-symmetric transport in non- -symmetric bi-layer optical arrays

We study transport properties of an array created by alternating (a, b) layers with balanced loss/ gain characterized by the key parameter γ. It is shown that for non-equal widths of (a, b) layers, i.e., when the corresponding Hamiltonian is non- -symmetric, the system exhibits the scattering properties similar to those of truly  -symmetric models provided that without loss/ gain the structure presents the matched quarter stack. The inclusion of the loss/gain terms leads to an emergence of a finite number of spectral bands characterized by real values of the Bloch index. Each spectral band consists of a central region where the transmission coefficient  T 1 N , and two side regions with  T 1 N . At the borders between these regions the unidirectional reflectivity occurs. Also, the set of Fabry–Perot resonances with TN=1 are found in spite of the presence of loss/gain.