Pulsating self-coupled lasers

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Abstract
We consider a system of two lasers. The output of each laser is injected in the other laser after a possible attenuation of the field intensity. We formulate the laser equations in the good-cavity limit and show that there is a coupling between intensities and phases. If the coupling is small, the long-time response of each laser is time periodic and is similar to the response of a laser with periodic loss modulations. Resonance effects are possible and may lead to interesting bifurcation diagrams when the free lasers are different. We investigate the weak-coupling limit for arbitrary values of the pump parameters. The resonance problem is analyzed for values of the pump parameters close to the laser first threshold. If the coupling is moderate, stable steady-state solutions are possible. The transition from time-periodic to steady-state responses appears at a critical coupling amplitude. We propose an asymptotic analysis of the laser equations which is valid for values of the pump parameters close to the laser first threshold.