide core 16 is buried in the buried oxide layer 14 and functions as a waveguide. The waveguide core 16 is part of the silicon layer. The silicon layer includes a platform not shown. The waveguide core 16 is separated from the platform. The thickness T1 of the waveguide core 16 is, for example, 220 nm. The distance T0 from the substrate 12 to the waveguide core 16 is, for example, 2 μm.

[0060] Light is incident on the incident port 1. The incident light propagates in the waveguide 20. In the coupler 30, the light is divided into the waveguide 24 and the waveguide 26. The ratio of the intensity of the divided light is, for example, 1:1.

[0061] Light propagates in the waveguide 24 and the waveguide 26. There are two or more light modes. For example, the mode of light propagating in the section 24a of the waveguide 24 is the TE0 mode. The mode of light propagating in the section 24b is the TE1 mode. The mode of light propagating in the section 26a of the waveguide 26 is, for example, the TE0 mode. The mode of light propagating in the section 26b is, for example, the TE1 mode. The mode conversion of light is performed between the section 24a and the section 24b of the waveguide 24. The mode conversion of light is performed between the section 26a and the section 26b of the waveguide 26.

[0062] The light propagating through the waveguide 24 and the light propagating through the waveguide 26 are incident on the coupler 32 and are combined in the coupler 32. The combined light propagates through the waveguide 28 and is emitted from the emission port 2.

[0063] As described above, the optical filter 100 branches incident light into a plurality of waveguides, propagates the light in two different modes (for example, TE0 mode and TE1 mode), and combines the two lights to output the combined light.

[0064] (Design device) Figure 3A This is a block diagram illustrating a design device 110 for the optical filter 100 . The design device 110 designs the length of the section of the optical filter 100 .

[0065] The design device 110 includes a control unit 111. The control unit 111 is a computer or the like, and functions as a design unit 112. The design unit 112 includes a first calculation unit 113, a second calculation unit 114, and a third calculation unit 115. The functions of each unit of the control unit 111 will be described later.

[0066] Figure 3B 1 is a block diagram showing the hardware configuration of the control unit 111. Figure 3B As shown, the control unit 111 includes a CPU (Central Processing Unit) 116, a RAM (Random Access Memory) 117, a ROM (Read Only Memory) 118, a storage device 119, and an interface 120. The CPU 116, the RAM 117, the ROM 118, the storage device 119, and the interface 120 are connected to each other via a bus or the like. The RAM 117 is a volatile memory that temporarily stores programs and data. The storage device 119 is a solid state drive (SSD: Solid State Drive) such as a flash memory, a hard disk drive (HDD: Hard Disk Drive), etc. The storage device 119 stores programs, etc.

[0067] The CPU 116 executes the program stored in the RAM 117, thereby realizing the design unit 112 in the control unit 111. Each part of the control unit 111 may be hardware such as a circuit.

[0068] (Calculation of interval length) The design device 110 designs the length of the interval of the optical filter 100 based on the following equation 2. The matrix on the left side of equation 2 may be expressed as matrix A. The column vector on the left side may be expressed as L. The first term on the right side may be expressed as B and the second term may be expressed as C.

[0069] [Formula 2]

[0070] In Mathematical Formula 2, β1 to βn are propagation constants of the interval. L1 to Ln are the lengths of the intervals. Suffixes 1 to n in β and L are numbers corresponding to the intervals. For example, β1 is the propagation constant in the interval 24a of the waveguide 24. L1 is the length of the interval 24a. T represents the temperature of the optical filter 100. λ is the wavelength of light propagating in the optical filter 100. k is the wave number. w is the width of the interval. FSR is the interval between adjacent peaks in the transmission spectrum of the optical filter 100. φ is the sum of the changes in the phase of light generated when connecting different intervals.

[0071] The matrix A on the left is explained. Matrix A is a matrix with 4 rows and n columns. The components of the first row of matrix A are partial differentials of the propagation constant related to temperature T. The components of the second row are partial differentials of the propagation constant related to temperature T and wavelength λ. The components of the third row are partial differentials of the propagation constant related to wave number k. The components of the fourth row are partial differentials of the propagation constant related to temperature T and width w of the interval. The components of the column vector L on the left are the lengths of the intervals.

[0072] The first term on the right is the column vector B. The numerator of the third row of the column vector B is the square of the wavelength λ. The denominator is the FSR. The first, second, and fourth rows are zero.

[0073] The second term on the right is the column vector C, which is sometimes recorded as a correction term. The first row of the column vector C is the partial differential of the phase change φ with respect to temperature T. The second row is the partial differential of the phase change φ with respect to temperature T and wavelength λ. The third row is the partial differential of the phase change φ with respect to wave number k. The fourth row is the partial differential of the phase change φ with respect to temperature T and the width w of the interval.

[0074] The propagation constant is proportional to the refractive index of the interval and depends on the width of the interval. The propagation constant is determined by determining the width of the interval and the matrix elements of the matrix A are determined. The elements of the column vector B are determined by the wavelength λ of the light propagating in the optical filter 100 and the size of the FSR. The phase change φ depends on the shape of the waveguide. The phase change φ is determined by determining the shape of the waveguide, and the components of the column vector C are also determined.

