WO2023240772A1 - 基于稀疏度计算的硅基光学微环滤波器逆向设计方法 - Google Patents

基于稀疏度计算的硅基光学微环滤波器逆向设计方法 Download PDF

Info

Publication number
WO2023240772A1
WO2023240772A1 PCT/CN2022/110582 CN2022110582W WO2023240772A1 WO 2023240772 A1 WO2023240772 A1 WO 2023240772A1 CN 2022110582 W CN2022110582 W CN 2022110582W WO 2023240772 A1 WO2023240772 A1 WO 2023240772A1
Authority
WO
WIPO (PCT)
Prior art keywords
micro
ring
cascaded
microring
filter
Prior art date
Application number
PCT/CN2022/110582
Other languages
English (en)
French (fr)
Inventor
刘宁
陈宇
Original Assignee
苏州大学
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 苏州大学 filed Critical 苏州大学
Publication of WO2023240772A1 publication Critical patent/WO2023240772A1/zh

Links

Images

Classifications

    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/0012—Optical design, e.g. procedures, algorithms, optimisation routines
    • 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
    • G02B6/24—Coupling light guides
    • G02B6/26—Optical coupling means
    • G02B6/28—Optical coupling means having data bus means, i.e. plural waveguides interconnected and providing an inherently bidirectional system by mixing and splitting signals
    • G02B6/293—Optical coupling means having data bus means, i.e. plural waveguides interconnected and providing an inherently bidirectional system by mixing and splitting signals with wavelength selective means
    • G02B6/29331—Optical coupling means having data bus means, i.e. plural waveguides interconnected and providing an inherently bidirectional system by mixing and splitting signals with wavelength selective means operating by evanescent wave coupling
    • G02B6/29335—Evanescent coupling to a resonator cavity, i.e. between a waveguide mode and a resonant mode of the cavity
    • G02B6/29338—Loop resonators
    • 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
    • G02B6/24—Coupling light guides
    • G02B6/26—Optical coupling means
    • G02B6/28—Optical coupling means having data bus means, i.e. plural waveguides interconnected and providing an inherently bidirectional system by mixing and splitting signals
    • G02B6/293—Optical coupling means having data bus means, i.e. plural waveguides interconnected and providing an inherently bidirectional system by mixing and splitting signals with wavelength selective means
    • G02B6/29331—Optical coupling means having data bus means, i.e. plural waveguides interconnected and providing an inherently bidirectional system by mixing and splitting signals with wavelength selective means operating by evanescent wave coupling
    • G02B6/29335—Evanescent coupling to a resonator cavity, i.e. between a waveguide mode and a resonant mode of the cavity
    • G02B6/29338—Loop resonators
    • G02B6/2934—Fibre ring resonators, e.g. fibre coils
    • 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
    • G02B6/24—Coupling light guides
    • G02B6/26—Optical coupling means
    • G02B6/28—Optical coupling means having data bus means, i.e. plural waveguides interconnected and providing an inherently bidirectional system by mixing and splitting signals
    • G02B6/293—Optical coupling means having data bus means, i.e. plural waveguides interconnected and providing an inherently bidirectional system by mixing and splitting signals with wavelength selective means
    • G02B6/29331—Optical coupling means having data bus means, i.e. plural waveguides interconnected and providing an inherently bidirectional system by mixing and splitting signals with wavelength selective means operating by evanescent wave coupling
    • G02B6/29335—Evanescent coupling to a resonator cavity, i.e. between a waveguide mode and a resonant mode of the cavity
    • G02B6/29338—Loop resonators
    • G02B6/29343—Cascade of loop resonators

