Rate-equation theory of a feedback insensitive unidirectional semiconductor ring laser

Abstract

For our recently designed continuous-wave and single-frequency ring laser with intra-cavity isolator, we have formulated a rate-equation theory which accounts for two sources of mutual back-scattering between the clockwise and counterclockwise modes, i.e. induced by side-wall irregularities and due to inversion-grating-induced spatial hole burning. With this theory we first confirm that for a ring laser without intra-cavity isolation, from sufficiently large pumping strength on, the inversion-grating-induced bistable operation (i.e. either clockwise or counterclockwise) will overrule the back-reflection-induced coupled-mode operation (i.e. both clockwise and counterclockwise). We then analyze the robustness of unidirectional operation in case of intra-cavity isolation against the intra-cavity back-reflection mechanism and grating-induced mode coupling and derive for this case an explicit expression for the directionality in the presence of external optical feedback, valid for sufficiently strong isolation. The predictions posed in the second reference remain unaltered in the presence of the mode coupling mechanisms here considered.

Toward a Feedback-Insensitive Semiconductor Laser

“…Most of the theory for our laser can be found in [51], [58], [59] and will be summarized here. In [58] it is assumed that neither back scattering nor hole-burning-induced cross saturation is present.…”

“…In [59] a theoretical study is given as to what extent the main predictions are robust against the inevitable presence of back scattering and cross saturation. In case of sufficiently strong isolation an analytic expression for the directionality in the presence of EOF is derived, which shows that the effects of EOF and back scattering are similar in structure and corroborates the predictions in [58].…”

“…It is shown in [59] that if the laser operates close to the steady-state equilibrium and the isolation is strong enough that ΔΓ ξT 1 ΔJ while ΔΓ K and I ccw I cw , the following expression holds in good approximation:…”

Multi-Stable Operation of a Semiconductor Ring Laser Due to Spatial Hole-Burning

“…The rate equations were originally derived for the weakly time-dependent field amplitudes in [12] in the context of a feedback-insensitive semiconductor laser and extended for the inclusion of coherent back scattering in [13]. The relevant equations for the present study are…”

Simultaneous Chaos Time-Delay Signature Cancellation and Bandwidth Enhancement in Cascade-Coupled Semiconductor Ring Lasers

“…Unlike any lasers mentioned above, a semiconductor ring laser (SRL) supports clockwise (CW) and counter clockwise (CCW) propagation modes in a cavity with a circular geometry [45]- [51]. Both modes can be readily destabilized by the feedback, thereby enabling a large variety of complex dynamics including chaos.…”