Optical multiplexing circuit

Abstract

Disclosed is an optical multiplexing circuit that has a new configuration using a PLC and that achieves further reduction in size. This optical multiplexing circuit uses a multimode interferometer (MMI) as an optical multiplexing element. The MMI alone multiplexes two or more input light beams having different wavelengths and outputs multiplexed light beams to a main port and a monitor port. By modulating the width of the MMI along the light traveling direction, the light beams are bifurcated, at an arbitrary bifurcation ratio, into a main multiplexed light beam for the main port and a monitor light beam for the monitor port. The modulated width of the MMI is determined by a modified wavefront matching method. By using the MMI alone, it is possible to collectively perform the multiplexing and the bifurcation without the need to perform wavelength multiplexing on three or more input light beams in multiple stages. It is possible to shorten the length of the optical multiplexing circuit in the light traveling direction.

Description

optical multiplexing circuit

[0001] The present invention relates to an optical circuit, and more particularly to an optical multiplexing circuit capable of branching and monitoring output.

[0002] One of the devices that has supported the development of the optical communications field is the silica-based planar lightwave circuit (PLC). PLCs have an embedded waveguide consisting of a high-refractive-index core and a low-refractive-index cladding formed on a substrate such as silicon. PLCs are fabricated using proven glass deposition and semiconductor microfabrication technologies (Non-Patent Document 1). By changing the shape of the core, PLCs can achieve various functions on a single chip, such as branching of light, multiplexing / demultiplexing of wavelengths, and switching of optical paths.

[0003] PLCs now handle not only infrared light used in optical communications but also wavelengths in the visible range, increasing the opportunities to process light of a wider range of wavelengths within a single chip. For example, their applications are expanding to include RGB couplers that combine three primary colors (Patent Document 1) and optical combining circuits used for atomic cooling in optical lattice clocks. RGB couplers in particular are used in a wide range of products, from large projectors to small smart glasses.

[0004] International Publication WO 2017 / 142076 A1

[0005] A. Himeno, et al., J. Sel. Top. QE, vol. 4, 1998, pp.913-924Y. Fujiwara, et al., Jpn. J. Appl. Phys. 61, SK1021Y. Sakamaki, T. Saida, T. Hashimoto, and H. Takahashi, "New Optical Waveguide Design Based on Wavefront Matching Method", Journal of Lightwave Technology, vol. 25, No.11, pp.3511-3518, Nov. 2007

[0006] As the range of applications expands to small devices such as smart glasses, there is a growing demand for miniaturization of optical multiplexing circuits such as RGB couplers. In conventional RGB couplers, the length of wavelength multiplexing elements such as directional couplers and mode couplers limited the size of the PLC. In addition, higher-level operation is required for the input and output light of the RGB coupler. A new optical multiplexing circuit configuration using PLC was needed.

[0007] SUMMARY OF THE INVENTION The present invention has been made in view of the above problems, and has as its object to provide an optical multiplexing circuit that is miniaturized and suitable for high-level operation.

[0008] One embodiment of the present invention is an optical multiplexing circuit comprising: a multi-mode interferometer waveguide (MMI waveguide) having at least two or more input ports and a first output port and a second output port; input waveguides connected to each of the at least two or more input ports and accepting input light of different wavelengths; a main output waveguide connected to the first output port and outputting multiplexed light of the input light of the different wavelengths; and a monitor output waveguide connected to the second output port and outputting branched light of the multiplexed light at a predetermined branching ratio, wherein the width of the MMI waveguide is modulated along the light propagation direction.

[0009] Another embodiment of the present invention is a method for determining a structure of an optical multiplexing circuit, the optical multiplexing circuit having a multi-mode interferometer waveguide (MMI waveguide) having at least two or more input ports and a first output port and a second output port, input waveguides connected to each of the at least two or more input ports and receiving input light of different wavelengths, a main output waveguide connected to the first output port and outputting multiplexed light of the input light of the different wavelengths, and a monitor output waveguide connected to the second output port and outputting branched light of the multiplexed light at a predetermined branching ratio, and a step of setting an initial shape of the MMI waveguide, in which a region of the MMI waveguide is divided into a plurality of grids in a light traveling direction. setting an input field of the input light at the input port, an output field of the combined light at the first output port, and an output field of the branched light at the second output port; updating a waveguide structure by wavefront matching; updating the output fields at the first output port and the second output port based on the updated structure, respectively; further repeating updating of the waveguide structure by wavefront matching a predetermined number of times for the updated structure and the updated output fields; and determining the finally updated structure as a width-modulated MMI waveguide structure.

[0010] The present invention makes it possible to realize an optical multiplexing circuit that is small in size and suitable for high-level operation.

[0011] FIG. 1 is a diagram showing the configurations of various wavelength multiplexing elements used in PLC. FIG. 2 is a diagram showing the overall configuration of an RGB coupler of the prior art. FIG. 3 is a diagram showing the configuration of a multiplexing section of an RGB coupler of the prior art. FIG. 4 is a diagram showing the basic configuration of a multiplexing section in an optical multiplexing circuit of the present disclosure. FIG. 5 is a diagram showing the transmission spectrum of a multiplexing section realized by a single MMI. FIG. 6 is a diagram explaining boundary conditions for determining the structure of a refractive index-modulated MMI. FIG. 7 is a diagram showing the configuration of a multiplexing section using a refractive index-modulated MMI of the present disclosure. FIG. 8 is a diagram showing the transmission spectrum of a multiplexing section using a refractive index-modulated MMI. FIG. 9 is a diagram showing another configuration of a multiplexing section using a refractive index-modulated MMI of the present disclosure. FIG. 10 is a diagram showing the configuration of an RGB coupler realized by the PLC of embodiment 1. FIG. 11 is a diagram showing the configuration of an RGB coupler realized by the PLC of embodiment 2. FIG. 12 is a diagram showing the configuration of an RGB coupler realized by the PLC of embodiment 3. FIG. 13 is a flowchart of a procedure for determining a modulated waveguide width structure using a WFM method.

