## Generalized Lorenz–Mie theory for infinitely long elliptical cylinders

JOSA A, Vol. 16, Issue 6, pp. 1333-1341 (1999)

http://dx.doi.org/10.1364/JOSAA.16.001333

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### Abstract

A generalized Lorenz–Mie theory for infinite elliptical cylinders is presented. This theory describes the interaction between arbitrary shaped beams and infinitely long cylinders having an elliptical cross section.

© 1999 Optical Society of America

**OCIS Codes**

(260.0260) Physical optics : Physical optics

(290.0290) Scattering : Scattering

**History**

Original Manuscript: October 12, 1998

Revised Manuscript: January 19, 1999

Manuscript Accepted: January 21, 1999

Published: June 1, 1999

**Citation**

G. Gouesbet and L. Mees, "Generalized Lorenz–Mie theory for infinitely long elliptical cylinders," J. Opt. Soc. Am. A **16**, 1333-1341 (1999)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-6-1333

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### References

- G. Gouesbet, B. Maheu, G. Gréhan, “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]
- G. Gouesbet, G. Gréhan, B. Maheu, “Generalized Lorenz–Mie theory and applications to optical sizing,” in Combustion Measurements, N. Chigier, ed. (Hemisphere, New York, 1991), pp. 339–384.
- G. Gouesbet, G. Gréhan, “Sur la généralisation de la théorie de Lorenz–Mie,” J. Opt. (Paris) 13, 97–103 (1982). [CrossRef]
- J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988). [CrossRef]
- 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]
- F. Onofri, G. Gréhan, G. Gouesbet, “Electromagnetic scattering from a multilayered sphere located in an arbitrary beam,” Appl. Opt. 34, 7113–7124 (1995). [CrossRef] [PubMed]
- G. Gouesbet, “Interaction between Gaussian beams and infinite cylinders, by using the theory of distributions,” J. Opt. (Paris) 26, 225–239 (1995). [CrossRef]
- G. Gouesbet, “Interaction between an infinite cylinder and an arbitrary shaped beam,” Appl. Opt. 36, 4292–4304 (1997). [CrossRef] [PubMed]
- K. F. Ren, G. Gréhan, G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder in the framework of generalized Lorenz–Mie theory: formulation and numerical results,” J. Opt. Soc. Am. A 14, 3014–3025 (1997). [CrossRef]
- J. A. Lock, “Scattering of a diagonally incident focused Gaussian beam by an infinitely long homogeneous circular cylinder,” J. Opt. Soc. Am. A 14, 640–652 (1997). [CrossRef]
- J. B. Barton, “Internal and near-surface electromagnetic fields for a spheroidal particle with arbitrary illumination,” Appl. Opt. 34, 5542–5551 (1995). [CrossRef] [PubMed]
- H. Mignon, G. Gréhan, G. Gouesbet, T. H. Hu, C. Tropea, “Measurement of cylindrical particles with phase-Doppler anemometry,” Appl. Opt. 25, 5180–5190 (1996). [CrossRef]
- N. Gauchet, T. Girasole, K. F. Ren, G. Gréhan, G. Gouesbet, “Application of generalized Lorenz–Mie theory for cylinders to cylindrical characterization by phase-Doppler anemometry,” Opt. Diag. Eng. 2, 1–10 (1997).
- X. Han, K. F. Ren, Z. Wu, F. Corbin, G. Gouesbet, G. Gréhan, “Characterization of initial disturbances in liquid jet by rainbow sizing,” Appl. Opt. 37, 8498–8503 (1998). [CrossRef]
- J. A. Lock, C. L. Adler, B. R. Stone, P. D. Zajak, “Amplification of high-order rainbows of a cylinder with an elliptical cross-section,” Appl. Opt. 37, 1527–1533 (1998). [CrossRef]
- S. Lange, G. Schweiger, “Structural resonances in the total Raman- and fluorescence-scattering cross section: concentration-profile dependence,” J. Opt. Soc. Am. B 13, 1864–1872 (1996). [CrossRef]
- G. Gouesbet, L. Mees, G. Gréhan, “Partial-wave description of shaped beams in elliptical-cylinder coordinates,” J. Opt. Soc. Am. A 15, 3028–3038 (1998). [CrossRef]
- C. Yeh, “The diffraction of waves by a penetrable ribbon,” J. Math. Phys. (N.Y.) 4, 65–71 (1963). [CrossRef]
- C. Yeh, “Backscattering cross section of a dielectric elliptical cylinder,” J. Opt. Soc. Am. A 55, 309–314 (1965). [CrossRef]
- P. M. Morse, H. Feshbach, Methods of Theoretical Physics, Part I (McGraw-Hill, New York, 1953).
- T. J. Bromwich, “Electromagnetic waves,” Philos. Mag. 38, 143–164 (1919). [CrossRef]
- F. E. Borgnis, “Elektromagnetische Eigenschwingungen dielektrischer Raüme,” Ann. Phys. (Leipzig) 35, 359–384 (1939). [CrossRef]
- G. Gouesbet, G. Gréhan, B. Maheu, K. F. Ren, “Electromagnetic scattering of shaped beams (generalized Lorenz–Mie theory),” available from G. Gouesbet, LESP, UMR 6614-CNRS, INSA de Rouen, B.P. 08, 76131 Mont-Saint-Aignan Cedex, France.
- R. Campbell, Théorie générale de l’équation de Mathieu (Masson et Cie, Paris, 1955).
- N. W. McLachlan, Theory and Application of Mathieu Functions (Clarendon, Oxford, UK, 1951).
- M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972), pp. 723–745.
- G. Gouesbet, “Theory of distributions and its application to beam parametrization in light scattering,” Part. Part. Syst. Charact. (to be published).
- G. Gouesbet, L. Mees, G. Gréhan, “Partial wave expansions of higher-order Gaussian beams in elliptical cylinder coordinates,” J. Opt. (to be published).
- L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. 19, 1177–1179 (1979). [CrossRef]
- J. P. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989). [CrossRef]
- G. Gouesbet, J. A. Lock, G. Gréhan, “Partial wave representations of laser beams for use in light scattering calculations,” Appl. Opt. 34, 2133–2143 (1995). [CrossRef] [PubMed]
- G. Gouesbet, L. Mees, G. Gréhan, K. F. Ren, “Description of arbitrary beams in elliptical cylinder coordinates, by using a plane wave spectrum approach,” Opt. Commun. 161, 63–78 (1999). [CrossRef]
- J. A. Lock, G. Gouesbet, “Rigorous justification of the localized approximation to the beam shape coefficients in generalized Lorenz–Mie theory. 1. On-axis beams,” J. Opt. Soc. Am. A 11, 2503–2515 (1994). [CrossRef]
- G. Gouesbet, J. A. Lock, “Rigorous justification of the localized approximation to the beam shape coefficients in generalized Lorenz–Mie theory. 2. Off-axis beams,” J. Opt. Soc. Am. A 11, 2516–2525 (1994). [CrossRef]
- G. Gouesbet, G. Gréhan, K. F. Ren, “Rigorous justification of the cylindrical localized approximation to speed up computations in the generalized Lorenz–Mie theory for cylinders,” J. Opt. Soc. Am. A 15, 511–523 (1998). [CrossRef]

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