It is important to observe that any pair of Fresnel coefficients can be directly interrelated by the elimination of their common variable v.
In the Nebraska (Muller) conventions, the ejwt time dependence is chosen (see Ref. 4).
Zero reflection at normal incidence (z = 0) leads, as expected, to zero reflection at oblique incidence (w = 0). Notice that z → 0 as v → 1, i.e., when the difference between the refractive indices of the two media that surround the interface tends to zero.
Points along the real axis of the z plane represent normal-incidence reflection of s-polarized light at a dielectric/dielectric interface (v real, hence z real) and the image points in the w plane represent the reflection of that light from the same interface at an angle ø. The oblique reflection is total (i.e., |w| = 1) if the refractive index ratio v ≥ sinø or z ≤ (1 - sinø)/(1 + sinø).
Total reflection at normal incidence (|z| = 1) leads, as expected, to total reflection at oblique incidence (|w| = 1). Notice that |z| → 1 as v → ∞ which happens when light is reflected from the interface between a medium with a finite refractive index and another which is perfectly conducting.
These lines are the loci of constant normal-incidence phase shift.
These circles are the loci of constant normal-incidence (amplitude or intensity) reflectance.
O. S. Heavens, Optical Properties of Thin Solid Films. (Dover, New York, 1965), p. 85.
Various two reflectance methods for determining the optical properties of materials have been previously described. See, for example, Refs. 14–16. Although we assume s-polarized light, identical procedures apply for p-polarized light. The sensitivity of the TRM is known to be poorer with the s polarization than with the p polarization, but straightforward extension of the method to anisotropic media is possible only with s-polarized light (as is illustrated in this section).
A. Fresnel, "Mémoire sur la loi des modifications que la réflection imprime a la lumière polarisée," in Oeuvres Complètes de Fresnel, Vol. 1, H. Senarmont, É. Verdet, and L. Fresnel, 1866, pp. 767–775 (Johnson Reprint Corporation, New York, 1965).
See, for example, R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), Sec. 4.2.
It will be significant to study the relationship between each Fresnel coefficient and the refractive index ratio v as a conformal mapping between two complex planes.