Optical momentum and angular momentum in complex media: from the Abraham–Minkowski debate to unusual properties of surface plasmon-polaritons

Abstract

We examine the momentum and angular momentum (AM) properties of monochromatic optical fields in dispersive and inhomogeneous isotropic media, using the Abraham-and Minkowski-type approaches, as well as the kinetic (Poynting-like) and canonical (with separate spin and orbital degrees of freedom) pictures. While the kinetic Abraham-Poynting momentum describes the energy flux and the group velocity of the wave, the Minkowski-type quantities, with proper dispersion corrections, describe the actual momentum and AM carried by the wave. The kinetic Minkowski-type momentum and AM densities agree with phenomenological results derived by Philbin. Using the canonical spinorbital decomposition, previously used for free-space fields, we find the corresponding canonical momentum, spin and orbital AM of light in a dispersive inhomogeneous medium. These acquire a very natural form analogous to the Brillouin energy density and are valid for arbitrary structured fields. The general theory is applied to a non-trivial example of a surface plasmon-polariton (SPP) wave at a metal-vacuum interface. We show that the integral momentum of the SPP per particle corresponds to the SPP wave vector, and hence exceeds the momentum of a photon in the vacuum. We also provide the first accurate calculation of the transverse spin and orbital AM of the SPP. While the intrinsic orbital AM vanishes, the transverse spin can change its sign depending on the SPP frequency. Importantly, we present both macroscopic and microscopic calculations, thereby proving the validity of the general phenomenological results. The microscopic theory also predicts a transverse magnetization in the metal (i.e. a magnetic moment for the SPP) as well as the corresponding direct magnetization current, which provides the difference between the Abraham and Minkowski momenta.

Spin and momentum of the light fields in inhomogeneous dispersive media with application to surface plasmon-polariton waves

“…Note a remarkably compact and unified character of expressions (17) and (19): they merely reproduce a scheme in which the dispersion has been taken into account in the Brillouin formula (2) for the energy. In this form, equations for the field momentum and the AM have been derived and used for the analysis of the SPP [16,17]. However, there are some imperfections in the pattern described by Eqs.…”

“…Nonetheless, a genuine value of their approach becomes clear only in conjunction with a so-called canonical decomposition of the field momentum, when it is subdivided into the spin and canonical (orbital) components [16,17]. With further elaboration and microscopic substantiation, this approach has resulted in unified, compact and physically transparent expressions for the canonical linear momentum, as well as the orbital and spin AMs of optical fields in lossless, inhomogeneous dispersive media.…”

“…The methods and results of Refs. [16,17] have enabled elaborating a rigorous, consistent theory of surface plasmon-polaritons (SPPs), analyzing thoroughly their non-trivial properties (e.g., a transverse spin) and predicting a number of novel phenomena (e.g., an SPP-induced magnetization of media).…”

“…[16,17]. In particular, we enhance their general scheme to include a linear spin momentum whose description in the dispersive media has earlier been omitted.…”

“…The present consideration is essentially based on the materials of Refs. [16,17]; we not only employ their main ideas but, where possible, adhere to their notation and terminology.…”