Finite element modeling methods for photonics
By: B. M. Azizur Rahman, Arti Agrawal
Contributors: Agrawal, Arti, author
Publisher: Artech House; Artech House Publishers
Published: 2013
Place of publication: Boston
Language: eng
Number of pages: 247
ISBN-13: 9781608075317
Copyright date: 2013
Subjects: Photonics; Finite element method
Notes: Includes bibliographical references and index.
Table of contents: title: Machine generated contents note: 1.Introduction; title: 1.1.Significance of Numerical Methods; title: 1.2.Numerical Methods; title: 1.3.Maxwell's Equations and Boundary Conditions; title: 1.3.1.Maxwell's Equations; title: 1.3.2.Boundary Conditions across Material Interfaces; title: 1.3.3.Boundary Conditions: Natural and Forced; title: 1.3.4.Boundary Conditions: Truncation of Domains; title: 1.4.Basic Assumptions of Numerical Methods and Their Applicability; title: 1.4.1.Time Harmonic and Time-Dependent Solutions; title: 1.4.2.The Wave Equations; title: 1.4.3.Scalar and Vector Nature of the Equations/Solutions; title: 1.4.4.Modal Solutions; title: 1.4.5.Beam Propagation Methods; title: 1.5.Choosing a Modeling Method; title: 1.6.Finite-Element-Based Methods; title: References; title: 2.The Finite-Element Method; title: 2.1.Basic Concept of FEM: Essence of FEM-based Formulations; title: 2.2.Setting up the FEM; title: 2.2.1.The Variational Approach; title: 2.2.2.The Galerkin Method; title: 2.3.Scalar and Vector FEM Formulations; title: 2.3.1.The Scalar Formulation; title: 2.3.2.The Vector Formulation; title: 2.4.Implementation of FEM; title: 2.4.1.Flowchart of Main Steps in FEM; title: 2.4.2.Meshing and Shape Functions; title: 2.4.3.Shape Functions; title: 2.4.4.Examples of Meshing; title: 2.5.Formation of Element and Global Matrices; title: 2.5.1.Mass and Stiffness Matrix Evaluation for First-order Triangular Elements; title: 2.5.2.Mass and Stiffness Matrix Evaluation for Second-order Triangular Elements; title: 2.5.3.Assembly of Global Matrices: Bandwidth and Sparsity of Matrices; title: 2.5.4.Penalty Function Method for Elimination of Spurious Modes; title: 2.6.Solution of the System of Equations; title: 2.7.Implementation of Boundary Conditions; title: 2.7.1.Natural Boundary Condition and Symmetry: Electric and Magnetic Wall; title: 2.7.2.Absorbing Boundary Condition and Perfectly Matched Layer (PML) Boundary Condition; title: 2.7.3.Periodic Boundary Conditions (PBC); title: 2.8.Practical Illustrations of FEM Applied to Photonic Structures/devices; title: 2.8.1.The Rectangular Waveguide: Si Nanowire; title: 2.8.2.Waveguide with a Circular Cross Section: Photonic Crystal Fiber (PCF); title: 2.8.3.Plasmonic Waveguides; title: 2.8.4.Photonic Crystal Waveguide and Periodic Boundary Conditions; title: 2.9.FEM Analysis of Bent Waveguides; title: 2.10.Perturbation Analysis for Loss/gain in Optical Waveguides; title: 2.10.1.Perturbation Method with the Scalar FEM; title: 2.10.2.Perturbation Method with the Vector FEM; title: 2.11.Accuracy and Convergence in FEM; title: 2.11.1.Discretisation and Interpolation Errors in FEM Analysis; title: 2.11.2.Element Shape Quality and the Stiffness Matrix; title: 2.11.3.Error Dependence on Element Size, Order and Arrangement; title: 2.11.4.Adaptive Mesh Refinement; title: 2.12.Computer Systems and FEM Implementation; title: References; title: 3.Finite-Element Beam Propagation Methods; title: 3.1.Introduction; title: 3.2.Setting up BPM Methods; title: 3.3.Vector FE-BPM with PML Boundary Conditions; title: 3.3.1.Semi-vector and Scalar FE-BPM; title: 3.3.2.Wide-angle FE-BPM; title: 3.3.3.Paraxial FE-BPM; title: 3.3.4.Implementation of the BPM and Stability; title: 3.3.5.Practical Illustrations of FE-BPM applied to Photonic Structures/devices; title: 3.4.Junction Analysis with FEM: The LSBR Method; title: 3.4.1.Analysis of High Index Contrast Bent Waveguide; title: 3.5.Bi-directional BPM; title: 3.6.Imaginary Axis/distance BPM; title: 3.6.1.Analysis of 3D Leaky Waveguide by the Imaginary Axis BPM; title: References; title: 4.Finite-Element Time Domain Method; title: 4.1.Time Domain Numerical Methods; title: 4.2.Finite-Element Time Domain (FETD) BPM Method; title: 4.2.1.Wide Band and Narrow Band Approximations; title: 4.2.2.Implementation of the FETD BPM Method: Implicit and Explicit Schemes; title: 4.3.Practical Illustrations of FETD BPM Applied to Photonic Structures/devices; title: 4.3.1.Optical Grating; title: 4.3.2.90° Sharp Bends; title: References; title: 5.Incorporating Physical Effects within the Finite-Element Method; title: 5.1.Introduction; title: 5.2.The Thermal Model; title: 5.2.1.Thermal Modeling of a VCSEL; title: 5.3.The Stress Model; title: 5.3.1.Stress Analysis of a Polarization Maintaining Bow-tie Fiber; title: 5.4.The Acoustic Model; title: 5.4.1.Acousto-optic Analysis of a Silica Waveguide; title: 5.4.2.SBS Analysis of a Silica Nanowire; title: 5.5.The Electro-optic Model; title: 5.5.1.Analysis of a Lithium Niobate (LN) Electro-optic Modulator; title: 5.6.Nonlinear Photonic Devices; title: 5.6.1.Analysis of a Strip-loaded Nonlinear Waveguide; title: 5.6.2.Analysis of a Nonlinear Directional Coupler; title: 5.6.3.Analysis of Second Harmonic Generation in an Optical Waveguide; title: References; title: 6.FE-based Methods: The Present and Future Directions; title: 6.1.Introduction; title: 6.2.Salient Features of FE-based Methods; title: 6.3.Future Trends and Challenges for FE-based Methods; title: Appendix A Scalar FEM with Perturbation; title: TE Modes; title: TM Modes; title: Appendix B Vector FEM with Perturbation; title: Appendix C Green's Theorem.