Abstract

Following the recent results in generalized Lorenz–Mie theory concerning the description of an arbitrary shaped electromagnetic beam propagating in an arbitrary orientation, a theoretical investigation of morphology- dependent resonances (MDRs) excited in a sphere with an eccentrically located spherical inclusion illuminated by a tightly focused Gaussian beam is presented. Calculations of extinction efficiency spectra and backward- scattering intensity spectra are made for different locations and radii of the inclusion with respect to the host sphere. Exemplifying field distributions inside of the scatterer under both off-resonance and on-resonance conditions are exhibited. The influences of the relative size of the inclusion with respect to the host sphere and of the separation distance between the two sphere centers on the positions and on the amplitudes of the MDRs peaks are studied. As are the cases for spheres and concentrically multilayered spheres, the resonance positions of MDRs in an eccentrically layered sphere are located at the same size parameter for Gaussian beam illumination and for plane-wave illumination. In contrast with the lift of azimuthal modes m degeneracy in MDR peaks for an eccentric sphere illuminated obliquely by a plane wave, we display a kind of lift that cannot be observed in extinction efficiency spectra with an oblique illumination of a tightly focused Gaussian beam. Nevertheless, asymmetric distributions of the internal field inside of the eccentric sphere at resonance conditions are observed both with an oblique illumination of a tightly focused beam and with an oblique illumination of a plane-wave illumination. Interpretation from a perspective of the localization principle is applied to the simulation results.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Ashkin and J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351–1354 (1977).
    [CrossRef]
  2. P. Chýlek, J. T. Kiehl, and M. K. W. Ko, “Optical levitation and partial-wave resonance,” Phys. Rev. A 18, 2229–2233 (1978).
    [CrossRef]
  3. P. Chýlek, B. Ramaswamy, A. Ashkin, and J. M. Dziedzic, “Simultaneous determination of refractive index and size of spherical dielectric particles from light scattering data,” Appl. Opt. 22, 2302–2307 (1983).
    [CrossRef] [PubMed]
  4. H.-M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, “Evaporation and condensation rates of liquid droplets deduced from structure resonances in the fluorescence spectra,” Opt. Lett. 9, 273–275 (1984).
    [CrossRef] [PubMed]
  5. G. Chen, M. M. Mazumder, R. K. Chang, J. C. Swindal, and W. P. Acker, “Laser diagnostics for droplet characterization: application of morphology dependent resonances,” Progr. Energy Combust. Sci. 22, 163–188 (1996).
    [CrossRef]
  6. J. Ducastel, “Etude des résonances morphologiquement dépendantes et application à la caractérisation de microparticules en milieu diphasique,” Ph.D. thesis (Institut National des Sciences Appliquées de Rouen, 2007).
  7. D. Ngo and R. G. Pinnick, “Suppression of scattering resonances in inhomogeneous microdroplets,” J. Opt. Soc. Am. A 11, 1352–1359 (1994).
    [CrossRef]
  8. 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]
  9. V. S. C. M. Rao and S. D. Gupta, “Broken azimuthal degeneracy with whispering gallery modes of microspheres,” J. Opt. A 7, 279–285 (2005).
    [CrossRef]
  10. G. Chen, R. K. Chang, S. C. Hill, and P. W. Barber, “Frequency splitting of degenerate spherical cavity mode: stimulated Raman scattering spectrum of deformed droplets,” Opt. Lett. 16, 1269–1271 (1991).
    [CrossRef] [PubMed]
  11. M. I. Mishchenko and A. A. Lacis, “Morphology-dependent resonances of nearly spherical particles in random orientation,” Appl. Opt. 42, 5551–5556 (2003).
    [CrossRef] [PubMed]
  12. Y. P. Han, L. Méès, G. Gouesbet, Z. S. Wu, and G. Gréhan, “Resonant spectra of a deformed spherical microcavity,” J. Opt. Soc. Am. B 23, 1390–1397 (2006).