[0012] The optical multiplexing circuit disclosed herein utilizes a multi-mode interferometer (MMI) as an optical multiplexing element. A single MMI multiplexes two or more input light beams with different wavelengths and outputs the multiplexed light beam to a main port and a monitor port. By modulating the width of the MMI along the light propagation direction in the MMI, the light beam is split into a main multiplexed light beam from the main port and a monitor light beam from the monitor port at an arbitrary splitting ratio. The modulated waveguide width of the MMI is determined using a modified wavefront matching method. Even when multiplexing three or more input light beams, multi-stage multiplexing using cascaded wavelength multiplexing elements, as in conventional technology, is not required. Because multiplexing and splitting can be performed simultaneously using a single MMI, the length of the optical multiplexing circuit in the light propagation direction can be shortened. Using a wide MMI waveguide distributes the propagating optical power in the width direction, improving blue light resistance. Furthermore, the adoption of MMI allows for the relaxation of microfabrication precision, making it possible to adopt an optical waveguide structure with a core doped with Zr. This improves light resistance to blue light, enabling higher-level operation of input and output light to and from the optical multiplexing circuit.

[0013] In the following, we will first outline the problems with conventional optical multiplexing circuits, and then explain the configuration and operation of the optical multiplexing circuit of the present disclosure. In the following explanation, we will explain an RGB optical multiplexing circuit (hereinafter referred to as an RGB coupler) as an example, but the optical multiplexing circuit of the present disclosure can also be applied to optical multiplexing circuits for various other purposes that require a large number of multiplexed lights, and is not limited to RGB couplers.

[0014] Figure 1 shows the configuration of various wavelength multiplexing elements used in RGB couplers using PLC. Each of these elements is a basic element used in optical multiplexing circuits such as RGB couplers, and is a wavelength multiplexing element that performs the wavelength multiplexing function. An RGB coupler is constructed by combining these wavelength multiplexing elements with peripheral optical circuits such as input waveguides, output waveguides, and branching circuits.

[0015] FIG. 1A shows the principle of wavelength multiplexing of two waves (G light and B light) using a directional coupler. The directional coupler 60 is composed of two closely spaced waveguides, and for G light and B light from the input end, coupling of the B light and recombination of the G light occur at one output end. The waveguide width, gap, and length are designed so that the coupling position of the B light and the recombination position of the G light coincide. The length of the coupling waveguide must be adjusted to match the period of the light of different wavelengths, and a certain element length is required. To multiplex three or more waves, further cascade-connected directional couplers are required.

[0016] Figure 1(b) illustrates the principle of wavelength multiplexing of two waves (G light and B light) using an MMI. The MMI 70 is composed of an input waveguide, a wide planar waveguide, and an output waveguide. Light is equally divided within the planar waveguide, causing interference. The self-imaging length is the length of the MMI required to restore the same field (phase) as that in the input waveguide immediately before entering the MMI. By designing the length of the MMI so that the number of self-imaging events between the G light entering through port 1 and the B light entering through port 2 is shifted by one, G and B light can be multiplexed. The MMI 70 also requires a certain element length to match the length of the MMI to the wavelengths of the two lights to be multiplexed. Multiplexing three or more waves requires cascading two or more MMIs, which increases the overall element length.

[0017] FIG. 1C illustrates the principle of wavelength multiplexing of three waves (R, G, B) using a mode coupler. The mode coupler 80 includes a mode converter 81 located between two coupled waveguides. It is designed to satisfy the mode transition conditions for only specific wavelengths, allowing multiplexing from the shortest wavelength (see Patent Document 1). In FIG. 1C, the mode coupler is designed to satisfy the transition conditions for only the R light, and the R light is then transitioned to the waveguide where the G and B lights are multiplexed, resulting in multiplexing. Since mode couplers do not require matching the period between two lights of different wavelengths, they can be more compact than directional couplers or MMIs. However, they still multiplex light for each wavelength individually, requiring a separate mode coupler to multiplex the G and B lights prior to the mode coupler 80. Increasing the number of wavelengths necessitates multiple connections, increasing the overall length of the device. Furthermore, mode couplers that multiplex light from the shortest wavelengths have the drawback of reduced blue light resistance because short-wavelength light always passes through the coupler at high intensity.

[0018] FIG. 2 shows the overall configuration of a conventional RGB coupler. The RGB coupler 400 includes three input waveguides 401-1 to 401-3 for inputting R, G, and B light, corresponding optical branches 402-1 to 402-3, a multiplexing section 410, and an output waveguide 403 for the main multiplexed light. The RGB coupler 400 further includes monitor output waveguides 404 for each of the R, G, and B light beams branched by the optical branch before multiplexing, in order to check the intensity of the beam emitted from the main output waveguide 403. It should be noted that the RGB coupler shown in FIG. 2 is a schematic diagram, and the relative sizes of the various components and the aspect ratio are not accurately depicted.

[0019] FIG. 3 is a diagram showing the configuration of a multiplexing section of a conventional RGB coupler. The multiplexing section in FIG. 3 corresponds to the multiplexing section 410 in the overall RGB coupler 400 in FIG. 2. In the multiplexing section 410, a GB multiplexing element 411 that multiplexes B light and G light, and an R-GB multiplexing element 412 that multiplexes GB multiplexed light and R light are cascade-connected. The two multiplexing elements can be the wavelength multiplexing elements shown in FIGS. 1(a) to 1(c). In the following description, the central wavelength of blue light (B light) is 450 nm, the central wavelength of green light (G light) is 520 nm, and the central wavelength of red light (R light) is 638 nm. Depending on the application, the central wavelengths may deviate from the wavelengths described above.

[0020] Returning to Figure 2, in the configuration of the RGB coupler 400, R light, G light, and B light are each branched by optical branching before being multiplexed. Since the branching ratio can be freely designed for each color in the separate optical branching, highly accurate monitor light can be easily obtained. However, the need for the branching unit 404 makes the PLC chip that constitutes the RGB coupler 400 longer in the light propagation direction. The monitor outputs from the monitor waveguides 414 and 415 from each multiplexing element in Figure 3 can also be used, but the branching ratio (tap ratio) of each wavelength cannot be freely set because it is determined by the transition period of the directional coupler, etc.

[0021] As described above, in any of the wavelength multiplexing elements shown in Figures 1(a) to 1(c), the element length in the propagation direction of each light becomes long, and even in a configuration in which a simple monitor light that is branched before multiplexing is extracted, the overall length of the RGB coupler becomes long. If the number of wavelengths of light to be multiplexed increases, the size of the PLC will inevitably increase. The optical multiplexing circuit disclosed below solves or alleviates the above-mentioned problems of the conventional optical multiplexing circuits shown in Figures 1 to 3.

