WO2024043215A1 - 光素子の設計方法、光素子の製造方法及び光素子の設計プログラム - Google Patents

光素子の設計方法、光素子の製造方法及び光素子の設計プログラム Download PDF

Info

Publication number
WO2024043215A1
WO2024043215A1 PCT/JP2023/030056 JP2023030056W WO2024043215A1 WO 2024043215 A1 WO2024043215 A1 WO 2024043215A1 JP 2023030056 W JP2023030056 W JP 2023030056W WO 2024043215 A1 WO2024043215 A1 WO 2024043215A1
Authority
WO
WIPO (PCT)
Prior art keywords
optical
optimization
individuals
optical device
normal distribution
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Ceased
Application number
PCT/JP2023/030056
Other languages
English (en)
French (fr)
Japanese (ja)
Inventor
充 竹中
悠人 宮武
信一 高木
カシディット トープラサートポン
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
University of Tokyo NUC
Original Assignee
University of Tokyo NUC
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by University of Tokyo NUC filed Critical University of Tokyo NUC
Priority to JP2024542814A priority Critical patent/JPWO2024043215A1/ja
Publication of WO2024043215A1 publication Critical patent/WO2024043215A1/ja
Anticipated expiration legal-status Critical
Ceased legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
    • G02B6/10—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings of the optical waveguide type
    • G02B6/12—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings of the optical waveguide type of the integrated circuit kind
    • G02B6/13—Integrated optical circuits characterised by the manufacturing method
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/06—Multi-objective optimisation, e.g. Pareto optimisation using simulated annealing [SA], ant colony algorithms or genetic algorithms [GA]

