Analytical model of direct-Bragg, exchange-Bragg, and evanescent coupling in a dual-waveguide structure and its application to single-mode lasing

Abstract

Single-mode distributed-feedback lasing is explored for an asynchronous dual-waveguide uniform-grating structure that exhibits exchange-Bragg and evanescent coupling between optical modes of the two waveguides as well as direct-Bragg coupling between optical modes within each waveguide. Coupled-mode equations governing all coupling processes are presented and solved, yielding an analytical solution that is applicable to a variety of single-mode lasing mechanisms. We leverage this solution to elucidate the lasing mechanism in which the photonic bandgap (PBG) due to exchange-Bragg coupling is aligned to and suppresses a degenerate lasing mode associated with the direct-Bragg PBG of the active waveguide. PBG alignment and mode suppression are achieved for a range of values of Henry’s alpha, direct-Bragg coupling, exchange-Bragg coupling, and evanescent coupling that yield at-threshold gain margin and longitudinal power flatness superior to those of the benchmark λ/4-shifted DFB lasing structure. Such performance includes a gain margin ΔαL=0.88 for a minimum flatness F=0.0006, enabled by the power-transfer action of evanescent coupling. The dual-waveguide geometry and superior predicted performance make the structure compelling for both III-V and heterogeneous III-V-on-silicon platforms.