[0075] The temperature of the optical filter 100 may change, and the width of the waveguide may have errors. By designing the interval length based on the above-mentioned mathematical formula, even when the temperature changes and the width changes, the change in characteristics can be suppressed.

[0076] like Figure 1 As shown, the optical filter 100 has interval 24a, interval 24b, interval 26a and interval 26b. The lengths L1, L2, L3 and L4 of these four intervals are calculated. By setting n=4 in mathematical formula 2, mathematical formula 3 is obtained. In mathematical formula 3, matrix A is a 4×4 matrix. Vector L, vector B and vector C are column vectors of 4 rows respectively.

[0077] [Formula 3]

[0078] In design, the second terms (correction terms) on the right sides of equations 2 and 3 may be considered or ignored. When each component of the second term on the right side of equation 2 is set to zero, equation 4 is obtained.

[0079] [Formula 4]

[0080] When n=3 in Math 4, Math 5 is obtained. Math 5 is used in the design example described later.

[0081] [Formula 5]

[0082] (Manufacturing method) Figure 4A as well as Figure 4B 2 is a flow chart illustrating a method for manufacturing the optical filter 100. Figure 4A As shown, a design process is performed to design the length and width of the waveguide (process S1). The wafer is processed to form the waveguide based on the design (process S2).

[0083] Figure 5A as well as Figure 5B 2 is a cross-sectional view illustrating a method for manufacturing the optical filter 100. Figure 5A As shown in FIG. 1 , a buried oxide layer 14a and a silicon layer 16a are sequentially stacked on one surface of the substrate 12. A resist pattern (not shown) is provided on the silicon layer 16a. Figure 5B As shown, the silicon layer 16a is etched to form the waveguide core 16 from the silicon layer 16a. A silicon oxide layer is further stacked on the buried oxide layer 14a to form the buried oxide layer 14. The optical filter 100 is formed by cutting the wafer.

[0084] As described above, the waveguide core 16 is manufactured by etching the silicon layer 16a. The width may vary. In the first embodiment, the deterioration of characteristics due to the variation in width is suppressed.

[0085] Figure 4B This is a flowchart that illustrates the design process. Figure 4A The first calculation unit 113 of the control unit 111 calculates the matrix A and the column vector B (step S10). The first calculation unit 113 sweeps the width of the interval and calculates the matrix elements of the matrix A corresponding to each width. The first calculation unit 113 calculates the λ of the column vector B based on the wavelength of the light and the FSR. 2 / FSR.

[0086] The third calculation unit 115 calculates L1, L2, L3, and L4 in the column vector L using the matrix A and column vector B obtained in step S10 (step S12). At the time of step S12, the correction term (column vector C) is not considered, and the lengths L1, L2, L3, and L4 of the intervals corresponding to the width of the sweep are calculated.

[0087] The second calculation unit 114 calculates the correction term (process S14). The third calculation unit 115 also calculates the length of the interval in consideration of the correction term (process S16). In detail, an appropriate value is selected from the width and interval length obtained by process S12. If the width is larger, it is easier to manufacture the waveguide. The shorter the interval of the waveguide, the more the size of the optical filter 100 can be suppressed. In order to strike a balance between productivity and miniaturization, a larger width and a shorter interval is effective. For example, the third calculation unit 115 selects a width and interval length that meet such requirements, and adds the column vector C to the selected interval length. That is, the interval length is calculated using mathematical formula 2 (process S16). As described above, Figure 4B The processing is finished.

[0088] (Comparative Example) Figure 6Schematic diagram illustrating an optical filter 101 involved in a comparative example. The optical filter 101 has three sections. The waveguide 26 has a section 26a and a section 26b. The waveguide 24 functions as a section. The mode of light propagating in the waveguide 24 is the TE1 mode. The mode of light propagating in the section 26a of the waveguide 26 is the TE0 mode. The mode of light propagating in the section 26b is the TE0 mode. The width of the waveguide 24 is 600nm. The width of the section 26a is 400nm. The width of the section 26b is 270nm.

[0089] In the calculation of the interval length in the comparative example, the mathematical formula 6 is used. [Formula 6]

[0090] Mathematical formula 6 includes three interval lengths L1, L3, and L4, and does not include the interval length L2, nor the differential of the propagation constant related to temperature and width. The interval lengths L1, L3, and L4 are calculated by mathematical formula 6. The result of the calculation is that the interval length L1 of the waveguide 24 is 253.6 μm. The interval length L3 of the interval 26a is 31.7 μm. The interval length L4 of the interval 26b is 326.7 μm.

[0091] (spectrum) The optical filter is applied to the wavelength division multiplexing method (WDM) to calculate the spectrum in the wavelength band of the C band.

[0092] (CWDM) 7A to 8D It is an example of CWDM (Coarse Wavelength Division Multiplexing).