[0022] FIG. 4 illustrates the configuration of the multiplexing section in the optical multiplexing circuit disclosed herein. The multiplexing section 10 multiplexes R, G, and B light beams with different wavelengths and outputs RGB multiplexed light. Furthermore, a portion of the RGB multiplexed output is branched off to output monitor light. The multiplexing section 10 is composed of an MMI 10-0 with a wide waveguide structure approximately 6 μm wide (y-direction) and 700 μm long (x-direction). One end of the MMI has an input section 10-1 with three input ports, and the other end has an output section 10-2 with two output ports, a main and a monitor. The input sections 10-1, labeled R, G, and B, are each part of the input waveguides 101-1 to 101-3, indicated by dotted lines, and are continuous and not structurally separate. Note that there are no defined protrusions at the ends of the rectangular MMI 10-0. Similarly, output waveguides 103 and 104 are continuously formed in output section 10-2, and the entire multiplexing section 10 is made up of PLC. Note that in Figure 4, the width direction (y direction) is significantly enlarged relative to the length direction (x direction).

[0023] The MMI is a waveguide that is wider than a normal waveguide and corresponds to the rectangular MMI body in Fig. 4, and the MMI waveguide also means the same thing. The input port corresponds to the boundary between the input waveguide and the MMI to which the input waveguide in the MMI is connected, and is not intended to be a terminal having a specific structure. The same applies to the output port.

[0024] The multiplexing section 10 in the optical multiplexing circuit of the present disclosure multiplexes three light beams of different wavelengths using a single MMI, thereby achieving the functions of the multiplexing section 410 and the branching section 405 in the conventional optical multiplexing circuit 400 shown in Figure 2. This eliminates the need for the branching section 405, which occupies a large area on the PLC, and the waveguide connecting the branching section 405 and the multiplexing section 410, thereby reducing the PLC chip size. The overall configuration of the wavelength multiplexing circuit will be described later with reference to Figures 10 to 12.

[0025] 4 has the following configuration example when branching into the main port and the monitor port at a power branching ratio of 95:5: the core thickness is 1.5 μm, the relative refractive index difference between the cladding and the core is 1.0%, the input waveguide width is 1.5 μm, the pitch between the input waveguides is 3.0 μm, the output waveguide width is 1.5 μm, the center-to-center distance between the output waveguides is 6.0 μm, the MMI length is 700 μm, and the lengths of the input straight waveguide and the output straight waveguide are each 100 μm.

[0026] Figure 5 shows the transmission spectra between the input and output ports of the multiplexer. Figure 5(a) shows the transmittance spectra from each of the three R, G, and B input ports to the main port. Figure 5(b) shows the transmittance spectra from each of the three R, G, and B input ports to the monitor port. The bands labeled R, G, and B indicate the wavelength ranges nominally referred to as R light, G light, and B light. This figure shows the results of a three-dimensional beam propagation method (BPM) simulation of the transmittance of the MMI configuration of the multiplexer shown in Figure 4. The transmittance of the main port for R light, G light, and B light varies greatly for each wavelength, ranging from -1 to -6 dB, and uniform multiplexing among the three wavelengths is not achieved. The same is true for the monitor port; uniform branching among R light, G light, and B light is not achieved.

[0027] Therefore, the inventors attempted to achieve a desired optical output distribution by modulating the refractive index distribution along the light propagation direction in order to achieve a more accurate branching ratio while constructing a compact multiplexing section using a single MMI. It is known that the refractive index distribution in an MMI can be modulated by modulating the waveguide width of the MMI. In this study, a modified wavefront matching method (WFM) was used to calculate the specific shape of the refractive index distribution.

[0028] In the WFM method, for an optical circuit with certain input / output conditions (boundary conditions), the refractive index distribution (waveguide structure) is determined so as to match the wavefronts of light propagating from the input side (forward propagation) and light propagating from the output side (reverse propagation). By calculating the refractive index distribution, the width of the MMI can be determined, and the waveguide structure can be specified. This is a simulation technique that calculates the refractive index distribution that maximizes the transmittance of the circuit for the desired boundary conditions, and is also used in PLC design (Non-Patent Document 3).

[0029] [Specific example of determining MMI structure using WFM method] To calculate a refractive index profile for improving transmittance using WFM method, for example, BPM is used to propagate light with a desired mode field in the forward and reverse directions, and the width of the waveguide is changed so that the wavefronts of the two lights match within the circuit. By repeating this procedure multiple times, it is possible to determine the refractive index profile that will produce the desired optical output distribution at the output port of the MMI.

[0030] FIG. 6 is a diagram illustrating the boundary conditions for determining the structure of a refractive index-modulated MMI. When determining the refractive index-modulated structure using the WFM method for the MMI of the multiplexing section shown in FIG. 4, electric field distributions are set on the input and output sides for each of the R, G, and B light. As indicated by "input side" in FIG. 6, the input boundary condition is set to light with an amplitude of 1 in the fundamental (0th-order) mode of each wavelength, relative to the input port position (y direction) at the left end of the MMI in FIG. 4. For example, for R light, at the input port indicated as R in FIG. 4, light with an amplitude of 1 in the 0th order is set at a position y = -3 (μm) in the width direction.

[0031] As shown in FIG. 6 as "output side," the output port at the right end of the MMI in FIG. 4 has an amplitude of √0.95 (0.95) for the R light relative to the main port at y=+3 (μm). 1 / 2 ) to the monitor port at y = -3 (μm), and the amplitude is √0.05 (0.05 1 / 2) are set to the zeroth mode light, respectively. On the output side, the sum of the squares of the electric field is normalized to be the same as the sum of the squares of the electric field on the input side. By setting the boundary conditions for each of the three lights as shown in Figure 6, the three waves are multiplexed at the main port and the monitor port with equal electric field strength. Simultaneously with the multiplexing, the RGB multiplexed light is output from the main port and the monitor port at a branching ratio of 95:5.

[0032] Under the boundary conditions shown in Figure 6, the main output port is set to be located on an extension of the B light input port in the width direction. This is because the short-wavelength B light has a high tendency to propagate in a straight line, making it difficult to manipulate the light using WFM. The main port, which needs to collect light at the output port with greater power, is located on an extension of the B light input port in the light propagation direction (x direction). Because the branching ratio to the monitor port side is small at 0.05, each port must be positioned so that excess light is less likely to enter the monitor port side. The monitor port was located at the end opposite the main port in the width direction of the MMI and at the farthest position from the main port.

