## Scattering by a slab containing randomly located cylinders: comparison between radiative transfer and electromagnetic simulation

JOSA A, Vol. 18, Issue 2, pp. 374-384 (2001)

http://dx.doi.org/10.1364/JOSAA.18.000374

Enhanced HTML Acrobat PDF (690 KB)

### Abstract

This study is devoted to the examination of scattering of waves by a slab containing randomly located cylinders. For the first time to our knowledge, the complete transmission problem has been solved numerically. We have compared the radiative transfer theory with a numerical solution of the wave equation. We discuss the coherent effects, such as forward-scattering dip and backscattering enhancement. It is seen that the radiative transfer equation can be used with great accuracy even for optically thin systems whose geometric thickness is comparable with the wavelength. We have also shown the presence of dependent scattering.

© 2001 Optical Society of America

**OCIS Codes**

(030.5620) Coherence and statistical optics : Radiative transfer

(030.5630) Coherence and statistical optics : Radiometry

(210.3820) Optical data storage : Magneto-optical materials

(290.0290) Scattering : Scattering

(320.5540) Ultrafast optics : Pulse shaping

(320.7100) Ultrafast optics : Ultrafast measurements

**History**

Original Manuscript: September 25, 2000

Manuscript Accepted: October 9, 2000

Published: February 1, 2001

**Citation**

Laurent Roux, Philippe Mareschal, Nicolas Vukadinovic, Jean-Baptiste Thibaud, and Jean-Jacques Greffet, "Scattering by a slab containing randomly located cylinders: comparison between radiative transfer and electromagnetic simulation," J. Opt. Soc. Am. A **18**, 374-384 (2001)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-18-2-374