[0093] FIG. 7A to FIG. 7D Shows a comparative example. FIG. 7A to FIG. 7D The horizontal axis represents the wavelength of light. 7A to 7C This is a diagram illustrating an example of a spectrum calculated for the optical filter 101 of the comparative example. 7A to 7C The vertical axis of represents the transmittance of light. The solid line is an example of a temperature of 20°C. The dashed line is an example of a temperature of 40°C. The dotted line is an example of a temperature of 60°C. The FSR is 10 nm.

[0094] Fig. 7A This is the spectrum when the error in the width of the interval is 0 nm (Δw=0 nm). That is, the width of all intervals is equal to the designed value. Figure 7B This is the spectrum when the error in the width of the interval is -10nm (Δw = -10nm). The width of each of the three intervals is 10nm narrower than the designed value. Figure 7CThis is the spectrum when the error in the width of the interval is +10 nm (Δw = +10 nm). The width of each of the three intervals is 10 nm wider than the designed value.

[0095] Fig.7D is a graph showing the displacement amount in the comparative example, showing that 7A to 7C The wavelength shift is calculated from the spectrum. Fig.7D The vertical axis represents the shift of the spectrum, which indicates the amount of deviation of the wavelength of the spectrum relative to the temperature change of 1K. The solid line represents the example of Δw=0nm, which is Fig. 7A The dotted line represents the case where Δw = -10nm. Figure 7B The dotted line represents the case of Δw=+10nm. Figure 7C The amount of displacement in .

[0096] like Fig. 7A as well as Fig.7D As shown in the figure, when Δw = 0 nm, the shift of the spectrum is close to zero at any wavelength in the wavelength range shown in the graph. Figure 7B As shown in the figure, when Δw = -10nm, as the temperature rises, the spectrum shifts to the negative direction at any wavelength in the wavelength range in the graph. Fig.7D As shown in Figure 1, the shift is less than -20 pm per 1K temperature. Figure 7C As shown in the figure, when Δw = +10nm, as the temperature rises, the spectrum shifts in the positive direction at any wavelength in the wavelength range in the graph. Fig.7D As shown, the shift amount is more than +10 pm per 1K temperature.

[0097] FIG. 8A to FIG. 8D The calculation results for the optical filter 100 of the first embodiment are shown. The parameters used for the calculation are as follows. Figure 1 In the optical filter 100, the mode of light propagating in the section 24a of the waveguide 24 is the TE0 mode, and the mode of light propagating in the section 24b is the TE1 mode. The mode of light propagating in the section 26a of the waveguide 26 is the TE0 mode, and the mode of light propagating in the section 26b is the TE1 mode. The width of the section 24a is 390nm. The width of the section 24b is 720nm. The width of the section 26a is 1200nm. The width of the section 26b is 600nm.

[0098] In the calculation of the interval lengths L1 to L4 in the first embodiment, Formula 5 is used with the components of the vector C (the second term on the right side) in Formula 3 being zero. In other words, Figure 4BThe steps S10 and S12 are performed, and the steps S14 and S16 are not performed, and the interval lengths are calculated. The result of the calculation is that the interval length L1 of the interval 24a is 723.7 μm. The interval length L2 of the interval 24b is 237.5 μm. The interval length L3 of the interval 26a is 525.9 μm. The interval length L4 of the interval 26b is 109.4 μm.

[0099] FIG. 8A to FIG. 8C This is a diagram illustrating an example of a spectrum in Embodiment 1. The spectrum of the optical filter 100 when the parameters are set to the above-mentioned values ​​is shown in the diagram. FIG. 8A to FIG. 8D The horizontal axis represents the wavelength of light. FIG. 8A to FIG. 8C The vertical axis represents the transmittance of light. Fig. 8A This is the spectrum when the error in the width of the interval is 0 nm (Δw = 0 nm). The width of each of the four intervals is equal to the design value. Figure 8B This is the spectrum when the error in the width of the interval is -10nm (Δw = -10nm). The width of each of the four intervals is 10nm narrower than the design value. Figure 8C This is the spectrum when the error in the width of the interval is +10 nm (Δw = +10 nm). The width of each of the four intervals is 10 nm wider than the design value. Fig.8D is a diagram showing the displacement amount in the first embodiment, indicating FIG. 8A to FIG. 8C The wavelength shift of the spectrum. Fig.8D The vertical axis represents the shift amount of the spectrum, which indicates the amount by which the wavelength of the spectrum deviates from the temperature change of 1K.

[0100] exist FIG. 8A to FIG. 8C In each case, the three spectra almost overlap. Fig.8D As shown, when Δw=0nm, the shift of the spectrum is within about -1pm per 1K temperature. When Δw=-10nm, the shift is within about -2pm per 1K temperature. When Δw=+10nm, the shift is within -2pm per 1K temperature. The shift of the first embodiment is about 1 / 10 of the shift of the comparative example.

[0101] (DWDM) Next, an example in which the optical filter 100 is used for DWDM (Dense Wavelength Division Multiplexing) will be described.