[0033] A modified WFM method was applied to design the multiplexing section in the optical multiplexing circuit of the present disclosure. As an example, a method for setting the R light will be described. The electric field distribution of the light at the left end (the left end of the input section 10-1, R port in FIG. 4) of the region where the waveguide width is obtained by applying the WFM method is defined as Φ in,R , the electric field distribution of light at the right end (the right end of the output section 10-2 in FIG. 4) is Φ target,R Here, Φ in,R is the electric field distribution of the fundamental mode of R light in the input waveguide of R light. target,R For the main port and the monitor port, the desired branching ratio is achieved and the total intensity is Φ in,R The electric field distributions at the main port and monitor port are normalized as follows: Φ main,R , Φ moni,R Let's say.

[0034] In this case, the following equation holds: Φ target,R =Φ main,R + Φ moni,R Formula (1)

[0035] In the WFM method, the input condition Φ in,R But the output condition Φ target,R Normally, when a target value is set as in equation (1) in the WFM method, Φ main,R and Φ moni,R The output conditions are set so that the phases of the two signals are 0 or the same. However, in an RGB coupler with a branching function, the phases of the electric fields do not need to be the same between the two ports, the main and the monitor. In an RGB coupler, it is sufficient that the R light, G light, and B light are multiplexed at a uniform level into the main port and a predetermined branching ratio is realized for the monitor port.

[0036] When optimizing the branching ratio toward the target value, the normal WFM method calculates so that the phases of the two electric fields are also aligned. This results in a lower transmittance compared to optimization that takes into account only the branching ratio. Therefore, each time a calculation is performed using the WFM method, the phases at the main port and monitor port when light is propagated are set to ψmain and ψmoni, respectively, and calculations are performed so that the following equation holds true: Φ target,R = e iψmain Φ main,R + e iψmoni Φ moni,R Formula (2)

[0037] By correcting the target value of the electric field distribution in the WFM method as in equation (2), it is no longer necessary to match the phase of the light at the two ports, and the calculation simply involves matching the branching ratio to the target value. As a result, the transmittance can be increased. The above procedure is performed for each wavelength of R light, G light, and B light.

[0038] Next, an overview of the steps for determining the waveguide width using the WFM method will be described. It is assumed that the shape and size of the grid that divides the entire region of the MMI waveguide into a mesh are predetermined. The entire region for which the waveguide width is to be determined is divided into M rectangular grids along the light propagation direction of the waveguide. For example, in the MMI waveguide 10 of FIG. 4, the region is divided into M grids with a width Δx in the x direction. Although details are omitted, in actual calculations, the grid is further divided into finer meshes, and the "phase difference" is determined for each mesh in step 4 described below. Specifically, one grid can be divided into L meshes in the y direction to form one mesh. For example, the mesh size can be 0.1 μm in the x direction (light propagation direction) and 0.025 μm in the y direction (width direction).

[0039] The entire region for which the waveguide width is to be calculated includes the MMI 10-0, the input section 10-1, and the output section 10-2, as in the multiplexing section 10 shown in Fig. 4. In addition to the main body of the MMI, grids and meshes are also defined for the part 10-1 of the input waveguide and the part 10-2 of the output waveguide.

[0040] Fig. 13 is a flow chart showing the procedure for determining the modulated waveguide width structure using the WFM method. Below, the calculation procedure will be outlined with reference to the flow chart 500 in Fig. 13. It should be noted that the flow chart 500 is a simplified overview of the procedure and does not include all of the content described in the following steps. Also, the loop configuration of the repetitive processing in the flow chart in Fig. 13 is one example, and other algorithms are possible depending on the calculation process.

[0041] *Step 1: Set the initial value of the refractive index profile. That is, set the initial shape of the MMI waveguide for determining the modulated waveguide width. In the above example, set the shape of the MMI waveguide 10 in Fig. 4. In Fig. 13, this corresponds to S501.

[0042] ★Step 2: Input field (Φ in the above example) in,R ) and the output field (Φ in the example above) target,R) is set. Input fields and output fields are set for each of the R light, G light, and B light. This corresponds to S501 in FIG. 13.

[0043] ★Step 3: Set the number of times to perform WFM. In other words, determine in advance how many times to repeat the WFM calculation to perform the overall optimization of the waveguide structure. Before performing the first WFM, initialize the WFM number counter to 1 and start the WFM calculation process. After loopback, increment the number counter before starting the next WFM. In Figure 13, this corresponds to S502.

[0044] ★ Step 4: For one of the grids, in order to match the wavefront of the input field propagating in the forward direction with the wavefront of the output field propagating in the backward direction, a decision is made as to whether to widen, narrow, or maintain the waveguide width for that grid. To decide this operation, a decision is made sequentially on the operation to be performed on the waveguide width for each rectangular grid. In Figure 13, this corresponds to S503. Note that in S503 after loopback, the process changes to the next target grid.

[0045] For each grid, a decision is made as to whether to widen the grid width outward, narrow it inward, or maintain it as is, in order to minimize the wavefronts of the two fields, i.e., the phase difference, and make it zero. Determining the manipulation content of the waveguide structure to match the wavefronts is the core of the WFM method. By sequentially manipulating the waveguide structure for all grids of the MMI waveguide, it is possible to approach the respective target fields at the two output ports.

[0046] In an RGB multiplexer, boundary conditions must be satisfied for three light beams as shown in FIG. 6 , so the determination of minimizing the phase difference described above may conflict with the determination of minimizing the phase difference for R light, G light, and B light. As an example, the phase difference described above may be calculated for each of the three light beams, and a determination of how to change the width of each grid based on the sum of the phase differences may be made. Therefore, step 4 may include a substep of determining the phase differences for R light, G light, and B light with respect to the target grid, and a substep of determining how to change the width of the grid based on the sum of the phase differences.

[0047] The phase difference for one grid is determined for each mesh that constitutes the grid and is arranged in the y direction, and the phase differences for all meshes in the y direction are summed to obtain the phase difference for one grid. The calculation of the phase difference corresponds to S504 in FIG. 13.

[0048] *Step 5: Repeat step 4 for all grids to determine the operation on the waveguide width for each grid. The operation on the waveguide width corresponds to S505 in FIG. 13. The repeated operation on each grid corresponds to the loopback operation from the No determination in S506 in FIG. 13.

[0049] Once the operation to the waveguide width (widening, narrowing, or maintaining the same width) has been determined for all grids, one WFM run is completed. By performing one WFM run, the temporally modulated waveguide width for the entire MMI waveguide can be obtained. The amount of change in the waveguide width can be determined in advance to a predetermined change range.

