Transport mean free path for magneto-transverse light diffusion

Abstract

PACS. 78.20.Ls -Magneto-optical effects. PACS. 42.68.Ay -Propagation, transmission, attenuation, and radiative transfer.Abstract. -We derive an expression for the transport mean free path ℓ * ⊥ associated with magneto-transverse light diffusion for a random collection of Faraday-active Mie scatterers. This expression relates the magneto-transverse diffusion in multiple scattering directly to the magneto-transverse scattering of a single scatterer.Magneto-transverse light diffusion -more popularly known as the "Photonic Hall Effect" (PHE) -has been predicted theoretically some three years ago [1], and has been confirmed experimentally one year later [2]. Phenomenologically, the effect has many similarities to the well-known electronic Hall effect: given a diffusion current J, the presence of an external and constant magnetic field creates a flow in the "magneto-transverse" direction qB × J, with q the charge of the current carriers. By the non-existence of photon charge, the physics of the PHE seems different, and compares perhaps better to the so-called Beenakker-Senftleben effect in dilute gazes [3]. The evident driver behind the electronic Hall effect is the Lorentz force acting on a charged particle while colliding with the impurities. According to Ref.[1] the PHE finds its origin in the Faraday effect for dielectric scatterers, that slightly changes their scattering amplitude. The charge q is replaced by a material parameter V with the symmetry of charge, quantifying the Faraday effect of the particle's material. In a homogeneous medium the Faraday effect implies a rotation V B per unit length of the polarization vector of linearly polarized light. Two other magneto-optical effects in multiple scattering, such as the suppression of coherent backscattering in a magnetic field [4,5], and "Photonic MagnetoResistance" [6] are known to exist, and basically originate from the same Faraday effect.In an isotropic medium, Fick's phenomenological law relates the diffusion current to the energy-density gradient ∇ρ according to J = −D 0 ∇ρ [7]. D 0 is the conventional diffusion constant for radiative transfer and is usually related to the transport mean free path ℓ * and the transport velocity v E according to D = 1 3 v E ℓ * . The velocity is relevant only for dynamical experiments. Fick's law applies to media much larger than ℓ * and, when supplied by boundary Typeset using EURO-L A T E X

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