Definitions

  • the present invention relates to a method for designing an optical device, a method for manufacturing an optical device, and a program for designing an optical device.
  • Optical integrated circuits that integrate optical elements formed on silicon semiconductors are called silicon photonics, and have been attracting attention in recent years.
  • This optical integrated circuit is an optical circuit that has optical elements formed on an SOI (Si-on-insulator: silicon layer on an insulating layer) substrate, and can strongly confine light within a silicon optical waveguide, making it extremely compact. can create optical circuits.
  • Photonic integrated circuits can be produced using silicon semiconductor CMOS processes, making large-scale photonic integrated circuits possible.
  • the optical waveguide may be simply referred to as a waveguide.
  • Designing optical devices that are small and have high characteristics is important for realizing large-scale optical integrated circuits.
  • the following non-patent documents 1 and 2 are known as methods for designing optical elements.
  • Non-Patent Document 3 the covariance matrix adaptive evolution strategy (CMA-ES) is applied to the optimization of a diffraction grating coupler, which is one of the optical elements, and the pitch of the teeth of the diffraction grating and the width and depth of the grooves are It is described to optimize the In this example, CMA-ES is applied with the pitch of the teeth of the diffraction grating and the width and depth of the grooves as optimization parameters.
  • CMA-ES covariance matrix adaptive evolution strategy
  • Non-Patent Document 1 uses the length and width of the planar view shape (planar shape) of an optical waveguide, which is a basic component of an optical device, as parameters, and calculates each characteristic by simulation by changing the parameter values. , to search for parameter values with optimal characteristics, and to search for the optimal planar shape of the waveguide.
  • the planar shape of the searched optical element is very large, making it unsuitable as an optical element for the above-mentioned large-scale optical integrated circuit.
  • Non-Patent Document 2 uses the permittivity distribution in an optical waveguide, which is a component of an optical device, as a parameter, searches for an optimal permittivity distribution from an extremely wide parameter space, and determines the plane of the waveguide having the permittivity distribution. It explores shapes. However, in the optical devices that have been searched, disordered holes are formed in the multimode waveguides of photocouplers and optical splitters, for example. Therefore, although the planar shape of the optical element is very small, the holes formed in the optical waveguide cause large scattering of light, resulting in poor light transmittance. Also, initialization in the optimization process is very complex and difficult.
  • Non-Patent Document 3 uses CMA-ES to optimize the pitch, tooth width, and depth of a diffraction grating of a diffraction grating coupler, which is a special optical element.
  • the pitch and width of the teeth of the diffraction grating are not the outer periphery of the planar shape of the waveguide, but the depth of the teeth is the value in the film thickness direction of the waveguide, and the planar shape of the optical waveguide is widely used in the structure of optical devices. It is not intended to optimize the shape of the outer periphery.
  • Non-patent document 4 is a paper that describes CMA-ES in detail.
  • the purpose of the first aspect of the present embodiment is to provide an optical device design method, an optical device manufacturing method, and an optical device design program that can design an optical device with a simple optimization process and excellent characteristics. There is a particular thing.
  • a first aspect of the present embodiment is a method for designing an optical element having an optical waveguide composed of a cladding layer and a core layer, wherein a first The position coordinates of a plurality of control points that specify the outer periphery are selected as the optimization target parameters, and the computer is configured to adaptively change the multivariate normal distribution in the parameter space of the optimization target parameters to determine the optimization target parameters. Optimization processing is performed using a covariance matrix adaptive evolution strategy to search for a solution close to the optimal solution of the parameters, and the optical waveguides are associated with vectors whose components are the values of the parameters to be optimized in the parameter space.
  • the optimization process includes evaluation of the predetermined number of sampled individuals from the predetermined number of individuals sampled from the multivariate normal distribution in the g-th generation of the covariance matrix adaptive evolution strategy.
  • the process of evolving into the multivariate normal distribution in the g+1th generation is repeatedly executed according to a plurality of elite individuals selected based on the goodness of the value, and the process of evolving into the multivariate normal distribution in the predetermined Nth generation is performed. This is a method of designing an optical element in which an individual or an individual having a predetermined evaluation value or more is extracted as a solution close to the optimal solution.
  • the optimization process is simple and the optical device can be optimized to have excellent characteristics.
  • FIG. 2 is a diagram showing a structural example of a 2 ⁇ 2 optical coupler, which is an example of an optical element.
  • 1 is a diagram showing a configuration example of an optical integrated circuit.
  • FIG. 3 is a diagram illustrating data of an optical device optimized by an optical device design method using CMA-ES.
  • 1 is a diagram illustrating a configuration example of an optical device design apparatus according to the present embodiment.
  • FIG. 2 is a diagram showing a schematic flowchart of the optical device design method and program processing steps in the present embodiment.
  • FIG. 2 is a diagram illustrating an outline of processing steps of an optical device design program.
  • FIG. 6 is a diagram showing details of processing steps S2 and S4 in the flowchart.
  • FIG. 6 is a diagram showing details of processing steps S2 and S4 in the flowchart.
  • FIG. 6 is a diagram showing details of processing steps S2 and S4 in the flowchart.
  • FIG. 6 is a diagram showing details of processing steps S2 and S4 in the flowchart.
  • FIG. 2 is a diagram showing an example of a design method for optimizing a 2 ⁇ 2 optical coupler using CMA-ES. Changes in the Y coordinates of control points C0 to C7 on edge EG1 to be optimized and control points C10 to C11 on edge EG2 during initialization and after optimization when applying the optimization process using the CMA-ES algorithm It is a figure showing an example.
  • FIG. 2 is a diagram showing an example of a design method for optimizing a 2 ⁇ 2 optical coupler using CMA-ES. Changes in the Y coordinates of control points C0 to C7 on edge EG1 to be optimized and control points C10 to C11 on edge EG2 during initialization and after optimization when applying the optimization process using
  • FIG. 7 is a diagram showing the outer periphery of the planar shape of the optimal 2 ⁇ 2 optical coupler and the electric field intensity distribution of the light calculated by simulation, in which input light is split by a multimode interference section and emitted from a pair of output ports.
  • FIG. 7 is a diagram showing a comparison between a transmittance spectrum improved by optimization using CMA-ES in this example and a transmittance spectrum of a conventional directional coupler.
  • FIG. 3 is a diagram showing the manufacturing durability of transmittance (top) and the temperature stability of transmittance (bottom) comparing the present example and a conventional DC.
  • FIG. 7 is a diagram showing a second example of a design method for optimizing an S-shaped waveguide using CMA-ES.
  • FIG. 3 is a diagram showing an example of control points for specifying the outer periphery of the S-shaped waveguide 22.
  • FIG. FIG. 7 is a diagram showing a transmittance spectrum of an optimal solution searched for by executing an optimization program using CMA-ES for the S-shaped bent waveguide of this example.
  • FIG. 3 is a diagram showing an optimal solution extracted by optimization of an S-shaped waveguide using CMA-ES.
  • FIG. 7 is a diagram showing a third example of a design method for optimizing an optical demultiplexer using CMA-ES.
