Fresnel power transmission coefficient

Love, J. D. and Winkler, C. (1980) Generalized Fresnel power transmission coefficients for curved graded-index media. I.E.E.E. Trans. Microwave Theory Tech., 28, 689-94. 

The fraction of beam power transmitted across the interface depends on the product of E, and H and is given by the Fresnel power transmission coefficient T of Eq. (35-21) with and n replaced by Uj and n o, respectively. 

Consider two semi-infinite media of refractive indices and < n , separated by the planar interface x = 0 in Fig. 35-3(a). A ray, or plane wave, is incident on the interface from the denser medium at angle 6 to the z-direction. Plane wave reflection in this situation is well-known and the power transmission coefficient of Eq. (35-11) is identical to the classical Fresnel coefficient [2]. 

The interface and turning-point caustic are curved surfaces. They are defined by two principal radii of curvature which depend on both the core radius p and the bend radius R. Under these conditions we use the localized transmission coefficients of Section 7-14 each time a ray loses power by tunneling. When power is lost by refraction, we employ the Fresnel coefficient of Eq. (35-50) for the step profile, and assume complete power loss for the clad parabolic profile, i.e. T= 1. 

The ray tubes formed by the incident and reflected rays in Fig. 35-3 (a) have the same z-directed cross-section, and, since 4 is complex, the power density in each varies as 14 p, as is clear from Table 13-2, page 292. We deduce from Eqs. (35-11) and (35-18) that the transmission coefficient is given by 1 — B/A for 0. < 0 < n/2, leading to the Fresnel coefficient... 

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