Phase-slip induced distributed feedback resonator modes with tilted modulation

Transversely bounded λ/4 distributed feedback (DFB) resonator with tilted index modulation is considered. By treating the modulation as a weak perturbation and averaging the wave equation with respect to the transverse field distribution we obtain an effective coupled-wave equations with spatially varying coupling constant. We analyze these equations both analytically and numerically for a specific case of transverse confinement. The evolution of the frequency of the lowest threshold laser mode with the tilt angle is studied. It is demonstrated that the dependence of the frequency of the intra-gap localized mode on the tilt angle originates from the mode-conversion mechanism in the DFB process.