Definitions

  • the invention relates to the technical field of micro-ring filters, and in particular to a silicon-based optical micro-ring filter reverse design method based on sparsity calculation.
  • Microring filters were first proposed by Marcatili in 1969. It was not until the past decade that, thanks to the advancement of process technology, related research on microrings developed rapidly. Now microrings have become a research area in the field of silicon-based photonics. Hotspot.
  • the design points of silicon-based microrings focus on the free spectrum range (FSR) of the microring, the extinction ratio of the microring, and the thermal tuning of the microring.
  • Francesco Morichetti of Milan Polytechnic proposed to use the vernier effect of non-integer ratios to expand the free spectrum range of the microring filter to achieve FSR-free in theory, that is, the microring filter does not operate within the spectrum range of interest. Shows periodic resonance.
  • the existing technology proposes a thermal tuning control method for a cascaded microring array, which realizes the rapid calibration and tuning functions of the cascaded microring array.
  • a vernier cascade microring filter is proposed, which reduces thermal crosstalk by placing the two-stage microrings of the fourth-order filter far enough apart to achieve simpler and more accurate microring tuning.
  • Dai Daozin's team at Zhejiang University proposed using curved waveguides to replace straight waveguides or multi-mode interferometers in the microring coupling part in high-order microring filters, which can achieve flexible coupling ratios in the coupling area. Choose and reduce losses.
  • Reverse design can realize the design automation of silicon-based optical components, thereby facilitating the large-scale integration of silicon-based optical devices.
  • reverse design has been increasingly applied to silicon-based photonic design.
  • Reverse design is a concept proposed relative to forward design.
  • Reverse design is generally improved based on the original product model or existing products generated by the forward design concept. It is obtained by directly modifying, testing and analyzing the model that caused the problem. Relatively ideal results are obtained, and then the final model is obtained through a series of methods such as scanning and modeling based on the revised model or sample.
  • the reverse design method provides a new design method for the design of silicon-based optoelectronic devices, which can realize new micro-nano devices such as ultra-small size, ultra-high performance and rich functions.
  • silicon-based cascaded microring filters mainly adopt the forward design method, that is, the structure is designed completely according to the relevant a priori theoretical knowledge of microring filters.
  • the cascaded microrings are designed in When considering the bending loss caused by reducing the radius of the microring, the vernier effect can be used to expand the free spectrum range.
  • Figure 1 is a schematic diagram of the cascaded double rings. The vernier effect is shown in Figure 2.
  • Figure 2 the two cascaded microrings If the radii are different, their FSR will also be different. Only when the wavelength of the incident light satisfies the resonance conditions of the two rings at the same time, the light can be transmitted to the output end, thus achieving the effect of expanding the FSR.
  • the forward-designed silicon-based cascaded microring filter has the following problems:
  • the silicon-based cascaded microring filter using forward design has low design freedom.
  • the FSR ratio of the cascaded microring can only be selected as an integer ratio, which cannot ensure the optimal performance of the designed cascaded microring filter.
  • the technical problem to be solved by the present invention is to provide a silicon-based optical micro-ring based on sparsity calculation that designs the micro-ring structure according to the design goal, improves the degree of freedom of silicon-based cascade micro-ring filter design, and improves filter design efficiency. Filter reverse design method.
  • the present invention provides a silicon-based optical micro-ring filter reverse design method based on sparsity calculation.
  • the silicon-based optical micro-ring filter reverse design method based on sparsity calculation includes the following steps:
  • step S4 Based on the sparsity obtained by the summation, iterate the micro-ring radius according to the optimization goal of maximizing sparsity, and use the iterated micro-ring radius to recalculate the coupling coefficient, and return to step S2 until the maximum number of iterations is reached to obtain the final Microring radius and coupling coefficient.
  • step S1 the initial radius of each microring in the cascaded microring filter is determined by the following formula:
  • each coupling coefficient of the cascaded micro-ring filter is determined through the following formula:
  • K 1 is the coupling coefficient between the first microring and the bus waveguide
  • K n+1 is the coupling coefficient between the nth microring and the bus waveguide
  • K q represents the qth microring Coupling coefficient with q-1 microrings
  • parameter g can be expressed as:
  • ⁇ is related to the designed in-band loss, expressed as:
  • step S2 the cascaded micro-ring filter is split into several directional couplers and transmission lines using the transmission matrix method.
  • the directional couplers and transmission lines are both four-port components.
  • the couplers and transmission lines are arranged at intervals in sequence.
  • the transfer function of the cascaded micro-ring filter is expressed by the transfer matrix method as:
  • input 1 and input 2 are the two input ports of the first directional coupler
  • output 1 and output 2 are the two output ports of the last directional coupler
  • M 1 , M 3 ,..., M 2n+1 are The matrix representation of the current directional coupler
  • M 2 , M 4 ,..., M 2n are the matrix representation of the current transmission line
  • M is the matrix representation of the entire cascaded micro-ring filter
  • P d is the transmission spectrum of the cascaded micro-ring filter.
  • k the coupling coefficient
  • t the transmission coefficient
  • * conjugation
  • ⁇ represents the microring cavity loss
  • e represents the natural index
  • ⁇ represents the phase shift in one circle of the microring.
  • ⁇ is expressed as:
  • neff represents the effective refractive index of the waveguide
  • R represents the radius of the microring
  • ⁇ represents the central wavelength
  • step S2 and step S3 the following steps are also included:
  • P d is the transmission spectrum of the cascaded micro-ring filter.
  • step S3 a composite inverse proportional function is used to characterize the sparsity of the transmission spectrum.
  • the form of the composite inverse proportional function is:
  • ⁇ is a parameter that controls the approximation effect.
  • ⁇ 0 the properties of this function are described as:
  • the present invention also provides an electronic device, including a memory, a processor and a computer program stored in the memory and executable on the processor.
  • the processor executes the program, the steps of any one of the above methods are implemented. .
  • the present invention also provides a computer-readable storage medium on which a computer program is stored, which is characterized in that when the program is executed by a processor, the steps of any one of the above methods are implemented.
  • the present invention also provides a silicon-based optical micro-ring filter, which is designed using any of the above-mentioned reverse design methods of silicon-based optical micro-ring filters based on sparsity calculation.
  • the present invention introduces reverse design thinking into the design of silicon-based cascaded microrings, and transforms the problem of designing cascaded microring filters into the problem of solving the microring structure corresponding to the sparsest spectrum of the cascaded microring filter in the design band. .
  • the invention can improve the degree of freedom in the design of silicon-based cascade micro-ring filters, and can flexibly adjust the structure of the micro-rings according to actual manufacturing processes and application requirements, thereby improving the performance of the designed filter.
  • the present invention can design the micro-ring structure according to the design target, so it can realize design automation and improve the filter design efficiency.
  • Figure 1 is a schematic diagram of cascaded double rings
  • Figure 2 is a schematic diagram of the cascade double-ring cursor effect
  • Figure 3 is a schematic diagram of the silicon-based optical micro-ring filter reverse design method based on sparsity calculation according to the present invention
  • Figure 4 is a schematic diagram of cascaded microrings
