Incoming and reflected light waves superimpose to form a standing-wave pattern normal to a reflecting surface. For total internal reflection, a cosine distribution of the electric field amplitude in the denser medium joins onto the exponential distribution of the penetrating field in the rarer medium. The electric field amplitude at the reflecting interface is a maximum at the critical angle and decreases to zero at grazing incidence. In this paper, theoretical expressions are given for the electric field amplitudes, near the surface, which depend both on polarization and on angle of incidence. These expressions enable us to calculate from simple formulas, and without the aid of computers, the reflectivity losses resulting from the interaction of these standing waves with absorbing species, near the surface either in the rarer or denser medium. They also give us physical insight into the nature of the absorption mechanism at the reflecting interface when the reflection is frustrated. This is helpful in the fields of internal reflection optical spectroscopy and fiber optics. Experimental results, which agree with theoretical expectations, are presented. Strongest coupling is obtained by working near the critical angle for either polarization, and the absorption in the rarer medium is greater for parallel polarization than for perpendicular polarization.
N. J. HARRICK, "Electric Field Strengths at Totally Reflecting Interfaces," J. Opt. Soc. Am. 55, 851-856 (1965)