[0102] The optical filter is designed based on Mathematical Formula 5. The following represents the parameters used for calculating the spectrum. The mode of light propagating in the section 24a of the waveguide 24 is the TE0 mode, and the mode of light propagating in the section 24b is the TE1 mode. The mode of light propagating in the section 26a of the waveguide 26 is the TE0 mode, and the mode of light propagating in the section 26b is the TE1 mode. The width w1 of the section 24a of the waveguide 24 is 390nm, and the section length L1 is 9.0mm. The width w2 of the section 24b of the waveguide 24 is 720nm, and the section length L2 is 3.0mm. The width w3 of the section 26a of the waveguide 26 is 1200nm, and the section length L3 is 6.6mm. The width w4 of the section 26b of the waveguide 26 is 600nm, and the section length L4 is 1.4mm.

[0103] 9A to 9C This is a diagram illustrating an example of the spectrum in the first embodiment, and illustrates the spectrum of the optical filter 100 when the parameters are set to the above-mentioned values. The FSR is 0.8 nm. Fig. 9A This is the spectrum when the error in the width of the interval is 0 nm (Δw=0 nm). Fig. 9B This is the spectrum when the error in the width of the interval is -10 nm (Δw = -10 nm). Fig. 9C This is the spectrum when the error in the width of the interval is +10 nm (Δw=+10 nm). Fig.9D It is a graph showing the shift amount of the spectrum.

[0104] exist 9A to 9C In each case, the three spectra almost overlap. Fig.9D As shown, when Δw=0nm, the shift of the spectrum is within about -1pm per 1K temperature. When Δw=-10nm, the shift is within the range of -2pm to 0.5pm per 1K temperature. When Δw=+10nm, the shift is within the range of -3pm to 0.5pm per 1K temperature. According to the first embodiment, even in the case where the width of the waveguide changes by ±10nm from the design value in both DWDM and CWDM, the absolute value of the wavelength shift of the spectrum relative to the temperature change can be suppressed to a few pm / K.

[0105] According to the first embodiment, the optical filter 100 has a waveguide 24 and a waveguide 26. The waveguide 24 has a section 24a and a section 24b. The waveguide 26 has a section 26a and a section 26b. Two modes (TE0 mode and TE1 mode) propagate in four sections. The length of the section is designed based on the differential of the propagation constant βn with respect to the temperature T and the width w of the section. By making the section length an appropriate size, the tolerance with respect to the manufacturing error can be improved. Even if the width of the waveguide deviates from the design value, the temperature dependency can be suppressed and the change of the characteristics can be suppressed.

[0106] For example, Fig.8D as well as Fig.9D As shown, when the width of the waveguide changes by ±10 nm from the design value, the shift amount is about several pm per temperature 1 K. In other words, even when there is an error in the width, the shift of the spectrum caused by the temperature change can be suppressed.

[0107] The length of the interval is designed based on Math 2 to Math 5. The matrix A on the left includes the differential of the propagation constant related to temperature T, the differential related to temperature T and wavelength λ, the differential related to wave number k, and the differential related to temperature T and width w. The column vector on the left includes the interval lengths L1 to Ln. The first term on the right includes wavelength λ and FSR. The second term on the right of Math 2 and Math 4 includes the phase change φ. The interval lengths L1 to Ln can be calculated. The temperature dependence of the characteristics can be suppressed and the tolerance can be improved.

[0108] Figure 1 The optical filter 100 has four sections. When the number of sections is four (n=4), the section lengths L1 to L4 are designed using Mathematical Formula 3. In the optical filter 100 , even when the width of the waveguide changes, the temperature dependency can be suppressed.

[0109] In the design process, you can use Mathematical Formula 2 or Mathematical Formula 3, or you can use Mathematical Formula 4 or Mathematical Formula 5. Fig.8D as well as Fig.9D As shown, even without including the correction term (the second term on the right side of equation 2 and equation 3), the shift of the spectrum relative to the change in width can be suppressed. The amount of calculation when the design interval is long can be reduced. By considering the correction term and performing the design, the change in characteristics can be further suppressed.

[0110] like Figure 1 As shown, the optical filter 100 has two waveguides 24 and a waveguide 26, and has four intervals 24a, interval 24b, interval 26a, and interval 26b. The number of intervals can be more than 4, or more than 5. Let n in Mathematical Formula 2 and Mathematical Formula 4 be the number of intervals, and design the length of each interval. In Mathematical Formula 3 and Mathematical Formula 5, n=4, and the matrix on the left is a 4×4 square matrix. When the number of intervals n is more than 5, the matrix is ​​not a square matrix. By making the generalized inverse matrix of the matrix act from the left, the interval length can be calculated.

[0111] There are two or more modes of light propagating in four or more intervals. Figure 1 In the example, the TE0 mode and the TE1 mode are propagated. The modes may be three or more, and for example, the TM0 mode may be propagated in addition to the TE0 mode and the TE1 mode.

