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Simulation of enhanced backscattering of light by numerically solving Maxwell’s equations without heuristic approximations

Snow H. Tseng, Young L. Kim, Allen Taflove, Duncan Maitland, Vadim Backman, and Joseph T. Walsh

Open Access Open Access

Abstract

We report what we believe to be the first simulation of enhanced backscattering (EBS) of light by numerically solving Maxwell’s equations without heuristic approximations. Our simulation employs the pseudospectral time-domain (PSTD) technique, which we have previously shown enables essentially exact numerical solutions of Maxwell’s equations for light scattering by millimeter-volume random media consisting of micrometer-scale inhomogeneities. We show calculations of EBS peaks of random media in the presence of speckle; in addition, we demonstrate speckle reduction using a frequency-averaging technique. More generally, this new technique is sufficiently robust to permit the study of EBS phenomena for random media of arbitrary geometry not amenable to simulation by other approaches, especially with regard to extension to full-vector electrodynamics in three dimensions.

©2005 Optical Society of America

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Figures (3)
Fig. 1.
Fig. 1. PSTD simulation of the enhanced backscattering (EBS) numerical experiment. With dimensions of 800×400 µm, the rectangular cluster consists of N randomly positioned, non-contacting, infinitely long, dielectric cylinders with refractive index n=1.25; Each cylinder had a diameter of 1.2 µm with an average spacing of s=2.8 µm between cylinders (edge to edge). The rectangular cluster is illuminated by a coherent plane wave that is incident at 15° relative to the normal. Both the incident light and the backscattered light are polarized perpendicular to the plane of incidence, equivalent to collinear detection in EBS experiments. A standard anisotropic perfectly matched layer (APML) absorbing boundary condition is implemented to absorb outgoing waves, simulating a light scattering experiment in free space.

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Fig. 2.
Fig. 2. PSTD-computed enhanced backscattered light (EBS) as a function of backscattering angle. 0° corresponds to direct backscattering at 15° from the normal. (a) Two examples of scattered light intensities, corresponding to two different rectangular clusters each consisting of N=10,000 cylinders, as shown in Fig. 1. (b) Ensemble average of 40 different rectangular clusters, showing a significant amount of speckle that partially obscures the EBS peak. (c) After averaging over 50 closely spaced frequencies, the speckle is significantly reduced and the EBS peak can be clearly seen.

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Fig. 3.
Fig. 3. Comparison of PSTD-computed EBS peaks (solid lines) for three wavelengths with theoretical benchmark results (dash-dotted lines) for rectangular clusters consisting of N cylinders. (a)-(c) correspond to N=10,000 cylinders with ls ’=65.0 µm, 41.5 µm, and 37.7 µm, respectively; (d)-(e) correspond to N=20,000 cylinders with ls ’=32.5 µm, 20.7 µm, and 18.9 µm, respectively. The PSTD calculations are in good agreement with the benchmark theory.

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Equations (2)

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{ ∂ V ∂ x ∣ i } = − F − 1 ( j k ˜ x F { V i } )
α ( θ ) = 3 8 π [ 1 + 2 z 0 l + 1 ( 1 + q l ) 2 ( 1 + 1 − exp ( − 2 q z 0 ) q l ) ] * SF ( θ )
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