Whence the Minkowski momentum?

Masud Mansuripur, Armis R. Zakharian

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


Electromagnetic waves carry the Abraham momentum, whose density is given by pEM = S(r,t) / c2. 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 n2 + iκ2, submerged in a transparent dielectric of refractive index n1, through which light must travel to reach the absorber/reflector. Depending on the impedance-mismatch between the two media, which mismatch is dependent on n1, n 2, κ2, 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.

Original languageEnglish (US)
Pages (from-to)3557-3563
Number of pages7
JournalOptics Communications
Issue number19
StatePublished - Oct 1 2010


  • Electromagnetic theory
  • Lorentz force
  • Photon momentum
  • Radiation pressure

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Atomic and Molecular Physics, and Optics
  • Physical and Theoretical Chemistry
  • Electrical and Electronic Engineering


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