1 Fibers & Nonlinear Optics, Department of Photonics Engineering, Technical University of Denmark2 Department of Photonics Engineering, Technical University of Denmark3 Optofluidics Theory and Similation, Department of Micro- and Nanotechnology, Technical University of Denmark4 Department of Micro- and Nanotechnology, Technical University of Denmark5 Center for Nanostructured Graphene, Center, Technical University of Denmark
We present a method for calculating the transmission spectra, dispersion, and time delay characteristics of optical-waveguide gratings based on Green's functions and Dyson's equation. Starting from the wave equation for transverse electric modes we show that the method can solve exactly both the problems of coupling of counterpropagating waves (Bragg gratings) and co-propagating waves (long-period gratings). In both cases the method applies for gratings with arbitrary dielectric modulation, including all kinds of chirp and apodization and possibly also imperfections in the dielectric modulation profile of the grating. Numerically, the method scales as O(N) where N is the number of points used to discretize the grating along the propagation axis. We consider optical fiber gratings although the method applies to all one-dimensional (1D) optical waveguide gratings including high-index contrast gratings and 1D photonic crystals.
Physical Review E (statistical, Nonlinear, and Soft Matter Physics), 2006, Vol 74, Issue 3