  • Figure 5 is a schematic diagram of the directional coupler and transmission line split into cascaded microrings.
  • the preferred embodiment of the present invention discloses a silicon-based optical micro-ring filter reverse design method based on sparsity calculation, which includes the following steps:
  • the performance indicators include the free spectrum range of the filter, in-band loss, Microring radius, assuming that the total free spectrum range of the target is FSR total .
  • the cascaded microring filter is composed of n microrings cascaded. The relationship between the initial free spectrum range of each microring and FSR total is as follows: formula (1) .
  • the initial radius of each microring in the cascaded microring filter is determined by formulas (1) and (2). Among them, the obtained free spectrum range only needs to be the total free spectrum range of the target. That’s it, subsequent algorithm iterations can obtain the radius parameter that conforms to the target free spectrum range.
  • the coefficient ratio of the range which is an integer ratio in this step;
  • R i is the initial radius of the i-th microring;
  • ⁇ is the central wavelength, and
  • n g is the group refractive index of the waveguide.
  • step S1 determine each coupling coefficient of the cascaded micro-ring filter through the following formula:
  • K 1 is the coupling coefficient between the first microring and the bus waveguide
  • K n+1 is the coupling coefficient between the nth microring and the bus waveguide
  • K q represents the qth microring Coupling coefficient with q-1 microrings
  • parameter g can be expressed as:
  • ⁇ is related to the designed in-band loss, expressed as:
  • step S2 the cascaded micro-ring filter is split into several directional couplers and transmission lines using the transmission matrix method.
  • the directional couplers and transmission lines are both four-port components. Refer to Figure 5.
  • the directional coupler is on the left and the transmission line is on the right.
  • the directional coupler and the transmission line are arranged at intervals in sequence. Both ends of the cascaded micro-ring filter are directional couplers.
  • k the coupling coefficient
  • t the transmission coefficient
  • * conjugation
  • ⁇ represents the microring cavity loss
  • e represents the natural index
  • ⁇ represents the phase shift in one circle of the microring.
  • ⁇ is expressed as:
  • neff represents the effective refractive index of the waveguide
  • R represents the radius of the microring
  • ⁇ represents the central wavelength
  • the transfer function of the cascaded micro-ring filter is expressed by the transfer matrix method as:
  • input 1 and input 2 are the two input ports of the first directional coupler
  • output 1 and output 2 are the two output ports of the last directional coupler
  • M 1 , M 3 ,..., M 2n+1 are The matrix representation of the current directional coupler
  • M 2 , M 4 ,..., M 2n are the matrix representation of the current transmission line
  • M is the matrix representation of the entire cascaded micro-ring filter
  • P d is the transmission spectrum of the cascaded micro-ring filter.
  • step S2 the following steps are also included:
  • the data processing part includes data clipping and data normalization to ensure the efficiency of algorithm iteration.
  • Data clipping cuts out the part of the spectrum that exhibits particularly low crosstalk, and this part does not contribute to the optimization of the algorithm.
  • the data can be normalized using the linear normalization method, which can be expressed as:
  • the cascaded microring filter in order to ensure that the designed filter parameters can be tuned across the entire frequency spectrum, it is necessary to consider the performance of the designed filter in different frequency bands, so it is necessary to simultaneously calculate the performance of the designed filter at three frequency points: low frequency, medium frequency and high frequency.
  • the sparsity of the spectrum at three frequency points is calculated and summed to obtain the total sparsity at three frequency points as the basis for optimization.
  • the tuning of the low, medium and high frequency bands of the cascaded microring is achieved in the algorithm by modifying neff in equation (10).
  • the cascaded microring filter generally uses thermal tuning to tune the resonant wavelength. .
  • the neff of the microring will drift through heating, and its value will change.
  • neff is a parameter of the transfer function of the cascade microring.
  • neff is a parameter of the transfer function of the cascade microring.
  • the compound inverse proportional function (CIPF) is used to characterize the sparsity of the transmission spectrum.
  • the form of the compound inverse proportional function is:
  • ⁇ is a parameter that controls the approximation effect.
  • ⁇ 0 the properties of this function are described as:
  • step S4 Based on the sparsity obtained by summation, iterate the micro-ring radius according to the optimization goal of maximizing sparsity, and use the iterated micro-ring radius to recalculate the coupling coefficient according to formula (3) (4) (5) (6), And return to step S2 until the maximum number of iterations is reached, and the final microring radius and coupling coefficient are obtained.
  • use algorithms such as ant colony algorithm, particle swarm algorithm, genetic algorithm, simulated annealing algorithm or gradient descent for optimization iteration.
  • the silicon-based optical micro-ring filter reverse design method based on sparsity calculation in this embodiment is used to design a four-stage cascaded micro-ring filter in the C+L band, which includes the following steps:
  • the first step Determine the radius and coupling coefficient of each microring of the initial cascaded microring filter; according to the wavelength range of C+L, determine the radius of each microring of the initial cascaded microring filter according to equation (1), According to the 3dB bandwidth and in-band loss, determine each coupling coefficient of the microring according to formula (3) (4) (5) (6).
  • Step 2 Use the ant colony algorithm to optimize the microring radius based on sparsity; including the following steps:
  • Each ant has four search directions, representing the radii of the four micro-rings.
  • Equation (16) Use the composite inverse proportional function shown in Equation (16) as the cost function to calculate the spectrum sparsity. Sum up the sparsity of the microrings in the three frequency bands of low frequency (1490nm), medium (1540nm), and high frequency (1590nm) from 1480 to 1600nm.
  • T max represents the largest pheromone in the ant colony
  • Ti represents the pheromone of the i-th ant.
  • the pheromone is equivalent to the sparsity.
  • Pi When Pi is large, it means that the i-th ant is far away from the current global optimal, and global search is selected.
  • Global search refers to randomly selecting four micro-ring radii in the global scope.
  • Pi When Pi is small, it means that the i-th ant is closer to the current global optimal, and local search is selected.
  • Local search refers to randomly selecting four micro-ring radii near the result of the last iteration.
  • the present invention introduces reverse design thinking into the design of silicon-based cascaded microrings, and transforms the problem of designing cascaded microring filters into the problem of solving the microring structure corresponding to the sparsest spectrum of the cascaded microring filter in the design band. .
  • the invention can improve the degree of freedom in the design of silicon-based cascade micro-ring filters, and can flexibly adjust the structure of the micro-rings according to actual manufacturing processes and application requirements, thereby improving the performance of the designed filter.
  • the present invention can design the micro-ring structure according to the design target, so it can realize design automation and improve the filter design efficiency.
  • This embodiment discloses an electronic device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor.
  • the processor executes the program, it implements the sparse-based method described in the first embodiment. Steps of the reverse design method for silicon-based optical micro-ring filters based on degree calculation.
  • This embodiment discloses a computer-readable storage medium on which a computer program is stored.
  • the program is executed by a processor, the silicon-based optical micro-ring filter reverse design method based on sparsity calculation described in the first embodiment is implemented. A step of.
  • This embodiment discloses a silicon-based optical micro-ring filter, which is designed using the silicon-based optical micro-ring filter reverse design method based on sparsity calculation described in the first embodiment above.

