Orbital and spin parts of energy currents for electromagnetic waves through spatially inhomogeneous media

Abstract

We investigate electromagnetic waves propagating through non-magnetic and loss-free dielectric media, but with spatially inhomogeneous refractive indices. We derive hence a set of analytic formulae for conservation laws and energy-current (Poynting) vector. As a result, we deduce that the energy-current vector cannot be neatly separated into its orbital and spin parts in contrast to the cases with spatially homogeneous media. In addition, we present physical interpretations of the two additional terms due to spatial material inhomogeneity.

Keywords:

• Electromagnetic wave
• material inhomogeneity
• conservation law
• energy current
• orbital part
• spin part

Acknowledgements

We are grateful to the reviewers for guiding us to focus on the main theme of this study and for supplying additional references. We thank in particular one of the reviewers for recommending us to seek the physical implications expounded in Section 8.