Calculation and Experimental Proof of the Transverse Shift Induced by Total Internal Reflection of a Circularly Polarized Light Beam

TLDR: In this article, the transverse energy flux existing in total reflection of an elliptically polarized light beam was calculated by an energy-flux-conservation argument similar to Kristoffel's and to Renard's in their deduction of the longitudinal Goos-Hanchen shift, thus obtaining a formula different from those of the previous authors.

Abstract: Wiegrefe, Fedorov, Costa de Beauregard, and Schilling have discussed the transverse energy flux existing in total reflection of an elliptically polarized light beam, the latter two proposing formulas for the transverse shift of the reflected beam. We have calculated the transverse shift by an energy-flux-conservation argument similar to Kristoffel's and to Renard's in their deduction of the longitudinal Goos-H\"anchen shift, thus obtaining a formula different from those of the previous authors. We have also tested experimentally the existence of the transverse shift, in the optimal case of circular polarization and quasilimit total reflection, by using two slightly different multiplying procedures. Our measurements definitely vindicate our own formula for the transverse shift against both Costa de Beauregard's and Schilling's. The relevance of our results in connection with noncollinearity of velocity and momentum of the spinning photon inside the evanescent wave is very briefly discussed.