Lorentz invariance of absorption and extinction cross sections of a uniformly moving object

Timothy J. Garner, Akhlesh Lakhtakia, James K. Breakall, Craig F. Bohren

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Abstract

The energy absorption and energy extinction cross sections of an object in uniform translational motion in free space are Lorentz invariant, but the total energy scattering cross section is not. Indeed, the forward-scattering theorem holds true for comoving observers but not for other inertial observers. If a pulsed plane wave with finite energy density is incident upon an object, the energies scattered, absorbed, and removed from the incident signal by the object are finite. The difference between the energy extinction cross section and the sum of the total energy scattering and energy absorption cross sections for a non-comoving inertial observer can be either negative or positive, depending on the object's velocity, shape, size, and composition. Calculations for a uniformly translating, solid, homogeneous sphere show that all three cross sections go to zero as the sphere recedes directly from the source of the incident signal at speeds approaching c, whether the material is a plasmonic metal (e.g., silver) or simply a dissipative dielectric material (e.g., silicon carbide).

Original languageEnglish (US)
Article number053839
JournalPhysical Review A
Volume96
Issue number5
DOIs
StatePublished - Nov 20 2017

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All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics

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