## Study of scattering from a sphere with an eccentrically located spherical inclusion by generalized Lorenz–Mie theory: internal and external field distribution |

JOSA A, Vol. 28, Issue 1, pp. 24-39 (2011)

http://dx.doi.org/10.1364/JOSAA.28.000024

Enhanced HTML Acrobat PDF (1691 KB)

### Abstract

Based on the recent results in the generalized Lorenz–Mie theory, solutions for scattering problems of a sphere with an eccentrically located spherical inclusion illuminated by an arbitrary shaped electromagnetic beam in an arbitrary orientation are obtained. Particular attention is paid to the description and application of an arbitrary shaped beam in an arbitrary orientation to the scattering problem under study. The theoretical formalism is implemented in a homemade computer program written in FORTRAN. Numerical results concerning spatial distributions of both internal and external fields are displayed in different formats in order to properly display exemplifying results. More specifically, as an example, we consider the case of a focused fundamental Gaussian beam (

© 2011 Optical Society of America

**OCIS Codes**

(140.0140) Lasers and laser optics : Lasers and laser optics

(260.2110) Physical optics : Electromagnetic optics

(290.0290) Scattering : Scattering

**ToC Category:**

Scattering

**History**

Original Manuscript: October 19, 2010

Manuscript Accepted: November 11, 2010

Published: December 22, 2010

**Virtual Issues**

Vol. 6, Iss. 2 *Virtual Journal for Biomedical Optics*

**Citation**

J. J. Wang, G. Gouesbet, Y. P. Han, and G. Gréhan, "Study of scattering from a sphere with an eccentrically located spherical inclusion by generalized Lorenz–Mie theory: internal and external field distribution," J. Opt. Soc. Am. A **28**, 24-39 (2011)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-28-1-24

