Emergence of stable two-color states in mutually coupled lasers

We theoretically investigate a setup of two mutually delay-coupled semiconductor lasers in a face to face configuration, and study the multi-stabilities and symmetry-broken 1-colour and 2-colour states for this system, for the... [ view full abstract ]

We theoretically investigate a setup of two mutually delay-coupled semiconductor lasers in a face to face configuration, and study the multi-stabilities and symmetry-broken 1-colour and 2-colour states for this system, for the development of mutually coupled lasers for integration in a Photonic Integrated Circuit (PIC).

The lasers are coherently coupled via their optical fields, where the time delay τ arises from the finite propagation time of the light from one laser to the other. This system is well described by single mode rate equations, which are a system of delay differential equations (DDEs) with one fixed delay. Yanchuk et al. 2004 predicted 1-color symmetric states for very small delays. In Erzgräber et al. 2006 the bifurcations of 1-color states were studied for large delay. Moreover, for zero delay, stable symmetric and symmetry-broken 1-color and 2-color states have been predicted recently by Clerkin et al. 2014.

In particular, symmetry-broken 2-color states are highly interesting from an application point of view, for example in the context of all-optical switching. Here we show that these states continue to exist for finite delays. We performed a detailed study of the relevant bifurcations of the system with finite delay in the range of τ from 0 to 1 (in units of photon lifetime), by means of the continuation Matlab package DDE-BIFTOOL.

Bifurcations and stability regions with the two bifurcation parameters, coupling strength κ and coupling phase Cp are shown in the figure for τ=1. In regions a and b, in-phase and antiphase 1-color states are stable, respectively. For very high coupling strength κ, these two regions are separated by two supercritical Hopf bifurcations. The very small area between these two Hopf lines contains region c with stable symmetric 2-color states. More importantly, the model predicts that symmetry-broken 2-color states are stable in the two large regions d and e, which are bounded by torus, period-doubling and pitchfork of limit cycle bifurcations.

Acknowledgements: We thank Bernd Krauskopf and Hartmut Erzgräber for helpful discussions and for help with the DDE-BIFTOOL implementation. This work was supported by the Science Foundation Ireland under grant SFI 13/IA/1960 .