Frequency-Domain Model of Longitudinal Mode Interaction in Semiconductor Ring Lasers

A general and comprehensive frequency-domain model of longitudinal mode interactions in semiconductor ring lasers (SRLs) is presented, including nonlinear terms related to third order nonlinear susceptibilities
$\chi^{3}$
and also linear terms due to back scattering between counter-propagating modes. The model can handle a large number of modes and complex third order nonlinear processes such as self-suppression, cross-suppression and four wave mixing occurring due to both interband and intraband effects. Every aspect of the lasing characteristics of SRLs, including lasing spectra, light-current curves and lasing direction hysteresis, can be reproduced by the model. To assess the performance and validity of the model, several miniaturized SRLs are designed, fabricated and tested. Stable unidirectional lasing in SRLs is also demonstrated by introducing asymmetric feedback from external facets. Good agreement between theoretical and experimental results is demonstrated.