Sort: Year | Journal | Reset

### References

- G. Mie, “Beiträge zur optik trüben medien speziell kolloidaler metalösungen,” Ann. Phys. 25, 377–452 (1908). [CrossRef]
- J. A. Lock and G. Gouesbet, “Generalized Lorenz–Mie theory and applications,” J. Quant. Spectrosc. Radiat. Transfer 110, 800–807 (2009). [CrossRef]
- G. Gouesbet, “Generalized Lorenz–Mie theories, the third decade: a perspective,” J. Quant. Spectrosc. Radiat. Transfer 110, 1223–1238 (2009). [CrossRef]
- G. Gouesbet, B. Maheu, and 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]
- B. Maheu, G. Gouesbet, and G. Gréhan, “A concise presentation of the generalized Lorenz–Mie theory for arbitrary location of the scatter in an arbitrary incident profile,” J. Opt. 19, 59–67 (1988). [CrossRef]
- G. Gouesbet, “Validity of the localized approximation for arbitrary shaped beams in the generalized Lorenz–Mie theory for spheres,” J. Opt. Soc. Am. A 16, 1641–1650 (1999). [CrossRef]
- L. Méès, G. Gouesbet, and G. Gréhan, “Transient internal and scattered fields from a multi-layered sphere illuminated by a pulsed laser,” Opt. Commun. 282, 4189–4193 (2009). [CrossRef]
- J. P. Barton, D. R. Alexander, and 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]
- G. Gouesbet, “Interaction between an infinite cylinder and an arbitrary-shaped beam,” Appl. Opt. 36, 4292–4304 (1997). [CrossRef] [PubMed]
- G. Gouesbet and G. Gréhan, “Generalized Lorenz–Mie theory for a sphere with an eccentrically located spherical inclusion,” J. Mod. Opt. 47, 821–837 (2000).
- Y. P. Han, G. Gréhan, and G. Gouesbet, “Generalized Lorenz–Mie theory for a spheroidal particle with off-axis Gaussian-beam illumination,” Appl. Opt. 42, 6621–6629 (2003). [CrossRef] [PubMed]
- F. Xu, K. F. Ren, G. Gouesbet, G. Gréhan, and X. Cai, “Generalized Lorenz–Mie theory for an arbitrary oriented, located, and shaped beam scattered by homogeneous spheroid,” J. Opt. Soc. Am. A 24, 119–131 (2007). [CrossRef]
- K. F. Ren, G. Gréhan, and 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]
- L. Méès, K. F. Ren, G. Gréhan, and G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation: numerical results,” Appl. Opt. 38, 1867–1876 (1999). [CrossRef]
- G. Gouesbet and L. Méès, “Generalized Lorenz–Mie theory for infinitely long elliptical cylinders,” J. Opt. Soc. Am. A 16, 1333–1341 (1999). [CrossRef]
- 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]
- G. Gouesbet and 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]
- Y. P. Han, H. Y. Zhang, and G. X. Han, “The expansion coefficients of arbitrary shaped beam in oblique illumination,” Opt. Express 15, 735–746 (2007). [CrossRef] [PubMed]
- Y. P. Han, Y. Zhang, H. Y. Zhang, and G. X. Han, “Scattering of typical particles by beam shape in oblique illumination,” J. Quant. Spectrosc. Radiat. Transfer 110, 1375–1381 (2009). [CrossRef]
- G. Gouesbet, J. J. Wang, and Y. P. Han, “Transformations of spherical beam shape coefficients in generalized Lorenz–Mie theories through rotations of coordinate systems. I. General formulation,” Opt. Commun. 283, 3218–3225 (2010). [CrossRef]
- J. J. Wang, G. Gouesbet, and Y. P. Han, “Transformations of spherical beam shape coefficients in generalized Lorenz–Mie theories through rotations of coordinate systems. II. Axisymmetric beams,” Opt. Commun. 283, 3226–3234 (2010). [CrossRef]
- G. Gouesbet, J. J. Wang, and Y. P. Han, “Transformations of spherical beam shape coefficients in generalized Lorenz–Mie theories through rotations of coordinate systems. III. Special Euler angles,” Opt. Commun. 283, 3235–3243 (2010). [CrossRef]
- G. Gouesbet, J. J. Wang, Y. P. Han, and G. Gréhan, “Transformations of spherical beam shape coefficients in generalized Lorenz–Mie theories through rotations of coordinate systems. IV. Plane waves,” Opt. Commun. 283, 3244–3254 (2010). [CrossRef]
- G. Gouesbet, J. A. Lock, J. J. Wang, and G. Gréhan, “Transformations of spherical beam shape coefficients in generalized Lorenz–Mie theories through rotations of coordinate systems. V. Localized beam models,” Opt. Commun. (to be published).
- J. G. Fikioris and N. K. Uzunoglu, “Scattering from an eccentrically stratified dielectric sphere,” J. Opt. Soc. Am. A 69, 1359–1366 (1979). [CrossRef]
- F. Borghese, P. Denti, R. Saija, and O. I. Sindoni, “Optical properties of spheres containing several spherical inclusions,” Appl. Opt. 33, 484–493 (1994). [CrossRef] [PubMed]
- K. A. Fuller, “Morphology-dependent resonances in eccentrically stratified sphere,” Opt. Lett. 19, 1272–1274 (1994). [CrossRef] [PubMed]
- G. Videen, D. Ngo, P. Chylek, and R. G. Pinnick, “Light scattering from a sphere with an irregular inclusion,” J. Opt. Soc. Am. A 12, 922–928 (1995). [CrossRef]
- A. Doicu, T. Wriedt, and Y. A. Eremin, Light Scattering by Systems of Particles: Null-Field Method with Discrete Sources: Theory and Programs (Springer, 2006).
- S. M. Hasheminejad and Y. Mirzaei, “Exact 3D elasticity solution for free vibrations of eccentric hollow sphere,” J. Sound Vib. (to be published).