  • FIG. 7 is a diagram showing the transition of the figure of merit FOM for generations and the transmittance of the output port for two wavelengths ⁇ in the optimization process using CMA-ES.
  • FIG. 3 is a diagram showing optimization results of the optical demultiplexer of this example.
  • FIG. 1 is a diagram showing an example of the structure of a 2 ⁇ 2 optical coupler, which is an example of an optical element.
  • FIG. 1 shows a front sectional view (1), side sectional views (2) and (3), and a plan view (3) of the optical coupler.
  • the 2 ⁇ 2 optical coupler has a pair of input/output ports IO_11, IO_12, IO_21, and IO_22 provided on the left and right, and a multi-channel optical coupler provided between the input/output ports on the left and right. It has a mode interference section MMI.
  • the pair of input/output ports IO_11, IO_12 and IO_21, IO_22 are single mode optical waveguides, and are connected to the optical waveguide of the central multimode interference unit MMI.
  • the power of the light incident on the input port IO_11 is separated by the multimode interference unit MM1, and guided to a pair of output ports IO_21 and IO_22 and output.
  • the optical coupler can also have a pair of input ports on the right side and a pair of output ports on the left side.
  • the 2 ⁇ 2 optical coupler has a symmetrical shape vertically and horizontally, and can cause incident light and output light to enter and exit symmetrically vertically and horizontally.
  • cross-sectional views along A-A', B-B', and C-C' of the plan view are shown in (2), (4), and (1), and in each case, the inside of the silicon oxide film 12 formed on the surface of the silicon substrate 10 is shown.
  • a silicon film 14 having the shape of the outer peripheral edge indicated by the broken line shown in the plan view (3) is formed on. Since the refractive index of the silicon film 14 is higher than that of the silicon oxide film 12, light is confined within the silicon film 14.
  • the input and output ports and the multimode interference section are constituted by an optical waveguide consisting of a core layer of silicon film 14 and a cladding layer of silicon oxide film 12 surrounding it.
  • the planar outer periphery of the core layer is the planar outer periphery of the optical waveguide.
  • the silicon film 14 which is the core layer of the optical waveguide, has a flat structure with a constant film thickness.
  • a silicon oxide film and a silicon film 14 of a predetermined thickness are formed on the surface of a silicon substrate 10 by a bonding process and patterned, and the patterned silicon film 14 is further covered with a silicon oxide film. It is not necessary to form a silicon oxide film covering the patterned silicon film 14, and even in that case, light is confined within the silicon film 14 and can be used as an optical waveguide.
  • the characteristics of the optical coupler are optimized by optimizing the planar shape (pattern) of the silicon film 14 serving as the core layer.
  • the silicon film 14 is processed into an optimized shape in the patterning process.
  • the thickness of the silicon film 14 is constant and is set to a predetermined value in advance.
  • FIG. 2 is a diagram showing an example of the configuration of an optical integrated circuit.
  • FIG. 2 shows a pattern of an optical waveguide of an optical element of an optical integrated circuit.
  • a combination of a linear optical waveguide 20, an S-shaped optical waveguide 22, and a 2 ⁇ 2 optical coupler optical waveguide 24 is shown.
  • a resistive layer 26 for causing a phase shift of light based on the thermo-optic effect, for example, is disposed on the upper optical waveguide of the pair of linear optical waveguides 20 disposed in the center.
  • phase shifter circuit 28 is composed of the S-shaped optical waveguides 22_3 and 22_4 and the linear optical waveguides 20_3 and 20_4.
  • the two lights with a phase difference propagate through the S-shaped optical waveguides 22_5 and 22_6, enter the optical coupler 24_2, and are combined. Depending on the magnitude of the generated phase shift, the two lights propagate into the S-shaped optical waveguides 22_5 and 22_6.
  • the power ratio of the light coupled to the optical waveguides 22_7 and 22_8 is determined.
  • Both the straight optical waveguide and the S-shaped optical waveguide are single-mode optical waveguides. It is desirable that the S-shaped optical waveguide and optical coupler have high light transmittance and low loss of propagating light. Further, it is desirable that the desired characteristics be obtained with propagating light in a wide wavelength band. Furthermore, it is desirable that the optical waveguide has resistance to the manufacturing process (manufacturing tolerance) that allows desired characteristics to be obtained against variations in the manufacturing process.
  • FIG. 3 is a diagram illustrating data of an optical device optimized by the CMA-ES optical device design method.
  • the optical element shown in FIG. 3 is the 2 ⁇ 2 optical coupler 24 described in FIGS. 1 and 2.
  • FIG. 3 shows the planar shape (planar shape) (left) and cross section (right) of the waveguide of the optical coupler 24.
  • the planar shape includes a pair of input/output ports IO_11, IO_12 and IO_21, IO_22 provided on the left and right sides, and a multimode interference unit MMI arranged between both the pairs of ports.
  • the input/output port is a single mode waveguide
  • the multimode interference section is a wide multimode waveguide.
  • the core layer 14 of the waveguide is formed within a silicon oxide film 12 formed on the surface of the silicon substrate 10.
  • the film thicknesses TZ1 and TZ2 of the core layer 14 are fixed values determined for standard SOI wafers and are not subject to optimization. However, in the case of a wafer made of a material other than silicon, the film thicknesses of the core layer, etc. TZ1 and TZ2 may also be selected as optimization parameters.
  • a plurality of control points that specify the first outer periphery of at least a part of the outer periphery of the planar shape are selected as optimization target parameters. Ru. Whether a control point that specifies an outer circumferential edge other than the first outer circumferential edge or the size of the outer circumferential edge is to be optimized may be selected based on whether or not the optimization process converges. When not included in the optimization target, one or an arbitrary number of fixed values are given to those control points and sizes.
  • the outer peripheral edge of the planar shape of the waveguide of the optical coupler is the edge between points A1 and A2, the edge between points A2 and A3, and the edge between points A3 and A4. , has a set of edges between points A4 and A5, edges between points A5 and A6, and edges between points A6 and A7 in each of the four quadrants of the X-Y coordinates. Since the planar shape of the waveguide of the optical coupler is symmetrical in the X-axis direction and the Y-axis direction, the six edges between the aforementioned points A1 to A7 in the second quadrant shown in FIG. , also in the third and fourth quadrants.
  • a plurality of control points C0 to C5 specify at least a part of the first outer periphery (the edge between points A1 and A2).
  • the position coordinates of are selected as parameters to be optimized.
  • the plurality of control points C0 to C5 are points on the first outer peripheral edge (the edge between points A1 and A2).
  • a control point of a Bezier curve may be selected as the control point to be optimized.
  • the X coordinate may be a fixed value
  • the Y coordinate may be selected as the parameter to be optimized.
  • points C6, C7, etc. that specify a second outer circumferential edge other than the first outer circumferential edge among the six outer circumferential edges may be set to fixed coordinates without being included in the optimization target parameters, for example.
  • points C6 and C7 may also be included in the optimization target parameters.
  • the length LX1 in the X direction and the lengths LY1 to LY3, LY6 in the Y direction, which specify the planar shape of the waveguide of the optical coupler 24, may be included in the optimization parameters, or they may be included in the optimization parameters.
  • the hyperparameter may be selected as a hyperparameter to which a predetermined value is given in advance.
  • the length etc. of the hyperparameters may be set to any number of fixed values, and an optimization process may be performed using each fixed value to search for the optimal solution for the Y coordinates of the optimization target parameters C0 to C5. In that case, the evaluation results of the respective optimal solutions are compared and the fixed value of the best evaluation result is selected.