[0112] In the design process, the width of the interval is determined to determine the propagation constant βn and calculate each term in the matrix A. The interval length L1 to Ln corresponding to the width is calculated using Mathematical Formula 2. Figure 5A as well as Figure 5B As shown, the waveguide is manufactured by etching the silicon layer 16a. If the width is small, it is difficult to manufacture the waveguide. The one with a larger width is easy to manufacture. For example, the width is swept and the interval length of each width is calculated. A value of the width that is easy to manufacture is selected, and the interval length corresponding to the width is adopted. A waveguide having the width and interval length is manufactured by etching the silicon layer 16a. It is possible to suppress temperature dependence and improve tolerance.

[0113] It is also possible to calculate a correction term for all swept widths (the second term on the right side of Mathematical Formula 2) when sweeping the width and searching for an appropriate interval length. In order to reduce the amount of calculation, it is also possible to calculate correction terms for only a part of the swept width instead of all the swept widths. For the swept width, calculate the interval length without considering the correction term. Among the calculated interval lengths, for example, a group of smaller values ​​is used as a candidate for the interval length. Calculate the correction term corresponding to the candidate for the interval length, and calculate the interval length using the correction term and the candidate ( Figure 4B ). As mentioned above, the interval length can also be calculated without considering the correction term.

[0114] Alternatively, a matrix A corresponding to the assumed width candidate may be calculated in advance and stored in the control unit 111. Alternatively, the wavelength of light propagating in the optical filter 100 and the FSR of the spectrum may be determined, and the column vector B may be calculated in advance and stored in the control unit 111. The interval length is proportional to the square of the wavelength λ and inversely proportional to the FSR. The FSR may be greater than 10 nm, less than 10 nm, or less than 1 nm. The spectrum has peaks periodically. By appropriately designing the interval length, the temperature dependence of the characteristics can be suppressed even when the width changes.

[0115] The optical filter may be formed on the SOI substrate or may be formed on a component other than the SOI substrate. The waveguide may include a waveguide core 16 of Si or may be formed of other materials.

[0116] <Second embodiment> Fig.10 2 is a top view illustrating an optical filter 200 according to the second embodiment. The same configuration as that of the first embodiment will be omitted. Fig.10 As shown, the optical filter 200 includes waveguides 40, 42, 44, and 46. These four waveguides are provided on the substrate 10. The waveguide 40 extends from one end to the other end of the substrate 10 in the X-axis direction and has an input port 1 and an output port 2.

[0117] The waveguide 42, the waveguide 44, and the waveguide 46 are arranged in parallel with the waveguide 40 in the Y-axis direction. The waveguide 42, the waveguide 44, and the waveguide 46 are arranged in this order from the side close to the input port 1.

[0118] The waveguide 40 includes a portion 50, a portion 52, a section 54, a portion 56, a section 57, and a portion 58. The portion 50, the portion 52, the section 54, the portion 56, the section 57, and the portion 58 are arranged in this order along the X-axis direction. The portion 50 includes an input port 1. The portion 58 includes an output port 2.

[0119] The width w2 of the interval 54 is wider than the widths of the portion 50 and the interval 57, for example, 800 nm. The width w1 of the interval 57 is smaller than the width w2, for example, 400 nm. The portion 52 and the portion 56 have a tapered shape. The portion 52 is connected to the portion 50 and the interval 54. The width of the portion 52 widens from the portion 50 toward the interval 54. The portion 56 is connected to the interval 54 and the interval 57. The width of the portion 56 narrows from the interval 54 toward the interval 57.

[0120] The waveguide 42 includes a portion 60, a portion 61, a section 62, a portion 63, and a portion 64. The portions 60, 61, the section 62, the portion 63, and the portion 64 are arranged in sequence along the X-axis direction. The widths of the portions 60 and 64 of the waveguide 42 are greater than the widths of the portions 50 and 58 of the waveguide 40. The width w4 of the section 62 is smaller than the widths w2 of the portions 60 and 64 and the width w2 of the section 54 of the waveguide 40, and is greater than the width w1 of the section 57 of the waveguide 40, and is, for example, 600 nm.

[0121] The portion 61 and the portion 63 have a tapered shape. The portion 61 is connected to the portion 60 and the section 62. The width of the portion 61 becomes narrower from the portion 60 toward the section 62. The portion 63 is connected to the section 62 and the portion 64. The width of the portion 63 becomes wider from the section 62 toward the portion 64.

[0122] The waveguide 44 includes a portion 66, a portion 67, a section 68, a portion 69, and a portion 70. The portion 66, the portion 67, the section 68, the portion 69, and the portion 70 are sequentially arranged along the X-axis direction. The widths of the portion 66 and the portion 70 are smaller than the widths of the portion 60 and the portion 64 of the waveguide 42. The width w3 of the section 68 is larger than the widths of the portion 66 and the portion 70, and larger than the width w2 of the section 54 of the waveguide 40, and is, for example, 1200 nm.

[0123] Portion 67 and portion 69 have a tapered shape. Portion 67 is connected to portion 66 and section 68. The width of portion 67 increases from portion 66 toward section 68. Portion 69 is connected to section 68 and portion 70. The width of portion 69 decreases from section 68 toward portion 70.

