Whence the Minkowski momentum?

• Published in: Optics communications 2010-10, Vol.283 (19), p.3557-3563
• Main Authors: Mansuripur, Masud, Zakharian, Armis R.
• Format: Article
• Language: English
• Subjects: Density; Electromagnetic fields; Electromagnetic theory; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Lorentz force; Mathematical analysis; Optical elements, devices, and systems; Optics; Photon momentum; Physics; Radiation pressure; Reflectors; Reflectors, beam splitters, and deflectors; Refractive index; Refractivity; Submerged
• ISSN: 0030-4018; 1873-0310
• DOI: 10.1016/j.optcom.2010.04.059

Electromagnetic waves carry the Abraham momentum, whose density is given by p EM = S ( r , t) / c 2. Here S ( r , t) = E ( r , t) × H ( r , t) is the Poynting vector at point r in space and instant t in time, E and H are the local electromagnetic fields, and c is the speed of light in vacuum. The above statement is true irrespective of whether the waves reside in vacuum or within a ponderable medium, which medium may or may not be homogeneous, isotropic, transparent, linear, magnetic, etc. When a light pulse enters an absorbing medium, the force experienced by the medium is only partly due to the absorbed Abraham momentum. This absorbed momentum, of course, is manifested as Lorentz force (while the pulse is being extinguished within the absorber), but not all the Lorentz force experienced by the medium is attributable to the absorbed Abraham momentum. We consider an absorptive/reflective medium having the complex refractive index n 2 + i κ 2, submerged in a transparent dielectric of refractive index n 1, through which light must travel to reach the absorber/reflector. Depending on the impedance-mismatch between the two media, which mismatch is dependent on n 1, n 2, κ 2, either more or less light will be coupled into the absorber/reflector. The dependence of this impedance-mismatch on n 1 is entirely responsible for the appearance of the Minkowski momentum in certain radiation pressure experiments that involve submerged objects.