Unbreakable -symmetry and its consequence in a -symmetric dimer

Abstract

This article presents a finite dimensional unbreakable -symmetric waveguide system with linear and nonlinear coupling. In traditional -symmetric systems, a balance (or a symmetric state) among the waveguides with loss and gain can be achieved only when the coupling among the waveguides is sufficiently strong. But the coupled waveguide system that we report here obtains the balance (or symmetry preservation) as soon as the couplings are established and this symmetric nature is undisturbed even for arbitrarily large values of loss–gain strength. We here show that the -symmetry in the system is unbreakable in the presence of linear and nonlinear coupling. Interestingly, in the absence of linear coupling, the system shows contrast behavior where -symmetry is spontaneously broken for all parametric values. As the considered system is integrable, we illustrate the symmetry unbroken and broken nature of the system using their integrals of motion. Importantly, we illustrate the possibility to have high power oscillations by weakening the couplings among the waveguides.