Thursday, November 3, 2011

Question everything

As you may know, my major field is optics, which concerns the study and application of light. Throughout my studies I've been constantly amazed that Maxwell's electromagnetic theory of light, which has been around since the late 1800's, still contains features that have not been settled or have been simply overlooked by scientists. One such artifact is the dissimilarity between Minkowski's and Abraham's descriptions of the momentum carried by an electromagnetic wave.

In a 2010 PRA Rapid Communication, Chaumet et al. expand on earlier work by Hinds and Barnett that examines the force on a dipole in a time-varying (i.e. pulsed) plane wave. This force is written completely as

where Pj is the dipole moment, E is the electric field, B is the magnetic induction, and ε is the Levi-Civita tensor. The first term in the sum relates to both the radiation pressure and the gradient force. The second term, according to Hinds and Barnett, is usually absent in laser trapping and cooling texts because it is proportional to the time-derivative of the Poynting vector, which is zero in common cooling setups. This term is responsible for repulsion of systems such as a two-level atom from the leading edge of the wave when the first term alone predicts an attraction.

Works like this make me wary of blindly using formulas when performing calculations since it reminds me that a theory may not be complete or its assumptions explicit when presented to a niche audience.