Spectral Singularity in confined PT symmetric optical potential    [PDF]

Anjana Sinha, R. Roychoudhury
We present an analytical study for the scattering amplitudes (Reflection |R| and Transmission |T|), of the periodic PT symmetric optical potential V(x) = W_0 cos^2 x + i W_0 V_0 sin 2x confined within the region 0 < x < L, embedded in a homogeneous medium having uniform potential W_0. The confining length L is considered to be some multiple of the period D. We give some new and interesting results. Scattering is observed to be normal (|T|^2 \leq 1, |R|^2 \leq 1) for V_0 < 0.5, when the above potential can be mapped to a Hermitian potential by a similarity transformation. However, |R|^2 and |T|^2 do not necessarily add up to unity. Beyond this point (V_0 > 0.5) scattering is found to be anomalous (|T|^2, |R|^2 not necessarily \leq 1). Additionally, in this parameter regime of V_0, one observes infinite number of spectral singularities E_{SS} at different values of V_0. Furthermore, for L = 2n \pi, the transition point V_0 = 0.5 shows unidirectional invisibility with zero reflection when the beam is incident from the absorptive side (Im[V(x)] < 0) but finite reflection when the beam is incident from the emissive side (Im[V(x)] > 0), transmission being identically unity in both cases.
View original: http://arxiv.org/abs/1307.1844