Resonant mode conversion in the waveguides with an unbroken and broken -symmetry

We study resonant mode conversion in the -symmetric multimode waveguides, where symmetry breaking manifests itself in sequential destabilization (appearance of the complex eigenvalues) of the pairs of adjacent guided modes. We show that the effi-cient mode conversion is possible even in the presence of the resonant longitudinal modulation of the complex refractive index. The distinguishing feature of the resonant mode conversion in the -symmetric structure is a drastic growth of the width of the resonance curve when the gain/losses coefficient approaches a critical value, at which symmetry breaking occurs. We found that in the system with broken symmetry the resonant coupling between exponentially growing mode with stable higher-order one effectively stabilizes dynamically coupled pair of modes and remarkably diminishes the average rate of the total power growth. In the end of nineties it was established that non-Hermitian Hamiltonians satisfying a specific parity-time symmetry condition can possess purely real eigenvalue spectrum- an indispensable attribute of any stable physical quantum sys-tem [1]. Optical systems, such as couplers, built as the bal-anced pairs of amplifying and absorbing waveguides, serve as analogs of quantum systems with -symmetric poten-tials and are capable of supporting guided modes whos