[0050] ★Step 6: When performing WFM for the second or subsequent times, after a new structure of the temporarily modulated waveguide width has been obtained, the target field expressed by equation (2) is updated. Specifically, the set input field is entered for the updated structure with the new waveguide width after WFM, and the electric field distribution when light is propagated to the right end is calculated using BPM or the like. The phases after the kth WFM, ψmain,k and ψmoni,k, obtained from this calculation, are used as the phases in equation (2) to reset the target field in equation (2). The update of the target field and the waveguide structure corresponds to S507 in Figure 13.

[0051] By updating the phases of the target fields at the two output ports each time WFM is performed, optimization can be performed taking into account only the branching ratio. Whether or not a specified number of WFMs have been performed is determined based on the set number of WFMs and the current value of the WFM count counter, and steps 3 to 5 are repeated for the reconfigured target field and structure as the next WFM. This corresponds to the loopback calculation resulting from the determination of No in S508 of FIG. 13. The count counter is updated in S502, and the above-described steps 3 to 5 are repeated. For the new WFM, steps S502 to S507 of FIG. 13 are performed.

[0052] Each time WFM is performed, the temporary modulated waveguide width is updated. In a conventional WFM method, the output field setting in step 2 is performed only the first time WFM is performed. In determining the structure of the optical multiplexing circuit of the present disclosure, the procedure is modified so that the phase of the target field is calculated and the target field is reset in S507 of FIG. 13 each time WFM is performed on the entire target MMI waveguide.

[0053] *Step 7: Determine the MMI structure with modulated waveguide width. By performing WFM a set number of times, an MMI structure with modulated waveguide width is obtained. This corresponds to S509 in Figure 13. Specifically, a multiplexing section with a refractive index-modulated MMI as shown in Figure 7, which will be described next, is obtained.

[0054] The above-described procedure of the WFM method is one example, and for example, the determination of the phase difference in each grid and the operation on the waveguide structure can be varied in many ways in terms of how the judgments for R light, G light, and B light are combined. As described above, the present invention also has an aspect of a method for determining an MMI waveguide structure in which the waveguide width in an optical multiplexing circuit is modulated.

[0055] That is, the present invention provides a method for determining a structure of an optical multiplexing circuit, the optical multiplexing circuit having a multimode interferometer waveguide (MMI waveguide) having at least two or more input ports and a first output port and a second output port, input waveguides connected to each of the at least two or more input ports and receiving input light of different wavelengths, a main output waveguide connected to the first output port and outputting multiplexed light of the input light of different wavelengths, and a monitor output waveguide connected to the second output port and outputting branched light of the multiplexed light at a predetermined branching ratio, the method comprising: a step (S501) of setting an initial shape of the MMI waveguide, in which an area of ​​the MMI waveguide is divided into a plurality of grids in the light traveling direction; The method can be implemented as a method comprising the steps of: setting an input field of input light, an output field of the combined light at the first output port, and an output field of the branched light at the second output port (S501); updating a waveguide structure by wavefront matching (S504-S506) (S507); updating the output fields at the first output port and the second output port based on the updated structure (S507); further repeating updating of the waveguide structure by wavefront matching a predetermined number of times for the updated structure and the updated output field (S506); and determining the finally updated structure as a width-modulated MMI waveguide structure (S509).

[0056] The step of updating the waveguide structure by wavefront matching also includes a first step (S504) of obtaining a phase difference between the input field and the output field for each of the input light of the different wavelengths at one grid of interest, a second step (S505) of determining an operation for the width of the grid of interest based on the phase difference for each of the input light of the different wavelengths, a third step (S506) of determining the operation for all of the plurality of grids, and a fourth step (S507) of determining an updated structure of the MMI waveguide based on the operation determined for the plurality of grids.

[0057] [Basic Configuration of a Refractive Index-Modulated Wave-Coupling Section] FIG. 7 is a diagram showing the configuration of a wave-coupling section using a refractive index-modulated MMI. The graph shows the shape of the wave-coupling section 11 in the length and width directions of the MMI. The wave-coupling section 11 was obtained by the WFM method using the wave-coupling section 10 of FIG. 4 , in which the refractive index is not modulated, as the initial shape. In FIG. 7 , the width direction (vertical axis) is enlarged by approximately 100 relative to the length direction (horizontal axis). Therefore, the actual outline of the width-modulated MMI is barely visible. The modulation of the MMI waveguide width using the WFM method modulates the widths of not only the rectangular MMI 11-0 but also a portion 11-1 of the input waveguide and a portion 11-2 of the output waveguide formed contiguously with the MMI. As will be described later in conjunction with FIG. 10 , an RGB coupler is constructed from the wave-coupling section 11 using the width-modulated MMI shown in FIG. 7 , including the input and output waveguides formed contiguously with the MMI.

[0058] FIG. 8 shows the transmission spectrum of a multiplexer using a refractive index-modulated MMI. (a) of FIG. 8 shows the transmittance spectrum from each of the three R, G, and B input ports to the main port. (b) of FIG. 8 shows the transmittance spectrum from each of the three R, G, and B input ports to the monitor port. As with FIG. 5, this figure shows the results of a simulation of the transmittance spectrum using 3D BPM. The transmittance of the main port for R, G, and B light is approximately -1.2 dB, resulting in the multiplexing of the three colors at a nearly uniform level. At the monitor port, the levels of R, G, and B light are consistent within the range of -13 to 15 dB, achieving a branching ratio of approximately 95:5. Compared to the transmission spectrum shown in FIG. 5 for a multiplexer 10 without refractive index modulation, the multiplexing of R, G, and B light at a uniform level is achieved at the desired branching ratio according to the boundary conditions described in FIG. 6.

[0059] In the refractive index-modulated multiplexer 11 shown in Figure 7, the minimum width and minimum gap of the input waveguide 11-1 and the output waveguide 11-2 are limited to 1 μm, respectively, to facilitate manufacturability. Under the boundary conditions described in Figure 6, three beams of R, G, and B light are multiplexed, and the branching ratio between the main port and the monitor port is set to 95:5. However, the number of wavelengths and branching ratio are not limited to this example. The wavelengths of the multiplexed R, G, and B light vary depending on the application of the optical multiplexer. Furthermore, refractive index modulation of an MMI using the WFM method can also be applied to visible light with wavelengths different from those of the R, G, and B light. If the number of wavelengths is increased too much or the wavelength spacing between the multiplexed beams is too narrow, the element length increases and the transmittance decreases. However, the length in the optical waveguide direction can be shortened compared to conventional directional couplers and mode couplers.

