GREEN'S FUNCTION INTEGRAL EQUATION METHODS IN NANO OPTICS
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- Author: THOMAS M. SONDERGAARD
- ISBN: 9780815365969
- Availability: In Stock
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ABOUT THE BOOK
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.
Each
presented method is accompanied by examples from nano-optics, including:
resonant metal nano-particles placed in a homogeneous medium or on a surface or
waveguide; a microstructured gradient-index-lens; the Purcell effect for an
emitter in a photonic crystal; the excitation of surface plasmon polaritons by
second-harmonic generation in a polymer fiber placed on a thin metal film; and
anti-reflective, broadband absorbing or resonant surface microstructures. Each
presented method is also accompanied by guidelines for software implementation
and exercises.
Features
- Comprehensive
introduction to Green’s function integral equation methods for scattering
problems in the field of nano-optics
- Detailed
explanation of how to discretize and solve integral equations using simple
and higher-order finite-element approaches
- Solution
strategies for large structures
- Guidelines
for software implementation and exercises
- Broad
selection of examples of scattering problems in nano-optics