Semiconductor ring lasers (SRLs) are interesting devices for their applications in photonic integrated circuits. For simulating and analysing the SRL one frequently uses a two-mode ODE model consisting of a pair of complex equations for the counter-propagating longitudinal modes and a rate equation for the carrier density . This model, however, cannot recover different multi-mode effects of SRLs such as mode locking or transitions between multiple longitudinal modes. Moreover, it is based on mean-field approximations and does not allow considering spatially inhomogeneous laser parameters and dynamical variables.
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