An optical method is introduced for observation of temporally and spatially resolved frames that show how light propagates in diffusely scattering materials. The method permits videos with 100-fs resolution in time to be produced. The method utilizes short-coherence interferometry. The source of information is the speckle contrast. The temporal and spatial evolution of the multiple scattering process is demonstrated for several biological and industrial samples. A major objective of the method is to investigate the conditions for optimum coherence and optimum apertures to achieve high resolution in the short-coherence interferometry. One important result is that during the propagation a sharp photon horizon evolves, which is useful for the morphological analysis of volume scatterers.
The magnetic behavior of bound shallow donors in CdS, a model S = i amorphous antiferromagnet, has been measured by a Faraday rotation technique down to T ~ 50 mK. The susceptibility, x 9 and dyJdT as well increase monotonically with decreasing T with no sign of an ordering transition even though the median exchange interaction of a spin is ~7K. The results agree with a hydrogeniclike exchange model which is solved in terms of exactly diagonalized weakly interacting clusters.A semiconductor lightly doped with shallow donors is an example of a simple and rather wellcharacterized S=| amorphous antiferromagnet. The amorphous character follows from the large donor orbits, random placement, and low concentration. The exchange interaction between neutral donors, J ij9 is essentially hydrogenic resulting in a well-described distribution of antiferromagnetic interactions which fall off basically exponentially with their separation. 1 Such a system has the essential element of "frustration" of competing interactions characteristic of spinglasses, 2 but differs in having exchange couplings of consistently negative sign and short range in contrast to the 1/r 3 behavior of Ruder man-Kittel-Kasuya-Yosida (RKKY) systems. An intriguing question is whether or not these systems undergo a spin-glass transition to an ordered state at finite temperature. 3 In RKKY systems, a discontinuity in d\/dT (usually a cusp at low fields) has been used by many as an earmark of such a proposed transition. By contrast, no such discontinuity in d\/dT has been observed in experiments on a variety of homogeneous random amorphous antiferromagnets 3 " 6 at temperatures well below the antiferromagnetic Curie-Weiss 0 extracted from the hightemperature behavior of x. Even more striking in these systems is the monotonic increase in \dx/dT\ with decreasing T, with x tending towards infinity. Our current experiments on donors in CdS, extended to temperatures two orders of magnitude lower than 9, show a similar behavior for x (see Fig. 1). These observations are in good quantitative agreement with a modified hydrogenic exchange model which is solved in terms of exactly diagonalized clusters with the intercluster interaction treated in a molecular-field approximation. For spins S = \ this approach has the important advantage over, e.g., Monte Carlo techniques, 7 of being quantum mechanical. Of course, the condition for a division into clusters is that the intercluster interaction be less than k B T. The special feature of the short-range interaction (as compared to RKKY) is that this condition persists down to a temperature two orders of magnitude lower than the median value of the closest-neighbor exchange interactions. Unusual percolative properties are also found as will be seen below.
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