Phase shifts that accompany total internal reflection at a dielectric-dielectric interface

The absolute, average, and differential phase shifts that p- and s-polarized light experience in total internal reflection (TIR) at the planar interface between two transparent media are considered as functions of the angle of incidence phi. Special angles at which quarter-wave phase shifts are achieved are determined as functions of the relative refractive index N. When the average phase shift equals pi/2, the differential reflection phase shift A is maximum, and the reflection Jones matrix assumes a simple form. For N > root3, the average and differential phase shifts are equal (hence delta(P) = 3delta(S)) at a certain angle phi that is determined as a function of N. All phase shifts rise with infinite slope at the critical angle. The limiting slope of the Delta-versus-phi curve at grazing incidence = (partial derivativeDelta/partial derivativephi) (phi=90degrees) = -(2/N)(N-2 - 1)(1/2) = -2 cos phi(C), where phi(C) is the critical angle and (partial derivative(2)Delta/partial derivativephi(2)) (phi=90degrees) = 0. Therefore Delta is proportional to the grazing incidence angle theta = 90degrees - phi (for small theta) with a slope that depends on N. The largest separation between the angle of maximum A and the critical angle is 9.88degrees and occurs when N = 1.55377. Finally, several techniques are presented for determining the relative refractive index N by using TIR ellipsometry. (C) 2004 Optical Society of America.