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 delta is maximum, and the reflection Jones matrix assumes a simple form. For N > square root 3, the average and differential phase shifts are equal (hence deltap = 3 deltas) 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 partial differential delta/partial partial differential phi)phi=90 degrees = -(2/N)(N2 - 1)1/2 = -2 cos phic, where phic is the critical angle and (partial partial differential2 delta/partial partial differential phi 2)phi=90 degrees = 0. Therefore delta is proportional to the grazing incidence angle theta = 90 degrees - phi (for small theta) with a slope that depends on N. The largest separation between the angle of maximum delta and the critical angle is 9.88 degrees and occurs when N = 1.55377. Finally, several techniques are presented for determining the relative refractive index N by using TIR ellipsometry.