  • the gap length LY2 between the pair of left and right input ports and the pair of output ports may be selected as a parameter subject to a constraint that it be less than a predetermined fixed length. This constraint is due to the fact that a gap length necessary for the manufacturing process needs to be ensured between the ports.
  • the input/output port distance LY3 is set to, for example, half the width LY6 of the MMI, LY6/2.
  • the thickness TZ1 of the core layer 14 of the waveguide and the thickness TZ2 of the cladding layer 12 below the core layer 14 be set to fixed values, for example, in the case of a standard SOI wafer. In the case of wear other than silicon, it may be selected as an optimization parameter.
  • FOM Figure of Merit
  • the evaluation value for evaluating the characteristics of an individual during the CMA-ES optimization process.
  • the sum of the excess loss of a pair of output ports and the transmittance difference of a pair of output ports is selected as the evaluation value.
  • the cumulative value of the figure of merit calculated for each wavelength in the wavelength band may be used as the evaluation value. In the above example, it is determined that the lower the figure of merit, the better the evaluation value. Therefore, as the evaluation value, the figure of merit representing the most desirable characteristics is selected in the optimization process.
  • the optimal solution for the waveguide of this optical device is searched for by having the computer execute the CMA-ES optimization process.
  • the optimization process of CMA-ES will be explained below.
  • FIG. 4 is a diagram illustrating an example of the configuration of the optical device design apparatus in this embodiment.
  • the optical device design apparatus 30 is, for example, a supercomputer, a high-performance computer, a personal computer, or the like.
  • the optical device design apparatus 30 has a processor 32, a main memory 34, a network interface 36, storages 38, 49, and 42 that are large-capacity auxiliary storage devices, and an internal bus 44 that connects them.
  • an optical device design program 38, an optical device simulation program 40, and optical device data 42 to be optimized are stored.
  • the optical device design program 38 is an optimization program using the CMA-ES algorithm.
  • the optical device simulation program 40 is, for example, a simulation program for the 3D-FDTD method (Finite Difference Time Domain Method). These programs 38 and 40 are loaded into the main memory 34 and executed by the processor 32.
  • the optical device design device 30 is accessible from terminal devices 48, 49, etc., and includes optical device data to be optimized inputted from the terminal devices, that is, optical device optimization parameters and hyperparameters in the optimization process. , constraints, evaluation values, etc., an optical device design program is executed to search for an optimal solution for the optical device.
  • the optical element design apparatus 30 executes an optical element simulation program in the optical element optimization process to calculate the evaluation value of the individual to be searched.
  • FIG. 5 is a diagram showing a schematic flowchart of the optical device design method and program processing steps in this embodiment.
  • FIG. 6 is a diagram illustrating an outline of the processing steps of the optical device design program.
  • 7, FIG. 8, FIG. 9, and FIG. 10 are diagrams showing details of processing steps S2 and S4 in the flowchart. The optical device design method and program processing steps will be described with reference to these figures.
  • a plurality of control points that specify the outer periphery of the planar shape of the waveguide of the optical device are selected as optimization parameters (S1.0).
  • the Y coordinates of control points C0 to C5 on the outer peripheral edge between points A1 and A2 are selected as optimization parameters.
  • the length of a predetermined portion of the outer periphery of the waveguide may be selected as an optimization parameter. Optimization parameters are selected depending on the convergence operation of the optimization process.
  • This process is not a process of an optical element design program, but is a pre-process that is performed manually. In this process S1.0, the preliminary process explained in FIG. 3 is performed.
  • the CMA-ES algorithm is executed to search for an optimal solution for the optical device.
  • CMA-ES is an algorithm that performs global optimization probabilistically without using derivatives, imitating the process of adaptive evolution in living organisms.
  • one set x of optimization target parameters that defines the outer periphery of the planar shape of a waveguide of an optical device corresponds to one individual in the parameter space.
  • CMA-ES adaptively changes the multivariate normal distribution that includes multiple individuals x in this parameter space so that the better individual x in the multivariate normal distribution is included. Search the distribution containing the optimal individual x, and find the optimal individual x.
  • the individual x corresponds to a vector whose components are the Y coordinates of control points C0 to C5 selected as parameters to be optimized.
  • FIG. 7 is a diagram showing the process of generating a population of individuals x in the g+1 generation.
  • the generation of a population of individuals x in the g+1th generation is performed by sampling from the multivariate normal distribution of the previous gth generation, as shown in equation (1) in FIG.
  • N(0,C (g) ) is the multivariate normal distribution in the gth generation
  • x (g+1) k is the kth individual in the g+1th generation
  • m (g) is the gth generation is the mean vector indicating the center of the multivariate normal distribution in the gth generation
  • ⁇ (g) is the step size indicating the size of the multivariate normal distribution in the gth generation
  • C (g) is the shape of the multivariate normal distribution in the gth generation.
  • the covariance matrix, ⁇ is the number of individuals in the population.
  • the processor executes the optical device design program and initializes the 0th generation multivariate normal distribution in the parameter space (S1.1). Note that in the following description, processing executed by a processor that executes an optical device design program will be described, but the description will be omitted with “running the optical device design program”.
  • the covariance matrix C (0) in the 0th generation is initialized by the unit matrix (perfect spherical distribution), and the mean vector m (0) in the 0th generation and the step size ⁇ (0 ) is appropriately determined depending on the case to be optimized.
  • the covariance matrix C (0) corresponds to the shape of the multivariate normal distribution N(0,C (0) )
  • the individual x is a vector whose components are a set of parameters
  • the mean vector m is It corresponds to the center of the multivariate normal distribution
  • the step size ⁇ corresponds to the size of the multivariate normal distribution.
  • the processor selects a 0th generation multivariate normal distribution N(0,C (0) ) is generated.
  • the parameter space P_SP shown in FIG. 6 is indicated by a star for the individual B_IND with the best evaluation value and a contour line of the evaluation value centered on the star. The evaluation value gradually worsens as it spreads around the asterisk.
  • the 0th generation multivariate normal distribution N(0,C (0) ) may be generated at any position in the parameter space, but the multivariate normal distribution that includes known individuals that have been optimized to some extent is It is preferable to choose. For example, let the initial value of the optimization parameter of a known optimized individual be the component of the average vector m (0) in the 0th generation.
  • the processor randomly samples ⁇ first generation individuals x from the initialized multivariate normal distribution (S2).
  • the processor randomly generates ⁇ first generation individuals from the plurality of individuals included in the 0th generation multivariate normal distribution N(0,C (0) ). sample.
  • a plurality of black points in the multivariate normal distribution N(0,C (0) ) are sampled as ⁇ first generation individuals x.
  • the process of randomly sampling ⁇ number of individuals x of the first generation after initialization is based on equation (1) explained with reference to FIG. This is done by running
