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 φ. 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 π/2, the differential reflection phase shift Δ is maximum, and the reflection Jones matrix assumes a simple form. For N\u3e√3, the average and differential phase shifts are equal (hence δp=3δs) at a certain angle φ that is determined as a function of N. All phase shifts rise with infinite slope at the critical angle. The limiting slope of the Δ-versus-φ curve at grazing incidence (∂Δ/∂φ)φ=90°=−(2/N)(N2−1)1/2=−2 cos φc, where φc is the critical angle and (∂2Δ/∂φ2)φ=90°=0. Therefore Δ is proportional to the grazing incidence angle θ=90°−φ (for small θ) with a slope that depends onN. The largest separation between the angle of maximum Δ and the critical angle is 9.88° and occurs when N=1.55377. Finally, several techniques are presented for determining the relative refractive index N by using TIR ellipsometry