    [CrossRef]
  13. M. M. Mazumder, S. C. Hill, and P. W. Barber, “Morphology-dependent resonances in inhomogeneous spheres: comparison of the layered T-matrix method and the time-independent perturbation method,” J. Opt. Soc. Am. A 9, 1844–1853 (1992).
    [CrossRef]
  14. K. A. Fuller, “Morphology-dependent resonances in eccentrically stratified sphere,” Opt. Lett. 19, 1272–1274 (1994).
    [CrossRef] [PubMed]
  15. 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]
  16. M. Hentschel and K. Richter, “Quantum chaos in optical systems: the annular billiard,” Phys. Rev. E 66, 056207 (2002).
    [CrossRef]
  17. S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415, 621–623 (2002).
    [CrossRef] [PubMed]
  18. 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]
  19. 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).
  20. 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]
  21. 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 11, 015705, 2009.
    [CrossRef]
  22. 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]
  23. 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]
  24. 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]
  25. 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]
  26. 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. 284, 411–417 (2011).
    [CrossRef]
  27. 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).
    [CrossRef]
  28. G. Gouesbet, “T-matrix formulation and generalized Lorenz–Mie theories in spherical coordinates,” Opt. Commun. 283, 517–521(2010).
    [CrossRef]
  29. 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]
  30. 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]
  31. 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]
  32. G. Gouesbet and G. Gréhan, Generalized Lorenz–Mie Theories (Springer, 2011).
    [CrossRef]
  33. 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]
  34. 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]
  35. 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]
  36. J. A. Lock, “An improved Gaussian beam scattering algorithm,” Appl. Opt. 34, 559–570 (1995).
    [CrossRef] [PubMed]
  37. G. Gouesbet, J. A. Lock, and G. Gréhan, “Generalized Lorenz–Mie theories and description of electromagnetic arbitrary shaped beams: localized approximations and localized beam models,” J. Quant. Spectrosc. Radiat. Transfer 112, 1–27 (2011).
    [CrossRef]
  38. P. W. Barber and S. C. Hill, Light Scattering by Particles: Computational Methods, Vol.  2 of Advanced Series in Applied Physics (World Scientific, 1990).
    [CrossRef]
  39. 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]
  40. E. E. M. Khaled, S. C. Hill, and P. W. Barber, “Light scattering by a coated sphere illuminated with a Gaussian beam,” Appl. Opt. 33, 3308–3314 (1994).
    [CrossRef] [PubMed]
  41. A. Ashkin and J. M. Dziedzic, “Observation of optical resonances of dielectric spheres by light scattering,” Appl. Opt. 20, 1803–1814 (1981).
    [CrossRef] [PubMed]
  42. J. P. Barton, D. R. Alexander, and S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
    [CrossRef]
  43. E. E. M. Khaled, S. C. Hill, and P. W. Barber, “Internal electric energy in a spherical particle illuminated with a plane wave or off-axis Gaussian beam,” Appl. Opt. 33, 524–532 (1994).
    [CrossRef] [PubMed]
  44. F. Onofri, G. Gréhan, and G. Gouesbet, “Electromagnetic scattering from a multilayered sphere located in an arbitrary beam,” Appl. Opt. 34, 7113–7124 (1995).
    [CrossRef] [PubMed]
  45. H. C. van de Hulst, Light Scattering by Small Particles (Peter Smith, 1982).
  46. G. Gouesbet, G. Gréhan, and B. Maheu, “Localized interpretation to compute all the coefficients gnm in the generalized Lorenz–Mie theory,” J. Opt. Soc. Am. A 7, 998–1007 (1990).
    [CrossRef]