Landscapes

  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Optics & Photonics (AREA)
  • Optical Integrated Circuits (AREA)

Abstract

一种基于稀疏度计算的硅基光学微环滤波器逆向设计方法，包括：S1、确定级联微环滤波器中各个微环的初始半径和级联微环滤波器的各个耦合系数；S2、根据初始半径和耦合系数，利用传输矩阵法得到级联微环滤波器的传输频谱；S3、计算级联微环在不同频点处的稀疏度，并进行求和；S4、基于求和得到的稀疏度，按照稀疏度最大的优化目标对微环半径进行迭代，并利用迭代的微环半径重新计算耦合系数，并返回步骤S2，直至达到最大迭代次数，得到最终的微环半径和耦合系数。根据设计目标来设计微环结构，提高了硅基级联微环滤波器设计的自由度，提高了滤波器设计效率。

Description

基于稀疏度计算的硅基光学微环滤波器逆向设计方法 技术领域
本发明涉及微环滤波器技术领域，特别涉及一种基于稀疏度计算的硅基光学微环滤波器逆向设计方法。
背景技术
微环滤波器早在1969年被Marcatili首次提出，直到近十年，得益于工艺技术的进步，微环的相关研究才迅速发展起来，如今微环已经成为了硅基光子学领域的一个研究热点。硅基微环的设计要点集中在微环的自由频谱范围(Free spectrum range,FSR)、微环的消光比以及微环的热调谐等方向。米兰理工学院的Francesco Morichetti提出了利用非整数比的游标效应来扩展微环滤波器的自由频谱范围从而在理论上实现了FSR-free，也即微环滤波器在感兴趣的频谱范围内并不表现周期性谐振。现有技术提出了一种级联微环阵列的热调谐控制方法，实现了级联微环阵列的快速标定与调谐功能。除此之外提出了一种游标级联微环滤波器，通过将四阶滤波器的两级微环放得足够远来减少热串扰，实现更加简单与精准的微环调谐。在国内，浙江大学的戴道锌团队提出了在高阶微环滤波器中，利用弯曲波导来代替微环耦合部分的直波导或者是多模干涉仪，这样可以实现耦合区的耦合比的灵活选择并且降低损耗。
逆向设计由于可以实现硅基光学元件的设计自动化，从而有助于硅上光器件的大规模集成，近年来越来越多地应用到硅基光子设计上来。逆向设计是相对于正向设计提出的概念，逆向设计一般是根据正向设计概念所产生的产品原始模型或者已有产品来进行改良，通过对产生问题的模型进行直接的修改、试验和分析得到相对理想的结果，然后再根据修正后的模型或样件通过扫描和造型等一系列方法得到最终的模型。逆向设计方法为硅基光电子器件的设计提供了全新的设计方法，可以实现例如超小尺寸，超高性能以及丰富功能的新型微纳器件。国内也有诸多优秀团队致力于光纤/硅基光学器件逆向设计与自动化设计领域，例如上海交通大学提出了基于粒子群算法的环芯结构OAM光纤设计、 基于搜索算法和神经网络的环芯结构OAM光纤设计以及少模光纤弱耦合优化设计等，取得了一系列优秀的成果。但是，当前逆向设计在硅基光子设计上的主要应用集中在耦合器、功率分束器、模分复用解复用器以及硅衬底上的减反射涂层系统等。逆向设计在硅基微环谐振器设计上的应用目前尚未见报道。
目前硅基级联微环滤波器主要采用正向设计的方法，也即完全按照微环滤波器的相关先验理论知识进行结构的设计，级联微环为了使得自由频谱范围满足设计要求，在考虑减小微环半径带来的弯曲损耗时可以采用游标效应来扩大自由频谱范围，图1为级联双环示意图，游标效应如图2，从图2可以看出，级联的两个微环半径不同，则它们的FSR也不一样，只有当入射光的波长同时满足两个环的谐振条件时，光才能传到输出端，这样就达到了扩大FSR的效果。
综上所述，正向设计的硅基级联微环滤波器存在以下问题：
(1)利用正向设计的硅基级联微环滤波器设计自由度低，级联微环的FSR比值只能选择整数比，无法确保设计的级联微环滤波器性能最优。
(2)正向设计过程需要依靠设计者的经验，不利于设计自动化与大规模集成设计的发展。
(3)正向设计的参数扫描没有明确的优化方向，设计效率低下，当级联微环的阶数增加时该问题更加突出。
发明内容
本发明要解决的技术问题是提供一种根据设计目标来设计微环结构、提高硅基级联微环滤波器设计的自由度、提高滤波器设计效率的基于稀疏度计算的硅基光学微环滤波器逆向设计方法。
为了解决上述问题，本发明提供了一种基于稀疏度计算的硅基光学微环滤波器逆向设计方法，所述基于稀疏度计算的硅基光学微环滤波器逆向设计方法包括以下步骤：
S1、确定级联微环滤波器中各个微环的初始半径和级联微环滤波器的各个耦合系数；
S2、根据初始半径和耦合系数，利用传输矩阵法得到级联微环滤波器的传输频谱；
S3、计算级联微环在不同频点处的稀疏度，并进行求和；
S4、基于求和得到的稀疏度，按照稀疏度最大的优化目标对微环半径进行迭代，并利用迭代的微环半径重新计算耦合系数，并返回步骤S2，直至达到最大迭代次数，得到最终的微环半径和耦合系数。
作为本发明的进一步改进，步骤S1中，通过以下公式确定级联微环滤波器中各个微环的初始半径：
Figure PCTCN2022110582-appb-000001
Figure PCTCN2022110582-appb-000002
其中，FSR total为目标的总自由频谱范围；n为级联微环滤波器中微环个数；FSR i为级联微环滤波器中第i个微环的初始自由频谱范围，i＝1,2，...，n；N 1、N 2、…、N n为各个微环的自由频谱范围的系数比；R i为第i个微环的初始半径；λ为中心波长，n g为波导的群折射率。
作为本发明的进一步改进，步骤S1中，通过以下公式确定级联微环滤波器的各个耦合系数：
Figure PCTCN2022110582-appb-000003
Figure PCTCN2022110582-appb-000004
Figure PCTCN2022110582-appb-000005
Figure PCTCN2022110582-appb-000006
Figure PCTCN2022110582-appb-000007
Figure PCTCN2022110582-appb-000008
其中，B为所设计的3dB带宽，K 1为第1个微环与总线波导的耦合系数，K n+1为第n个微环与总线波导的耦合系数，K q表示第q个微环与q-1个微环之间的耦合系数；参数g可以表示为：
Figure PCTCN2022110582-appb-000009
其中：
Figure PCTCN2022110582-appb-000010
Figure PCTCN2022110582-appb-000011
Figure PCTCN2022110582-appb-000012