Sort: Year | Journal | Reset

### References

- S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).
- K. D. Lathrop, “Use of discrete ordinates methods for the solution of neutron transport equations,” Nucl. Sci. Eng. 24, 381–388 (1966).
- A. Lagendijk, B. A. van Tiggelen, “Resonant multiple scattering of light,” Phys. Rep. 270, 143–216 (1996). [CrossRef]
- H. C. Hottel, A. F. Sarofim, I. A. Vasalos, W. H. Dalzell, “Multiple scatter: comparison of theory with experiment,” Trans. ASME, Ser. C J. Heat Transfer 92, 285–291 (1970). [CrossRef]
- A. K. Fung, Microwave Scattering and Emission Models and Their Applications (Artech House, Norwood, Mass., 1994).
- L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1985).
- U. Frisch, “Wave propagation in random media,” in Probabilistic Methods in Applied Mathematics, A. Bharucha-Reid, ed. (Academic, New York, 1968), pp. 75–198.
- A. Walther, “Radiometry and coherence,” J. Opt. Soc. Am. 58, 1256–1259 (1968). [CrossRef]
- L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1995).
- L. A. Apresyan, Y. A. Kravtsov, Radiation Transfer, Statistical and Wave Aspects (Gordon & Breach, Amsterdam, 1996).
- L. Ryzhik, G. Papanicolaou, J. B. Keller, “Transport equations for elastic and other waves in random media,” Wave Motion 24, 327–370 (1996). [CrossRef]
- M. I. Mishchenko, J. M. Dlugach, E. G. Yanovitskij, “Multiple light scattering by polydispersions of randomly distributed, perfectly-aligned, infinite Mie cylinders illuminated perpendicularly to their axes,” J. Quant. Spectrosc. Radiat. Transf. 47, 401–410 (1992). [CrossRef]
- J. Keller, “Stochastic equations and wave propagation in random media,” in Stochastic Processes in Mathematical Physics and Engineering, Vol. 16 of Proceedings of Symposia in Applied Mathematics, R. Bellman, ed. (American Mathematical Society, Providence, R.I., 1964), pp. 145–170.
- L. Tsang, J. A. Kong, “Scattering of electromagnetic waves from random media with strong permittivity fluctuations,” Radio Sci. 16, 303–320 (1981). [CrossRef]
- R. West, D. Gibbs, L. Tsang, A. K. Fung, “Comparison of optical scattering experiments and the quasi-crystalline approximation for dense media,” J. Opt. Soc. Am. A 11, 1854–1858 (1994). [CrossRef]
- C. E. Mandt, Y. Kuga, L. Tsang, A. Ishimaru, “Microwave propagation and scattering in a dense distribution of non-tenuous spheres: experiment and theory,” Waves Random Media 2, 225–234 (1992). [CrossRef]
- A. Nashshibi, K. Sarabandi, “Experimental characterization of the effective propagation constant of dense random media,” IEEE Trans. Antennas Propag. 47, 1454–1462 (1999). [CrossRef]
- L. Tsang, C. E. Mandt, K. H. Ding, “Monte Carlo simulations of the extinction rate of dense media with randomly distributed dielectric spheres based on solution of Maxwell’s equations,” Opt. Lett. 17, 314–316 (1992). [CrossRef] [PubMed]
- L. M. Zurk, L. Tsang, K. H. Ding, D. P. Winnebrener, “Monte Carlo simulations of the extinction rate of densely packed spheres with clustered and nonclustered geometries,” J. Opt. Soc. Am. A 12, 1772–1781 (1995). [CrossRef]
- L. Tsang, K. H. Ding, S. Shih, J. Kong, “Scattering of electromagnetic waves from dense distributions of spheroidal particles based on Monte Carlo simulations,” J. Opt. Soc. Am. A 15, 2660–2669 (1998). [CrossRef]
- P. R. Siqueira, K. Sarabandi, “T-matrix determination of effective pemittivity for three-dimensional dense random media,” IEEE Trans. Antennas Propag. 48, 317–327 (2000). [CrossRef]
- P. Sheng, Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena (Academic, San Diego, Calif., 1995).
- F. E. Nicodemus, “Directional reflectance and emissivity of an opaque surface,” Appl. Opt. 4, 767–773 (1965). [CrossRef]
- F. E. Nicodemus, “Reflectance nomenclature and directional reflectance and emissivity,” Appl. Opt. 9, 1474–1475 (1970). [CrossRef] [PubMed]
- C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, New York, 1983).
- H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
- A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).
- Z. Jin, K. Stamnes, “Radiative transfer in nonuniformly refracting layered media: atmosphere–ocean system,” Appl. Opt. 33, 431–442 (1994). [CrossRef] [PubMed]
- J. Moore, H. Ling, C. S. Liang, “The scattering and absorption characteristics of material coated periodic gratings under oblique incidence,” IEEE Trans. Antennas Propag. 41, 1281–1288 (1993). [CrossRef]
- P. Mareschal, “Étude de la diffraction électromagnétique par des géométries bidimensionnelles infinies,” Ph.D. dissertation (Ecole Centrale Paris, Paris, 1996).
- A. Ishimaru, Y. Kuga, “Attenuation constant of a coherent field in a dense distribution of particles,” J. Opt. Soc. Am. 72, 1317–1320 (1982). [CrossRef]
- J. J. Greffet, M. Nieto-Vesperinas, “Field theory for generalized bidirectional reflectivity: derivation of Helmholtz’s reciprocity principle and Kirchhoff’s law,” J. Opt. Soc. Am. A 15, 2735–2744 (1998). [CrossRef]
- L. M. Zurk, L. Tsang, D. P. Winebrenner, “Scattering properties of dense media from Monte Carlo simulations with application to active remote sensing of snow,” Radio Sci. 31, 803–819 (1996). [CrossRef]
- K. Stamnes, R. A. Swanson, “A new look at the discrete ordinate method for radiative transfer calculations in anisotropically scattering atmospheres,” J. Atmos. Sci. 38, 387–399 (1981). [CrossRef]
- D. A. DeWolf, “Electromagnetic reflections from an extended turbulent medium: cumulative forward-scatter single-backscatter approximation,” IEEE Trans. Antennas Propag. 19, 254–262 (1971). [CrossRef]
- E. Wolf, G. Maret, “Weak localisation and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55, 2696–2699 (1985). [CrossRef] [PubMed]
- M. P. V. van Albada, A. Lagendijk, “Observation of weak localisation of light in a random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985). [CrossRef] [PubMed]
- Y. Kuga, A. Ishimaru, “Retroreflectance from a dense distribution of spherical particles,” J. Opt. Soc. Am. A 1, 831–835 (1984). [CrossRef]
- Y. A. Kravtsov, L. A. Apresyan, “Radiative transfer: new aspects of the old theory,” in Progress in Optics, E. Wolf, ed. (Elsevier Science BV, Amsterdam, 1996), Vol. XXXVI, pp. 179–244.
- Ref. 7, Chap. 3.

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

### Figures

Fig. 1 |
Fig. 2 |
Fig. 3 |

Fig. 4 |
Fig. 5 |
Fig. 6 |

Fig. 7 |
Fig. 8 |
Fig. 9 |

Fig. 10 |
Fig. 11 |
Fig. 12 |

Fig. 13 |
||

« Previous Article | Next Article »

OSA is a member of CrossRef.