[0124] The shape of waveguide 46 is the same as that of waveguide 42. Waveguide 46 includes portion 72, portion 73, interval 74, portion 75, and portion 76. Portion 72, portion 73, interval 74, portion 75, and portion 76 are arranged in sequence along the X-axis direction. Portion 73 and portion 75 have a tapered shape. The width W4 of interval 74 is, for example, 600 nm.

[0125] The interval 57 of the waveguide 40 is Figure 1 The interval 62 of the waveguide 42 and the interval 74 of the waveguide 46 correspond to the interval 26b.

[0126] The portion 50 of the waveguide 40 and the portion 60 of the waveguide 42 form a directional coupler 80. The directional coupler 80 and Figure 1 The portion 64 of waveguide 42 and the portion 66 of waveguide 44 form a directional coupler 81. The portion 70 of waveguide 44 and the portion 72 of waveguide 46 form a directional coupler 82. The portion 76 of waveguide 46 and the portion 58 of waveguide 40 form a directional coupler 83. The directional coupler 83 and Figure 1 The coupler 32 corresponds to.

[0127] Light is injected into the waveguide 40 from the injection port 1. A part of the light propagates in the waveguide 40, and another part of the light is transferred to the waveguide 42 in the directional coupler 80. The mode of the light propagating in the waveguide 40 is the TE0 mode. The light in the TE0 mode propagates in the interval 54 and the interval 57.

[0128] The mode of light is converted in the directional coupler 80. The mode of light propagating in the waveguide 42 is the TE1 mode. In the directional coupler 81, light is transferred from the waveguide 42 to the waveguide 44, and the mode is converted from the TE1 mode to the TE0 mode. Light in the TE0 mode propagates in the waveguide 44. In the directional coupler 82, light is transferred from the waveguide 44 to the waveguide 46, and the mode is converted from the TE0 mode to the TE1 mode. Light in the TE1 mode propagates in the waveguide 46. In the directional coupler 83, light is transferred from the waveguide 46 to the waveguide 40, and the mode is converted from the TE1 mode to the TE0 mode. Light in the TE0 mode propagates in the waveguide 40 and is emitted from the emission port 2 to the outside of the optical filter 200.

[0129] The length L1 of the interval 57, the length L2 of the interval 54, the length L3 of the interval 68, and the length L4 of the interval 62 and the interval 74 are designed by the design device 110. The width of each interval is set to the above value, and the mathematical formula 5 is used. As a result of the calculation, the length L1 of the interval 57 is 8587μm. The length L2 of the interval 54 is 7358μm. The length L3 of the interval 68 is -15762μm. The length L4 of the interval 62 and the interval 74 is -865μm. The waveguide 40 with a positive interval length is Figure 1 The waveguides 42, 44, and 46 with negative interval lengths are Figure 1 The waveguide 26 corresponds to. Fig.10 In FIG. 4 , waveguide 40 is arranged at the top, and waveguide 42, waveguide 44, and waveguide 46 are arranged at the bottom. That is, a positive section length indicates a section length of a waveguide arranged at the top side of the optical filter, and a negative section length indicates a section length of a waveguide arranged at the bottom side of the optical filter ( Fig.11 The same also applies to ).

[0130] According to the second embodiment, the optical filter 200 has intervals 54, 57, 62, 68, and 74. The TE0 mode propagates to the intervals 54, 57, and 68. The TE1 mode propagates to the intervals 62 and 74. The length of the interval is designed based on the differential of the propagation constant βn with respect to the temperature T and the width w of the interval. By making the interval length an appropriate size, the tolerance can be improved. Even when the width of the waveguide changes, the temperature dependency can be suppressed and the change of the characteristics can be suppressed.

[0131] <Third Embodiment> Fig.11 This is a plan view illustrating an optical filter 300 according to the third embodiment. The description of the same configuration as that of the first embodiment or the second embodiment will be omitted.

[0132] exist Fig.11 In the example of FIG. 4 , the length of the section 54 of the waveguide 40 is L3, and the width of the section 54 is w3. The length of the section 68 of the waveguide 44 is L2, and the width of the section 68 is w2.

[0133] The width w1 of the section 57 of the waveguide 40 is, for example, 410 nm. The width w2 of the section 68 of the waveguide 44 is, for example, 800 nm. The width w3 of the section 54 of the waveguide 40 is, for example, 1200 nm. The width w4 of the section 62 of the waveguide 42 and the section 74 of the waveguide 46 is, for example, 600 nm.

[0134] The mode of light propagating in the sections 54 and 57 of the waveguide 40 is the TE0 mode. The mode of light propagating in the section 62 of the waveguide 42 and the section 74 of the waveguide 46 is the TE1 mode. The mode of light propagating in the section 68 of the waveguide 44 is the TE0 mode.

[0135] The length L1 of the interval 57, the length L2 of the interval 68, the length L3 of the interval 54, and the length L4 of the interval 62 and the interval 74 are designed by the design device 110. As a result of calculation, the length L1 of the interval 57 is 13016 μm. The length L2 of the interval 68 is -24829 μm. The length L3 of the interval 54 is 12760 μm. The length L4 of the interval 62 and the interval 74 is -1312 μm. The waveguide 40 having a positive interval length is Figure 1 The waveguides 42, 44, and 46 with negative interval lengths are Figure 1 The waveguide 26 corresponds to. Fig.11 In the diagram, the waveguide 40 is arranged at the upper part, and the waveguide 42, the waveguide 44 and the waveguide 46 are arranged at the lower part.

