Dephased index and gain coupling in distributed feedback lasers

In this paper, we study the reflection coefficient of a periodic Bragg reflecting structure in which there exists both an index-of-refraction grating as well as a gain grating. Most past studies have assumed that these two gratings were in phase with each other. In the present work we investigate the effects that arise when a phase shift is purposely introduced between the two gratings. We use a normal coupled-wave analysis to calculate the reflection coefficient as a function of the detuning away from the Bragg frequency when this grating phase difference is varied from 0 to 2π. We find particular phase difference values for which essentially a single-line reflection coefficient results, which in turn should produce narrow-band, single-mode operation of any device utilizing this Bragg structure for distributed feedback purposes