Fourier factorization with complex polarization bases in modeling optics of discontinuous bi-periodic structures

Fourier Factorization with Complex Polarization Bases in Calculating 2D Photonic Bandgap Structures and Devices

The plane wave expansion method for calculating photonic bandgap structures is reformulated by using the method of Fourier factorization with complex polarization bases. A brief description of the method is shown, and then two examples of photonic crystals are calculated, one with square and another with hexagonal periodicity of arranged elements. The convergence of the presented approach is di...

Polarization Optics of Periodic Media

A Spectral Volume Integral Equation Meth- Od for Arbitrary Bi-periodic Gratings with Explicit Fourier Factorization

For dielectric periodic gratings, we propose the combination of a spectral-domain volume integral equation and Fourier factorization rules to address the Gibbs phenomenon caused by jumps in both the fields and the permittivity. From a theoretical point of view we discuss two ways to overcome the computational complexity caused by the inverse rule by changing the fundamental unknowns of the unde...

Periodic structures in integrated optics

Thin-film dielectric waveguides with a periodic refractive index, a periodic substrate, or periodic surface are studied. The field is determined from Maxwell's equations using Floquet's theorem. The Brillouin diagram and the interaction regions are investigated. The bandwidth and the attenuation coefficients of the interaction regions are given as a function of the optical wavelength. A number ...

Periodic Structures for Integrated Optics

This paper deals with the theory and device applications of periodic thin-film waveguides. Topics treated include mode solutions, optical fiiters, distributed feedback lasers (DFB), distzibuted B r a g reflector (DBR) lasers, grating couplers, and phase matching in nonlinear interactions.