Photonic Hall effect of inactive Mie scatterers in a Faraday active matrix

Abstract

We describe an experimental study of the photonic Hall effect in media consisting of a magneto-optically active matrix and magneto-optically inert Mie scatterers. We call such media reversed with respect to the normal media having magneto-optically active Mie scatterers in inert matrices in which the photonic Hall effect has been studied so far. We show the photonic Hall effect in reversed media to be proportional to VBl*, where V is the Verdet constant of the matrix, l(*) the transport mean free path of the liquid, and B the applied magnetic field. We further propose an empirical expression that unifies the results obtained in normal and reversed media and present a simple analytic model to illustrate the photonic Hall effect.

Magnetotransverse Scattering of Surface Plasmon Polaritons

“…Although there is no rigorous theoretical prediction for the magnitude of such an effect, dimensionality arguments suggest that the ratio of the magnetotransverse flux and the incident flux should be of the order of GVBl, where l is some characteristic length of the scattering process and G is a dimensionless geometry parameter. In the case of the three-dimensional photonic Hall effect, such a relation has indeed been observed with G 5 3 10 23 [14]. The microscopic mechanism underlying this effect is the influence of the Lorentz force at the SPP oscillation frequency on the collective free electron motion, and thereby on the propagation and scattering of SPP.…”

“…[3] but no magnetic field had been taken into account; and as the cobalt islands of our samples are large compared to the wavelength, this calculation does not apply to our experiment. However, in a scattering crosssection model for the three-dimensional photonic Hall effect [14,15], the influence of the perpendicular magnetic field on photon scattering could be described by rotating the differential scattering cross section around the magnetic field axis over an angle b ഠ VBs, where V is the Verdet constant of the scattering medium, and s is a characteristic scattering length. This results in a net magnetotransverse current of photons, i.e., a photonic Hall effect.…”