Longitudinal and transverse shifts of an 8 cm parallel bounded beam of 34.2 GHz (8.77 mm) microwaves totally reflected from a paraffin prism have been investigated. The 45°–45°–90° prism is 18 cm high by 25 cm on the sides and the index of refraction is 1.491. Longitudinal shifts as large as 3 cm have been measured in a single reflection near the critical angle for a beam linearly polarized in the plane of incidence. The shift for perpendicular polarization is approximately half this value. The results are in general agreement with the classical theory for the Goos-Hanchen effect. An incident beam polarized at 45° to the incidence plane produces both parallel and perpendicular polarization shifts with values similar to the above. The shifts for both polarizations are reduced but are still distinctly separate if either a second prism or a metallic reflector is brought into the evanescent wave at millimeter distances from the interface. These results are in accordance with stationary phase calculations for two interfaces. It is found that a small (6 mm) transverse shift results if the prism is illuminated with circularly polarized microwaves.

Longitudinal and transverse displacements of a bounded microwave beam at total internal reflection

A general expression for the Goos–Hanchen lateral shift of a Gaussian wave beam, applicable for incident angle θ equal to, near, or larger than the critical angle θc, is obtained It yields finite and smooth results around θc and coincides with Artmann’s classical result otherwise Another expression for the lateral shift of a different beam-field distribution is also obtained and shown to be quite similar to that of the Gaussian beam Comparisons with an existing theoretical expression and with available experimental data (for θ ≃ θc) are made Discussion of a different expression for θ away from θc obtained through an energy method is also presented

Goos–Hänchen effect around and off the critical angle

We study the lateral shift of a light beam transmitted from an indefinite medium slab. The analytic expressions for the transmission coefficient and the lateral shift are obtained by using the stationary-phase method, and different conditions for the occurrence of a negative lateral shift are deduced. It is shown that the thickness of the indefinite medium strongly affects the properties of the lateral shift. For a larger thickness, the sign of the lateral shift depends only on the signs of the permittivity and permeability, while, for a smaller thickness, the sign of the lateral shift is determined by the combined effect of the incident angle of the light, the signs of the permittivity and permeability, and the thickness of the indefinite medium slab. In addition, the lateral shift at the transmitted resonance points is found to be enhanced greatly, and the sign of the lateral shift around the transmitted resonance points is strongly dependent on the permittivity and permeability of the indefinite medium. Some examples are given to validate the obtained theoretical results.

Negative and positive Goos-Hänchen shifts of a light beam transmitted from an indefinite medium slab

The longitudinal displacement of an elelctromagnetic beam upon reflection from a dielectric slab has been investigated. The experimental results, using 3 cm microwaves, are compared to those predicted by a theory based on a plane-wave approach. The experiment has been completed for both perpendicular and parallel polarization using a slab several wavelengths thick for angles of incidence around 45°. The agreement between experimental values and theoretical predictions is good.

Displacement of an electromagnetic beam upon reflection from a dielectic slab

We report on the Goos–Hanchen (GH) shift of a beam reflected from ferrofluids composed of Fe3O4 nanoparticles coated with Ag, based on the stationary-phase method. We found that both the magneto and structural approaches can effectively control the GH shift. In particular, a larger negative GH shift can be obtained by changing the external magnetic field and the volume factor. The magneto-controllable GH shift provides a possibility for obtaining a desirable GH shift in a fixed configuration.

https://iopscience.iop.org/article/10.1088/2040-8978/15/3/035103/pdf

Large and negative Goos–Hänchen shift with magneto-controllability based on a ferrofluid

Longitudinal Shift of a Microwave Beam at Total Internal Reflection

We have measured the longitudinal shift of a microwave beam at total internal reflection. Good agreement with the prediction of classical electromagnetic theory is provided. The magnitude of the effect at microwave frequencies is conveniently large and the experimental setup used is sufficiently straightforward to allow this experiment to be repeated in an undergraduate laboratory program.

T. M. Knasel

Papers

Longitudinal Shift of a Microwave Beam at Total Internal Reflection

Measurement of the longitudinal shift of radiation at total internal reflection by microwave techniques