PHYSICAL REVIEW E 86, 011401 (2012) Energy transport velocity in bidispersed magnetic colloids Hem Bhatt, 1 Rajesh Patel, 2,3,* and R. V. Mehta 2 1 Shantilal Shah Engineering College, Sidsar, Bhavnagar-364060, India 2 Department of Physics, Bhavnagar University, Bhavnagar- 364002, India 3 Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA (Received 3 May 2012; published 5 July 2012) Study of energy transport velocity of light is an effective background for slow, fast, and diffuse light and exhibits the photonic property of the material. We report a theoretical analysis of magnetic field dependent resonant behavior in forward-backward anisotropy factor, light diffusion constant, and energy transport velocity for bidispersed magnetic colloids. A bidispersed magnetic colloid is composed of micrometer size magnetic spheres dispersed in a magnetic nanofluid consisting of magnetic nanoparticles in a nonmagnetic liquid carrier. Magnetic Mie resonances and reduction in energy transport velocity accounts for the possible delay (longer dwell time) by field dependent resonant light transport. This resonant behavior of light in bidispersed magnetic colloids suggests a novel magnetophotonic material. DOI: 10.1103/PhysRevE.86.011401 PACS number(s): 83.80.Hj, 42.25.Bs, 42.25.Fx, 75.50.Mm I. INTRODUCTION Nearly five decades ago, Wigner calculated the properties of a quantum particle captured in a potential resonant to its wavelength [1]. He found that the resonant scattering of photonlike particles on the potential leads to increased dwell time. In recent years this has been implemented, using photons as the scattering particles. In many different experimental circumstances, it has been possible to slow down light transport by many orders of magnitude in cold atomic gases [2] and to create optical cavities with high Q value using properly tuned microspheres [3], in photonics [4,5] as well as in biosensing [6]. Most of the recent advances are towards disordered, strongly scattering, random optical media [7]. Some new effects in light scattering by magnetic spheres and vanishing of energy transport velocity in disordered magnetic particles have been studied by Pinheiro et al. [8,9]. Very few have used magnetic tuning of magnetic spheres to predict theoretical and experimental photonic effects [10–12]. Recently, an interesting work on the non-Rayleigh limit of the Mie solution and suppression of scattering by spheres having negative refractive index was published by Miroshnichenko [13]. The case of single as well as multiple scattering by magnetic spheres surrounded by a magnetically passive medium is also treated by several groups [14–16]. However, scattering by a magnetizable sphere dispersed in a magnetically active medium has not been treated until now. Our recent experiment has shown as magnetic field dependent some unusual light transport in bidispersed magnetic colloids [17–19]. We have also reported photonic band gap [20] and optical capacitance [21] for the bidispersed magnetic colloids. Laskar et al. [22] has also studied light scattering in a magnetically polarizable nanoparticle suspension and observed resonant behavior of anisotropy factor as a function of size parameter and magnetic permeability. They have also observed the oscillatory behavior of extinction parameters as a function of the size parameter. However, they have not studied the oscillatory behavior in energy transport velocity or diffusion constant of light * Corresponding author: rjp@bhavuni.edu; rpat7@yahoo.com as a function of an externally applied magnetic field for a magnetic colloid. Here we report a numerical analysis of magnetic field dependent light transport in micrometer size magnetic particles suspended in a magnetic nanofluid (Fig. 1, inset). Magnetic field dependent Mie resonances in forward-backward anisotropy factor, diffusion constant, and energy velocity is observed. A decrease in the energy transport velocity is also observed, which accounts for the longer dwell time of light in such medium. Earlier reports suggest light transport is studied as a function of wavelength, size parameter, or magnetic permeability. However, magnetic field dependent resonant light transport and energy transport velocity are not much explored. This suggests a novel magnetophotonic effect in a bidispersed magnetic colloid. The reason behind choosing bidispersed magnetic colloids is that the micronmeter size magnetic sphere will behave as a Mie scatterer and the magnetic nanofluid consisting of magnetic nanoparticles will be the hydrodynamically continuous medium for the micrometer size scatterer; further, the refractive index of the micrometer size scatterer can be tuned relatively by tuning the refractive index of magnetic nanofluid by the externally applied magnetic field. Thus, results are explained based on two parameters specifically, as the magnetically tunable refractive index of the scatterer via magnetic nanofluid and magnetic field dependent Mie resonances. Magnetic nanoparticles of the magnetic nanofluid will behave like a Rayleigh scatterer and the dispersed micrometer size magnetic sphere will behave like a Mie scatterer. The combined effect may produce the oscillatory behavior in the light transport parameters. II. THEORY Transport of light in dielectric systems is described cor- rectly neither by the group velocity nor by the phase velocity. It has been shown that the correct velocity in that case is the energy transport velocity (v E )[23,24], given by the ratio of the energy flux to the energy density, which takes into account a possible very strong delay by resonant scattering. Resonant behavior of energy transport velocity of diffused light for monodisperse dielectric sphere is studied [7]. We 011401-1 1539-3755/2012/86(1)/011401(4) ©2012 American Physical Society