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

TLDR

Transverse energy flux in total internal reflection of elliptically polarized light has been theoretically described by Wiegrefe, Fedorov, Costa de Beauregard, and Schilling, with recent discussions linking it to the noncollinearity of photon velocity and momentum in evanescent waves. The authors derived a new transverse‑shift formula using an energy‑flux‑conservation approach analogous to Kristoffel and Renard, and experimentally verified it for circularly polarized light in near‑limit total reflection with two distinct measurement methods. Experimental results confirm the authors’ formula, disproving the earlier expressions by Costa de Beauregard and Schilling.

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.