Light Intensity Distributions in Bragg Gratings and Distributed-feedback Resonators

Periodic optical structures are employed in numerous photonic applications. The coupled-mode theory was developed to calculate the electric-field distributions within such structures. However, for more complex, nonperfectly periodic optical structures it merely provides approximated solutions. The characteristic-matrix approach provides exact solutions but is cumbersome to apply. We introduce a simple method to obtain the exact electric-field and intensity distributions in an arbitrary multi-resonator structure by considering the structure as a combination of multiple Fabry-Pérot resonators of various lengths and refractive indices. The circulating-field approach can be applied recursively to obtain the electric-field distribution of such structures. As each resonator is considered separately, this method can be easily applied to structures with non-uniform resonator lengths and refractive indices, such as chirped and tapered gratings, thereby greatly simplifying their analysis. We apply this method to the calculation of reflectivity spectra and electric-field, intensity, and phase distributions of Bragg gratings and distributed-feedback (DFB) structures.