Optimization of multiple exposure gratings for widely tunable lasers

A theoretical study of the reflection spectra of multiple holographic exposure distributed Bragg reflector gratings is presented. We will show that such a grating can exhibit a uniform reflection comb if the relative phases of the superimposed gratings are well chosen. The tolerances on the optimal phases are of the order of 0.09 radians for six superimposed gratings to 0.04 radians for ten gratings.