Multiple-mode behavior of circular-grating-coupled distributed feedback lasers

Multimode characteristics of circular-grating-coupled distributed feedback (CGC DFB) lasers are studied theoretically. A modified time-domain finite-difference method is used to solve the time-dependent coupled-mode equations and carrier rate-equation in a self-consistent manner. It is found that, at a moderate injection current density (≤ 4 times its threshold), the high-order radial modes with fundamental azimuthal profile can be excited when either 1) the grating duty cycle is in the range between 0.35 and 0.5, 2) the phase shift of the grating center is greater than π, or 3) the facet reflectivity is greater than 0.2. On the other hand, switching between the modes with fundamental and first-order azimuthal profiles is observed when the grating duty cycle is either ∼0.08 or ∼ 0.45. Switching of azimuthal modes is also observed if facet reflectivity is greater than 0.02. Outside these conditions or the lasers with duty cycle greater than 0.5, stable single-mode operation is observed. Therefore, the design of single-radial and azimuthal mode CGC DFB lasers can be realized.