其中，ε与所设计的带内损耗loss有关，表示为：
Figure PCTCN2022110582-appb-000013
通过公式(3)(4)(5)(6)得到所设计的光学微环滤波器各个微环的各个耦合系数。
作为本发明的进一步改进，在步骤S2中，利用传输矩阵法将级联微环滤波器拆分成若干定向耦合器和传输线，所述定向耦合器和传输线均为四端口元器件，所述定向耦合器和传输线依次间隔排列，所述级联微环滤波器的传输函数用传输矩阵法表示为：
Figure PCTCN2022110582-appb-000014
其中，input 1和input 2为第一个定向耦合器的两个输入端口，output 1和output 2和最后一个定向耦合器的两个输出端口；M 1、M 3、…、M 2n+1为当前定向耦合器的矩阵表示；M 2、M 4、…、M 2n为当前传输线的矩阵表示；M为整个级联微环滤波器的矩阵表示；
当n为奇数时，output 1口为drop口，此时级联微环滤波器的传输频谱为：
Figure PCTCN2022110582-appb-000015
当n为偶数时，output 2口为drop口，此时级联微环滤波器的传输频谱为：
Figure PCTCN2022110582-appb-000016
其中，P d为级联微环滤波器的传输频谱。
作为本发明的进一步改进，
Figure PCTCN2022110582-appb-000017
Figure PCTCN2022110582-appb-000018
其中，k表示耦合系数，t表示透射系数，*表示共轭，在不考虑耦合区损耗的情况下，耦合系数与透射系数的关系为：
k 2+t 2＝1
其中，α表示微环腔体损耗，e表示自然指数，θ表示微环内一圈产生相移，在微环中，θ表示为：
Figure PCTCN2022110582-appb-000019
其中，neff表示波导的有效折射率，R表示微环的半径，λ表示中心波长。
作为本发明的进一步改进，在步骤S2和步骤S3中，还包括以下步骤：
对传输频谱进行数据的裁剪和归一化处理；
其中，归一化处理表示为：
Figure PCTCN2022110582-appb-000020
其中，P d为级联微环滤波器的传输频谱。
作为本发明的进一步改进，在步骤S3中，利用复合反比例函数来表征传输频谱的稀疏度，复合反比例函数的形式为：
Figure PCTCN2022110582-appb-000021
其中，σ为控制逼近效果的参数，则当σ→0时，该函数的性质描述为：
Figure PCTCN2022110582-appb-000022
将总的传输频谱代入上式的x中得到传输频谱的稀疏度。
本发明还提供了一种电子设备，包括存储器、处理器及存储在存储器上并可在处理器上运行的计算机程序，所述处理器执行所述程序时实现上述任意一项所述方法的步骤。
本发明还提供了一种计算机可读存储介质，其上存储有计算机程序，其特征在于，该程序被处理器执行时实现上述任意一项所述方法的步骤。
本发明还提供了一种硅基光学微环滤波器，其采用上述任一所述的基于稀疏度计算的硅基光学微环滤波器逆向设计方法设计得到。
本发明的有益效果：
本发明将逆向设计思维引入硅基级联微环的设计中，将设计级联微环滤波器问题转化为求解级联微环滤波器在设计波段的最稀疏光谱所对应的微环结构的问题。
本发明可以提高硅基级联微环滤波器设计的自由度，可以根据实际制造工艺与应用需求灵活调整微环的结构从而提高所设计的滤波器的性能。
本发明可以根据设计目标来设计微环结构，所以可以实现设计自动化，提高滤波器设计效率。
上述说明仅是本发明技术方案的概述，为了能够更清楚了解本发明的技术手段，而可依照说明书的内容予以实施，并且为了让本发明的上述和其他目的、特征和优点能够更明显易懂，以下特举较佳实施例，并配合附图，详细说明如下。
附图说明
图1是级联双环示意图；
图2是级联双环游标效应示意图；
图3是本发明基于稀疏度计算的硅基光学微环滤波器逆向设计方法的示意图；
图4是级联微环示意图；
图5是级联微环拆分的定向耦合器与传输线示意图。
具体实施方式
下面结合附图和具体实施例对本发明作进一步说明，以使本领域的技术人员可以更好地理解本发明并能予以实施，但所举实施例不作为对本发明的限定。
实施例一
如图3所示，本发明优选实施例公开了一种基于稀疏度计算的硅基光学微环滤波器逆向设计方法，包括以下步骤：
S1、确定级联微环滤波器中各个微环的初始半径和级联微环滤波器的各个耦合系数；具体地，首先确定设计目标，性能指标包括滤波器的自由频谱范围、带内损耗、微环半径，设目标的总自由频谱范围为FSR total，该级联微环滤波器由n个微环级联而成，则各个微环的初始自由频谱范围与FSR total关系如公式(1)。
Figure PCTCN2022110582-appb-000023
Figure PCTCN2022110582-appb-000024
通过公式(1)和(2)确定级联微环滤波器中各个微环的初始半径。其中，所得到的自由频谱范围只需要为目标的总自由频谱范围的
Figure PCTCN2022110582-appb-000025
即可，后续通过算法迭代可以得到符合目标自由频谱范围的半径参数。FSR i为级联微环滤波器中第i个微环的初始自由频谱范围，i＝1,2，...，n；N 1、N 2、…、N n为各个微环的自由频谱范围的系数比，该系数比在本步骤中为整数比；R i为第i个微环的初始半径；λ为中心波长，n g为波导的群折射率。
步骤S1中，通过以下公式确定级联微环滤波器的各个耦合系数：
Figure PCTCN2022110582-appb-000026
其中，B为所设计的3dB带宽，K 1为第1个微环与总线波导的耦合系数，K n+1为第n个微环与总线波导的耦合系数，K q表示第q个微环与q-1个微环之间的耦合系数；参数g可以表示为：
Figure PCTCN2022110582-appb-000027
其中：
Figure PCTCN2022110582-appb-000028
Figure PCTCN2022110582-appb-000029
Figure PCTCN2022110582-appb-000030
其中，ε与所设计的带内损耗loss有关，表示为：
Figure PCTCN2022110582-appb-000031
通过公式(3)(4)(5)(6)得到所设计的光学微环滤波器各个微环的各个耦合系数。
S2、根据初始半径和耦合系数，利用传输矩阵法得到级联微环滤波器的传输频谱；
如图4所示，在步骤S2中，利用传输矩阵法将级联微环滤波器拆分成若干 定向耦合器和传输线，所述定向耦合器和传输线均为四端口元器件，参照图5，左侧为定向耦合器，右侧为传输线，所述定向耦合器和传输线依次间隔排列，级联微环滤波器的两端均为定向耦合器，
