森本 佳太

In this paper, a rigorous two-dimensional full-vectorial finite difference time domain (2D-FVFDTD) method is developed for an efficient analysis of nonradiative dielectric waveguide (NRD guide) devices with three-dimensional structure. A Convolutional perfectly matched layer is employed as an absorbing boundary condition. Furthermore, we have established a rigorous formulation for estimating the modal power of each LSM01 and LSE01 mode. We confirmed the validity of the proposed method through the analysis of NRD crossing and T-branch guide devices. Excellent accuracy is achieved by the cross comparison of 2D-FVFDTD results with recently developed two-dimensional full vectorial finite element method.

In order to increase communication capacity, the use of millimeter-wave and terahertz-wave bands are being actively explored. Non-radiative dielectric waveguide known as NRD guide is one of promising platform of millimeter-wave integrated circuits thanks to its nonradiative and low loss nature. In order to develop millimeter wave circuits with various functions, various circuit components have to be efficiently designed to meet requirements from application side. In this paper, for efficient design of NRD guide devices, we develop a topology optimal design technique based on function-expansion-method which can express arbitrary structure with arbitrary geometric topology. In the present approach, recently developed two-dimensional full-vectorial finite element method (2D-FVFEM) for NRD guide devices is employed to improve computational efficiency and several evolutionary approaches, which do not require appropriate initial structure depending on a given design problem, are used to optimize design variables, thus, NRD guide devices having desired functions are efficiently obtained without requiring designer’s special knowledge.

小型で高性能な光デバイスの開発を目指して，計算機シミュレーションを利用した最適設計法に関する研究が活発に行われている．中でも構造のトポロジーまで含めて設計が可能なトポロジー最適設計法は，これまで考えられたことのない全く新しい構造を見出せる可能性がある．一方で，トポロジー最適設計法はその自由度の高さから大域的最適解を見出すことが難しいこと，3次元光デバイスの設計においては設計に要する時間が飛躍的に増大することが問題となる．本検討では，3次元光デバイスのトポロジー最適設計を効率的に行うため，3次元構造をより精度良く2次元近似するための改良型の等価屈折率法を提案し，2次元近似設計された構造を3次元解析を基に反復改良することで，3次元光デバイスのトポロジー最適設計の効率化を図っている．計算負荷の軽い2次元設計においては，進化的手法に感度情報に基づく効率的な解の改良を組み合わせたトポロジー最適設計法を提案し，より大域的な最適解の探索を効率的に行うための検討も行っている．

In this paper, we propose an optimal design approach based on a concept of mosaic-like structure for achieving high performance NRD devices. In order to improve design efficiency, we employ the recently proposed two-dimensional full vectorial finite element method (2D-FVFEM) which can accurately model 3D structure of NRD as a numerical simulation method. As an optimization method, we employ either direct binary search (DES) algorithm or genetic algorithm (GA) depending on design problems. In order to show the usefulness of our approach, design examples of crossing and T-branch waveguides are considered and high transmission efficiency greater than 99.9% for crossing waveguide and 49.8%: 49.8% for T-branch waveguide is achieved. The numerical results by 2D-FVFEM are verified by 3D-FVFEM.

We first present a bidirectional beam propagation method (BiBPM) based on axially symmetric full-vectorial finite element method (Axi-FVFEM). The Axi-FVFEM based BiBPM is a more versatile method than previous scalar BiBPM for axi-symmetric structure. It has potential to offer more efficient analysis than widely used FEM or finite difference based techniques, especially for a large scale waveguide such as a long periodic structure. An air gap in an axi-symmetric waveguide and a fibre Bragg grating (FBG) are analyzed using the Axi-FVFEM based BiBPM for numerical validation, and we compare the numerical results with those of a 3D finite-difference time-domain (FDTD) method and a modal-based method.

In recent years, various kinds of optimal design approaches are intensively studied for exploring novel and higher performance microwave and optical devices beyond human knowledge. In this article, we first apply a design approach based on Bayesian optimization (BO) to design of dielectric flat lens which is expected to be used in microwave and millimeter wave region because of its excellent features, such as thin and light weight. BO is able to efficiently search optimal values of design variables compared with population based optimization, without requiring sensitivity analysis which is mandatory in the gradient method.

An efficient finite-element-method-based scattering operator (FEM-SO) is proposed. Utilizing field based propagation operators as boundary conditions, arbitrary light waves including radiation and evanescent waves can be treated at input and output ports. In contrast to conventional scattering operator techniques, the FEM-SO is applicable to arbitrary structures by using finite element models. In addition, considering structural discontinuities at the connecting boundary of scattering operators, an interface matrix to satisfy the boundary conditions between unit structures is introduced. To verify the present approach, numerical examples are shown for propagation characteristics of high-index-contrast waveguide facet and power spectrum of a photonic-crystal Fabry-Perot (FP) cavity filter.

Nonradiative dielectric waveguide (NRD guide) is a promising platform for realizing compact millimeter waveguide circuits. NRD guide devices have been simulated by several numerical simulation approaches so far and these approaches treat 3-D structure because electric and magnetic fields in NRD guides vary in whole directions. In this letter, we propose a 2-D full-vectorial finite element analysis for efficient simulation of NRD guide devices.

