Green s Function Integral Equation Methods in Nano Optics 1st Edition by Thomas M Sndergaard ISBN 9780815365969 0815365969

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Product details:

ISBN 10:  0815365969

ISBN 13: 9780815365969

Author:  Thomas M Sndergaard

 This book gives a comprehensive introduction to Green’s function integral equation methods (GFIEMs) for scattering problems in the field of nano-optics. First, a brief review is given of the most important theoretical foundations from electromagnetics, optics, and scattering theory, including theory of waveguides, Fresnel reflection, and scattering, extinction, and absorption cross sections. This is followed by a presentation of different types of GFIEMs of increasing complexity for one-, two-, and three-dimensional scattering problems. In GFIEMs, the electromagnetic field at any position is directly related to the field at either the inside or the surface of a scattering object placed in a reference structure. The properties of the reference structure, and radiating or periodic boundary conditions, are automatically taken care of via the choice of Green’s function. This book discusses in detail how to solve the integral equations using either simple or higher-order finite-element-based methods; how to calculate the relevant Green’s function for different reference structures and choices of boundary conditions; and how to calculate near-fields, optical cross sections, and the power emitted by a local source. Solution strategies for large structures are discussed based on either transfer-matrix-approaches or the conjugate gradient algorithm combined with the Fast Fourier Transform. Special attention is given to reducing the computational problem for three-dimensional structures with cylindrical symmetry by using cylindrical harmonic expansions.

Table of contents: 

1. Introduction

2. Theoretical foundation

3. Onedimensional scattering problems

4. Surface integral equation method for 2D scattering problems

5. Area integral equation method for 2D scattering problems

6. Volume integral equation method for 3D scattering problems

7. Volume integral equation method for cylindrically symmetric structures

8. Surface integral equation method for the quasistatic limit

9. Surface integral equation method for 3D scattering problems

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Tags: Thomas M Sndergaard, Green s Function, Integral, Equation, Methods, Nano Optics