Low reflection at zero or low-energies in the well-barrier scattering potentials

Abstract

Probability of reflection R(E) off a finite attractive scattering potential at zero or low energies is ordinarily supposed to be 1. However, a fully attractive potential presents a paradoxical result that R(0) = 0 or R(0) < 1, when an effective parameter q of the potential admits special discrete values.Here, we report another class of finite potentials which are well-barrier (attractive-repulsive) type and which can be made to possess much less reflection at zero and low energies for a band of low values of q. These well-barrier potentials have only two real turning points for E ∈ (V min , V max ), excepting E = 0. We present two exactly solvable and two numerically solved models to confirm this phenomenon.

Supersymmetry, half-bound states, and grazing incidence reflection

“…In this section, we use the factorisation method usually applied in supersymmetric quantum mechanics [20] to design a family of HBS supporting dielectric profiles, which do not reflect TE waves at grazing incidence. We note that our approach connects with recent work in quantum mechanics by Ahmed et al where zero energy reflectionless potentials have been investigated in several cases [34][35][36], and where HBS supporting potentials have been subject to supersymmetric transformations to generate e.g. potentials supporting no bound states at all [37].…”

Supersymmetry, half-bound states, and grazing incidence reflection

“…In this section, we use the factorisation method usually applied in supersymmetric quantum mechanics [20] to design a family of HBS supporting dielectric profiles, which do not reflect TE waves at grazing incidence. We note that our approach connects with recent work in quantum mechanics by Ahmed et al where zero energy reflectionless potentials have been investigated in several cases [30][31][32], and where half-bound state supporting potentials have been subject to supersymmetric transformations to generate e.g. potentials supporting no bound states at all [33].…”