Abraham-based momentum and spin of optical fields under conditions of total reflection

Abstract

This memo contains a collection of formulas describing the electromagnetic energy, momentum and spin distribution of an optical field formed in dielectric media separated by a plane interface when an incident monochromatic plane wave is totally reflected. The formulas are based on the Abraham momentum definition and include the momentum decomposition into the orbital (canonical) and spin parts as well as explicit dual-symmetric separation of the electric and magnetic contributions. This material was prepared in February 2013 but it had not been finalized and published because of the difficulties in physical interpretation of singular terms in the spin and orbital momentum expressions associated with the sharp interface. Meanwhile, it has become clear that the "naive" Abraham approach is not correct for this problem and the electromagnetic spin and momentum in inhomogeneous media are better characterized by the more elaborated relations based on the Minkowski paradigm [see, e.g., Phys. Rev. A 83, 013823 (2011); 86, 055802 (2012); arXiv:1706.05493]. In application to the total-reflection situation this Minkowski-based description was recently illustrated in arXiv:1706.06263, so the present material is mainly of historical interest. However, it seems useful to make it known for a wide audience, at least for comparison with the recent improved approaches and for suitable references. The last section, treating the ponderomotive action experienced by a Mie particle in the evanescent wave, is independent of the Abraham - Minkowski controversy. The numerical calculations preserve their validity, and association of the various force and torque components with corresponding components of the optical momentum and spin remains legal in the Minkowski pattern. The results of the last section were partly used in other published works [e.g., Nature Commun. 5, 3300 (2014)].