Finite Element Modeling Methods for Photonics

Name: Finite Element Modeling Methods for Photonics
Brand: Artech House
Price: 247.99 EUR
Availability: OnlineOnly

B. M. Azizur Rahman(Autor*in)

Artech House (Verlag)

1. Auflage

Erschienen am 1. Januar 2013

268 Seiten

E-Book

PDF mit Adobe-DRM

Systemvoraussetzungen

978-1-60807-532-4 (ISBN)

247,99 €inkl. 7% MwSt.

Systemvoraussetzungen

für PDF mit Adobe-DRM

E-Book Einzellizenz

Als Download verfügbar

Beschreibung

Weitere Details

Weitere Ausgaben

Inhalt

Finite Element Modeling Methods for Photonics
Contents
Preface
Acknowledgments
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
2.10 Perturbation Analysis for Loss/Gain in Optical Waveguides
2.10.1 Perturbation Method with the Scalar FEM
2.10.2 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
2.12 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 90° 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
About the Authors
Index

Systemvoraussetzungen

Als PDF speichern Als Link merken