Analysis of Multiple Waveguide Discontinuities Using Propagation Operator Method and Beam Propagation Method

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

Full-vectorial analysis of optical waveguide discontinuities using a propagation operator method based on the finite element scheme discontinuities using a propagation operator method based on the finite element scheme

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

A Study on Topology Optimization of Plasmonic Waveguide Devices Using Function Expansion Method and Evolutionary Approach

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

Propagation Operator Based Boundary Condition for Finite Element Analysis

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

Novel Scattering Operator for Arbitrary Finite Element Models in Optical Waveguides

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

Sensitivity-Based Structural Optimal Design With Bi-Directional Beam Propagation Method for Photonic Devices in High-Index-Contrast Waveguides

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)

Bidirectional Beam Propagation Method Based on Axi-Symmetric Full-Vectorial Finite Element Method

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

Tests of human auditory temporal resolution: preliminary investigation of ZEST parameters for amplitude modulation detection

Auditory temporal resolution plays a critical role in the everyday experience of listening to complex acoustic patterns. Amplitude modulation detection thresholds are widely used to measure auditory temporal resolution. In an attempt to develop a standardized clinical test of auditory temporal resolution, we used ZEST (Zippy Estimation by Sequential Testing, a Bayesian threshold estimation procedure, to measure amplitude modulation detection thresholds. ZEST utilizes prior knowledge about a listener’s thresholds, as represented by a probability density function of the thresholds, and psychometric functions of the listener’s responses. This paper reports a preliminary study in which ZEST parameters that could be used for measurements of amplitude modulation detection thresholds were sought. For this purpose, we created histograms of the detection thresholds for a wide range of modulation frequencies, measured the psychometric functions of amplitude modulation detection, and performed computer simulations of ZEST threshold estimation. The results suggested that, with appropriately-set parameters, ZEST allows for the accurate estimation of amplitude modulation detection thresholds within 20 trials

A Study on Optimal Design of Optical Devices Utilizing Coupled Mode Theory and Machine Learning

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 3dB 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)

A Study on Function-Expansion-Based Topology Optimization without Gray Area for Optimal Design of Photonic Devices

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