Scattering of light by a parity-time-symmetric dipole beyond the first Born approximation

Abstract

The scattering of light by localized three-dimensional dielectrics having gain and loss defies the usual Born approximation, since the material can increase the amplitude of the incident field within the scatterer, making the weak-scattering assumption invalid. The convergence of the Born series is rarely discussed in analytical treatments, as the state of exhaustion is reached after calculating the very first few terms of the series. Even if all the terms are obtained, the series will certainly be of a divergent type in general, thus invalidating the equality of the scattered field to its Taylor-series representation. We present here a simple localized material model of a dielectric having parity-time ($\mathcal{PT}$) symmetry, consisting of a $\mathcal{PT}$-symmetric dipole, such that all the terms in the Born series are analytically evaluated and a closed-form expression is obtained in the far-zone approximation. The scattered field is then analyzed by using Pad\'e approximants in order to obtain convergent representations of the scattered radiation and to compare with the exact solution. This allows us to study the role of the gain and loss parameter in strong-scattering regimes and to demonstrate the remarkable properties of Pad\'e approximants when applied to scattering.