以input 1为输入端口为例，此时定向耦合器与传输线的传输矩阵分别为式(7)和(8)所示。
Figure PCTCN2022110582-appb-000032
Figure PCTCN2022110582-appb-000033
其中，k表示耦合系数，t表示透射系数，*表示共轭，在不考虑耦合区损耗的情况下，耦合系数与透射系数的关系为：
k 2+t 2＝1     (9)
其中，α表示微环腔体损耗，e表示自然指数，θ表示微环内一圈产生相移，在微环中，θ表示为：
Figure PCTCN2022110582-appb-000034
其中，neff表示波导的有效折射率，R表示微环的半径，λ表示中心波长。
所述级联微环滤波器的传输函数用传输矩阵法表示为：
Figure PCTCN2022110582-appb-000035
其中，input 1和input 2为第一个定向耦合器的两个输入端口，output 1和output 2和最后一个定向耦合器的两个输出端口；M 1、M 3、…、M 2n+1为当前定向耦合器的矩阵表示；M 2、M 4、…、M 2n为当前传输线的矩阵表示；M为整个级联微环滤波器的矩阵表示；
Figure PCTCN2022110582-appb-000036
Figure PCTCN2022110582-appb-000037
当n为奇数时，output 1口为drop口，此时级联微环滤波器的传输频谱为：
Figure PCTCN2022110582-appb-000038
当n为偶数时，output 2口为drop口，此时级联微环滤波器的传输频谱为：
Figure PCTCN2022110582-appb-000039
其中，P d为级联微环滤波器的传输频谱。
可选地，在步骤S2和步骤S3之间，还包括以下步骤：
对传输频谱进行数据的裁剪和归一化处理；
数据处理部分包括数据的裁剪和数据的归一化，以确保算法迭代的效率。数据的裁剪将频谱上表现得特别低的串扰的部分裁剪掉，这部分对于算法的优化是没有贡献的。数据的归一化可以采用线性归一化方法，该方法可以表示为：
Figure PCTCN2022110582-appb-000040
在本发明中，为了确保所设计的滤波器参数能够在整个频谱上进行调谐，需要考虑所设计的滤波器性能在不同频段的性能，所以需要同时计算在低频，中频和高频三个频点处的频谱的稀疏度并且进行求和，得到三个频点处的总稀疏度来作为优化的依据。级联微环的低、中、高三个频段的调谐在算法中是通过修改式(10)中的neff来实现的，其中，级联微环滤波器一般采用热调谐的方式对谐振波长进行调谐。微环的neff通过加热会产生漂移，数值会发生改变。如式(10)所示，neff是级联微环的传输函数的一个参量，我们在程序中直接将neff加上或者减去一定的数值来模拟这一调谐过程，并将谐振波长分别调谐到低、中、高三个波段。则总的传输谱表示为三个频段的传输谱的和，也即：
P d(总)＝P d(低)+P d(中)+P d(高)    (15)
S3、计算级联微环在不同频点处的稀疏度，并进行求和；
具体地，利用复合反比例函数(compound inverse proportional function,CIPF)来表征传输频谱的稀疏度，复合反比例函数的形式为：
Figure PCTCN2022110582-appb-000041
其中，σ为控制逼近效果的参数，则当σ→0时，该函数的性质描述为：
Figure PCTCN2022110582-appb-000042
也即随着的σ逐渐减小，该函数逐步逼近L0范数，可以用来表征稀疏度。将总的传输频谱代入上式的x中得到传输频谱的稀疏度。
S4、基于求和得到的稀疏度，按照稀疏度最大的优化目标对微环半径进行迭代，并利用迭代的微环半径按照公式(3)(4)(5)(6)重新计算耦合系数，并返回步骤S2，直至达到最大迭代次数，得到最终的微环半径和耦合系数。可选地，利用蚁群算法、粒子群算法、遗传算法、模拟退火算法或梯度下降等算法进行优化迭代。
具体地，利用本实施例中的基于稀疏度计算的硅基光学微环滤波器逆向设计方法设计一个C+L波段的四阶级联微环滤波器，包括以下步骤：
第一步：确定初始的级联微环滤波器的各个微环半径与耦合系数；根据C+L的波长范围，根据式(1)确定初始级联微环滤波器的各个微环的半径，根据3dB带宽和带内损耗按照公式(3)(4)(5)(6)确定微环的各个耦合系数。
第二步：利用蚁群算法根据稀疏性进行微环半径的优化；包括以下步骤：
1.首先对算法进行初始化，每只蚂蚁有四个搜索方向，代表着四个微环的半径。
2.利用式(16)所示的复合反比例函数作为代价函数用于计算频谱稀疏度。对于微环在1480-1600nm的低频(1490nm)、中(1540nm)、高(1590nm)三个频段的稀疏度进行求和。
3.根据蚁群算法的转移概率选择局部搜索还是全局搜索。算法一次迭代结束后，重新计算耦合系数。转到第2步。第i个蚂蚁的转移概率为：
Figure PCTCN2022110582-appb-000043
式中，T max表示蚁群中最大的信息素，T i表示第i只蚂蚁的信息素，在本实施例中，信息素等价于稀疏度的大小。当P i较大时，代表第i只蚂蚁距离当前全局最优较远，选择全局搜索，全局搜索是指在全局范围内随机选取四个微环 半径。当P i较小时，代表第i只蚂蚁距离当前全局最优较近，选择局部搜索，局部搜索是指在上次迭代的结果附近随机选取四个微环半径。
达到最大迭代次数后得到的半径和耦合系数即是最后的设计结果。
本发明将逆向设计思维引入硅基级联微环的设计中，将设计级联微环滤波器问题转化为求解级联微环滤波器在设计波段的最稀疏光谱所对应的微环结构的问题。
本发明可以提高硅基级联微环滤波器设计的自由度，可以根据实际制造工艺与应用需求灵活调整微环的结构从而提高所设计的滤波器的性能。
本发明可以根据设计目标来设计微环结构，所以可以实现设计自动化，提高滤波器设计效率。
实施例二
本实施例公开了一种电子设备，包括存储器、处理器及存储在存储器上并可在处理器上运行的计算机程序，所述处理器执行所述程序时实现上述实施例一中所述基于稀疏度计算的硅基光学微环滤波器逆向设计方法的步骤。
实施例三
本实施例公开了一种计算机可读存储介质，其上存储有计算机程序，该程序被处理器执行时实现上述实施例一中所述基于稀疏度计算的硅基光学微环滤波器逆向设计方法的步骤。
实施例四
本实施例公开了一种硅基光学微环滤波器，其采用上述实施例一中所述的基于稀疏度计算的硅基光学微环滤波器逆向设计方法设计得到。
以上实施例仅是为充分说明本发明而所举的较佳的实施例，本发明的保护范围不限于此。本技术领域的技术人员在本发明基础上所作的等同替代或变换，均在本发明的保护范围之内。本发明的保护范围以权利要求书为准。

