Classes of Balanced Gain-and-Loss Waveguides as Non-Hermtian Potential Hierarchies

In this work, we report the construction of different classes complex-valued refractive index landscapes, with real spectra, in framework factorization method. The particular case guiding hyperbolic-type profiles is considered PT- and non-PT-symmetric configurations. both schemes, imaginary part satisfies zero-total-area condition indicating that total transverse optical power preserved, allowing stable propagating modes to be obtained. spectra guided modal field amplitudes are obtained their orthogonality relations established.