Rajkumar Roychoudhury

Spectral singularity in confined PT symmetric optical potential

We present an analytical study for the scattering amplitudes (Reflection |R| and Transmission |T|), of the periodic PT symmetric optical potential V(x)=W0cos2x+iV0sin2x confined within the region 0 ⩽ x ⩽ L, embedded in a homogeneous medium having uniform potential W0. The confining length L is considered to be some integral multiple of the period π. We give some new and interesting results. Scattering is observed to be normal (|T|2 ⩽ 1,u2009|R|2 ⩽ 1) for V0 ⩽ 0.5, when the above potential can be mapped to a Hermitian potential by a similarity transformation. Beyond this point (V0 > 0.5) scattering is found to be anomalous (|T|2,u2009|R|2 not necessarily ⩽1). Additionally, in this parameter regime of V0, one observes infinite number of spectral singularities ESS at different values of V0. Furthermore, for L = 2nπ, the transition point V0 = 0.5 shows unidirectional invisibility with zero reflection when the beam is incident from the absorptive side (Im[V(x)] < 0) but with finite reflection when the beam is incident...

An algebraic approach to the exponential cosine screened Coulomb potential

An analytical formula is obtained for the energy eigenvalues of the exponential cosine screened Coulomb potential by a method that is a combination of algebraic perturbation theory based on the Lie algebra of the SO(2,1) group and the scaling variational method. The results are found to be in excellent agreement with Pade approximation calculations.