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Exceptional points in a time-delayed anti-PT symmetric system

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.