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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References

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Appl. Opt. (2)

IEEE T. Geosci. Remote (1)

J.J. Guo, L. Tsang, K.H. Ding, A.T.C. Chang, and C.T. Chen, "Frequency dependence of scattering by dense media of small particles based on Monte Carlo simulation of Maxwell equations" IEEE T. Geosci. Remote 40, 153-161 (2002)
[CrossRef]

IEICE T. Electron. (1)

B.E. Barrowes, C.O. Ao, F.L. Teixeira, J.A. Kong, and L. Tsang, "Monte Carlo simulation of electromagnetic wave propagation in dense random media with dielectric spheroids" IEICE T. Electron. E83C, 1797-1802 (2000).

J. Opt. A-Pure Appl. Op. (1)

T. Khan and H.B. Jiang, "A new diffusion approximation to the radiative transfer equation for scattering media with spatially varying refractive indices" J. Opt. A-Pure Appl. Op. 5, 137-141 (2003).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Phys. A: Math. Gen. (1)

E. Amic, J.M. Luck, and T.M. Nieuwenhuizen, "Anisotropic multiple scattering in diffusive media" J. Phys. A: Math. Gen. 29, 4915-4955 (1996).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Opt. Technol. Let. (1)

Q.H. Liu, "The PSTD algorithm: A time-domain method requiring only two cells per wavelength" Microw. Opt. Technol. Let. 15, 158-165 (1997).
[CrossRef]

Phys. Rev. Lett. (1)

M. Haney and R. Snieder, "Breakdown of wave diffusion in 2D due to loops" Phys. Rev. Lett. 91 (2003).
[CrossRef] [PubMed]

submitted to Appl. Opt. (1)

S.H. Tseng, A. Taflove, D. Maitland, V. Backman, and J.T. Walsh, "Extraction of Single-Scatterer Signatures from Multiple-Scattering of Closely Packed Random Media" (submitted to Appl. Opt.)

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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.

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.

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.

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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