[0060] Specifically, when the mode coupler 80 shown in FIG. 1C is used as the wavelength multiplexing element, the length of the two cascaded stages, corresponding to the multiplexing section 410, is approximately 1.5 mm. Furthermore, the length of the branching section 405 shown in FIG. 2, including the waveguide expansion section, is approximately 0.5 mm. While the combined length of the branching section and multiplexing section is 2.0 mm, the element length of the multiplexing section using the refractive index-modulated MMI 11 shown in FIG. 7, which achieves the same multiplexing and branching functions, is only 0.7 to 0.9 mm. In the light propagation direction, the total chip length of the RGB coupler described below is approximately 3.5 mm, a reduction of more than 1 mm compared to conventional technology.

[0061] Therefore, the optical multiplexing circuit of the present disclosure can be implemented as comprising: a multi-mode interferometer waveguide (MMI waveguide) 11 having at least two or more input ports and a first output port and a second output port; input waveguides 101-1 to 101-3 connected to each of the at least two or more input ports and accepting input light of different wavelengths; a main output waveguide 103 connected to the first output port and outputting multiplexed light of the input light of different wavelengths; and a monitor output waveguide 104 connected to the second output port and outputting branched light of the multiplexed light at a predetermined branching ratio, wherein the width of the MMI waveguide is modulated along the light propagation direction. Also, obtaining an updated structure of the MMI waveguide by wavefront matching includes obtaining a phase difference between the input field and the output field for each of the input light of the different wavelengths at one grid of interest, determining an operation for a width of the grid of interest based on the phase difference for each of the input light of the different wavelengths, determining the operation for all of the plurality of grids, and determining an updated structure of the MMI waveguide based on the determined operation for the plurality of grids.

[0062] The multiplexing section 11 in the optical multiplexing circuit disclosed herein utilizes an MMI with a wide waveguide structure. This eliminates the need for precise processing of narrow gaps, as is required with directional couplers and mode couplers used in conventional technologies. Optical multiplexing circuits can be realized using difficult-to-process materials such as Zr-doped cores and LN (LiNbO3). PLCs with Zr-doped cores, in particular, are highly resistant to high-energy blue light and can handle higher levels of light. Furthermore, compared to directional couplers and mode couplers, the waveguide width of the MMI multiplexing section is wider, dispersing optical power. This reduces permanent refractive index changes caused by high-level blue light, thereby avoiding degradation of multiplexing characteristics.

[0063] 7, the initial shape when determining the refractive index-modulated shape by the WFM method, i.e., the shape when modulating the waveguide width, is a simple rectangular MMI with a constant waveguide width. When the branching ratio between the main port and the monitor port is about 1:1 or 9:1 and the output difference between the two ports is not large, a tapered shape can be used for the MMI.

[0064] FIG. 9 shows another configuration of a multiplexing section using a refractive index-modulated MMI in an optical multiplexing circuit according to the present disclosure. (a) of FIG. 9 shows a multiplexing section 12 in which the main body of the MMI is tapered, narrowing toward the output port. The multiplexing section 12 has a tapered MMI 12-0, an input section 12-1 with three input ports at one end of the MMI, and an output section 12-2 with two output ports, a main and a monitor, at the other end. Each of the input sections 12-1, labeled R, G, and B, has a continuous input waveguide (not shown). Similarly, the output section 12-1 also has a continuous output waveguide (not shown), and the entire multiplexing section 12 is constructed using a PLC. As with FIG. 4, the width direction is significantly enlarged relative to the length direction.

[0065] As shown in Figure 9(a), the self-imaging length can be shortened by providing a tapered structure to the MMI and narrowing the waveguide width toward the output side. The element length can be further shortened by tapering the initial shape before determining the modulated waveguide width using the WFM method. Specifically, the element length of 700 μm for the MMI without a tapered shape shown in Figures 4 and 7 can be shortened to 480 μm.

[0066] FIG. 9B shows a multiplexing section 13 having a tapered MMI body and an output waveguide with a tapered structure in the opposite direction. The multiplexing section 13 includes a tapered MMI 13-0, an input section 13-1 with three input ports at one end of the MMI, and an output section 13-2 with two output ports (main and monitor) at the other end. The output section 13-2 has output waveguides 103 and 104 formed continuously. When the MMI body 13-0 is tapered to narrow toward the output side, the spot size during self-imaging decreases at the rate (change ratio) of narrowing the MMI. Therefore, as shown in the output section 12-2 of FIG. 9B, the output waveguide width is narrowed toward the side connected to the MMI at the same change ratio as the MMI taper, and then returned to its original width, thereby reducing coupling loss.

[0067] In the multiplexing section 13, the MMI body 13-0 has a tapered shape in which the width gradually narrows in the light propagation direction. Furthermore, part of the main output waveguide 103 and part of the MMI waveguide side of the monitor output waveguide 104 have tapered portions 13-2 in which the width gradually narrows in the direction opposite to the light propagation direction. Here, the ratio between the maximum and minimum widths of the tapered shape of the MMI waveguide 13-0 matches the ratio between the maximum and minimum widths of the tapered portion 13-2 (claims 3 and 4).

[0068] Specifically, if the ratio of the width of the input side to the width of the output side of the MMI body 13-0 is 2:1, then the ratio of the width of the MMI side to the width of the output waveguide side of the output section 13-2 should be 1:2. By setting the initial shape before determining the waveguide width modulated by the WFM method to the configuration shown in Figure 9(b), it is possible to shorten the element length and realize a branching section with reduced coupling loss. For both the configurations shown in Figure 9(a) and (b), transmission spectra equivalent to those shown in Figure 8 were confirmed.

[0069] The configuration of an RGB coupler including a multiplexing section using the refractive index-modulated MMI described above will be described below. Embodiment 1

[0070] FIG. 10 is a diagram showing the configuration of an RGB coupler according to the first embodiment, implemented using a PLC. The RGB coupler 100 includes a multiplexing section 102 using a refractive index-modulated MMI and has a layout that allows for the integration of a semiconductor laser (LD) as a light source. The multiplexing section 102 can be any of the multiplexing sections 11, 12, and 13 shown in FIG. 7 or FIG. 9. The input side of the multiplexing section 102 is provided with three input waveguides 101-1 to 101-3, which constitute a Fan-IN section 106. The Fan-IN section 106 adapts the three input waveguides connected to three light sources (e.g., LDs) (not shown) to the spacing between the MMI ports of the multiplexing section 102. The output side of the multiplexing section 102 is provided with a main output waveguide 103 and a monitor output waveguide 104, which are directed toward predetermined positions, and which constitute a Fan-OUT section 107.

