Finite element modeling methods for photonics - Info and Reading Options

"Finite element modeling methods for photonics" Table Of Contents:

• 1- Machine generated contents note: 1.Introduction
• 2- 1.1.Significance of Numerical Methods
• 3- 1.2.Numerical Methods
• 4- 1.3.Maxwell's Equations and Boundary Conditions
• 5- 1.3.1.Maxwell's Equations
• 6- 1.3.2.Boundary Conditions across Material Interfaces
• 7- 1.3.3.Boundary Conditions: Natural and Forced
• 8- 1.3.4.Boundary Conditions: Truncation of Domains
• 9- 1.4.Basic Assumptions of Numerical Methods and Their Applicability
• 10- 1.4.1.Time Harmonic and Time-Dependent Solutions
• 11- 1.4.2.The Wave Equations
• 12- 1.4.3.Scalar and Vector Nature of the Equations/Solutions
• 13- 1.4.4.Modal Solutions
• 14- 1.4.5.Beam Propagation Methods
• 15- 1.5.Choosing a Modeling Method
• 16- 1.6.Finite-Element-Based Methods
• 17- References
• 18- 2.The Finite-Element Method
• 19- 2.1.Basic Concept of FEM: Essence of FEM-based Formulations
• 20- 2.2.Setting up the FEM
• 21- 2.2.1.The Variational Approach
• 22- 2.2.2.The Galerkin Method
• 23- 2.3.Scalar and Vector FEM Formulations
• 24- 2.3.1.The Scalar Formulation
• 25- 2.3.2.The Vector Formulation
• 26- 2.4.Implementation of FEM
• 27- 2.4.1.Flowchart of Main Steps in FEM
• 28- 2.4.2.Meshing and Shape Functions
• 29- 2.4.3.Shape Functions
• 30- 2.4.4.Examples of Meshing
• 31- 2.5.Formation of Element and Global Matrices
• 32- 2.5.1.Mass and Stiffness Matrix Evaluation for First-order Triangular Elements
• 33- 2.5.2.Mass and Stiffness Matrix Evaluation for Second-order Triangular Elements
• 34- 2.5.3.Assembly of Global Matrices: Bandwidth and Sparsity of Matrices
• 35- 2.5.4.Penalty Function Method for Elimination of Spurious Modes
• 36- 2.6.Solution of the System of Equations
• 37- 2.7.Implementation of Boundary Conditions
• 38- 2.7.1.Natural Boundary Condition and Symmetry: Electric and Magnetic Wall
• 39- 2.7.2.Absorbing Boundary Condition and Perfectly Matched Layer (PML) Boundary Condition
• 40- 2.7.3.Periodic Boundary Conditions (PBC)
• 41- 2.8.Practical Illustrations of FEM Applied to Photonic Structures/devices
• 42- 2.8.1.The Rectangular Waveguide: Si Nanowire
• 43- 2.8.2.Waveguide with a Circular Cross Section: Photonic Crystal Fiber (PCF)
• 44- 2.8.3.Plasmonic Waveguides
• 45- 2.8.4.Photonic Crystal Waveguide and Periodic Boundary Conditions
• 46- 2.9.FEM Analysis of Bent Waveguides
• 47- 2.10.Perturbation Analysis for Loss/gain in Optical Waveguides
• 48- 2.10.1.Perturbation Method with the Scalar FEM
• 49- 2.10.2.Perturbation Method with the Vector FEM
• 50- 2.11.Accuracy and Convergence in FEM
• 51- 2.11.1.Discretisation and Interpolation Errors in FEM Analysis
• 52- 2.11.2.Element Shape Quality and the Stiffness Matrix
• 53- 2.11.3.Error Dependence on Element Size, Order and Arrangement
• 54- 2.11.4.Adaptive Mesh Refinement
• 55- 2.12.Computer Systems and FEM Implementation
• 56- References
• 57- 3.Finite-Element Beam Propagation Methods
• 58- 3.1.Introduction
• 59- 3.2.Setting up BPM Methods
• 60- 3.3.Vector FE-BPM with PML Boundary Conditions
• 61- 3.3.1.Semi-vector and Scalar FE-BPM
• 62- 3.3.2.Wide-angle FE-BPM
• 63- 3.3.3.Paraxial FE-BPM
• 64- 3.3.4.Implementation of the BPM and Stability
• 65- 3.3.5.Practical Illustrations of FE-BPM applied to Photonic Structures/devices
• 66- 3.4.Junction Analysis with FEM: The LSBR Method
• 67- 3.4.1.Analysis of High Index Contrast Bent Waveguide
• 68- 3.5.Bi-directional BPM
• 69- 3.6.Imaginary Axis/distance BPM
• 70- 3.6.1.Analysis of 3D Leaky Waveguide by the Imaginary Axis BPM
• 71- References
• 72- 4.Finite-Element Time Domain Method
• 73- 4.1.Time Domain Numerical Methods
• 74- 4.2.Finite-Element Time Domain (FETD) BPM Method
• 75- 4.2.1.Wide Band and Narrow Band Approximations
• 76- 4.2.2.Implementation of the FETD BPM Method: Implicit and Explicit Schemes
• 77- 4.3.Practical Illustrations of FETD BPM Applied to Photonic Structures/devices
• 78- 4.3.1.Optical Grating
• 79- 4.3.2.90° Sharp Bends
• 80- References
• 81- 5.Incorporating Physical Effects within the Finite-Element Method
• 82- 5.1.Introduction
• 83- 5.2.The Thermal Model
• 84- 5.2.1.Thermal Modeling of a VCSEL
• 85- 5.3.The Stress Model
• 86- 5.3.1.Stress Analysis of a Polarization Maintaining Bow-tie Fiber
• 87- 5.4.The Acoustic Model
• 88- 5.4.1.Acousto-optic Analysis of a Silica Waveguide
• 89- 5.4.2.SBS Analysis of a Silica Nanowire
• 90- 5.5.The Electro-optic Model
• 91- 5.5.1.Analysis of a Lithium Niobate (LN) Electro-optic Modulator
• 92- 5.6.Nonlinear Photonic Devices
• 93- 5.6.1.Analysis of a Strip-loaded Nonlinear Waveguide
• 94- 5.6.2.Analysis of a Nonlinear Directional Coupler
• 95- 5.6.3.Analysis of Second Harmonic Generation in an Optical Waveguide
• 96- References
• 97- 6.FE-based Methods: The Present and Future Directions
• 98- 6.1.Introduction
• 99- 6.2.Salient Features of FE-based Methods
• 100- 6.3.Future Trends and Challenges for FE-based Methods
• 101- Appendix A Scalar FEM with Perturbation
• 102- TE Modes
• 103- TM Modes
• 104- Appendix B Vector FEM with Perturbation
• 105- Appendix C Green's Theorem.

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