[0136] According to the third embodiment, the length of the interval of the optical filter 300 is designed based on the differential of the propagation constant βn with respect to the temperature T and the width w of the interval. By making the interval length an appropriate size, the tolerance can be improved. When the width of the waveguide changes, the temperature dependency can be suppressed and the change in characteristics can be suppressed.

[0137] exist Fig.10 as well as Fig.11 In the example, a portion of the waveguide has a taper. In the taper portion, the phase of the light changes. By including the second term (correction term) on the right side as in equations 2 and 3, the length of the interval that takes the phase change into account can be calculated.

[0138] The above-mentioned functions related to the design can be realized by a computer. In this case, a program is provided in which the processing contents of the functions that the processing device should have are recorded and described. The above-mentioned processing functions are realized on the computer by executing the program on the computer. The program in which the processing contents are recorded and described can be recorded in advance on a computer-readable storage medium (excluding the carrier wave).

[0139] When distributing a program, for example, it can be sold in the form of a portable storage medium such as a DVD (Digital Versatile Disk) or a CD-ROM (Compact Disc Read Only Memory) that records the program. Alternatively, the program can be stored in advance in a storage device of a server computer and transmitted from the server computer to other computers via a network.

[0140] The computer executing the program stores the program recorded on the mobile storage medium or the program transmitted from the server computer in its own storage device. Then, the computer reads the program from its own storage device and executes the processing in accordance with the program. It should be noted that the computer can also directly read the program from the mobile storage medium and execute the processing in accordance with the program. In addition, the computer can also sequentially execute the processing in accordance with the received program each time the program is transmitted from the server computer.

[0141] Based on the description of the embodiment, the following supplementary notes are further disclosed.

[0142] (Note 1) A method for manufacturing an optical filter, wherein: The optical filter has two or more waveguides. The two or more waveguides have four or more sections, The modes of light propagating in the four or more intervals are two or more, The manufacturing method comprises the steps of designing the lengths of the four or more sections and forming the two or more waveguides based on the lengths of the four or more sections. The designing step includes the step of designing the lengths of the four or more intervals based on the differentials of the propagation constants of the intervals with respect to temperature and the widths of the intervals.

[0143] (Note 2) In the method for manufacturing an optical filter according to Supplementary Note 1, the step of designing the lengths of the four or more sections includes the step of designing the lengths of the four or more sections based on Mathematical Formula 1.

[0144] (Note 3) Based on the method for manufacturing an optical filter described in Supplement 1 or Supplement 2, wherein the four or more intervals include a first interval, a second interval, a third interval, and a fourth interval, The step of designing the lengths of the four or more sections is a step of designing the length of the first section, the length of the second section, the length of the third section, and the length of the fourth section.

[0145] (Note 4) A method for designing an optical filter, wherein: The optical filter has two or more waveguides. The two or more waveguides have four or more sections, The modes of light propagating in the four or more intervals are two or more, The lengths of the four or more intervals are designed based on the temperature-dependent differentials of the propagation constants of the intervals and the widths of the intervals.

[0146] (Note 5) Based on the optical filter design method described in Supplementary Note 4, designing the lengths of the four or more intervals includes designing the lengths of the four or more intervals based on Mathematical Formula 1.

[0147] (Note 6) Based on the design method of the optical filter described in Supplement 4 or Supplement 5, wherein: The four or more intervals include a first interval, a second interval, a third interval, and a fourth interval, Designing the lengths of the four or more sections includes designing the length of the first section, the length of the second section, the length of the third section, and the length of the fourth section.

[0148] (Note 7) A design device for an optical filter, wherein: The optical filter has two or more waveguides. The two or more waveguides have four or more sections, The modes of light propagating in the four or more intervals are two or more, The designing device designs the lengths of the four or more intervals based on the differentials of the propagation constants of the intervals with respect to temperature and the widths of the intervals.

[0149] (Note 8) In the optical filter designing device according to Supplementary Note 7, designing the lengths of the four or more intervals includes designing the lengths of the four or more intervals based on Mathematical Formula 1.

[0150] (Note 9) Based on the design device of the optical filter described in Supplement 7 or Supplement 8, wherein: The four or more intervals include a first interval, a second interval, a third interval, and a fourth interval, Designing the lengths of the four or more sections includes designing the length of the first section, the length of the second section, the length of the third section, and the length of the fourth section.

[0151] (Note 10) A computer-readable storage medium stores a design program for an optical filter, wherein: The optical filter has two or more waveguides. The two or more waveguides have four or more sections, The modes of light propagating in the four or more intervals are two or more, The computer is caused to function as a design unit that designs the lengths of the four or more intervals based on the differentials of the propagation constants of the intervals with respect to temperature and the widths of the intervals.

