Integrated Bragg Grating Spectra

In this paper, we present a general methodology suitable for analyzing any IBG (Integrated Bragg Grating) as a linear time-invariant (LTI) system using the effective refractive index (ERI) and transfer matrix method (TMM). This approach is based on the translation of the IBG’s physical structure into a matrix of effective refractive indexes, neff, which is wavelength-dependent and describes the behavior of light in the IBG while avoiding the use of approximations like Coupled Mode Theory does. This procedure allows to obtain very accurate reflection and transmission spectra, regardless of the perturbation complexity of the grating. Using this methodology, different apodization and chirp methods are revised and compared. Its generality is considered by analyzing two distinct technological platforms, silicon-on-insulator (SOI) and aluminum oxide (Al2O3).