- D. R. Secker, P. H. Kaye, R. S. Greenaway, E. Hirst, D. L. Bartley, and G. Videen, “Light scattering from deformed droplets and droplets with inclusions. I. Experimental results,” Appl. Opt. 39, 5023–5030 (2000). [CrossRef]
- G. Videen, W. Sun, Q. Fu, D. R. Secker, R. S. Greenaway, P. H. Kaye, E. Hirst, and D. Bartley, “Light scattering from deformed droplets and droplets with inclusions. II. Theoretical treatment,” Appl. Opt. 39, 5031–5039 (2000). [CrossRef]
- N. Riefler, R. Schuh, and T. Wriedt, “Investigation of a measurement technique to estimate concentration and size of inclusions in droplets,” Meas. Sci. Technol. 18, 2209–2218 (2007). [CrossRef]
- A. A. Riziq, M. Trainic, C. Erlick, E. Segre, and Y. Rudich, “Extinction efficiencies of coated absorbing aerosols measured by cavity ring down aerosol spectrometry,” Atmos. Chem. Phys. 8, 1823–1833 (2008). [CrossRef]
- D. Ngo, G. Videen, and P. Chýlek, “A FORTRAN code for the scattering of EM waves by a sphere with a nonconcentric spherical inclusion,” Comput. Phys. Commun. 99, 94–112(1996). [CrossRef]
- G. X. Han, Y. P. Han, J. Y. Liu, and Y. Zhang, “Scattering of an eccentric sphere arbitrarily located in a shaped beam,” J. Opt. Soc. Am. B 25, 2064–2072 (2008). [CrossRef]
- B. Yan, X. Han, and K. F. Ren, “Scattering of a shaped beam by a spherical particle with an eccentric spherical inclusion,” J. Opt. A Pure Appl. Opt. 11, 015705 (2009). [CrossRef]
- S. Saengkaew, G. Godard, J. B. Blaisot, and G. Gréhan, “Experimental analysis of global rainbow technique: sensitivity of temperature and size distribution measurements to non-spherical droplets,” Exp. Fluids 47, 839–848 (2009). [CrossRef]
- G. Gouesbet, S. Meunier-Guttin-Cluzel, and G. Gréhan, “Generalized Lorenz–Mie theory for a sphere with an eccentrically located inclusion, and optical chaos,” Part. Part. Syst. Charact. 18, 190–195 (2001). [CrossRef]
- G. Gouesbet, S. Meunier-Guttin-Cluzel, and G. Gréhan, “Periodic orbits in Hamiltonian chaos of the annular billiard,” Phys. Rev. E 65, 016212 (2001). [CrossRef]
- G. Gouesbet, S. Meunier-Guttin-Cluzel, and G. Gréhan, “Morphology-dependent resonances and/or whispering gallery modes for a two-dimensional dielectric cavity with an eccentrically located circular inclusion, a Hamiltonian point of view with Hamiltonian (optical) chaos,” Opt. Commun. 201, 223–242(2002). [CrossRef]
- P. T. Leung, S. W. Ng, and K. M. Pang, “Morphology-dependent resonances in dielectric spheres with many tiny inclusions,” Opt. Lett. 27, 1749–1751 (2002). [CrossRef]
- V. S. C. M. Rao, Gupta, and S. Dutta, “Broken azimuthal degeneracy with whispering gallery modes of microspheres,” J. Opt. A Pure Appl. Opt. 7, 279–285 (2005). [CrossRef]
- G. Gouesbet, “T-matrix formulation and generalized Lorenz–Mie theories in spherical coordinates,” Opt. Commun. 283, 517–521(2010). [CrossRef]
- S. Stein, “Addition theorems for spherical wave functions,” Quart. Appl. Math. 19, 15–24 (1961).
- O. R. Cruzan, “Translational addition theorems for spherical vector wave functions,” Quart. Appl. Math. 20, 33–44 (1962).
- P. A. Bobbert and J. Vlieger, “Light scattering by a sphere on a substrate,” Physica A (Amsterdam) 137, 209–241 (1986). [CrossRef]
- D. W. Mackowski, “Analysis of radiative scattering from multiple sphere configurations,” Proc. R. Soc. Lond. 433, 599–614 (1991). [CrossRef]
- G. Gouesbet, C. Letellier, K. F. Ren, and G. Gréhan, “Discussion of two quadrature methods of evaluating beam-shape coefficients in generalized Lorenz–Mie theory,” Appl. Opt. 35, 1537–1542(1996). [CrossRef] [PubMed]
- G. Gouesbet, G. Gréhan, and B. Maheu, “Expressions to compute the coefficients gmn in the generalized Lorenz–Mie theory using finite series,” J. Opt. 19, 35 (1988). [CrossRef]
- K. F. Ren, G. Gouesbet, and G. Gréhan, “Integral localized approximation in generalized Lorenz–Mie theory,” Appl. Opt. 37, 4218–4225 (1998). [CrossRef]
- 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). [CrossRef] [PubMed]
- H. Y. Zhang and Y. P. Han, “Addition theorem for the spherical vector wave functions and its application to the beam shape coefficients,” J. Opt. Soc. Am. B 25, 255–260 (2008). [CrossRef]
- G. Gouesbet, “Higher-order descriptions of Gaussian beams,” J. Opt. 27, 35–50 (1996). [CrossRef]
- J. A. Lock, “An improved Gaussian beam scattering algorithm,” Appl. Opt. 34, 559–570 (1995). [CrossRef] [PubMed]
- T. Wriedt, “The website maintained by Thomas Wriedt,” http://www.scattport.org.
- M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (Academic, 2000).
- R. Schuh and T. Wriedt, “Computer programs for light scattering by particles with inclusions,” J. Quant. Spectrosc. Radiat. Transfer 70, 715–723 (2001). [CrossRef]
- P. W. Barber and S. C. Hill, Light Scattering by Particles: Computational Methods, Advanced Series in Applied Physics (World Scientific, 1990), Vol. 2. [CrossRef]
- J. A. Lock and E. A. Hovenac, “Internal caustic structure of illuminated liquid droplets,” J. Opt. Soc. Am. A 8, 1541–1552 (1991). [CrossRef]

## 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.