Claims (10)

  1. 一种基于稀疏度计算的硅基光学微环滤波器逆向设计方法，其特征在于，包括以下步骤：
    S1、确定级联微环滤波器中各个微环的初始半径和级联微环滤波器的各个耦合系数；
    S2、根据初始半径和耦合系数，利用传输矩阵法得到级联微环滤波器的传输频谱；
    S3、计算级联微环在不同频点处的稀疏度，并进行求和；
    S4、基于求和得到的稀疏度，按照稀疏度最大的优化目标对微环半径进行迭代，并利用迭代的微环半径重新计算耦合系数，并返回步骤S2，直至达到最大迭代次数，得到最终的微环半径和耦合系数。
  2. 如权利要求1所述的基于稀疏度计算的硅基光学微环滤波器逆向设计方法，其特征在于，步骤S1中，通过以下公式确定级联微环滤波器中各个微环的初始半径：
    Figure PCTCN2022110582-appb-100001
    Figure PCTCN2022110582-appb-100002
    其中，FSR total为目标的总自由频谱范围；n为级联微环滤波器中微环个数；FSR i为级联微环滤波器中第i个微环的初始自由频谱范围，i＝1,2，...，n；N 1、N 2、…、N n为各个微环的自由频谱范围的系数比；R i为第i个微环的初始半径；λ为中心波长，n g为波导的群折射率。
  3. 如权利要求2所述的基于稀疏度计算的硅基光学微环滤波器逆向设计方法，其特征在于，步骤S1中，通过以下公式确定级联微环滤波器的各个耦合系数：
    Figure PCTCN2022110582-appb-100003
    其中，B为所设计的3dB带宽，K 1为第1个微环与总线波导的耦合系数，K n+1为第n个微环与总线波导的耦合系数，K q表示第q个微环与q-1个微环之间的耦合系数；参数g可以表示为：
    Figure PCTCN2022110582-appb-100004
    其中：
    Figure PCTCN2022110582-appb-100005
    Figure PCTCN2022110582-appb-100006
    Figure PCTCN2022110582-appb-100007
    其中，ε与所设计的带内损耗loss有关，表示为：
    Figure PCTCN2022110582-appb-100008
    通过公式(3)(4)(5)(6)得到所设计的光学微环滤波器各个微环的各个耦合系数。
  4. 如权利要求1所述的基于稀疏度计算的硅基光学微环滤波器逆向设计方法，其特征在于，在步骤S2中，利用传输矩阵法将级联微环滤波器拆分成若干定向耦合器和传输线，所述定向耦合器和传输线均为四端口元器件，所述定 向耦合器和传输线依次间隔排列，所述级联微环滤波器的传输函数用传输矩阵法表示为：
    Figure PCTCN2022110582-appb-100009
    其中，input 1和input 2为第一个定向耦合器的两个输入端口，output 1和output 2和最后一个定向耦合器的两个输出端口；M 1、M 3、…、M 2n+1为当前定向耦合器的矩阵表示；M 2、M 4、…、M 2n为当前传输线的矩阵表示；M为整个级联微环滤波器的矩阵表示；
    当n为奇数时，output 1口为drop口，此时级联微环滤波器的传输频谱为：
    Figure PCTCN2022110582-appb-100010
    当n为偶数时，output 2口为drop口，此时级联微环滤波器的传输频谱为：
    Figure PCTCN2022110582-appb-100011
    其中，P d为级联微环滤波器的传输频谱。
  5. 如权利要求4所述的基于稀疏度计算的硅基光学微环滤波器逆向设计方法，其特征在于，
    Figure PCTCN2022110582-appb-100012
    Figure PCTCN2022110582-appb-100013
    其中，k表示耦合系数，t表示透射系数，*表示共轭，在不考虑耦合区损耗的情况下，耦合系数与透射系数的关系为：
    k 2+t 2＝1
    其中，α表示微环腔体损耗，e表示自然指数，θ表示微环内一圈产生相移，在微环中，θ表示为：
    Figure PCTCN2022110582-appb-100014
    其中，neff表示波导的有效折射率，R表示微环的半径，λ表示中心波长。
  6. 如权利要求1所述的基于稀疏度计算的硅基光学微环滤波器逆向设计方法，其特征在于，在步骤S2和步骤S3中，还包括以下步骤：
    对传输频谱进行数据的裁剪和归一化处理；
    其中，归一化处理表示为：
    Figure PCTCN2022110582-appb-100015
    其中，P d为级联微环滤波器的传输频谱。
  7. 如权利要求1所述的基于稀疏度计算的硅基光学微环滤波器逆向设计方法，其特征在于，在步骤S3中，利用复合反比例函数来表征传输频谱的稀疏度，复合反比例函数的形式为：
    Figure PCTCN2022110582-appb-100016
    其中，σ为控制逼近效果的参数，则当σ→0时，该函数的性质描述为：
    Figure PCTCN2022110582-appb-100017
    将总的传输频谱代入上式的x中得到传输频谱的稀疏度。
  8. 一种电子设备，包括存储器、处理器及存储在存储器上并可在处理器上运行的计算机程序，其特征在于，所述处理器执行所述程序时实现权利要求1-7中任意一项所述方法的步骤。
  9. 一种计算机可读存储介质，其上存储有计算机程序，其特征在于，该程序被处理器执行时实现权利要求1-7任意一项所述方法的步骤。
  10. 一种硅基光学微环滤波器，其特征在于，采用如权利要求1-7任一所述的基于稀疏度计算的硅基光学微环滤波器逆向设计方法设计得到。
PCT/CN2022/110582 2022-06-16 2022-08-05 基于稀疏度计算的硅基光学微环滤波器逆向设计方法 WO2023240772A1 (zh)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
CN202210680459.5 2022-06-16
CN202210680459.5A CN114967126B (zh) 2022-06-16 2022-06-16 基于稀疏度计算的硅基光学微环滤波器逆向设计方法

