Classical and Nonclassical Optical Diffusion
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CLASSICAL AND NONCLASSICAL OPTICAL DIFFUSION J. M. DRAKE* AND A. Z. GENACK** *Exxon Research and Engineering Co., Annandale, NJ 08801 USA **Department of Physics, Queens College of the City University of New York, Flushing, NY 11367 USA ABSTRACT We present a brief summary of our *recent work on classical and nonclassical optical diffusion in disorder metal oxides. Results on the optical transmission through a slab of titania spheres is presented and discussed in some detail illustrating the experimental method for obtaining the optical diffusion coefficient and photon absorption time from the transmission data. We conclude that the optical field-field correlation function with frequency is the Fourier transform of the time of flight distribution. INTRODUCTION Transport in granular materials is a common theme in many areas of solid state physics. This subject encompasses electronic conductance in granular metals, viscous flow, acoustic propagation in sedimentary rocks to mention only a few. We present a brief summary of our work on optical photon propagation In samples composed of dielectric metal oxide microparticles. This subject has been of intense interest recently due to the prospect that photon localization may occur in disordered dielectric microparticle systems. It has been recognized that a universal description of transport in random media should encompass classical as well as quantum mechanical waves [1-3]. The enhancement of reflected light in a narrow cone about the incident beam was shown to be a consequence of coherent backscattering [4-6]. This is the origin of weak localization, which had previously been observed only for electrons [7]. The scale dependence of the total optical transmission in slab systems is directly measurable [8] and is analogous to electronic conductance. Beyond this, the use of laser sources makes possible the measurement of the time of flight distribution for transmitted photons [9] and the intensity fluctuations with frequency [8,10-13] at a point, in the sample or in the far field speckle pattern. These are statistical properties of the optical intensity at a point in contrast to the total transmission or conductance, which represent spatial averages over the sample. Considering the possibility of photon localization, the loffe and Regel criterion [14] suggests that the onset of localization should occur when K9=1, where K=2w/f is the wave vector and e is the transport mean free path. The uncertainty in K, 1/e, is then as large as K itself so that an extended traveling-wave description is not appropriate. Since the lowest order scattering of light is P wave, maximum scattering is achieved when the scatter is several times larger than 1/K. Indices of refraction in the visible are less than 3 and the scattering cross-section is not much larger than the geometrical cross-section. Thus, it is not clear whether the loffe-Regel criterion can be satisfied for optical photon propagation in random dielectric media. To date, all measurements of optical propagation have been in the lim
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