Lavrinenko A.V., Lægsgaard J., Gregersen N., Schmidt F., Søndergaard T. Numerical Methods in Photonics

CRC Press, 2015. — 355.Simulation and modelling using numerical methods running on computers is today one of the key approaches in scientific work within practically all fields of research. In particular, in the field of photonics, a wide range of numerical methods are needed for studying both fundamental optics and applied branches such as the design, development, and optimization of photonic components. The topic of numerical modelling is thus becoming an increasing priority in photonics education.
This book evolved from research activities and teaching at three different research institutions. Part of the material (the finite-difference time-domain method, the finitedifference frequency-domain method, and the method for nonlinear propagation) was originally developed for a 5 ECTS course entitled ‘Numerical Methods in Photonics’, which has already been running for 7 years for graduate and undergraduate students at the Department of Photonics Engineering, the Technical University of Denmark (DTU). When it was decided to write a textbook on numerical methods, it was natural to include the popular and powerful modal method also employed at DTU, the finiteelement method, which has been used in research and teaching at Zuse Institute Berlin, Germany, for more than 10 years, and the Green’s function integral equation methods that have been applied for 10 years in both research and teaching at Aalborg University, Denmark. The book thus covers a wide range of important numerical tools employed in photonics modelling nowadays.
The aim of this textbook is to provide an introduction to a range of numerical methods that are used in photonics for the modelling of propagation and scattering of light in micro- and nano-structures. The propagation and interaction of light at optical wavelengths with such structures is governed by Maxwell’s equations, and thus the theoretical methods presented in this book are techniques that either directly solve Maxwell’s equations or solve equations deduced from those. While the material in this book can be employed to compute optical modes used, for example, in the quantization of the electromagnetic field or in a semi-classical model of lasing, we will focus only on solving Maxwell’s equations. A dedicated treatment of quantum phenomena and branches of photonics which requires going beyond Maxwell’s equations and using, for example, quantum mechanics is considered beyond the scope of the book.
This book also aims to provide an introduction to a range of important numerical methods to undergraduate and graduate students with an interest in the photonics and optics of micro- and nano-structures. It assumes that the reader has prior knowledge of optics and Maxwell’s equations. A basic knowledge of linear algebra and of programming will also be an advantage. We hope that the book will be useful for engineers and specialists in electromagnetism and optics, as well as for those who prefer to model physical processes using their own tools.Maxwell’s Equations
Finite-Difference Time-Domain Method
Finite-Difference Modelling of Straight Waveguides
Modelling of Nonlinear Propagation in Waveguides
The Modal Method
Green’s Function Integral Equation Methods for Electromagnetic Scattering Problems
Finite Element Method