## Light Scattering from an Optically Active Sphere into a Circular Aperture

Applied Optics, Vol. 37, Issue 33, pp. 7897-7905 (1998)

http://dx.doi.org/10.1364/AO.37.007897

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### Abstract

To show how apertures affect measurements of the circularly polarized components of light scattered to a detector, we develop two methods of averaging the <i>V</i> and <i>I</i> Stokes parameters over a circular aperture that collects light scattered from an optically active sphere. One method uses a two-dimensional numerical integration that is appropriate for small apertures, and the other gives analytical expressions for scattering into a solid angle of any size. We identify the aperture locations that, independent of aperture size, give an average <i>V</i> (and an effective degree of circular polarization) of zero for scattering from an optically inactive sphere and of nonzero for scattering from an optically active sphere.

© 1998 Optical Society of America

**OCIS Codes**

(010.1110) Atmospheric and oceanic optics : Aerosols

(260.2110) Physical optics : Electromagnetic optics

(260.5430) Physical optics : Polarization

(290.0290) Scattering : Scattering

(290.4020) Scattering : Mie theory

**Citation**

J. David Pendleton and David L. Rosen, "Light Scattering from an Optically Active Sphere into a Circular Aperture," Appl. Opt. **37**, 7897-7905 (1998)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-37-33-7897

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### References

- A. Vitkin, “Polarized light and the asymmetry of life,” Opt. Photon. News 7(7), 30–33 (1996).
- A. Lakhtakia, ed., Selected Papers on Natural Optical Activity (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1990).
- D. L. Rosen and J. D. Pendleton, “Detection of biological particles by the use of circular dichroism measurements improved by scattering theory,” Appl. Opt. 34, 5875–5884 (1995).
- C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, New York, 1983), pp. 45–53, 62–65, 94–95, 100–101, 114, 185–193.
- C. F. Bohren, “Light scattering by an optically active sphere,” Chem. Phys. Lett. 29, 458–462 (1974).
- D. J. Gordon, “Mie scattering by optically active particles,” Biochemistry 11, 413–420 (1972).
- C. F. Bohren, “Scattering of electromagnetic waves by an optically active spherical shell,” J. Chem. Phys. 62, 1566–1571 (1975).
- C. F. Bohren, “Scattering of an optically active cylinder,” J. Colloid Interface Sci. 66, 105–109 (1978).
- M. S. Kluskens and E. H. Newman, “Scattering by a multilayer chiral cylinder,” IEEE Trans. Antennas Propag. 39, 91–96 (1991).
- M. F. R. Cooray and I. R. Ciric, “Wave scattering by a chiral spheroid,” J. Opt. Soc. Am. A 10, 1197–1203 (1993).
- W. H. Pierce, “Numerical integration over the planar annulus,” J. Soc. Ind. Appl. Math. 5, 66–73 (1957).
- P. Chylek, “Mie scattering into the backward hemisphere,” J. Opt. Soc. Am. 63, 1467–1471 (1973).
- W. J. Wiscombe and P. Chylek, “Mie scattering between any two angles,” J. Opt. Soc. Am. 67, 572–573 (1977).
- W. P. Chu and D. M. Robinson, “Scattering from a moving spherical particle by two crossed coherent plane waves,” Appl. Opt. 16, 619–626 (1977).
- J. D. Pendleton, “Mie scattering into apertures,” J. Opt. Soc. Am. 72, 1029–1033 (1982).
- J. D. Pendleton, “A generalized Mie theory solution and its application to particle sizing interferometry,” Ph.D. dissertation (University of Tennessee, Knoxville, Tenn. 1982), p. 90.
- J. Y. Son, W. M. Farmer, and T. V. Giel, Jr., “New optical geometry for the particle sizing interferometer,” Appl. Opt. 25, 4332–4337 (1986).
- J. Y. Son, “Multiple methods for obtaining particle size distribution with a particle sizing interferometer,” Ph.D. dissertation (University of Tennessee, Knoxville, Tenn., 1985).
- J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), p. 746.
- J. D. Pendleton and S. C. Hill, “Collection of emission from an oscillating dipole inside a sphere: analytical integration over a circular aperture,” Appl. Opt. 36, 8729–8737 (1997).
- M. E. Rose, Elementary Theory of Angular Momentum (Dover, New York, 1995), p. 50.
- G. Arfken, Mathematical Methods for Physicists, 3rd. ed. (Academic, San Diego, Calif., 1985), pp. 198–200, 253, 678.
- H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), pp. 34, 124.
- A. N. Lowan, N. Davids, and A. Levenson, “Table of the zeros of the Legendre polynomials of order 1–16 and the weight coefficients for Gauss’ mechanical quadrature formula,” Bull. Am. Math. Soc. 48, 739–743 (1942); errata 49, 939 (1943).
- S. L. Belousov, Tables of Normalized Associated Legendre Polynomials (Pergamon, New York, 1962).
- J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), p. 401.
- M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1964).
- I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980), pp. 1005, 1008.

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