OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 31, Iss. 1 — Jan. 1, 2014
  • pp: 89–100

Scattering of an electromagnetic plane wave by a homogeneous sphere made of an orthorhombic dielectric–magnetic material

A. D. Ulfat Jafri and Akhlesh Lakhtakia  »View Author Affiliations

JOSA A, Vol. 31, Issue 1, pp. 89-100 (2014)

View Full Text Article

Enhanced HTML    Acrobat PDF (694 KB) Open Access

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



An exact transition matrix was formulated for electromagnetic scattering by an orthorhombic dielectric–magnetic sphere whose permeability dyadic is a scalar multiple of its permittivity dyadic. Calculations were made for plane waves incident on the sphere. As the size parameter increases, the role of anisotropy evolves; multiple lobes appear in the plots of the differential scattering efficiency in any scattering plane; the total scattering, extinction, and forward-scattering efficiencies exhibit a prominent maximum each; and the absorption efficiency generally increases with weak undulations. Certain orientations of the sphere with respect to the directions of propagation and the electric field of the incident plane wave make it highly susceptible to detection in a monostatic configuration, whereas other orientations make it much less vulnerable to detection. Impedance match to the ambient free space decreases backscattering efficiency significantly, although anisotropy prevents null backscattering.

© 2013 Optical Society of America

OCIS Codes
(160.1190) Materials : Anisotropic optical materials
(260.2110) Physical optics : Electromagnetic optics
(290.5825) Scattering : Scattering theory

ToC Category:

Original Manuscript: October 8, 2013
Revised Manuscript: November 8, 2013
Manuscript Accepted: November 8, 2013
Published: December 10, 2013

A. D. Ulfat Jafri and Akhlesh Lakhtakia, "Scattering of an electromagnetic plane wave by a homogeneous sphere made of an orthorhombic dielectric–magnetic material," J. Opt. Soc. Am. A 31, 89-100 (2014)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. O. F. Mossotti, “Recherches théoriques sur l’induction électro-statique, envisagée d’après idées de Faraday,” Supp. Biblio. Univer. Genève Arch. Sci. Phys. Natur. 16, 193–198 (1847).
  2. O. F. Mossotti, “Discussione analitica sull influenza che l’azione di un mezzo dielettrico ha sulla distribuzione dell’elettricita alla superficie di più corpi elettrici disseminati in esso,” Mem. Mat. Fis. Modena 24, 49–74 (1850).
  3. M. Faraday, “Experimental relations of gold (and other materials) to light,” Philos. Trans. R. Soc. London 147, 145–181 (1857). [CrossRef]
  4. A. Walther, “Optical applications of solid glass spheres,” Ph.D. thesis (Delft University of Technology, 1959).
  5. “Spherical glass solar energy generator by andre rawlemon,” August25, 2012, http://www.designboom.com/technology/spherical-glass-solar-energy-generator-by-rawlemon/ (accessed on June 3, 2013).
  6. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, 1957).
  7. M. Kerker, ed., Selected Papers on Light Scattering, Part 1 (SPIE, 1988).
  8. L. V. Lorenz, “Lysvevægelsen i og uden for en af plane lysbølger belyst kugle,” K. Dan. Vidensk. Selsk. Forh. 6, 1–62 (1890).
  9. G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. Lpz. 25, 377–445 (1908).
  10. G. Mie, “Contributions on the optics of turbid media, particularly colloidal metal solutions—translation,” Sandia Laboratories, Albuquerque, New Mexico, 1978, SAND78-6018. National Translation Center, Chicago, Illinois, Translation 79–21946.
  11. J. A. Stratton, Electromagnetic Theory (McGraw–Hill, 1941), Chap. 7.
  12. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983), Chap. 4.
  13. C. F. Bohren, “Light scattering by an optically active sphere,” Chem. Phys. Lett. 29, 458–462 (1974). [CrossRef]
  14. A. Lakhtakia and T. G. Mackay, “Vector spherical wavefunctions for orthorhombic dielectric-magnetic material with gyrotropic-like magnetoelectric properties,” J. Opt. 41, 201–213 (2012). [CrossRef]
  15. T. G. Mackay and A. Lakhtakia, Electromagnetic Anisotropy and Bianisotropy: A Field Guide (World Scientific, 2010).
  16. A. Lakhtakia, V. K. Varadan, and V. V. Varadan, “Plane waves and canonical sources in a gyroelectromagnetic uniaxial medium,” Int. J. Electron. 71, 853–861 (1991). [CrossRef]
  17. C. D. Gribble and A. J. Hall, Optical Mineralogy, Principles and Practice (University College London Press, 1992).
  18. J. C. Bose, “On the rotation of plane of polarisation of electric waves by a twisted structure,” Proc. R. Soc. London, Ser. A 63, 146–152 (1898). [CrossRef]
  19. O. S. Ivanova, C. B. Williams, and T. A. Campbell, “Additive manufacturing (AM) and nanotechnology: promises and challenges,” Rapid Prototyping 19, 353–364 (2013). [CrossRef]
  20. F. Brochard and P. G. de Gennes, “Theory of magnetic suspensions in liquid crystals,” J. Phys. 31, 691–708 (1970). [CrossRef]
  21. K. Aydin and A. Hizal, “On the completeness of the spherical vector wave functions,” J. Math. Anal. Appl. 117, 428–440 (1986). [CrossRef]
  22. P. M. Morse and H. Feshbach, Methods of Theoretical Physics, Vol. II (McGraw-Hill, 1953).
  23. S. H. Schot, “Eighty years of Sommerfeld’s radiation condition,” Hist. Math. 19, 385–401 (1992).
  24. A. Rubinowicz, “A weaker formulation of the electromagnetic radiation conditions,” Rep. Math. Phys. 2, 63–77 (1971). [CrossRef]
  25. G. W. Ford and S. A. Werner, “Scattering and absorption of electromagnetic waves by a gyrotropic sphere,” Phys. Rev. B 18, 6752–6769 (1978).
  26. J. L.-W. Li, W.-L. Ong, and K. H. R. Zheng, “Anisotropic scattering effects of a gyrotropic sphere characterized using the T-matrix method,” Phys. Rev. E 85, 036601 (2012). [CrossRef]
  27. J. Van Bladel, Electromagnetic Fields (Hemisphere, 1985).
  28. V. V. Varadan, A. Lakhtakia, and V. K. Varadan, eds., Field Representations and Introduction to Scattering (North-Holland, 1991).
  29. C. F. Bohren, “Multiple scattering of light and some of its observable consequences,” Am. J. Phys. 55, 524–533 (1987). [CrossRef]
  30. C. F. Bohren, “Understanding colors in nature,” Pigment Cell Res. 1, 214–222 (1988).
  31. H. Frohlich, Theory of Dielectrics (Oxford University Press, 1958).
  32. L. Ward, The Optical Constants of Bulk Materials and Films (Adam Hilger, 1988).
  33. A. Lakhtakia, “Rayleigh scattering by a bianisotropic ellipsoid in a biisotropic medium,” Int. J. Electron. 71, 1057–1062 (1991). [CrossRef]
  34. V. H. Weston, “Theory of absorbers in scattering,” IEEE Trans. Antennas Propag. 11, 578–584 (1963). [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.

CrossCheck Deposited