Non-hermitian dynamics in delay coupled semiconductor lasers

This paper describes our work on the realization of a non-hermitian Hamiltonian system in time-delay coupled semiconductor lasers consisting of two identical lasers, operated with a small frequency detuning between them, and bidirectionally coupled to each other through optical injection. The effective Hamiltonian for this system is non-hermitian, and, under some assumptions and conditions, reminiscent of two-site parity-time (PT) symmetric Hamiltonians, a topic that is under intense investigation. The dynamical response of the intensity of the lasers as a function of the detuning between them reveals characteristics of a PT symmetric system, and our emphasis is on the features that arise from the delayed coupling. Experimental measurements are in good agreement with numerical simulation of the nonlinear rate equation model that describes the coupled system. models and exceptional (EP) and few recent experiments fabricated synthetic mircocavity lasers on an integrated The laser novel when phase We now report a laboratory realization of a time-delayed, non-hermitian, system in a bulk optical configuration that is comprised of two optically coupled semiconductor lasers (SCLs), and an experimental and theoretical investigation of the properties of this system with special attention to the novel features that arise from the time delayed coupling between oscillators. We show that the rate equation model that is typically used to describe these coupled lasers, can, under certain conditions, lead to an effective non-hermitian Hamiltonian that is strongly reminiscent of the Hamiltonians that arise in the study of conventional PT-symmetric systems. Our experiments demonstrate not only that the coupled SCL system possesses many of the features that PT-symmetric systems do, but also reveals key signatures associated with the time-delayed coupling. Time-delayed differential equations are generally not amenable to analytic solutions and hence we resort to numerical methods to solve the relevant equations that model our system. The predictions of the numerical modeling are compared to the experiments, and the results of are in very good agreement. It is anticipated that the outcomes of our work will be important for systems described by non-Hermitian rate equations, local and nonlocal, and their laboratory implementations.