Goos-Hänchen shifts in reflection and transmission of gain assisted parity time symmetric conductive medium

The theoretical study of the manuscript explores the coefficients of reflection, transmission and their corresponding GH-shifts in a parity time ( PT )-symmetric gain assisted four-level conductive medium. The dielectric function of a conductive medium is calculated using density matrix formalism and Maxwell’s equations. The conductivity dependent coefficients of reflection, transmission and their corresponding GH-shifts are calculated from dielectric function of two media and free space permittivity. The reflection and transmission spectra obey PT -symmetry conditions \(R(x,y)-R^{*}(-x,-y)=0\) and \(T(x,y)-T^{*}(-x,-y)=0\) at the interface of a lossy medium of \(|A| \approx 0\) and polystyrene. Enhancement in GH-shifts is calculated with phase and amplitude of conductivity. Giant positive and negative GH-shifts in reflection are calculated to \(S_r=2696\lambda\) and \(S_r=-1848\lambda\) . Similarly, giant positive and negative GH-shifts in transmission are calculated to \(S_t=1346\lambda\) and \(S_t=-924\lambda\) . The GH-shifts in reflection and transmission spectra also satisfy PT -symmetry conditions \(S_r(x,y)=S_r^{*}(-x,-y)\) and \(S_t(x,y)=S_t^{*}(-x,-y)\) . The results of the manuscript are useful for nano-processor technology.