A rigorous analysis of DFB lasers with large and aperiodic corrugations

A rigorous electromagnetic analysis of the distributed-feedback (DFB) laser in which the corrugations, seen as a cascade of interacting discontinuities, need not be periodic or small is presented. The analysis takes into account the continuous spectrum of radiation modes excited at each discontinuity and their interaction between successive discontinuities without assuming periodicity. The analysis of the individual discontinuity is based on the concept of the transition function. The analysis of the cascade of discontinuities takes place by generalized transfer-matrix methods (including the continuum), bypassing the need for a periodic unit cell. This enables the total diffraction generated by the grating to be modeled exactly. Particular attention is devoted to the threshold analysis of a ridge-waveguide DFB laser, for the case of a rectangular and a trapezoidal grating