Decomposition of Abraham momentum into complex orbital and spin momenta in evanescent wave

TL;DR

This paper reexamines the decomposition of Abraham momentum in electromagnetic fields, revealing that orbital and spin momenta are inherently complex in evanescent waves, and introduces new exact expressions applicable to various media.

Contribution

It provides the first exact expressions for complex orbital and spin momenta in evanescent fields, extending Abraham momentum decomposition to lossy media and proposing a complex group velocity concept.

Findings

Orbital and spin momenta are inherently complex in evanescent fields.

Derived exact expressions for orbital and spin momenta applicable to propagating and evanescent fields.

Introduced a complex group velocity with real and imaginary parts representing energy flux and osmotic velocity.

Abstract

The Abraham momentum of electromagnetic field represents the decomposition property into real-valued orbital and spin contributions. However, we found that the orbital and spin momenta of evanescent electromagnetic fields are inherently complex. Consequently, the decomposition of Abraham momentum was reexamined and the exact expressions of orbital and spin momenta were obtained, which are applicable to both propagating and evanescent electromagnetic fields. Furthermore, we also justified the newly-derived decomposition of Abraham momentum for lossy media, which was further demonstrated by a concrete example of surface polariton of metal. In addition, by means of the complex orbital momentum of surface polariton the complex group velocity was tentatively put forward with its real part representing the energy flux velocity and its imaginary part denoting the osmotic velocity of energy penetrating the corresponding media