Exploiting Multistability to Stabilize Chimera States in All-to-All Coupled Laser Networks

Abstract

Large networks of optically coupled semiconductor lasers can be realized as on-chip solutions. They serve as general testbeds for delay-coupled networks but may also be candidates for new methods in signal processing. Our work focuses on all-to-all networks where the individual units are coupled to each other by a common mirror with very short delay times. Using the well-known Lang-Kobayashi-model for the local laser dynamics, we investigate the occurring bifurcation structure of the complex network in terms of numerical integration and path continuation techniques. We especially focus on the interrelation between material parameters of the laser and occurring synchronization patterns. In this respect we identify the time scale separation between photon and electron lifetimes T as well as the amplitude-phase coupling $\alpha$ to be the driving forces for multi-stability between different cluster solutions. As an example quantum-dot lasers with strongly damped relaxation oscillations are found to present less rich dynamics when coupled to a network. Depending on the initial conditions, one-color symmetric states (all lasers emit the same constant waves), inhomogeneous one-color symmetry-broken states (clusters form that emit at different constant wave intensities), and multi-color symmetry-broken states (clusters with different period pulsations) are found. Those solutions can be analytically understood by reducing the equations to two coupled lasers, where the dynamic bifurcation scenarios have been discussed (Clerkin et al. Phys Rev E 89:032919, 2014 [2]). Additionally we find chimera states, i.e. partially synchronized cluster solutions, where the desynchronized clusters are chaotic in phase, amplitude and carrier inversion (Böhm et al. Phys Rev E 91(4):040901(R), 2015 [1]). They form from random initial conditions within the regions of multistability for the case of large enough amplitude-phase coupling. These chimera states defy several of the previously established existence criteria. While chimera states in phase oscillators generally demand non-local coupling, large system sizes, and specially prepared initial conditions, we find chimera states that are stable for global coupling in a network of only four coupled lasers for random initial conditions.