In this paper we report on a method for quantitative measurement and characterization of the Goos-Hanchen effect based upon the real world performance of optical sources. A numerical model of a nonideal plane wave is developed in terms of uniform divergence properties. This model is applied to the Goos-Hanchen shift equations to determine beam shift displacement characteristics, which provides quantitative estimates of finite shifts near critical angle. As a potential technique for carrying out a meaningful comparison with experiments, a classical method of edge detection is discussed. To this end a line spread Green’s function is defined which can be used to determine the effective transfer function of the near critical angle behavior of divergent plane waves. The process yields a distributed (blurred) output with a line spread function characteristic of the inverse square root nature of the Goos-Hanchen shift equation. A parameter of interest for measurement is given by the edge shift function. Modern imaging and image processing methods provide suitable techniques for exploiting the edge shift phenomena to attain refractive index sensitivities of the order of 10−6, comparable with the recent results reported in the literature.
Phys. Rev. A
Phys. Rev. A 75 063826 (2007)