  • the multivariate normal distribution N(0,C (0) ) of the 0th generation is ⁇ (0) N(0,C (0) ) considering ⁇ (0) corresponding to the size of the distribution, and this
  • the multivariate normal distribution is located at the center of the 0th generation, m (0) .
  • the processor evaluates the performance index for each of the sampled ⁇ first generation individuals x (S3).
  • the figure of merit FOM which is the evaluation value, is the sum of the loss ratio of the total power of output light to the power of input light and the difference in transmittance of a pair of output ports.
  • the processor executes an optical device simulation program to perform a simulation for calculating the above-mentioned figure of merit.
  • the processor simulates the operation of each of the ⁇ optical elements having the shape of the outer periphery of the waveguide corresponding to the parameter value of the first generation individual x, and calculates the figure of merit FOM of each optical element.
  • the optical characteristics of each optical element are calculated based on electromagnetic field calculation.
  • the processor sorts the ⁇ individuals x in descending order of figure of merit FOM.
  • the order of the highest evaluation value is the order of the lowest performance index FOM.
  • some individuals with good evaluation values have changed to white dots.
  • the processor updates the multivariate normal distribution (S4). Specifically, the processor calculates the multivariate g+1 generation based on the ⁇ ( ⁇ ) individuals x with the highest evaluation value (figure of merit) out of the evaluated g+1 generation ⁇ individuals. Update to normal distribution. As shown in distribution update S4 in Figure 6, the g-th generation multivariate normal distribution N(0,C (g) ) is It is updated to a multivariate normal distribution N(0,C (g+1) ) with g+1 generations.
  • the center m (g+1) of the multivariate normal distribution of the g+1st generation is updated from the center m (g) of the gth generation based on elite individuals as described later, and the size of the distribution is determined by the step size ⁇ (g +1) , and the shape of the distribution is determined based on the covariance matrix C (g+1) .
  • Update S4 of the multivariate normal distribution includes updating S4.1 ( Figure 8) to the mean vector m (g+1) , updating S4.2 ( Figure 9) to the covariance matrix C (g+1) , with update S4.3 (FIG. 10) to step size ⁇ (g+1) .
  • Update S4.1 Figure 8
  • S4.2 Figure 9
  • C the covariance matrix C
  • update S4.3 FIG. 10
  • the processor updates the g-th generation average vector m (g) to the g+1-th generation average vector m (g+1) using equation (2).
  • the variables in equation (2) are as illustrated in FIG. According to equation (2), the difference between ⁇ elite individuals x of the g+1th generation and the average vector m (g) of the gth generation is weighted with a weighting coefficient w i that decreases in the sort order, and the sum is used for learning.
  • the average vector m (g+1) of the g+1 generation is calculated by multiplying by the rate c m and adding it to the average vector m (g) of the g- th generation. Therefore, the next average vector m (g+1) is calculated according to the amount and direction of movement from the average vector m (g) of the white point elite individual shown in individual evaluation S3 in FIG.
  • the ⁇ elite individuals are the parents of the g+1 generation.
  • the processor updates the g-th generation covariance matrix C (g) to the g+1-th generation covariance matrix C (g+1) using equations (3) to (5).
  • the variables in equations (3)-(5) are as illustrated in FIG. Note that P -c (g+1) is the evolution path of the covariance matrix in the g+1th generation. This evolution path of the covariance matrix is a parameter used to accumulate information on past average vectors and update the covariance matrix based on this information.
  • the processor updates the g-th generation step size ⁇ (g) to the g+1-th generation step size ⁇ (g+1) using equations (6) and (7).
  • the variables in equations (3)-(5) are as illustrated in FIG. Note that P - ⁇ (g+1) is the evolution path of the step size in the g+1th generation. This step size evolution path is a parameter used to accumulate information on past average vectors and update the step size based on this information.
  • the processor updates the number of generations g to g+1 (S5.1), and generates individuals S2 until the number of generations reaches a predetermined number of generations n gen (S5.2).
  • Individual evaluation S3 and distribution update S4 are repeated.
  • S2 to S4 may be repeated until the performance index of the elite individual reaches a desired level.
  • the g+1st generation multivariate normal distribution is such that the greater the distance of the g+1st generation elite individuals from the center of the gth generation multivariate normal distribution, the further away the optimal solution may be. Therefore, the distribution is larger and centered further away. Conversely, the smaller the distance, the closer the optimal solution is likely to be, so the distribution is centered closer and smaller. Since the optimal solution is searched for by repeatedly moving the multivariate normal distribution to the next generation multivariate normal distribution based on elite individuals, there may be local minimum values in the parameter space where the evaluation value (index of merit) is not optimal. Even if there are multiple solutions, it is possible to search for the optimal solution with the best evaluation value.
  • FIG. 11 is a diagram showing an example of a design method for optimizing a 2 ⁇ 2 optical coupler using CMA-ES.
  • the 2 ⁇ 2 optical coupler 24 of this embodiment has a pair of input ports 240_in and 241_in on the left side, a multimode interference section 244 (MMI) in the center, and a pair of output ports 248_bar and 248_cross on the right side.
  • tapered waveguides 242_tp and 243_tp are arranged between the pair of input ports and the multimode interference section 244, respectively, and similarly between the multimode interference section 244 and the pair of output ports 248_bar and 248_cross, respectively.
  • tapered waveguides 246_tp and 247_tp arranged.
  • a pair of input ports and output ports are single mode waveguides, and the tapered waveguide is tapered to suppress leakage of light to the outside of the waveguide between the single mode waveguide and the multimode interference section. has.
  • the planar shape of the optical coupler is shown in FIG. 11, its cross-sectional shape is the same as that in FIG.
  • FIG. 11 shows control points C0 to C11 arranged on the outer peripheral edge of a part of the planar shape of the optical coupler in the second quadrant. These control points are placed at X coordinate positions at intervals of resolution r points . Control points similar to those in the second quadrant are also arranged in the first, third, and fourth quadrants at positions symmetrical to the X and Y axes.
  • the Y coordinates of control points C0 to C6 on the outer periphery of the multimode interference part MMI and control points C7, C10, and C11 on the outer periphery of the tapered waveguide are the parameters to be optimized. selected.
  • the X coordinates of these control points are set to fixed values based on the hyperparameter resolution r points .
  • the initial value W MMI,init of the width in the Y-axis direction of the multimode interference part 244, the length l MMI in the same X-axis direction, the length l taper in the Y-axis direction of the tapered part 242_tp, and the resolution r points are hyperparameters. selected. Among these hyperparameters, the width and length W MMI,init , l MMI , and l taper are given an arbitrary number of values. An optimization process is performed for each combination of these hyperparameter values.
  • the values of these hyperparameters are fixed during the optimization process.
  • the evaluation values of the optimal solutions extracted in each optimization process are compared, and the optimal solution corresponding to the best evaluation value is extracted.
  • the distance between output ports dwg is 1/2 of the width W MMI,init of the multimode interference section, and is one of the hyperparameters.
  • the initial value W MMI_init of the width of the multimode interference part is 1.5 ⁇ m
  • the initial value l MMI,init of the same length is 8 or 2.2 ⁇ m
  • the tapered part The initial value l tape,iniy of the length in the Y-axis direction was set to 1 ⁇ m
  • the resolution r points was set to 417 nm between control points C0 and C8, and 500 nm between C9 and C10.
