Calculation of optical-waveguide grating characteristics using Green's functions and the Dyson's equation

TL;DR

This paper introduces a Green's function and Dyson's equation-based method for precisely calculating the optical-waveguide grating characteristics, accommodating complex grating profiles and imperfections with efficient numerical scaling.

Contribution

It presents a novel exact computational approach for optical-waveguide gratings that handles arbitrary dielectric modulations, including chirp, apodisation, and imperfections.

Findings

Method scales as O(N), efficient for large discretizations

Applicable to all 1D optical waveguide gratings, including high-index contrast

Can solve both Bragg and long-period grating problems exactly

Abstract

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 counter-propagating 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 apodisation 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 1D optical waveguide gratings including high-index contrast gratings and 1D photonic crystals.