[0071] The widths of the input waveguides 101-1 to 101-3 are set so that the coupling with the LD (not shown) is the desired value. The mode field diameter (MFD) of the LD and the MFD of the waveguide on the PLC having the configuration of Figure 10 often differ. For this reason, by arranging mode filters 105-1 to 105-3, such as thin waveguides, on the input waveguides to cut off higher-order modes generated at the connection points and achieve single-mode conditions, it is possible to reduce ripples and suppress misalignment of the output beam.

[0072] In the FanIN unit 102, the input point (R in , G in , B inThe positions of all input points are shifted so that the multiplexing unit 102 is not located on an extension of the incident light direction from the input point 110-1 to 110-3. Taking the LD radiation angle into consideration, not being located on an extension of the incident light direction means not being within the diffraction ranges 110-1 to 110-3 of the uncoupled light shown in Figure 10 . The multiplexing unit 102, which uses a refractive index-modulated MMI, has a small waveguide width modulation, resulting in small scattering losses across the entire MMI region. Therefore, when stray light, such as uncoupled light between the LD and PLC, passes through the MMI, it causes optical interference, resulting in wavy transmission spectra. In particular, when the branching ratio to the monitor output is small (95:5), as in the boundary condition setting illustrated in Figure 6 , the amount of stray light described above is constant, while the monitor output is small. Therefore, the effect of interference becomes relatively significant, resulting in significant wavy transmission spectra. It is important to avoid interference between the stray light generated in the Fan-IN unit 102 and the low-level monitor output light.

[0073] Furthermore, in each input waveguide in the FanIN section 102, the final bent portion 107 near the input port of the MMI is not an offset connection, but a clothoid connection in which the curvature gradually becomes infinitesimal and the connection is made into a straight line. In the case of an offset, a small loss occurs, but this is to generate a small amount of stray light near the MMI. Also, at the end of the output side of the multiplexing section 102 by the MMI, light 111 that could not be collected to each output port leaks out from the "fork" portion where there is no output waveguide. For this reason, the main port is connected to the input point (R in , G in , B in ) and the extension of the multiplexing section 102.

[0074] As mentioned above, the element length of the multiplexing section using the refractive index-modulated MMI 11 in Fig. 7 is 0.7 to 0.9 mm, and if a tapered shape is further given to the MMI as in Fig. 9, the element length of the multiplexing section using MMIs 112 and 113 will be 0.5 to 0.7 mm. In the light propagation direction, a significant reduction of 1 mm or more can be achieved compared to the total length of 2 mm of the branching section 405 + multiplexing section 410, which is the corresponding part of the conventional RGB coupler in Fig. 2. Embodiment 2

[0075] The RGB coupler of embodiment 1 has a circuit layout suitable for suppressing stray light and undesired interference that can lead to deterioration of characteristics, but due to chip size and the positional relationship with other circuits, it may not always be possible to achieve the layout shown in Figure 10. An embodiment that allows for greater flexibility in the layout of circuit elements is shown below.

[0076] FIG. 11 is a diagram showing the configuration of an RGB coupler according to a second embodiment, which is realized using a PLC. It is a top view of the optical circuit, looking at the PLC substrate surface. The RGB coupler 200 includes a multiplexing section 202 using a refractive index-modulated MMI, and has a layout that allows for the integration of a semiconductor laser (LD) as a light source. The multiplexing section 202 can be any of the multiplexing sections 11, 12, and 13 shown in FIG. 7 or FIG. 9. The layout of the three input waveguides 201-1 to 201-3, the main output waveguide 203, and the monitor output waveguide 204 is the same as that shown in FIG. 10.

[0077] The difference from the RGB coupler 100 in Figure 10 is that it has a light-shielding groove where the cladding portion is removed by etching or the like, which allows for greater freedom in layout while maintaining stable optical multiplexing and branching characteristics.

[0078] In the RGB coupler 200, for example, for R light, uncoupled light exiting the input waveguide 201-1 is totally reflected by the light-shielding grooves 211-1 and 212-1, preventing it from reaching the multiplexing section 202 or the output port. The light-shielding groove 211-1, which is the first to be hit by light, is not linear, but curved like a lens to satisfy the collimation condition, thereby preventing the stray light beam 215 from spreading. Furthermore, the second light-shielding groove 212-1 allows stray light to exit the chip, suppressing characteristic degradation due to stray light. If the light-shielding groove is too wide, stray light will escape vertically upward from the substrate surface, so the width of the light-shielding groove is preferably approximately 10 μm or less.

[0079] The above-mentioned light-shielding grooves can also be provided with similar light-shielding grooves for G light and B light. Furthermore, at the output end of the MMI multiplexing unit 202, the light-shielding grooves 211-4 and 214-2 can also be used to extract stray light from the "fork" portion where there is no output waveguide, as with the input waveguide, to the outside of the chip.

[0080] The cross-section of the PLC substrate showing the light-shielding grooves is also shown in the lower part of Figure 11. The light-shielding grooves can be formed by removing the cladding layer by etching. Embodiment 3

[0081] FIG. 12 is a diagram showing the configuration of an RGB coupler according to a third embodiment, which is realized using a PLC. The RGB coupler 300 includes a multiplexing section 302 using a refractive index-modulated MMI, and has a layout that allows for the integration of a semiconductor laser (LD) as a light source. The multiplexing section 302 can be any of the multiplexing sections 11, 12, and 13 shown in FIG. 7 or FIG. 9. The layout of the three input waveguides 301-1 to 301-3, the main output waveguide 303, and the monitor output waveguide 304 is the same as that of the RGB couplers shown in FIGS. 10 and 11.

[0082] In the RGB coupler 200 shown in Figure 11, light leaks perpendicular to the substrate surface from the openings of each light-shielding groove. Therefore, as shown in Figure 12, by forming a light-absorbing film 313 on the surface of the entire PLC and on part of the side surface inside the groove, it is possible to suppress stray light leaking upward from the substrate surface. The light-absorbing film 313 can be made of a simple metal film such as Cr, or a multilayer film made of Si, Nb, SiO2, or Nb2O5.

