First an intuitive explanation. The phenomenon is actually wholly analogous to quantum tunnelling by a first quantised particle field described by e. Indeed, if you have a sandwich of lower refractive index material between two higher index materials such that an incoming wave is "totally internally reflected" from the first high-index to lower-index interface, then some of the light tunnels through the sandwich and again propagates freely i. The power transmitted through the layer decreases exponentially with layer thickness, as with analogous quantum tunnelling through high but thin potential barrier problems. So, given that the field penetrates some distance into the lower refractive index medium, the "effective" interface actually lies a small distance into the lower refractive index medium. Now for some details.
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Newton gave both a theoretical basis and experimental evidence for penetration of light into medium 2 under conditions of total internal reflection. Theories of a lateral shift in total internal reflection of electromagnetic waves were developed by Picht Picht J, and by Schaefer and Pich Schaefer and Pich, Their experimental work inspired new theoretical work by Artmann Artmann K, and v.
Fragstein v. Fragstein C, , in which expressions for the lateral shift were obtained, with different shifts predicted for field polarization parallel to or perpendicular to the plane of incidence. It is but one of a large class of non-specular processes, including the Imbert-Federov effect and reflection by multi-layered media [see, for example, the articles by Tamir Tamir T, , Li Li C-F, , and Krayzel et al.
Krayzel et al. In effect, the GHS is connected with the propagation parallel to the surface of an evanescent wave in medium 2. Two distinct cases need be considered, polarization of the electric field perpendicular to the plane of incidence TE or transverse electric polarization and polarization parallel to the plane of incidence TM or transverse magnetic polarization.
By matching boundary conditions at the interface, one obtains the standard Fresnel equations for transmission and reflection at an interface. There is energy flow parallel to the surface in medium 2, but no energy flow perpendicular to the surface; the transmitted wave is an evanescent wave. The orange line is the interface and there is an evanescent wave in medium 2, above the interface. Image provided by A. An alternative explanation of the GHS can be given in terms of the time delay associated with the scattering of a radiation pulse at the interface.
Renard Renard RH, questioned the validity of Eqs. The existence of a nonvanishing GHS at grazing incidence was further supported by the work of Lai et al.
Lai et al. Further validation of the Artmann result was provided by the numerical simulations of Shi et al. Shi et al. The expressions for the GHS given above diverge at the critical angle where the approximations used in their derivation break down.
Early generalizations to include angles near the critical angle were given by Artmann Artmann K, and by Wolter Wolter H, Both these results reflect the fact that a beam having finite width contains a range of angles of incidence about some average angle of incidence. Hence at angles near the critical angle, there are components in the incident beam that undergo both normal as well as total internal reflection. As in the optical case, the GHS can be related to the phase of the reflection coefficient of the corresponding plane wave problem.
There is a probability current density parallel to the surface in medium 2, but no probability flow perpendicular to the surface; the transmitted wave is an evanescent wave. The quantum GHS has the same form as that of the optical GHS for the case of electric field polarization perpendicular to the plane of incidence. They compared total internal reflection from the back surface of a prism with the reflection from a silver strip that was deposited on the back of the prism.
Since the effect is very small, on the order of several optical wavelengths, they multiplied the relative shift between the light that was totally internally reflected and the light that was reflected from the silver by using an "optical waveguide" parallel surfaces between which many reflections occurred that allowed them to increase the relative shift by a factor of 70 or so, limited mainly by losses in reflections from the silver strip.
Thus, by , the GHS had been firmly established. The GHS continued to attract attention as new technologies became available. Cowan and Anicin Cowan and Anicin, observed the GHS shifts for both TE and TM polarizations for microwave radiation incident on a paraffin prism using a single reflection of the beam. Much of this work is motivated by the possibility that the GHS can serve as a probe of scattering and excitations that occur at and near the interface of two bulk materials. An experiment has been carried out in which evidence for the GHS in neutron scattering was claimed deHaan et al.
References Artmann, K. Physik , Beenaker, C. Berman, P. E 66, ; Bretenaker, F. Carnaglia, C. Chiu, K. Cowan, J. Goos, F. Ann Physik , Hora, H. Optik 17, Horowitz, B. Ignatovich, V. A , Krayzel, F.
Lai, H. A 3, E 62, Lotsch, K. Lotsch, H. Optik 32, ; ; ; McGuirk, M. Picht, J. Puri, A. Renard, R. Amer 54, Rhodes, D. Schaefer, C. Schwefel, H. Shi, J. B21, Tamir, T. Fragstein, C. Wolter, H. Naturforsch 5a,
Journal of the Optical Society of America
Newton gave both a theoretical basis and experimental evidence for penetration of light into medium 2 under conditions of total internal reflection. Theories of a lateral shift in total internal reflection of electromagnetic waves were developed by Picht Picht J, and by Schaefer and Pich Schaefer and Pich, Their experimental work inspired new theoretical work by Artmann Artmann K, and v. Fragstein v.
Goos-Hänchen effect in microcavities
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