We propose a novel finite element method (FEM) for efficient optical waveguide analysis to improve the computational efficiency in inverse design of optical waveguide devices. In our formulation, applying slowly varying envelope approximation (SVEA) to FEM, an electromagnetic field expression is split into a slowly varying complex envelope amplitude and a steady-state oscillating term. Then, field profile can be obtained by just solving the slowly varying complex envelope amplitude and the number of unknown variables along the propagation direction can be greatly reduced. The proposed method can achieve efficient optical waveguide analysis. Furthermore, by employing this analysis method in the inverse design of optical waveguide devices, automatic optimization of device structure can be carried out with reasonable computational costs.

We propose a new design approach to improve the computational efficiency of an optimal design of optical waveguide devices utilizing coupled mode theory (CMT) and a neural network (NN). Recently, the NN has begun to be used for efficient optimal design of optical devices. In this paper, the eigenmode analysis required in the CMT is skipped by using the NN, and optimization with an evolutionary algorithm can be efficiently carried out. To verify usefulness of our approach, optimal design examples of a wavelength insensitive 3 dB coupler, a 1 : 2 power splitter, and a wavelength demultiplexer are shown and their transmission properties obtained by the CMT with the NN (NN-CMT) are verified by comparing with those calculated by a finite element beam propagation method (FE-BPM).

In this paper, we reformulate a sensitivity analysis method for function-expansion-based topology optimization method without using gray area. In the conventional approach based on function expansion method, permittivity distribution contains gray materials, which are intermediate materials between core and cladding ones, so as to let the permittivity differentiable with respect to design variables. Since this approach using gray area dose not express material boundary exactly, it is not desirable to apply this approach to design problems of strongly guiding waveguide devices, especially for plasmonic waveguides. In this study, we present function-expansion-method-based topology optimization without gray area. In this approach, use of gray area can be avoided by replacing the area integral of the derivative of the matrix with the line integral taking into acount the rate of boundary deviation with respect to design variables. We verify the validity of our approach through applying it to design problems of a T-branching power splitter and a mode order converter.

This paper presents structural optimization based on sensitivity analysis exploiting a bi-directional beam propagation method (Bi-BPM) to design efficiently passive components in high-index-contrast optical waveguides. In this study, the Bi-BPM based on scaled-version Denman-Beavers iteration (S-DBI) with branch-cut technique, and scattering operator formulation (SO-Bi-BPM) is employed to execute stable, accurate wave-propagation analysis. Comparing three computation approaches of sensitivity with respect to design variables, efficient way of sensitivity analysis is revealed when the SO-Bi-BPM is used. The application range of the presented design approach is studied by designing a wavelength filter with waveguide grating, and a polarizer based on 1D photonic crystal (1D-PhC).

A new efficient boundary condition of finite element method (FEM) by using propagation operator is proposed. In this method, input, and output ports are terminated on their own boundaries instead of using perfectly matched layer (PML) which requires expanding the computational window. Moreover, this boundary condition can consider all modes including radiation modes without mode expansion. The propagation operator is efficiently calculated by Denman-Beavers iteration (DBI). The electromagnetic field on the POM boundary can be accurately propagated outside the boundary by using the propagation operator. In addition, we present a technique based on scattering operator method which can reduce the computational complexity of FEM. Three numerical results show that the present scheme is more accurate, and stable than conventional approximate boundary conditions such as using Pade approximation in both TE, and TM modes.

We apply an analysis scheme combining propagation operator method (POM) and beam propagation method (BPM) to waveguide discontinuity problems. In this approach, finite element method (FEM) with higher adaptability to waveguide geometry is utilized for discretizing waveguide cross section. While BPM based on FEM (FE-BPM) can efficiently analyze waveguides with long propagation distance, it encounters serious degradation of accuracy when waveguides with discontinuous structure has to be analyzed. The presented method overcomes this defect by applying POM which can analyze discontinuous facets and sufficiently cover various mode coupling.

A signal output of optical devices with multi-input ports, such as a logic gate, depends on the phase difference between input ports. In order to cascade optical devices, it is essential to design such devices considering not only desired output power but also desired output signal phase. We propose a topology optimization method for optical devices considering the output signal phase. In our approach, the beam propagation method (BPM) is employed as a numerical simulation method and the adjoint variable method (AVM) is used to calculate the sensitivity of output power and signal phase to design parameters. The validity and the effectiveness of our approach are verified through design examples of a three-branching waveguide with linear media and an all-optical logic gate utilizing nonlinear media.

We propose an efficient numerical method for the full-vectorial analysis of three-dimensional (3-D) optical waveguide discontinuities. In this method, the finite element method with higher adaptability and flexibility is employed to discretize the waveguide cross section. In order to calculate the square root of the characteristic matrix, the Denman-Beavers iterative scheme is used. Applying this method to 3-D strongly guiding waveguide discontinuity problems, the modal reflectivities of the fundamental TE-like and TM-like modes are calculated. These results show unique vector properties and significantly differ from those of scalar analysis because various mode couplings between the field components occur at the discontinuity facet and they cannot be ignored. (C) 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

We propose a novel topology optimization method for plasmonic devices. Plasmonic devices that have a great potential to downsize various optical devices beyond the diffraction limit attract a lot of attention. In order to develop high-performance plasmonic devices, a novel design theory is expected to be established instead of the conventional theory for dielectric waveguide devices. In this paper, we employ the function expansion method to express a device structure in the design region and optimize the design variables by using several evolutionary approaches, which do not require the sensitivity analysis. The validity and usefulness of this approach are demonstrated through the design examples of optical diode and optical circulator.