[0083] When constructing an RGB coupler using the above-mentioned PLC and further integrating an LD light source, it is common to polish the input and output surfaces and apply an anti-reflection coating. However, when monitor ports 104, 204, and 304 are positioned on sides perpendicular to the input light input surface and the combined light output surface, as shown in Figures 10 to 12, they are often not polished and do not have an anti-reflection coating. In this case, the reflected light at the monitor port end surface becomes strong, causing light to return to the LD side and resulting in unstable characteristics. To avoid this problem, it is preferable to form the monitor port waveguide at an angle of, for example, about 8°. This effectively prevents light from returning to the LD side, even when, for example, a LD chip mounted on a subcarrier is directly connected to the input end surface of the PLC for single-chip integration.

[0084] Although the optical multiplexing circuit of the present disclosure has been described using an RGB coupler as an example in the above-described embodiment, the effect of miniaturizing the multiplexing section can be applied to other optical devices. For example, an ophthalmoscope for examining the fundus of the eye requires the use of light of 488 nm, 532 nm, 670 nm, and 790 nm to acquire fundus images at different depths. To multiplex four wavelengths, conventional technology requires four multiplexing elements connected in cascade, resulting in a very long multiplexing section. Even in such cases, the use of a multiplexing section with a refractive index-modulated MMI can significantly shorten the length of the PLC in the light propagation direction. Furthermore, flow cytometers used for observing and inspecting cells, for example, typically use wavelengths of 405 nm, 488 nm, and 640 nm. These wavelengths vary depending on the object being inspected. Furthermore, fluorescence microscopes require the multiplexing of multiple wavelengths, such as 405 nm, 488 nm, 560 nm, 640 nm, and 790 nm. In this way, the configuration of the optical multiplexing circuit of the present disclosure can be applied to combinations of various types and numbers of wavelengths.

[0085] As described above in detail, by configuring the multiplexing section using a single MMI with a modulated refractive index, the length of the PLC in the light propagation direction can be shortened, and the chip size can be reduced. By utilizing the MMI structure that distributes power and making it possible to adopt a Zr-doped core, it is also possible to achieve a high level of input and output light.

[0086] The present invention can be used in optical multiplexing circuits in video equipment, optical equipment, and the like.

Claims

1. A multi-mode interference waveguide (MMI waveguide) having at least two or more input ports, a first output port, and a second output port; an input waveguide connected to each of the at least two or more input ports for receiving input light of different wavelengths; a main output waveguide connected to the first output port for outputting combined light of the input light of different wavelengths; and a monitor output waveguide connected to the second output port for outputting branched light of the combined light at a predetermined branching ratio, wherein the width of the MMI waveguide is modulated along the light propagation direction.

2. The optical multiplexing circuit according to claim 1, wherein the MMI waveguide has three input ports, the input light of different wavelengths is red light, green light, and blue light, and the first output port is located on an extension line of the input port of the blue light along the light propagation direction.

3. The optical multiplexing circuit according to claim 1, wherein the MMI waveguide has a tapered shape in which the width gradually narrows along the light propagation direction.

4. A part of the main output waveguide and the monitor output waveguide on the MMI waveguide side has a tapered portion in which the width gradually narrows in a direction opposite to the light propagation direction, and a ratio of a maximum width to a minimum width of the tapered shape of the MMI waveguide coincides with a ratio of a maximum width to a minimum width of the tapered portion. The optical multiplexing circuit according to claim 1.

5. The optical multiplexing circuit according to claim 1, wherein the MMI waveguide, the input waveguide, the main output waveguide, and the monitor output waveguide contain Zr in a core dopant.

6. The width of the MMI waveguide is set to the initial shape of the MMI waveguide. The region of the MMI waveguide is divided into a plurality of grids in the light traveling direction. The input field of the input light at the input port, the output field of the combined light at the first output port, and the output field of the branched light at the second output port are set. The updated structure of the MMI waveguide is obtained by wavefront matching. Based on the updated structure, the output fields at the first output port and the second output port are updated respectively. The update of the structure of the MMI waveguide by wavefront matching is repeated a predetermined number of times for the updated structure and the updated output fields. Finally, the last updated structure is determined as the structure of the MMI waveguide with a modulated width. The optical multiplexing circuit according to claim 1 obtained thereby.

7. Obtaining the updated structure of the MMI waveguide by wavefront matching includes obtaining the phase difference between the input field and the output field for each of the input lights of different wavelengths in one grid of interest, determining an operation on the width of the grid of interest based on the phase difference for each of the input lights of different wavelengths, determining the operation for all of the plurality of grids, and determining the updated structure of the MMI waveguide based on the determined operations of the plurality of grids. The optical multiplexing circuit according to claim 6.

8. The optical multiplexing circuit according to claim 1, further comprising, for each of the input waveguides, collimating the uncoupled light emitted from the input waveguide and having a light-shielding groove that totally reflects in a direction opposite to that of the input light.

9. A method for determining the structure of a wavelength combining waveguide circuit, the wavelength combining waveguide circuit comprising: a multimode interference waveguide (MMI waveguide) having at least two or more input ports, a first output port, and a second output port; input waveguides connected to each of the at least two or more input ports for receiving input light of different wavelengths; a main output waveguide connected to the first output port for outputting the combined light of the input light of different wavelengths; and a monitor output waveguide connected to the second output port for outputting branched light of the combined light at a predetermined branching ratio, the method comprising: setting an initial shape of the MMI waveguide, wherein a region of the MMI waveguide is divided into a plurality of grids in a light traveling direction; setting an input field of the input light at the input port, an output field of the combined light at the first output port, and an output field of the branched light at the second output port; updating a waveguide structure by wavefront matching; updating the output fields at the first output port and the second output port respectively based on the updated structure; further repeating the update of the waveguide structure by wavefront matching a predetermined number of times for the updated structure and the updated output fields; and finally determining the last updated structure as the structure of the MMI waveguide with a modulated width.

10. The method according to claim 9, wherein the step of updating the waveguide structure by wavefront matching includes: a first step of obtaining a phase difference between the input field and the output field for each of the input light of different wavelengths in one target grid; a second step of determining an operation on the width of the target grid based on the phase difference for each of the input light of different wavelengths; a third step of determining the operation for all of the plurality of grids; and a fourth step of determining an updated structure of the MMI waveguide based on the operation determined for the plurality of grids.

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