Fresnel algorithm

In addition to the angular position and peak intensity (at the metal surface) of surface plasmon modes their extension into the dielectric medium is another important aspect for SPFS. Again, based on the Fresnel algorithm we have calculated the optical intensity normal to the layered architecture prism / Au layer / aqueous buffer and display the result obtained at resonance in Figure 4 (full curve). One can see that the intensity I, indeed, peaks at the metal /dielectric interface and decays exponentially into both media. 

An illustrative description of the implicit parameters was given by Harrick (1967) on the basis of a low-absorption approximation. This applies well for most organic materials, for materials of stronger absorption the Fresnel equations or the thereupon based layer algorithms mentioned in Sec. 6.4.3 should be applied. The depth from which analytical information can be gathered is conveniently characterized by the penetration depth dp. This is the distance in which the amplitude of an electric field decays to a fraction e of its initial value. For the evanescent field one finds... 

FIGURE 4 Diffraction pattern of a ring-shaped aperture with internal diameter 0.8 times the external one, illuminated by a plane wave at a distance corresponding to a Fresnel number of 15. The three-dimensional plot was obtained by using an improved fast Fourier transform algorithm. [From Luchini, P. (1984). Comp. Phys. Commun. 31,303.]... 

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