Publications (1)

Publication Number Publication Date
WO2023240772A1 true WO2023240772A1 (zh) 2023-12-21

Family

ID=82963572

Family Applications (1)

Application Number Title Priority Date Filing Date
PCT/CN2022/110582 WO2023240772A1 (zh) 2022-06-16 2022-08-05 基于稀疏度计算的硅基光学微环滤波器逆向设计方法

Country Status (2)

Country Link
CN (1) CN114967126B (zh)
WO (1) WO2023240772A1 (zh)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115189799B (zh) * 2022-09-08 2022-12-23 之江实验室 一种基于逆向设计及波长自动反馈的宽带波分解复用器

Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102183814A (zh) * 2011-05-27 2011-09-14 哈尔滨工业大学深圳研究生院 基于混合优化算法的光纤布拉格光栅的逆向设计方法
CN103941345A (zh) * 2014-05-06 2014-07-23 苏州大学 基于二维层状材料的soi基微环滤波器
JP2017015789A (ja) * 2015-06-26 2017-01-19 日本電信電話株式会社 光波長フィルタおよびその作製方法
CN110764191A (zh) * 2019-11-01 2020-02-07 灵芯光电(天津)有限公司 一种基于微环的矩形光滤波器及其设计方法
CN113128119A (zh) * 2021-04-21 2021-07-16 复旦大学 基于深度学习的滤波器逆向设计和优化方法
CN114611443A (zh) * 2022-02-21 2022-06-10 浙江大学 一种基于等效电路空间映射的片上滤波器逆向设计方法

Family Cites Families (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105917533A (zh) * 2013-11-20 2016-08-31 科锐安先进科技有限公司 硅光子平台上基于萨格纳克环形镜的激光腔
CN104270202B (zh) * 2014-10-21 2016-08-17 武汉邮电科学研究院 基于受激拉曼散射效应的多波长光源
CN113267908B (zh) * 2021-05-20 2022-07-15 燕山大学 基于金刚石波导的级联双微环谐振腔滤波器

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102183814A (zh) * 2011-05-27 2011-09-14 哈尔滨工业大学深圳研究生院 基于混合优化算法的光纤布拉格光栅的逆向设计方法
CN103941345A (zh) * 2014-05-06 2014-07-23 苏州大学 基于二维层状材料的soi基微环滤波器
JP2017015789A (ja) * 2015-06-26 2017-01-19 日本電信電話株式会社 光波長フィルタおよびその作製方法
CN110764191A (zh) * 2019-11-01 2020-02-07 灵芯光电(天津)有限公司 一种基于微环的矩形光滤波器及其设计方法
CN113128119A (zh) * 2021-04-21 2021-07-16 复旦大学 基于深度学习的滤波器逆向设计和优化方法
CN114611443A (zh) * 2022-02-21 2022-06-10 浙江大学 一种基于等效电路空间映射的片上滤波器逆向设计方法

Also Published As

Publication number Publication date
CN114967126A (zh) 2022-08-30
CN114967126B (zh) 2023-06-06

Similar Documents

Publication Publication Date Title
Rumpf Improved formulation of scattering matrices for semi-analytical methods that is consistent with convention
WO2023240772A1 (zh) 基于稀疏度计算的硅基光学微环滤波器逆向设计方法
CA2554553A1 (en) Planar lightwave circuit with mode coupling and mode re-coupling means
Amal et al. Ultra-Highly Efficient $1\times 3$ and $1\times 6$ Splitters for Terahertz Communication Applications
Leng et al. Ultra-broadband, fabrication tolerant optical coupler for arbitrary splitting ratio using particle swarm optimization algorithm
Yang et al. Guided-mode based arbitrary signal switching through an inverse-designed ultra-compact mode switching device
Chen et al. Ultra-compact spot size converter based on digital metamaterials
Jiang et al. Exploring high-performance slow light grating waveguides by means of deep learning
Wang et al. Optimal design of planar wavelength circuits based on Mach-Zehnder interferometers and their cascaded forms
Seifi Laleh et al. Modeling optical filters based on serially coupled microring resonators using radial basis function neural network
Andonegui et al. Inverse design and topology optimization of novel photonic crystal broadband passive devices for photonic integrated circuits
Krapez Sequences of exact analytical solutions for plane waves in graded media
Madsen A multiport frequency band selector with inherently low loss, flat passbands, and low crosstalk
Swillam et al. Filter design using multiple coupled microcavities
Wang et al. Optimal design of a flat-top interleaver based on cascaded M–Z interferometers by using a genetic algorithm
Seyringer Design and simulation of 128-channel 10 GHz AWG for ultra-dense wavelength division multiplexing
Kamalakis et al. Analytical expressions for the resonant frequencies and modal fields of finite coupled optical cavity chains
Ke et al. Photonic crystal broadband y-shaped 1× 2 beam splitter inversely designed by genetic algorithm
Lakra et al. Design and realization of vertically coupled quadruple micro optical ring resonators (VCQMORR) in Z-domain
Khavasi et al. Circuit model for efficient analysis and design of photonic crystal devices
CN106599465B (zh) 一种1×n分波/合波器优化方法
Ruocco et al. Multi-parameter extraction from SOI photonic integrated circuits using circuit simulation and evolutionary algorithms
Song et al. A planar waveguide demultiplexer with a flat passband, sharp transitions and a low chromatic dispersion
CN112100881B (zh) 一种基于局域耦合模理论的光子灯笼全矢量数值分析方法
Bekasiewicz et al. Fast optimization of integrated photonic components using response correction and local approximation surrogates

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: 22946445

Country of ref document: EP

Kind code of ref document: A1