  • the initial value l MMI,init of the length of the multimode interference section is determined by sweeping this initial value l MMI,init in a certain range and at certain intervals with other variables fixed, so that the evaluation value of the optical element is the best. The value for this case was determined as the initial value. Since the width W MMI of the multimode interference part changes during the optimization process of the control points C0 to C6 on the outer periphery, its initial value W MMI,init is taken as a hyperparameter. Furthermore, the number of generations n gen , which is a condition for terminating the optimization process, is set to 120.
  • the figure of merit FOM which is an evaluation value, is calculated by calculating the difference between the transmittance T bar and T cross at a pair of output ports and the loss obtained by subtracting the sum of the transmittances at both output ports from 1, as shown in Figure 11. , is the sum of the values accumulated for each number of frequencies of input light.
  • C is a weighting factor for cumulative loss. When this weight c is reduced, the figure of merit becomes a figure of merit that emphasizes the difference in transmittance between a pair of output ports.
  • the pair of input and output ports is a single-mode waveguide, and its width is set to 430 nm and thickness to 220 nm, and the thickness of the silicon oxide film under the core layer 14 of the waveguide is set to 2 ⁇ m. Ru. These values are standard values in photonics.
  • FIG. 3 is a diagram showing an example of a change in Y coordinate. Moved from the Y coordinate position at initialization to the Y coordinate position after optimization. The Y coordinate of the edge between the control points on the outer periphery of the optimized waveguide was determined by, for example, two-dimensional interpolation of the Y coordinate of the control points.
  • the performance of the optical coupler having the outer periphery determined to be the optimal solution was calculated using an optical element simulator, and the results are as follows.
  • FIG. 13 is a diagram showing the outer periphery of the planar shape of the optimal 2 ⁇ 2 optical coupler and the energy distribution of the light calculated by simulation, in which the input light is split by the multimode interference section and is emitted from a pair of output ports. It is.
  • the outer peripheral edge of the planar shape of the optimal optical coupler has a wave shape in both the first to fourth quadrants. Furthermore, according to the light energy distribution, the energy of the input light is almost not scattered and is evenly distributed to the pair of output ports.
  • FIG. 14 is a diagram showing a comparison between the transmittance spectrum improved by optimization using CMA-ES in this example and the transmittance spectrum of a conventional directional coupler.
  • the left side of FIG. 14 shows the transmittance spectra of the output port, bar port, and cross port of the 2 ⁇ 2 optical coupler at initial time and final after optimization.
  • the horizontal axis is the wavelength of light
  • the vertical axis is the transmittance
  • EL stands for Excessive Loss
  • IB Imbalance
  • FIG. 14 shows a comparison of the transmittance spectra between the optimized 2 ⁇ 2 optical coupler and a conventional directional coupler (DC).
  • the difference in the transmittance spectra of both output ports of a conventional DC varies greatly depending on the wavelength.
  • the transmittances of both output ports after optimization have little difference over the entire wavelength band and have little wavelength dependence.
  • FIG. 15 is a diagram showing the manufacturing durability of transmittance (top) and the temperature stability of transmittance (bottom) comparing this example and a conventional DC.
  • the left side shows the change in transmittance with respect to the waveguide width variation Delta
  • the right side shows the change in the transmittance with respect to the waveguide film thickness variation.
  • the optical coupler optimized by CMA-ES of this embodiment has an even transmittance of approximately 50% at both output ports.
  • the conventional directional coupler DC the transmittance varies greatly when the waveguide width and film thickness vary. Note that since there is a correlation between the wavelength of light and the width and film thickness of the waveguide, it was possible to obtain the transmittance for the above-mentioned variations in the width and film thickness of the waveguide.
  • the temperature stability of the transmittance compared between this example and the conventional DC shown at the bottom of Figure 15 shows that the optical coupler optimized by CMA-ES of this example has a transmittance of approximately 50% at both output ports. % and are equal.
  • the transmittance of the conventional directional coupler DC varies greatly. This result was achieved because the refractive index of the waveguide changes as the temperature changes, and the change in refractive index is substantially linked to the change in the wavelength of the light.
  • FIG. 16 is a diagram showing a second embodiment of a design method for optimizing an S-bend waveguide using CMA-ES.
  • the S-shaped waveguide 22 is used for a waveguide that widens the gap between the waveguides of a pair of output ports such as an optical coupler 24, and a waveguide that narrows the gap between the widened waveguides. be done.
  • the S-shaped waveguide 22 has a structure including waveguides 1/4C_GW each having a 1/4 arc shape above and below the center point, and straight waveguides S_GW connected to each waveguide 1/4C_GW.
  • the x and y coordinates of control points (not shown) that specify the outer periphery on both sides of the S-shaped waveguide except for the input and output ends were selected as the parameters to be controlled.
  • the coordinates of the control points at the input end and output end of the S-shaped waveguide are given fixed values based on the relationship with other optical elements to be connected. In this example, an arbitrary number of fixed values were set for the effective radius R eff of the hyperparameter, optimization was performed using each fixed value, and the performance index of each optimal solution was evaluated.
  • the figure of merit FOM which is an evaluation value, is calculated and accumulated for each wavelength by subtracting the transmittance T, which is the ratio of the output optical power to the input optical power of the S-shaped waveguide, from 1.
  • T which is the ratio of the output optical power to the input optical power of the S-shaped waveguide
  • FIG. 17 is a diagram showing an example of control points that specify the outer periphery of the S-shaped waveguide 22.
  • the upper outer circumferential edge U and the lower outer circumferential edge L of the S-shaped bent waveguide are drawn as Bezier curves.
  • the upper outer peripheral edge is drawn with a Bezier curve based on the control points U1 to U7 shown in the figure, and the lower outer peripheral edge is drawn with a Bezier curve based on the control points L1 to L7.
  • These control points are control points that respectively specify both outer peripheral edges.
  • the x and y coordinates of the control points U1, L7 and U7, L1 at the input end and output end of the S-shaped waveguide 22 are set to fixed values.
  • the x and y coordinates of the remaining control points U2 to U6 and L2 to L6 are set as parameters to be optimized.
  • examples of x and y coordinates of 14 control points U1 to U7 and L1 to L7 are shown.
  • the x and y coordinates of control points U1, L7 and U7, L1 are fixed values, and the x and y coordinates of the remaining control points U2 to U6 and L2 to L6 are subject to optimization, and the initial values are shown in the figure. This is the value.
  • the cross-sectional shape of the waveguide, the thickness of the core layer, and the thickness of the silicon oxide film under the core layer are set to 220 nm and 2 ⁇ m.
  • FIG. 18 is a diagram showing a transmittance spectrum of an optimal solution searched for by executing an optimization program using CMA-ES for the S-shaped waveguide of this example.
  • FIG. 18 shows transmittance spectra at initialization and after optimization when the effective radius R eff is varied into three types and optimized for each type.
  • the waveguide shape at the time of initialization is a 1/4 perfect circle based on the effective radius, while the waveguide shape after optimization has a shape with an outer periphery that bulges outward from that at the time of initialization.
  • the transmittance spectrum after optimization (final) has a transmittance close to 0 dB (100%) in all wavelength bands.
