GREENS FUNCTION INTEGRAL EQUATION METHODS IN NANO OPTICS (HB 2019) Hardcover

This book offers a thorough introduction to Green’s function integral equation methods (GFIEMs) for analyzing how light interacts with nanoscale objects (scattering) in nano-optics. It begins with a concise overview of key theories from electromagnetics, optics, and scattering, including waveguides, Fresnel reflection, and how to measure scattering, extinction, and absorption. The book then presents various GFIEMs, ranging from simple to more complex, designed for one, two, and three-dimensional scattering scenarios. In GFIEMs, the light field at any point is directly linked to the field either inside or on the surface of a nanoscale object within a defined background environment. The characteristics of this background and any boundary conditions (like radiation or repeating patterns) are automatically accounted for by selecting the appropriate Green’s function. The book provides detailed explanations on how to solve these integral equations using basic or more advanced finite-element methods. It also discusses how to determine the relevant Green’s function for different background structures and boundary conditions, and how to calculate near-fields, optical properties, and the power emitted by a localized light source. For analyzing large structures, the book explores solution techniques based on transfer-matrix methods or the conjugate gradient algorithm combined with the Fast Fourier Transform. It specifically focuses on simplifying calculations for 3D structures with cylindrical shapes by using cylindrical harmonic expansions. Each method discussed is illustrated with examples from nano-optics, such as: resonant metal nanoparticles in different environments (homogeneous medium, surface, or waveguide): a microstructured lens with a gradually changing refractive index: the Purcell effect for a light emitter in a photonic crystal: the generation of surface plasmon polaritons by a nonlinear optical process in a polymer fiber on a thin metal film: and surface structures designed to reduce reflection, absorb light across a wide range of wavelengths, or resonate at specific frequencies. Furthermore, each method includes guidance for developing software and practice exercises.