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 spin–orbital 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.
Highlights
Note that in some works the super-momentum was interpreted as a ‘superluminal group velocity’ [33, 88], our present analysis shows that it should rather be considered as a pure momentum property, while the group velocity is determined by the Poynting–Abraham energy flux and is always subluminal
This singularity is cancelled by another singularity in field gradients, and all dynamical properties of the surface plasmon-polariton (SPP) wave are determined by volume contributions in the metal and in the vacuum
Equation (4.30) completes the microscopic picture and explains the origin of the difference between the Abraham and Minkowski momenta in the medium. Since this difference is produced by the direct magnetization current, it cannot be attributed to the wave (Minkowski-type) momentum but it does contribute to the energy flux (Abraham–Poynting momentum) and the group velocity of SPPs
Summary
Orbital 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. While the intrinsic orbital AM vanishes, the transverse spin can change its sign depending on the SPP frequency. We present both macroscopic and microscopic calculations, thereby proving the validity of the general phenomenological results. The microscopic theory 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
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