  • the graph at the right end of FIG. 18 shows the effective radius on the horizontal axis and the insertion loss on the vertical axis, and shows the loss of the optimal solution detected by setting seven fixed values for the effective radius. The loss decreases as the effective radius increases.
  • the optimal solution with an effective radius of 2.75 ⁇ m is lower than the targeted insertion loss of 0.1 dB.
  • FIG. 19 is a diagram showing an optimal solution extracted by CMA-ES optimization of an S-shaped waveguide.
  • Figure 19 shows the outer edge shape of the optimal S-bend waveguide, the energy distribution of light propagating through the S-bend waveguide, the transmittance spectrum, and the increase in the number of generations in the optimization process.
  • the transmittance is almost 100% within the entire wavelength band. Furthermore, as the number of generations increases, the transmittance converges to 100%.
  • FIG. 20 is a diagram showing a third example of a design method for optimizing an optical demultiplexer using CMA-ES.
  • the optical demultiplexer 29 has an input port in at the left end, a pair of output ports O_bar and O_cross at the right end, a multimode interference section MMI at the center, and an input side between the input port in and the multimode interference section MMI. It has a taper part and a pair of output side taper parts between the multimode interference part MMI and the output port.
  • the input port and the output port are single mode waveguides, and the input side taper part and the output side taper part are waveguides that connect the multimode interference part MMI and the single mode waveguide.
  • the thickness of the core layer of these waveguides and the thickness of the silicon oxide film of the cladding layer below the core layer are fixed values similar to those of the above embodiments.
  • the outer periphery of the planar shape of the optical demultiplexer 29 is the outer periphery of the input port in, the input side taper part, the multimode interference part MMI, the outer periphery of the pair of output side taper parts, and the pair of output ports O_bar. , with the outer periphery of O_cross.
  • the first outer circumferential edge edge1 includes the upper outer circumferential edge of the multimode interference part MMI and the upper outer circumferential edges of the tapered parts on both sides, and the lower outer circumferential edge of the MMI and the lower outer circumferential edges of the tapered parts on both sides.
  • Control points on the second outer circumferential edge edge2 and the third and fourth outer circumferential edges edge3 and edge4 inside the pair of output-side tapered portions are selected as optimization target parameters.
  • the Y coordinates of each of the control points C50 to C52 on the outer periphery edge4 are selected as optimization target parameters.
  • the X coordinate of the control point on the outer periphery and the difference dx between the control points are selected as hyperparameters.
  • the distance y in between the lower edge of the input port in and the X axis, the distances y out1 and y out2 between the output port and the X axis, and the X axis of the multimode interference unit MMI are also selected as parameters to be optimized.
  • These parameters are hyperparameters given a plurality of values in the 2 ⁇ 2 optical coupler of FIG. 11, but in the optical demultiplexer of this embodiment, these parameters are targeted for optimization.
  • the number of parameters to be optimized increased and the dimension of the individual vector increased, but in this example, the optimization process was able to converge to an optimal solution.
  • the width MMI in the Y-axis direction of the multimode interference part MMI is the optimization parameter since the control points C0 to C13 and C20 to C33 are the optimization parameters. Not a parameter. However, the width MMI is given an initial value width MMI,init , 1.3 ⁇ m. Although not shown, several weeks are set as the optimization processing time. Note that, similarly to the 2 ⁇ 2 optical coupler, the edge shape between the control points whose Y coordinates are optimized is calculated by two-dimensional interpolation calculation.
  • initial values are given to the parameters to be optimized.
  • the initial value width MMI,init and 1000 nm is given to the distance dx in the Y-axis direction between control points
  • the Y coordinate of the control point of the parameter to be optimized is determined.
  • the individual x for the initial value of the optimization target parameter corresponds to the mean vector m (0) at the center of the initial distribution in the parameter space at the time of S1.1 initialization in FIG.
  • the hyperparameters are the Y-axis distance dx between control points and the coefficient c of the figure of merit FOM, which are set to 1000 nm and 1, respectively. Then, a constraint condition is set that the minimum value of the Y-axis direction gap between the control points C40 and C50 at the left end of the inner outer peripheral edge of the pair of output-side tapered portions is 120 nm or more. There is no restriction on the movement range of the Y coordinate of the control point of the parameter to be optimized. However, if this constraint condition is not satisfied, by setting the figure of merit FOM to the maximum value of 1, the movement range of the Y coordinate of the control point is effectively limited.
  • the control points are selected as hyperparameters.
  • the length MMI of the multimode interference part MMI , the length taper of the tapered part, the Y coordinate y in of the input port, and the y coordinates y out1 and y out2 of the output port were also included in the parameters to be optimized.
  • the optimization process in the optical demultiplexer is more advanced than in the 2 ⁇ 2 optical coupler, and the parameter space is further expanded.
  • an individual x sampled from a certain multivariate normal distribution has the value of each optimization target parameter as a vector component.
  • this vector includes the y coordinate of each control point and other length variables (yin, yout1, yout2, length MMI , length taper ). Therefore, the initial values of the Y coordinate and length variable are used as the initial value m (0) of the center vector of the multivariate normal distribution, and the Y coordinate and length variable are updated in the subsequent optimization process.
  • FIG. 21 is a diagram showing the transition of the figure of merit FOM for each generation and the transmittance of the output port for two wavelengths ⁇ in the optimization process using CMA-ES.
  • the figure of merit FOM rapidly decreases as the generations change, and its evolution has almost converged after the 110th generation.
  • the transmittance transition graph on the right the transmittance of both output ports increases rapidly in response to evolution, and almost converges after the 110th generation.
  • FIG. 22 is a diagram showing the optimization results of the optical demultiplexer of this example.
  • (1) shows the initial state of the waveguide of the optical demultiplexer and the planar shape outer periphery Optimized after optimization.
  • the outer circumferential edge in the initial state is the same as that shown in FIG. 20, while the outer circumferential edge after optimization has a wave-like outer circumferential edge in the X-axis direction.
  • the length l MMI of the multimode interference part MMI and the length l taper of the tapered part were used as hyperparameters. As such, they may be included in the optimization parameters.
  • the length l MMI of the multimode interference part MMI, the length l taper of the taper part, and the Y coordinates of the input port and output port may be used as hyperparameters.
  • the optical device is designed by optimization using the CMA-ES algorithm.
  • the optical element design process is performed by causing a computer to execute an optical element design program.
  • the optical device is manufactured based on the optimized shape of the outer periphery of the planar shape of the waveguide of the optical device.
  • a silicon oxide film and a silicon film that will become the core layer of the waveguide are formed on a silicon substrate through a bonding process, and the silicon film is patterned into the optimal shape for the outer periphery of the waveguide, which was explored during the design process. .
  • an optical element design method As described above, according to the present embodiment, it is possible to provide an optical element design method, an optical element manufacturing method, and an optical element design program that can design an optical element with excellent characteristics.