[0152] (Note 11) Based on the computer-readable storage medium described in Note 10, designing the lengths of the four or more intervals includes designing the lengths of the four or more intervals based on Mathematical Formula 1.

[0153] (Note 12) Based on the computer-readable storage medium described in Note 10 or Note 11, wherein: The four or more intervals include a first interval, a second interval, a third interval, and a fourth interval, Designing the lengths of the four or more sections includes designing the length of the first section, the length of the second section, the length of the third section, and the length of the fourth section.

[0154] (Note 13) An optical filter, wherein The optical filter comprises: Two or more waveguides; and four or more sections arranged in the two or more waveguides, At least two or more modes propagate in the four or more intervals.

[0155] As mentioned above, although embodiment of this invention is described in detail, this invention is not limited to the said specific embodiment, Various deformation|transformation and change are possible within the range of the summary of this invention described in a claim.

Claims

1. A method for manufacturing an optical filter, wherein: The optical filter has two or more waveguides. The two or more waveguides have four or more sections, The modes of light propagating in the four or more intervals are two or more, The manufacturing method of the optical filter comprises the following steps: designing the lengths of the four or more intervals; and The two or more waveguides are formed based on the lengths of the four or more sections, The step of designing the lengths of the four or more sections includes the step of designing the lengths of the four or more sections based on differentials of propagation constants of the sections with respect to temperature and widths of the sections.

2. The method for manufacturing an optical filter according to claim 1, wherein: The step of designing the lengths of the four or more intervals includes the step of designing the lengths of the four or more intervals based on Mathematical Formula 1, [Formula 1] L1 to Ln: length of the interval; β1 to βn: propagation constants for each interval; T: temperature; λ: wavelength; k: wave number; FSR: the interval between the peaks of the spectrum; w: The width of the interval.

3. The method for manufacturing an optical filter according to claim 1 or 2, wherein: The four or more intervals include a first interval, a second interval, a third interval, and a fourth interval, The step of designing the lengths of the four or more sections is a step of designing the length of the first section, the length of the second section, the length of the third section, and the length of the fourth section.

4. A method for designing an optical filter, wherein: The optical filter has two or more waveguides. The two or more waveguides have four or more sections, The modes of light propagating in the four or more intervals are two or more, The lengths of the four or more intervals are designed based on the temperature-dependent differentials of the propagation constants of the intervals and the widths of the intervals.

5. The method for designing an optical filter according to claim 4, wherein: Designing the lengths of the four or more intervals includes designing the lengths of the four or more intervals based on Mathematical Formula 1, [Formula 1] L1 to Ln: length of the interval; β1 to βn: propagation constants for each interval; T: temperature; λ: wavelength; k: wave number; FSR: the interval between the peaks of the spectrum; w: The width of the interval.

6. The method for designing an optical filter according to claim 4 or 5, wherein: The four or more intervals include a first interval, a second interval, a third interval, and a fourth interval, Designing the lengths of the four or more sections includes designing the length of the first section, the length of the second section, the length of the third section, and the length of the fourth section.

7. A design device for an optical filter, wherein: The optical filter has two or more waveguides. The two or more waveguides have four or more sections, The modes of light propagating in the four or more intervals are two or more, The design device includes a design unit that designs the lengths of the four or more sections based on a differential of a propagation constant of the section with respect to temperature and a width of the section.

8. The optical filter design device according to claim 7, wherein: Designing the lengths of the four or more intervals includes designing the lengths of the four or more intervals based on Mathematical Formula 1, [Formula 1] L1 to Ln: length of the interval; β1 to βn: propagation constants for each interval; T: temperature; λ: wavelength; k: wave number; FSR: the interval between the peaks of the spectrum; w: The width of the interval.

9. The optical filter design device according to claim 7 or 8, wherein: The four or more intervals include a first interval, a second interval, a third interval, and a fourth interval, Designing the lengths of the four or more sections includes designing the length of the first section, the length of the second section, the length of the third section, and the length of the fourth section.

10. A computer-readable storage medium storing a design program for an optical filter, wherein: The optical filter has two or more waveguides. The two or more waveguides have four or more sections, The modes of light propagating in the four or more intervals are two or more, The computer is caused to function as a design unit that designs the lengths of the four or more intervals based on the differentials of the propagation constants of the intervals with respect to temperature and the widths of the intervals.

11. The computer-readable storage medium of claim 10, wherein: Designing the lengths of the four or more intervals includes designing the lengths of the four or more intervals based on Mathematical Formula 1, [Formula 1] L1 to Ln: length of the interval; β1 to βn: propagation constants for each interval; T: temperature; λ: wavelength; k: wave number; FSR: the interval between the peaks of the spectrum; w: The width of the interval.

12. The computer-readable storage medium according to claim 10 or 11, wherein: The four or more intervals include a first interval, a second interval, a third interval, and a fourth interval, Designing the lengths of the four or more sections includes designing the length of the first section, the length of the second section, the length of the third section, and the length of the fourth section.

13. An optical filter, wherein: The optical filter has two or more waveguides; and four or more sections arranged in the two or more waveguides, At least two or more modes propagate in the four or more intervals.

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