## Propagation in correlated distributions of large-spaced scatterers

JOSA, Vol. 73, Issue 3, pp. 313-320 (1983)

http://dx.doi.org/10.1364/JOSA.73.000313

Acrobat PDF (902 KB)

### Abstract

Simple asymptotic approximations are derived for the bulk coherent propagation coefficient (*K*) in pair-correlated distributions of obstacles with minimum separation (*b*) between particle centers large compared to wavelength (λ). The size of the scatterer (maximum diameter 2*a* ≤ *b*) is arbitrary compared to λ. The functional equation for *K* involves only the forward-scattered and backscattered amplitudes of an obstacle and simple integrals of the total correlation function (*F*). For large particles with small refractive contrast, the leading terms differ from the leading terms for small-spaced particles in that the scattering cross-section term involves a different packing factor (*W*). The present *W* depends on 2*a*/*b* and the zeroth moment of *F*, whereas for small spacing *W* is the limit of the structure factor for small *b*/λ. Higher-order terms involving the first and second moments of *F* are also derived, and the forms are applied to obtain explicit results for spheroids in terms of the volume fraction of statistical pa ticles. More generally, the initial functional equation can be evaluated in terms of existing tabulated values of *F*.

© 1983 Optical Society of America

**Citation**

Victor Twersky, "Propagation in correlated distributions of large-spaced scatterers," J. Opt. Soc. Am. **73**, 313-320 (1983)

http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-73-3-313

Sort: Year | Journal | Reset

### References

- V. Twersky, "Coherent scalar field in pair-correlated random distributions of aligned scatterers," J. Math. Phys. 18,2468–2486 (1977).
- V. Twersky, "Coherent electromagnetic waves in pair-correlated random distributions of aligned scatterers," J. Math. Phys. 19, 215–230 1978).
- Lord Rayleigh, "On the transmission of light through the atmosphere containing small particles in suspension, and on the origin of the color of the sky," Philos. Mag. 47, 375–383 (1899).
- F. Reiche, "Zur Theorie der Dispersion in Gasen und Dampfen," Ann. Phys. 50, 1–121 (1916).
- L. L. Foldy, "The multiple scattering of waves," Phys. Rev. 67, 107–119 (1945).
- M. Lax, "Multiple scattering of waves," Rev. Mod. Phys. 23, 287–310 (1951); "The effective field in dense systems," Phys. Rev. 88, 621–629 (1952).
- H. L. Frisch and J. L. Lebowitz, The Equilibrium Theory of Fluids (Benjamin, New York, 1964); R. J. Baxter, "Distribution functions," in Physical Chemistry, H. Eyring, D. Henderson, and W. Jost, eds. (Academic, New York, 1971), Vol. VIII A, Chap. 4, pp. 267–334.
- M. S. Wertheim, "Exact solution of the Percus-Yevick integral equation for hard spheres," Phys. Rev. Lett. 10, 321–323 (1963); E. Thiele, "Equation of state for hard spheres," J. Chem. Phys. 39, 474–479 (1963).
- G. J. Throop and R. J. Bearman, "Numerical solution of the Percus–Yevick equation for the hard-sphere potential," J. Chem. Phys. 42, 2408–2411 (1965); F. Mandel, R. J. Bearman, and M. Y. Bearman, "Numerical solution of the Percus–Yevick equation for the Lennard–Jones (6-12) and hard sphere potentials," J. Chem. Phys. 52, 3315–3323 (1970); D. Levesque, J. J. Weis, and J. P. Hansen, "Simulation of classical fluids," in Monte Carlo Methods in Statistical Physics (Springer-Verlag, New York, 1979), pp. 121–144.
- Y. Uehara, T. Ree, and F. H. Ree, "Radial distribution function for hard disks from the BGY2 theory," J. Chem. Phys. 70, 1876–1883 (1979); J. Woodhead-Galloway and P. A. Machin, "X-ray scattering from a gas of uniform hard-disks using the Percus–Yevick approximation," Mol. Phys. 32, 41–48 (1976); F. Lado, "Equation of state for the hard-disk fluid from approximate integral equations," J. Chem. Phys. 49, 3092–3096 (1968).
- V. Twersky, "Acoustic bulk parameters in distributions of paircorrelated scatterers," J. Acoust. Soc. Am. 64, 1710–1719 (1978); "Transparency of pair-correlated random distributions of small scatterers with applications to the cornea," J. Opt. Soc. Am. 65, 524–530 (1975); "Propagation in pair-correlated distributions of small-spaced lossy scatterers," J. Opt. Soc. Am. 69, 1567–1572 (1979).
- V. Twersky, "Scattering theory and diagnostic applications," in Wave Propagation through Random Media, P. Chow, W. Kohler, and G. Papanicolaou, eds. (North-Holland, Amsterdam, 1981), pp. 267–286; "Propagation and attenuation in composite media," in Microscopic Properties of Disordered Media, R. Burridge, S. Childress, and G. Papanicolaou, eds. (Springer-Verlag, Berlin, 1982), pp. 258–271.
- V. Twersky, "Multiple scattering of waves and optical phenomena," J. Opt. Soc. Am. 52, 145–171 (1962); "Interface effects in multiple scattering by large, low-refracting, absorbing particles," J. Opt. Soc. Am. 60, 908–914 (1970); "Absorption and multiple scattering by biological suspensions," J. Opt. Soc. Am. 60, 1084–1093 (1970). The text cites equations of the last paper.
- G. Placzek, B. R. A. Nijboer, and L. Van Hove, "Effects of short wavelength interference on neutron scattering by dense systems of heavy nuclei," Phys. Rev. 82, 392–403 (1951).
- H. Reiss, H. L. Frisch, and J. L. Lebowitz, "Statistical mechanics of rigid spheres," J. Chem. Phys. 31, 369–380 (1959); E. Helfand, H. L. Frisch, and J. L. Lebowitz, "The theory of the two- and one-dimensional rigid sphere fluids," J. Chem. Phys. 34, 1037–1042 (1961).
- B. R. A. Nijboer and L. Van Hove, "Radial distribution function of a gas of hard spheres and the superposition approximation," Phys. Rev. 85, 777–783 (1952).
- B. Larsen, J. C. Rasaiah, and G. Stell, "Thermodynamic perturbatio theory for multipolar and ionic liquids," Mol. Phys. 33, 987–1027 (1977).
- G. Stell and K. C. Wu, "Padé approximant for the internal energy of a system of charged particles," J. Chem. Phys. 63, 491–498 (1975).
- C. I. Beard, T. H. Kays, and V. Twersky, "Scattering by random distributions of spheres versus concentration," IEEE Trans. Antennas Propag. AP-1S, 99–118 (1967); S. W. Hawley, T. H. Kays, and V. Twersky, "Comparison of distribution functions from scattering data on different sets of spheres," IEEE Trans. Antennas Propag. AP-15, 118–135 (1967).
- H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), pp. 175.
- H. D. Jones, "Method for finding the equation of state of liquid metals," J. Chem. Phys. 55, 2640–2642 (1971).

## 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.

« Previous Article | Next Article »

OSA is a member of CrossRef.