عنوان

Finite element modeling methods for photonics

electronic

author

Rahman, B. M. Azizur

Finite element modeling methods for photonics

Boston, MA

Artech House

2013

xv, 247 pages : illustrations ; 24 cm

Includes bibliographical references and index

B. M. Azizur Rahman, Arti Agrawal

Machine generated contents note: 1.Introduction -- 1.1.Significance of Numerical Methods -- 1.2.Numerical Methods -- 1.3.Maxwell's Equations and Boundary Conditions -- 1.3.1.Maxwell's Equations -- 1.3.2.Boundary Conditions across Material Interfaces -- 1.3.3.Boundary Conditions: Natural and Forced -- 1.3.4.Boundary Conditions: Truncation of Domains -- 1.4.Basic Assumptions of Numerical Methods and Their Applicability -- 1.4.1.Time Harmonic and Time-Dependent Solutions -- 1.4.2.The Wave Equations -- 1.4.3.Scalar and Vector Nature of the Equations/Solutions -- 1.4.4.Modal Solutions -- 1.4.5.Beam Propagation Methods -- 1.5.Choosing a Modeling Method -- 1.6.Finite-Element-Based Methods -- References -- 2.The Finite-Element Method -- 2.1.Basic Concept of FEM: Essence of FEM-based Formulations -- 2.2.Setting up the FEM -- 2.2.1.The Variational Approach -- 2.2.2.The Galerkin Method -- 2.3.Scalar and Vector FEM Formulations -- 2.3.1.The Scalar Formulation -- 2.3.2.The Vector Formulation -- 2.4.Implementation of FEM -- 2.4.1.Flowchart of Main Steps in FEM -- 2.4.2.Meshing and Shape Functions -- 2.4.3.Shape Functions -- 2.4.4.Examples of Meshing -- 2.5.Formation of Element and Global Matrices -- 2.5.1.Mass and Stiffness Matrix Evaluation for First-order Triangular Elements -- 2.5.2.Mass and Stiffness Matrix Evaluation for Second-order Triangular Elements -- 2.5.3.Assembly of Global Matrices: Bandwidth and Sparsity of Matrices -- 2.5.4.Penalty Function Method for Elimination of Spurious Modes -- 2.6.Solution of the System of Equations -- 2.7.Implementation of Boundary Conditions -- 2.7.1.Natural Boundary Condition and Symmetry: Electric and Magnetic Wall -- 2.7.2.Absorbing Boundary Condition and Perfectly Matched Layer )PML( Boundary Condition -- 2.7.3.Periodic Boundary Conditions )PBC( -- 2.8.Practical Illustrations of FEM Applied to Photonic Structures/devices -- 2.8.1.The Rectangular Waveguide: Si Nanowire -- 2.8.2.Waveguide with a Circular Cross Section: Photonic Crystal Fiber )PCF( -- 2.8.3.Plasmonic Waveguides -- 2.8.4.Photonic Crystal Waveguide and Periodic Boundary Conditions -- 2.9.FEM Analysis of Bent Waveguides -- 2.01.Perturbation Analysis for Loss/gain in Optical Waveguides -- 2.01.1.Perturbation Method with the Scalar FEM -- 2.01.2.Perturbation Method with the Vector FEM -- 2.11.Accuracy and Convergence in FEM -- 2.11.1.Discretisation and Interpolation Errors in FEM Analysis -- 2.11.2.Element Shape Quality and the Stiffness Matrix -- 2.11.3.Error Dependence on Element Size, Order and Arrangement -- 2.11.4.Adaptive Mesh Refinement -- 2.21.Computer Systems and FEM Implementation -- References -- 3.Finite-Element Beam Propagation Methods -- 3.1.Introduction -- 3.2.Setting up BPM Methods -- 3.3.Vector FE-BPM with PML Boundary Conditions -- 3.3.1.Semi-vector and Scalar FE-BPM -- 3.3.2.Wide-angle FE-BPM -- 3.3.3.Paraxial FE-BPM -- 3.3.4.Implementation of the BPM and Stability -- 3.3.5.Practical Illustrations of FE-BPM applied to Photonic Structures/devices -- 3.4.Junction Analysis with FEM: The LSBR Method -- 3.4.1.Analysis of High Index Contrast Bent Waveguide -- 3.5.Bi-directional BPM -- 3.6.Imaginary Axis/distance BPM -- 3.6.1.Analysis of 3D Leaky Waveguide by the Imaginary Axis BPM -- References -- 4.Finite-Element Time Domain Method -- 4.1.Time Domain Numerical Methods -- 4.2.Finite-Element Time Domain )FETD( BPM Method -- 4.2.1.Wide Band and Narrow Band Approximations -- 4.2.2.Implementation of the FETD BPM Method: Implicit and Explicit Schemes -- 4.3.Practical Illustrations of FETD BPM Applied to Photonic Structures/devices -- 4.3.1.Optical Grating -- 4.3.2.09 Sharp Bends -- References -- 5.Incorporating Physical Effects within the Finite-Element Method -- 5.1.Introduction -- 5.2.The Thermal Model -- 5.2.1.Thermal Modeling of a VCSEL -- 5.3.The Stress Model -- 5.3.1.Stress Analysis of a Polarization Maintaining Bow-tie Fiber -- 5.4.The Acoustic Model -- 5.4.1.Acousto-optic Analysis of a Silica Waveguide -- 5.4.2.SBS Analysis of a Silica Nanowire -- 5.5.The Electro-optic Model -- 5.5.1.Analysis of a Lithium Niobate )LN( Electro-optic Modulator -- 5.6.Nonlinear Photonic Devices -- 5.6.1.Analysis of a Strip-loaded Nonlinear Waveguide -- 5.6.2.Analysis of a Nonlinear Directional Coupler -- 5.6.3.Analysis of Second Harmonic Generation in an Optical Waveguide -- References -- 6.FE-based Methods: The Present and Future Directions -- 6.1.Introduction -- 6.2.Salient Features of FE-based Methods -- 6.3.Future Trends and Challenges for FE-based Methods -- Appendix A Scalar FEM with Perturbation -- TE Modes -- TM Modes -- Appendix B Vector FEM with Perturbation -- Appendix C Green's Theorem

، Finite element method

، Photonics

، Finite element method

، Photonics

AU

AU Agrawal, Arti author

TI