Landscapes

  • Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • Theoretical Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Geometry (AREA)
  • Computer Hardware Design (AREA)
  • Evolutionary Computation (AREA)
  • General Engineering & Computer Science (AREA)
  • Optics & Photonics (AREA)
  • Microelectronics & Electronic Packaging (AREA)
  • Computational Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Pure & Applied Mathematics (AREA)
  • Optical Integrated Circuits (AREA)
PCT/JP2023/030056 2022-08-24 2023-08-21 光素子の設計方法、光素子の製造方法及び光素子の設計プログラム Ceased WO2024043215A1 (ja)

Priority Applications (1)

Application Number Priority Date Filing Date Title
JP2024542814A JPWO2024043215A1 (https=) 2022-08-24 2023-08-21

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
JP2022-133689 2022-08-24
JP2022133689 2022-08-24

Publications (1)

Publication Number Publication Date
WO2024043215A1 true WO2024043215A1 (ja) 2024-02-29

Family

ID=90013343

Family Applications (1)

Application Number Title Priority Date Filing Date
PCT/JP2023/030056 Ceased WO2024043215A1 (ja) 2022-08-24 2023-08-21 光素子の設計方法、光素子の製造方法及び光素子の設計プログラム

Country Status (2)

Country Link
JP (1) JPWO2024043215A1 (https=)
WO (1) WO2024043215A1 (https=)

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2016021047A (ja) * 2014-07-15 2016-02-04 三菱電機株式会社 多モード干渉（ｍｍｉ）デバイス及び光信号を操作する方法
CN106650179A (zh) * 2017-01-23 2017-05-10 东南大学 一种基于cma‑es优化算法设计声学超材料单元的方法

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2016021047A (ja) * 2014-07-15 2016-02-04 三菱電機株式会社 多モード干渉（ｍｍｉ）デバイス及び光信号を操作する方法
CN106650179A (zh) * 2017-01-23 2017-05-10 东南大学 一种基于cma‑es优化算法设计声学超材料单元的方法

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
（社）電気学会 進化技術応用調査専門委員会（編）, 進化技術ハンドブック 第１巻 基礎編, 初版１刷, 株式会社近代科学社, 2010, ISBN: 978-4-7649-0385-2, pp. 77-78 section 5.5, (Institute of Electrical Engineers of Japan: Committee on application research of evolutionary technology (editor). Handbook of evolutionary technology : computation and applications vol. 1 Fundamentals. 1st edition 1 printing. KINDAI KAGAKU SHA CO., LTD.) *
MIYATAKE YUTO, KASIDIT TOPRASATPON, SHINICHI TAKAGI, TAKENAKA,: "Design of Compact and Low-loss 2×2 coupler based on CMA-ES S", 21A-A205-9. PROCEEDINGS OF THE 83RD JAPAN SOCIETY OF APPLIED PHYSICS AUTUMN ACADEMIC CONFERENCE (2022 TOHOKU UNIVERSITY KAWAUCHI KITA CAMPUS + ONLINE), 21 September 2022 (2022-09-21), XP093139736 *

Also Published As

Publication number Publication date
JPWO2024043215A1 (https=) 2024-02-29

Similar Documents

Publication Publication Date Title
JP7449374B2 (ja) マルチチャネルフォトニックデマルチプレクサ
JP7448644B2 (ja) ２チャネルフォトニックデマルチプレクサ、非一時的な機械アクセス可能記憶媒体、及び、コンピュータ実装方法
Hill et al. Optimizing imbalance and loss in 2× 2 3-dB multimode interference couplers via access waveguide width
Tang et al. Generative deep learning model for inverse design of integrated nanophotonic devices
US9784914B2 (en) Waveguide superlattices for high density photonics integrations
Michaels et al. Hierarchical design and optimization of silicon photonics
US20230058239A1 (en) Techniques for determining and using static regions in an inverse design process
Chen et al. Inverse design of free-form devices with fabrication-friendly topologies based on structure transformation
Liu et al. High-Q silicon photonic crystal ring resonator based on machine learning
WO2024043215A1 (ja) 光素子の設計方法、光素子の製造方法及び光素子の設計プログラム
CN114924408B (zh) 一种超宽带的光功率分束器的设计方法及设计系统
JP6341874B2 (ja) 多モード干渉（ｍｍｉ）デバイス及び光信号を操作する方法
Lo et al. Solutions of the quasi-vector wave equation for optical waveguides in a mapped infinite domains by the Galerkin's method
Hwang Relations between the reflectance and band structure of 2-D metallodielectric electromagnetic crystals
KR20230028245A (ko) 브릭형 서브-파장 주기적 도파관, 상기 도파관을 사용하는 모달 어댑터, 전력 분배기, 및 편광 스플리터
JP7814519B2 (ja) 製造されたデバイスの性能測定からのファウンドリ製造モデルの導出
Efseaff et al. Implementing commercial inverse design tools for compact, phase-encoded, plasmonic digital logic devices
US20260023220A1 (en) Inversely designed two-layer photonic grating coupler
Danis et al. Intrinsically DRC-Compliant Nanophotonic Design via Learned Generative Manifolds
Zhu et al. Inverse Design of Fabrication-Robust, Low-Loss, and Compact Waveguide Bends
Dubey et al. High-Performance Silicon Nitride Waveguides: A Platform for Nonlinear and Quantum Photonics
Cauchon Silicon photonic Bragg-based devices: hardware and software
Hafner et al. Simulation and Optimization of Photonic Crystals Using the Multiple Multipole Program
Wu et al. Constraints-aware Adaptive Routing with Hybrid Waveguides for Photonic Integrated Circuits
Weisshaar Impedance boundary method of moments for accurate and efficient analysis of planar graded-index optical waveguides

Legal Events

Date Code Title Description
121 Ep: the epo has been informed by wipo that ep was designated in this application

Ref document number: 23857326

Country of ref document: EP

Kind code of ref document: A1

WWE Wipo information: entry into national phase

Ref document number: 2024542814

Country of ref document: JP

NENP Non-entry into the national phase

Ref country code: DE

122 Ep: pct application non-entry in european phase

Ref document number: 23857326

Country of ref document: EP

Kind code of ref document: A1