This paper will report on some features of a platform for the realization of an anti parity-time (anti-PT) symmetric system in a pair of time-delay coupled semiconductor lasers, with special emphasis on the delay induced dynamics in the system. The system is modeled by a modified Lang-Kobayashi rate equations model, augmented to include delayed coupling. The role of a phase accumulation factor that arises from the delayed coupling is elucidated. Finally, the novel exceptional point(s) behavior that is characteristic of the time-delay is investigated via numerics as well as analytically via the Lambert W function.
The purpose of this paper is to examine the behavior of exceptional points (EPs) in a time delayed anti-parity-time symmetric system composed of two delay-coupled semiconductor lasers (SCLs). Starting from a pseudo-2x2 rate equation model for the lasers’ electric fields we analyze the eigenvalues and eigenvectors of the system’s effective Hamiltonian and numerically search for EPs. Recent experimental work has suggested that the EP landscape in this system may be significantly different from the typical anti-PT dimer due to the time delay. Exceptional points in these PT dimers mark global phase changes from overall oscillatory behaviour to exponential growth/decay; in contrast, the time delay renders our effective Hamiltonian infinite-dimensional and allows for more than one EP. Specifically, we numerically demonstrate that by tuning the delay time or coupling strength our time delayed system may exhibit one, two, or zero EPs.
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 paritytime (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.
Over the past five years, open systems with balanced gain and loss have been investigated for extraordinary properties that are not shared by their closed counterparts. Non-Hermitian, Parity-Time (PT ) symmetric Hamiltonians faithfully model such systems. Such a Hamiltonian typically consists of a reflection-symmetric, Hermitian, nearest-neighbor hopping profile and a PT-symmetric, non-Hermitian, gain and loss potential, and has a robust PT -symmetric phase. Here we investigate the robustness of this phase in the presence of long-range hopping disorder that is not PT-symmetric, but is periodic. We find that the PT-symmetric phase remains robust in the presence of such disorder, and characterize the configurations where that happens. Our results are found using a tight-binding model, and we validate our predictions through the beam-propagation method.
We experimentally demonstrate the realization of a parity-time (PT) symmetry breaking in optically coupled semiconductor lasers (SCLs). The two SCLs are identical except for a detuning between their optical emission frequencies. This detuning is analogous to the gain-loss parameter found in optical PT systems. To model the coupled SCLs, we employ the standard rate equations describing the electric field and carrier inversion of each SCL, and show that, under certain conditions, the rate equations reduce to the canonical, two-site PT- symmetric model. This model captures the global behavior of the laser intensity as the system parameters are varied. Overall, we find that this bulk system (coupled SCLs) provides an excellent test-bed to probe the characteristics of PT-breaking transitions, including the effects of time delay.
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