Unveiling the Angle Dependence of Anisotropic Transmission Resonances in 1D Photonic Structures

Anisotropic transmission resonances (ATRs) are energy conserving fluxes observed in PT symmetric systems, characterised by the transmittance reaching unity \(\:(T=1)\) while either the left or right reflectance vanishes \(\:({R}_{l}=0\:or\:{R}_{r}=0)\). This study focuses on the formation and behaviour of ATRs as a function of incident angle, examining a PT symmetric structure composed of two dielectric layers with equal amounts of gain and loss. As the incident angle varies, the separation between ATRs on the loss and gain side decreases, impacting both S & P-polarizations. However, P-polarization exhibits a distinct behaviour. For P-polarization, Brewster's angle prevents the realization of loss-side ATRs ensuring their exclusive formation on one side. The scattering properties of individual ATRs were analysed from both loss and gain side, revealing their differential dependence on the incident angle. Furthermore, ATRs coinciding with the phase transition point were achieved by tuning parameters such as incident angle, gain/loss contrast (\(\:n{\prime\:}\)) and wavelength resulting in a unidirectional transmission feature. Additionally, an analogous study of the \(\:\sqrt{ϵ}\) behaviour previously explored using couple mode theory was conducted using the scattering matrix theory to examine the transition point (exceptional point).