The term photonics can be used loosely to refer to a vast array of components, devices, and technologies that in some way involve manipulation of light. One of the most powerful numerical approaches available to engineers developing photonic components and devices is the Finite Element Method (FEM), which can be used to model and simulate such components/devices and analyze how they will behave in response to various outside influences. This resource provides a comprehensive description of the formulation and applications of FEM in photonics applications ranging from telecommunications, astronomy, and sensing, to chemistry, imaging, and biomedical R&D. This book emphasizes practical, problem-solving applications and includes real-world examples to assist readers in understanding how mathematical concepts translate to computer code for finite element-based methods applicable to a range of photonic structures. In addition, this is the perfect support to anyone using the COMSOL Multiphysics RF Module.
Introduction - Significance of Numerical Methods. Numerical Methods. Maxwell 's Equations and Boundary Conditions. Basic Assumptions of Numerical Methods and Their Applicability. Choosing a Modeling Method. Finite-Element-Based Methods.; The Finite-Element Method - Basic Concept of FEM: Essence of FEM-based Formulations. Setting up the FEM. Scalar and Vector FEM Formulations. Implementation of FEM. Formation of Element and Global Matrices. Solution of the System of Equations. Implementation of Boundary Conditions. Practical Illustrations of FEM Applied to Photonic Structures/devices. FEM Analysis of Bent Waveguides. Perturbation Analysis for Loss/gain in Optical Waveguides. Accuracy and Convergence in FEM. Computer Systems and FEM Implementation.; Finite-Element Beam Propagation Methods -Introduction. Setting up BPM Methods. Vector FE-BPM with PML Boundary Conditions. Junction Analysis with FEM: The LSBR Method. Bi-directional BPM. Imaginary Axis/distance BPM.; Finite-Element Time Domain Method - Time Domain Numerical Methods. Finite-Element Time Domain (FETD) BPM Method. Practical Illustrations of FETD BPM Applied to Photonic Structures/devices.; Incorporating Physical Effects within the Finite-Element Method -Introduction. The Thermal Model. The Stress Model. The Acoustic Model. The Electro-optic Model. Nonlinear Photonic Devices.; FE-based Methods: The Present and Future Directions -Introduction. Salient Features of FE-based Methods. Future Trends and Challenges for FE-based Methods.; ;
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Arti Agrawal
Arti Agrawal is a lecturer of photonics in the department of electrical, electronic and information engineering at City University London. She earned her Ph.D. in physics from Indian Institute of Technology Delhiand.
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B. M. Azizur Rahman
B. M. Azizur Rahman is a professor of photonics in the department of electrical, electronic and information engineering at City University London. He earned his Ph.D. in electronics at University College London.