## Scattering of a transversely confined Neumann beam by a spherical particle

JOSA A, Vol. 28, Issue 12, pp. 2577-2587 (2011)

http://dx.doi.org/10.1364/JOSAA.28.002577

Enhanced HTML Acrobat PDF (223 KB)

### Abstract

Various properties of an electromagnetic wave whose spherical multipole expansion contains only Riccati– Neumann functions are examined. In particular, the novel behavior of the beam phase during diffractive spreading is discussed. When a Neumann beam is scattered by a spherical particle, the diffraction and external reflection portions of the scattering amplitude constructively interfere for large partial waves. As a result, a set of rapidly decreasing beam shape coefficients is required to cut off the partial wave sum in the scattering amplitudes. Because of its strong singularity at the origin, a Neumann beam can be produced by a point source of radiation at the center of a spherical cavity in a high conductivity metal, and Neumann beam scattering by a spherical particle can occur for certain partial waves if the sphere is placed at the center of the cavity as well.

© 2011 Optical Society of America

**OCIS Codes**

(260.1960) Physical optics : Diffraction theory

(290.4020) Scattering : Mie theory

(290.5825) Scattering : Scattering theory

**ToC Category:**

Physical Optics

**History**

Original Manuscript: August 17, 2011

Manuscript Accepted: October 2, 2011

Published: November 17, 2011

**Virtual Issues**

Vol. 7, Iss. 2 *Virtual Journal for Biomedical Optics*

**Citation**

James A. Lock, "Scattering of a transversely confined Neumann beam by a spherical particle," J. Opt. Soc. Am. A **28**, 2577-2587 (2011)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=josaa-28-12-2577

