A system of two mutually coupled quantum dot lasers, each with corresponding longitudinal modes, has been studied in this article. Using multimode rate equation model, we demonstrate how this model in conjunction with coupled-mode theory lead to a set of effective Hamiltonians with characteristics inarguably akin to those Hamiltonians associated to the conventional PT-symmetric systems. A fixed frequency detuning has been introduced by a minute difference in cavity lengths in the current system and the strength of optical coupling plays a decisive role in the emergence of the exceptional points at which the so- called non-conventional PT-symmetry breaks. It has also been shown that the predictions about amplification or attenuation of supermodes associated to the longitudinal modes based on effective Hamiltonians, happen to be supported by the multimode rate equation model, yet in the presence of weak coupling. Eventually, the overall output spectrum is potent to be manipulated and in particular exhibit a single longitudinal mode behavior in the vicinity of the exceptional point through the interplay between the frequency detuning and the coupling coefficient. Owing to the inhomogeneous broadening of the optical spectrum, a considerable rise in the number of photons for the single amplified supermode is witnessed within time having the attenuated modes out of the picture via proper mode selection in the present non-conventional PT-symmetric system.

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