An Electromagnetic Crystal Green Function Multiple Scattering Technique for Arbitrary Polarizations, Lattices, and Defects

• Published in: Journal of lightwave technology Vol. 25; no. 2; pp. 571 - 583
• Main Authors: Pissoort, D., Michielssen, E., Grbic, A.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-02-2007; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Band pass filters; Crystal defects; Crystals; Cylinders; Detection, estimation, filtering, equalization, prediction; Devices; Electromagnetic devices; Electromagnetic scattering; Electromagnetic wave polarization; Electromagnetic waveguides; Exact sciences and technology; Green function; Green's functions; Information, signal and communications theory; Integral equations; Lattices; Magnetic devices; Mathematical analysis; Multiplexing; Numerical analysis; periodic structures; photonic band gap waveguides; photonic crystals; Plasmons; Scattering; Signal and communications theory; Signal, noise; Studies; Telecommunications and information theory; Free field; Chebyshev filter; Wireless telecommunication; Non linear filter; Numerical method; Crystal defect; Micromachine; TM mode; TE mode; Periodic structure; Finite element method; Triangular lattice; Wave propagation; Arbitrary shape body; Spread function; Band pass filter; Integral equation; photonic band gap waveguides; periodic structures; Third order; Multiple scattering; Green function; Equation system; Numerical analysis; Free space propagation; Simulation; Photonic crystal; photonic crystals; Scattering matrix
• ISSN: 0733-8724; 1558-2213
• DOI: 10.1109/JLT.2006.889364

A generalized electromagnetic crystal (EC) Green function (GF) multiple scattering technique (MST) that permits the simulation of transverse electric and magnetic waves in 2-D EC devices created by replacing crystal cylinders by nonconforming ones is presented. The EC may be defined on a square or triangular lattice. Both EC and nonconforming cylinders can be of arbitrary shape and composition. Integral equations in terms of equivalent currents residing on circular surfaces centered about the nonconforming cylinders are constructed using GFs innate to the background EC. Contrary to the (conventional) free-space GF MST, the proposed generalized EC GF MST yields sparse systems of equations that can be solved efficiently by multifrontal methods. A combination of the generalized EC GF MST with a volume integral-equation- and/or finite-element-based scheme to calculate scattering matrices of noncircular/inhomogeneous/plasmonic cylinders yields a very powerful tool that permits simulating wave propagation in a very broad class of EC devices. The generalized EC GF MST is applied to the analysis of a wide variety of practical EC devices, including a third-order Chebyshev bandpass filter, a pair of power dividers, two channel drop filters, a large multiplexer-demultiplexer, a set of bended waveguides, and waveguide filters comprising noncircular or plasmonic cylinders