Accumulation of Distributed Phase Shift in Distributed-Feedback Resonators

Abstract

Distributed-feedback waveguide lasers based on Bragg-grating resonators generate ultranarrow-linewidth emission. Oscillation at the center of the reflection band ensures maximum reflectivity, hence minimum linewidth. The required π/2 phase shift is often introduced by a distributed change in effective refractive index, e.g., by widening the waveguide. Despite careful design and fabrication, the experimentally observed resonance wavelength deviates from the designed wavelength. Even when thermally induced chirp or fabrication errors are negligible, this deviation is still present. Here, we show theoretically and experimentally that this deviation is of fundamental nature. The decay of light intensity during propagation from the phase-shift center into both sides of the Bragg grating due to reflection by the periodic grating and the refractive index change causes an incomplete accumulation of designed phase shift, thereby systematically shifting the resonance to a shorter wavelength. Considering the overlap integral between the distributed phase shift and light intensity in the design provides the desired performance.