Sort: Year | Journal | Reset

### References

- G. Gouesbet, “Partial-wave expansions and properties of axisymmetric laser beams,” Appl. Opt. 35, 1543–1555 (1996). [CrossRef] [PubMed]
- J. W. Goodman, “The angular spectrum of plane waves,” in Introduction to Fourier Optics (McGraw-Hill, 1968), pp. 48–51.
- G. Gouesbet, B. Maheu, and G. Grehan, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988). [CrossRef]
- E. Hecht, “Fresnel integrals and the rectangular aperture,” in Optics, 2nd ed. (Addison-Wesley, 1987), pp. 447–449.
- H. C. van de Hulst, “Solution for coefficients from boundary conditions,” in Light Scattering by Small Particles (Dover, 1981), p. 121.
- C. F. Bohren and D. R. Huffman, “The internal and scattered fields,” in Absorption and Scattering of Light by Small Particles (Wiley-Interscience, 1983), p. 93.
- M. Kerker, “Solution of the wave equation,” in The Scattering of Light and Other Electromagnetic Radiation (Academic, 1969), p. 44.
- M. Born and E. Wolf, “Mathematical solution of the problem,” in Principles of Optics, 6th ed. (Cambridge University, 1998), pp. 641–643.
- G. Arfken, “Spherical Bessel functions,” in Mathematical Methods for Physicists, 3rd ed. (Academic, 1985), pp. 622–630.
- H. Chew, P. J. McNulty, and M. Kerker, “Model for Raman and fluorescent scattering by molecules embedded in small particles,” Phys. Rev. A 13, 396–404 (1976). [CrossRef]
- M. Kerker and S. D. Druger, “Raman and fluorescent scattering of molecules embedded in spheres with radii up to several multiples of the wavelength,” Appl. Opt. 18, 1172–1179 (1979). [CrossRef] [PubMed]
- H. Chew, “Transition rates of atoms near spherical surfaces,” J. Chem. Phys. 87, 1355–1360 (1987). [CrossRef]
- S. D. Druger, S. Arnold, and L. M. Folan, “Theory of enhanced energy transfer between molecules embedded in spherical dielectric particles,” J. Chem. Phys. 87, 2649–2659 (1987). [CrossRef]
- S. C. Hill, H. I. Saleheen, and J. A. Fuller, “Volume current method for modeling light scattered by inhomogeneously perturbed spheres,” J. Opt. Soc. Am. A 12, 905–915 (1995). [CrossRef]
- S. C. Hill, H. I. Saleheen, M. D. Barnes, W. B. Whitten, and J. M. Ramsey, “Modeling fluorescence collection from single molecules in microspheres: effects of position, orientation, and frequency,” Appl. Opt. 35, 6278–6288 (1996). [CrossRef] [PubMed]
- S. C. Hill, G. Videen, and J. D. Pendleton, “Reciprocity method for obtaining the far fields generated by a source inside or near a microparticle,” J. Opt. Soc. Am. B 14, 2522–2529 (1997). [CrossRef]
- 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). [CrossRef]
- J. P. Barton, “Electromagnetic fields for a spheroidal particle with an arbitrary embedded source,” J. Opt. Soc. Am. A 17, 458–464 (2000). [CrossRef]
- B. Van der Pol and H. Bremmer, “The diffraction of electromagnetic waves from an electrical point source round a finitely conducting sphere, with applications to radiotelegraphy and the theory of the rainbow,” Philos. Mag. 24, 825–864 (1937).
- J. A. Lock, “Debye series analysis of scattering of a plane wave by a spherical Bragg grating,” Appl. Opt. 44, 5594–5603(2005). [CrossRef] [PubMed]
- J. A. Lock, “Scattering of an electromagnetic plane wave by a Luneburg lens. III. Finely stratified sphere model,” J. Opt. Soc. Am. A 25, 2991–3000 (2008). [CrossRef]
- R. W. Boyd, “Intuitive explanation of the phase anomaly of focused light beams,” J. Opt. Soc. Am. 70, 877–880 (1980). [CrossRef]
- H. M. Nussenzveig, “High-frequency scattering by a transparent sphere. I. Direct reflection and transmission,” J. Math. Phys. 10, 82–124 (1969). [CrossRef]
- H. C. van de Hulst, “Solution of coefficients from boundary conditions,” in Light Scattering by Small Particles (Dover, 1981), p. 123.
- H. C. van de Hulst, “Amplitude functions,” in Light Scattering by Small Particles (Dover, 1981), p. 124.
- G. N. Watson, “The degenerate form of the addition theorem,” in A Treatise on the Theory of Bessel Functions, 2nd ed.(Cambridge University, 1958), pp. 368–370.
- J. A. Lock and J. T. Hodges, “Far-field scattering of an axisymmetric laser beam of arbitrary profile by an on-axis spherical particle,” Appl. Opt. 35, 4283–4290 (1996). [CrossRef] [PubMed]
- M.Abramowitz and I.A.Stegun (eds.), “Asymptotic expansions for large orders,” in Handbook of Mathematical Functions(National Bureau of Standards, 1964), p. 366, Eq. (9.3.3).
- J. A. Lock and G. Gouesbet, “Rigorous justification of the localized approximation to the beam-shape coefficients in generalized Lorenz-Mie theory. I. On-axis beams,” J. Opt. Soc. Am. A 11, 2503–2515 (1994). [CrossRef]
- H. C. van de Hulst, “The localization principle,” in Light Scattering by Small Particles (Dover, 1981), pp. 208–209.
- J. A. Lock, “Partial-wave expansions of angular spectra of plane waves,” J. Opt. Soc. Am. A 23, 2803–2809 (2006). [CrossRef]
- G. Grehan, B. Maheu, and G. Gouesbet, “Scattering of laser beams by Mie scatter centers: numerical results using a localized approximation,” Appl. Opt. 25, 3539–3548 (1986). [CrossRef] [PubMed]
- J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. A 336, 165–190 (1974). [CrossRef]
- S. Hassani, “Classification of isolated singularities,” in Foundations of Mathematical Physics (Allyn and Bacon, 1991), p. 474.
- G. Gouesbet, J. A. Lock, and G. Grehan, “Partial-wave representations of laser beams for use in light-scattering calculations,” Appl. Opt. 34, 2133–2143 (1995). [CrossRef] [PubMed]
- J. A. Lock, “Cooperative effects among partial waves in Mie scattering,” J. Opt. Soc. Am. A 5, 2032–2044 (1988). [CrossRef]
- W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. 19, 1505–1509 (1980). [CrossRef] [PubMed]
- J. A. Lock, “Contribution of high-order rainbows to the scattering of a Gaussian laser beam by a spherical particle,” J. Opt. Soc. Am. A 10, 693–706 (1993). [CrossRef]
- L. Brillouin, “The scattering cross section of a sphere for electromagnetic waves,” J. Appl. Phys. 20, 1110–1125 (1949). [CrossRef]
- G. Gouesbet, “Hypotheses on the a priori rational necessity of quantum mechanics,” Principia 14, 393–404 (2010). [CrossRef]
- J. R. Wait, “Reflection of electromagnetic waves from inhomogeneous media with special profiles,” in Electromagnetic Waves in Stratified Media (MacMillan, 1962), pp. 64–86.

## 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.