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Investigation of the noise-like structures of the total scattering cross-section of random media

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

Open Access Open Access

Abstract

The pseudospectral time-domain (PSTD) algorithm is implemented to numerically solve Maxwell’s equations to obtain the optical properties of millimeter-scale random media consisting of hundreds of micron-scale dielectric scatterers. Our methodology accounts for near-field interactions and coherent interference effects that are not easily modeled using other techniques. In this paper, we show that the total scattering cross-section (TSCS) of a cluster of closely packed scatterers exhibits a high-frequency oscillation structure, similar to noise. Furthermore, the characteristics and origin of such noise-like oscillation structure have been analyzed and determined based on first-principles.

©2005 Optical Society of America

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Figures (4)
Fig. 1.
Fig. 1. Comparison of the total scattering cross-section (TSCS) of a cluster consisting of N dielectric cylinders. With an overall-diameter D = 280 μm, each cluster consists of randomly positioned, non-contacting, n = 1.2 dielectric cylinders of diameter d = 14 μm. Five cases are shown (a)–(e): N = 10, 20, 75, 125, and 150, respectively. (Each TSCS curve is offset on the vertical axis to facilitate comparison.) It is apparent that the high-frequency oscillation of the TSCS spectrum increases with increasing N.

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Fig. 2.
Fig. 2. Extracted oscillation structure of the TSCS spectra corresponding to various N. The high-frequency oscillations are extracted from the TSCS (as shown in Fig. 1) by subtracting out the smoothed TSCS curves. (The smoothed TSCS spectra are obtained by a running Gaussian-window average with FWHM of 20 THz.) Each curve is offset vertically with (from bottom to top) N = 10, 20, 50, 75, 100, 125, 150, 175, and 203, respectively. For larger N, the oscillation of the TSCS spectrum becomes more pronounced.

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Fig. 3.
Fig. 3. Characteristic correlation interval δω of the TSCS high-frequency oscillation of clusters consisting of various numbers of cylinders. With an overall diameter D = 280 μm, each cluster consists of N dielectric cylinders of diameter d. An example of the geometry is shown in (i)–(v), depicting the geometry of a cluster consisting of diameter d = 14 μm dielectric cylinders (n = 1.2), with various numbers of cylinders within each cluster [(i)–(v): N = 10, 50, 100, 150, and 203, respectively.] The characteristic correlation interval δω is shown in (a)–(c), corresponding to clusters consisting of d-μm-diameter cylinders: (a) d = 6 μm, (b) d = 10 μm, (c) d = 14 μm. It is apparent that the characteristic correlation interval δω decreases monotonically as the number of scatterers increases.

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Fig. 4.
Fig. 4. Characteristic correlation interval δω of the TSCS oscillation for a cluster of fixed number of cylinders (N = 64), with various cluster diameter D. (i)–(vi): depicts the geometry of a cluster consisting of diameter d = 14 μm dielectric cylinders (n = 1.2), with various cluster diameters: D = 160 μm, 200 μm, 240 μm, 280 μm, 320 μm, and 480 μm, respectively. The characteristic correlation interval δω is shown in (a)–(c), corresponding to clusters consisting of d-μm-diameter cylinders: (a) d = 6 μm, (b) d = 10 μm, (c) d = 14 μm. From (a)–(c) it is readily shown that the correlation length does not depend significantly on the overall cluster diameter D, or the spacing s between scatterers.

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Equations (1)

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{ ∂ V ∂ x | i } = − F − 1 ( j k ˜ x F { V i } )
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