## Computation of the beam-shape coefficients in the generalized Lorenz–Mie theory by using the translational addition theorem for spherical vector wave functions

Applied Optics, Vol. 36, Issue 13, pp. 2971-2978 (1997)

http://dx.doi.org/10.1364/AO.36.002971

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### Abstract

The generalized Lorenz–Mie theory describes the electromagnetic scattering of a Gaussian laser beam by a spherical particle. The most intensive computational aspect of the theory concerns the evaluation of the beam-shape coefficients in the general case of an off-axis location of the scatterer. These beam-shape coefficients can be computed starting from the set of beam-shape coefficients for an on-axis location by using the addition theorem for the spherical vector wave functions of the first kind under a translation of the coordinate origin.

© 1997 Optical Society of America

**History**

Original Manuscript: May 22, 1996

Revised Manuscript: October 1, 1996

Published: May 1, 1997

**Citation**

A. Doicu and T. Wriedt, "Computation of the beam-shape coefficients in the generalized Lorenz–Mie theory by using the translational addition theorem for spherical vector wave functions," Appl. Opt. **36**, 2971-2978 (1997)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-36-13-2971

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### References

- G. Gouesbet, G. Grehan, “Sur la generalisation de la theorie de Lorenz-Mie,” J. Opt. (Paris) 13, 97–103 (1982). [CrossRef]
- G. Gouesbet, G. Grehan, B. Maheau, “Scattering of a Gaussian beam by a Mie scatterer centre using a Bromwich formalism,” J. Opt. (Paris) 16, 89–93 (1985).
- G. Grehan, B. Maheau, G. Gouesbet, “Scattering of laser beams by Mie scatterer centers: numerical results using a localized approximation,” Appl. Opt. 25, 3539–3548 (1986). [CrossRef]
- G. Gouesbet, B. Maheau, 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 (1989). [CrossRef]
- J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal and near-surface electromagnetic fields for spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988). [CrossRef]
- E. E. M. Khaled, S. C. Hill, P. W. Barber, “Scattered an internal intensity of a sphere illuminated with a Gaussian beam,” IEEE Trans. Antennas Propag. 41, 295–303 (1993). [CrossRef]
- J. A. Lock, 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]
- G. Gouesbet, J. A. Lock, “Rigorous justification of the localized approximation to the beam shape coefficients in generalized Lorenz–Mie theory. II. Off-axis beams,” J. Opt. Soc. Am. A 11, 2516–2525 (1994). [CrossRef]
- B. Maheau, G. Gouesbet, G. Grehan, “A concise presentation of the generalized Lorenz–Mie theory for arbitrary location of the scatterer in an arbitrary incident beam,” J. Opt. (Paris) 19, 59–67 (1988). [CrossRef]
- G. Grehan, B. Maheau, G. Gouesbet, “Scattering of laser beams by Mie scatterer centers: numerical results using a localized approximation,” Appl. Opt. 25, 3539–3548 (1986). [CrossRef]
- G. Gouesbet, G. Grehan, B. Maheau, “A localized interpretation to compute all the coefficients gnm in the generalized Lorenz–Mie theory,” J. Opt. Soc. Am. A 7, 998–1007 (1990). [CrossRef]
- L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979). [CrossRef]
- G. Gouesbet, G. Grehan, B. Maheau, “Computation of the gn coefficients in the generalized Lorenz–Mie theory using three different methods,” Appl. Opt. 27, 4874–4883 (1988). [CrossRef] [PubMed]
- A. Doicu, S. Schabel, F. Ebert, “Generalized Lorenz–Mie theory for non-spherical particles with applications in the Phase-Doppler anemometrie,” in Proceedings of the Fourth International Congress on Optical Particle Sizing, F. Durst, J. Domnick, eds. (Nürnberg Messe GmbH, Nürnberg, Germany, 1995), pp. 119–128.
- B. Friedman, J. Russek, “Addition theorems for spherical waves,” Q. Appl. Math. 12, 13–23 (1954).
- S. Stein, “Addition theorems for spherical wave functions,” Q. Appl. Math. 19, 15–24 (1961).
- O. R. Cruzan, “Translational addition theorems for spherical vector wave functions,” Q. Appl. Math. 20, 33–40 (1962).
- J. H. Bruning, Y. T. Lo, “Multiple scattering of EM waves by spheres–Part I–Multipole expansion and ray-optical solution,” IEEE Trans. Antennas. Propag. 19, 378–390 (1971). [CrossRef]
- A. Messiah, Quantum Mechanics (Editura Stiintifica, Bucuresti, 1974).
- A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U. Press, Princeton, N.J., 1957).
- 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]
- M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).
- A. Doicu, T. Wriedt, “Plane wave spectrum method of electromagnetic beams,” in Proceedings of the First Workshop on Electromagnetic and Light Scattering—Theory and Applications, T. Wriedt, M. Quinten, K. Bauckhage, eds. (Universität Bremen, Bremen, Germany, 1996), pp. 33–37.

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