Klein Paradox for Optical Scattering from Excited Targets

TL;DR

This paper explores the optical analog of the Klein paradox, showing that in media with excited atoms, scattering can lead to negative cross sections due to amplification, analogous to pair production in relativistic quantum mechanics.

Contribution

It demonstrates the existence of a Klein paradox in optical scattering from excited targets and explains its resolution through matter-induced amplification effects.

Findings

Negative total cross sections occur within certain frequency bands.

Amplification results from decay of excited atoms increasing photon numbers.

The optical Klein paradox parallels the relativistic Klein paradox in quantum mechanics.

Abstract

The well known Klein paradox for the relativistic Dirac wave equation consists in the computation of possible ``negative probabilities'' induced by certain potentials in some regimes of energy. The paradox may be resolved employing the notion of electron-positron pair production in which the number of electrons present in a process can increase. The Klein paradox also exists in Maxwell's equations viewed as the wave equation for photons. In a medium containing ``inverted energy populations'' of excited atoms, e.g. in a LASER medium, one may again compute possible ``negative probabilities''. The resolution of the electromagnetic Klein paradox is that when the atoms decay, the final state may contain more photons then were contained the initial state. The optical theorem total cross section for scattering photons from excited state atoms may then be computed as negative within a frequency band with matter induced amplification.