Takashi Yasui

A wide-angle finite element beam propagation method with perfectly matched layers for nonlinear optical waveguides

A wide-angle finite-element beam propagation method based on the Pade approximation is developed. Considerable improvement in accuracy over the paraxial approximation is achieved with virtually no additional computation. In the present algorithm, the quadratic element, transparent boundary condition, adaptive reference index, and adaptive grid are effectively utilized.

Synthesis of One-Input M-Output Optical FIR Lattice Circuits

This paper presents a one-input M-output (1 x M)configuration and a synthesis algorithm for realizing an optical finite impulse response (FIR) lattice filter having M output channels (M ges 2). The circuit configuration has a multilayer structure consisting of multiple Mach-Zehnder interferometers with delay time differences of zero or Deltatau. It is a natural extension of the conventional two-port optical FIR lattice circuit (M = 2) . The proposed synthesis algorithm is based on factorizations of the paraunitary total transfer matrix. It realizes output responses having highest orders equal to the number of stages for all output channels. It is shown that such a synthesis algorithm maximizes the degrees of freedom for designing output responses. Two kinds of five-channel interleave filters are demonstrated as synthesized examples: one has a flat group delay response while the other has an inclined group delay response.

Three-dimensional vector beam-propagation method for second harmonic generation analysis

A full vectorial three-dimensional beam-propagation method (BPM) based on the finite-element method is described for the analysis of second harmonic generation (SHG). Quasi-phase-matched SHG devices with periodically domain-inverted GaAlAs- and LiTaO/sub 3/-based waveguides are analyzed. The influences of the shape of domain-inverted regions and of the inversion width on the conversion efficiencies are investigated in detail. The results of full-wave analysis are compared to those of approximate scalar analysis.

Design of ultra-compact triplexer with function-expansion based topology optimization

In this paper, in order to optimize wavelength selective photonic devices using the function-expansion-based topology optimization method, several expansion functions are considered and the influence on the optimized structure based on each expansion function was investigated. Although the Fourier series is conventionally used in the function-expansion-based method, the optimized structure sometimes has a complicated refractive index distribution. Therefore, we employed a sampling function and a pyramid function to obtain a simpler structure through the optimal design. A triplexer was designed by using our method, and the comparison between the optimized structures based on the three expansion functions was also discussed in detail.

Efficient finite-difference time-domain computation of resonant frequencies of rectangular Lamé mode resonators via a combination of the symmetry boundary conditions and the Padé approximation

Resonant frequency analysis of the fundamental and higher-order modes of Lame mode resonators on a lossless isotropic solid is carried out by the finite-difference time-domain (FD-TD) method with the staggered grid with collocated grid points of velocities (SGCV). The symmetry boundary condition is implemented to reduce the size of the computational domain for the FD-TD method with the SGCV. One spectrum estimation technique based on the Pade approximation is employed to effectively extract the resonant frequencies from a spectrum transformed from the time series data calculated by the FD-TD method. Numerical results show the validity and efficiency of these techniques.

FINITE ELEMENT BEAM PROPAGATION METHOD FOR NONLINEAR OPTICAL WAVEGUIDES

A new beam propagation method based on the finite element method (FE-BPM) has been developed for the analysis of nonlinear optical waveguides. A formulation for the FE-BPM that is applicable not only to the TE mode but also to the TM mode is presented. Various techniques for enhancing the performance of the FE-BPM are introduced, including the Pade equation of wide-angle beam propagation, the transparent boundary condition, the perfect matched layer condition for prevention of spurious reflection from the edge of the analysis region, and an algorithm for adaptive updating of the reference index of refraction and the finite-element grids. Beam propagation analysis of spatial soliton emission in a nonlinear optical waveguide is performed in order to investigate the performance of the new FE-BPM.

Expansion of the difference-field boundary element method for numerical analyses of various local defects in periodic surface-relief structures

We expand the difference-field boundary element method (DFBEM) to calculate wave scattering from a variety of local periodic structure defects. The DFBEM is a numerical method for simulating the diffraction caused by a periodic surface-relief structure with a defect. Although it is more efficient than conventional techniques such as the finite-difference time-domain (FDTD) method, the original DFBEM is limited to projection defects. Here, we derive the integral equations and expressions for crack and buried-pillar defects, and also demonstrate some numerical analyses, validating the results by comparison with results from the FDTD method and the dielectric interface boundary conditions.

A Study on Topology Optimization of Optical Circuits Consisting of Multi-Materials

A topology optimization method can be used to find out the optical waveguide structures which have the desired transmission characteristics. Using the function expansion method, we can avoid the problem of a gray area, which means that some areas having intermediate refractive index between those of usable materials appear in a design region. However, so far, topology optimization has mainly been studied for structures consisting of two isotropic materials. In this paper, we study the applicability of topology optimization to structures which include three or more materials, and demonstrate the optimal design of a waveguide crossing.

Topology Optimization of Optical Waveguide Devices Based on Beam Propagation Method With Sensitivity Analysis

We present a gradient-based topology optimization method of optical waveguide devices using the beam propagation method (BPM). Efficient topology optimization of an optical waveguide is available by using our approach because it utilizes the adjoint variable method for sensitivity analysis, and the BPM for numerical propagation analysis. In this paper, a way of evaluating sensitivities for a design of longitudinally varying waveguides is newly described in the case that a density method and finite difference BPM are employed. In addition, the validity and availability of our proposed method are verified by optimizing an S-bend and a Y-branch waveguides.

Design of Three-Dimensional Optical Circuit Devices by Using Topology Optimization Method With Function-Expansion-Based Refractive Index Distribution

We extend topology optimization method with function-expansion-based refractive index distribution to optimization for three-dimensional optical circuits, in which a refractive index distribution in a design region is expressed by an expansion with some analytical functions. Three-branch optical waveguides have been optimized as numerical examples. Equally branching three-branch waveguides are achieved using our method. A limitation of topology optimization in two dimensions and dependency of initial structure are also shown.