2011 (3)

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. 284, 411–417 (2011).
[CrossRef]

G. Gouesbet, J. A. Lock, and G. Gréhan, “Generalized Lorenz–Mie theories and description of electromagnetic arbitrary shaped beams: localized approximations and localized beam models,” J. Quant. Spectrosc. Radiat. Transfer 112, 1–27 (2011).
[CrossRef]

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).
[CrossRef]

2010 (5)

G. Gouesbet, “T-matrix formulation and generalized Lorenz–Mie theories in spherical coordinates,” Opt. Commun. 283, 517–521(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. 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]

2009 (2)

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]

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 11, 015705, 2009.
[CrossRef]

2008 (1)

2007 (1)

2006 (1)

2005 (1)

V. S. C. M. Rao and S. D. Gupta, “Broken azimuthal degeneracy with whispering gallery modes of microspheres,” J. Opt. A 7, 279–285 (2005).
[CrossRef]

2003 (1)

2002 (3)

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]

M. Hentschel and K. Richter, “Quantum chaos in optical systems: the annular billiard,” Phys. Rev. E 66, 056207 (2002).
[CrossRef]

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415, 621–623 (2002).
[CrossRef] [PubMed]

2001 (2)

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]

2000 (1)

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).

1999 (1)

1996 (2)

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. Chen, M. M. Mazumder, R. K. Chang, J. C. Swindal, and W. P. Acker, “Laser diagnostics for droplet characterization: application of morphology dependent resonances,” Progr. Energy Combust. Sci. 22, 163–188 (1996).
[CrossRef]

1995 (2)

1994 (6)

1992 (1)

1991 (1)

1990 (1)

1989 (1)

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
[CrossRef]

1988 (1)

1984 (1)

1983 (1)

1981 (1)

1978 (1)

P. Chýlek, J. T. Kiehl, and M. K. W. Ko, “Optical levitation and partial-wave resonance,” Phys. Rev. A 18, 2229–2233 (1978).
[CrossRef]

1977 (1)

A. Ashkin and J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351–1354 (1977).
[CrossRef]

Acker, W. P.

G. Chen, M. M. Mazumder, R. K. Chang, J. C. Swindal, and W. P. Acker, “Laser diagnostics for droplet characterization: application of morphology dependent resonances,” Progr. Energy Combust. Sci. 22, 163–188 (1996).
[CrossRef]

Alexander, D. R.

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
[CrossRef]

Ashkin, A.

Barber, P. W.

Barton, J. P.

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
[CrossRef]

Chang, R. K.

Chen, G.

G. Chen, M. M. Mazumder, R. K. Chang, J. C. Swindal, and W. P. Acker, “Laser diagnostics for droplet characterization: application of morphology dependent resonances,” Progr. Energy Combust. Sci. 22, 163–188 (1996).
[CrossRef]

G. Chen, R. K. Chang, S. C. Hill, and P. W. Barber, “Frequency splitting of degenerate spherical cavity mode: stimulated Raman scattering spectrum of deformed droplets,” Opt. Lett. 16, 1269–1271 (1991).
[CrossRef] [PubMed]

Chýlek, P.

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]

P. Chýlek, B. Ramaswamy, A. Ashkin, and J. M. Dziedzic, “Simultaneous determination of refractive index and size of spherical dielectric particles from light scattering data,” Appl. Opt. 22, 2302–2307 (1983).
[CrossRef] [PubMed]

P. Chýlek, J. T. Kiehl, and M. K. W. Ko, “Optical levitation and partial-wave resonance,” Phys. Rev. A 18, 2229–2233 (1978).
[CrossRef]

Ducastel, J.

J. Ducastel, “Etude des résonances morphologiquement dépendantes et application à la caractérisation de microparticules en milieu diphasique,” Ph.D. thesis (Institut National des Sciences Appliquées de Rouen, 2007).

Dziedzic, J. M.

Fuller, K. A.

Gouesbet, G.

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. 284, 411–417 (2011).
[CrossRef]

G. Gouesbet, J. A. Lock, and G. Gréhan, “Generalized Lorenz–Mie theories and description of electromagnetic arbitrary shaped beams: localized approximations and localized beam models,” J. Quant. Spectrosc. Radiat. Transfer 112, 1–27 (2011).
[CrossRef]

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).
[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, 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, “T-matrix formulation and generalized Lorenz–Mie theories in spherical coordinates,” Opt. Commun. 283, 517–521(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. I. General formulation,” Opt. Commun. 283, 3218–3225 (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]

Y. P. Han, L. Méès, G. Gouesbet, Z. S. Wu, and G. Gréhan, “Resonant spectra of a deformed spherical microcavity,” J. Opt. Soc. Am. B 23, 1390–1397 (2006).
[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, “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 and G. Gréhan, “Generalized Lorenz–Mie theory for a sphere with an eccentrically located spherical inclusion,” J. Mod. Opt. 47, 821–837 (2000).

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]

F. Onofri, G. Gréhan, and G. Gouesbet, “Electromagnetic scattering from a multilayered sphere located in an arbitrary beam,” Appl. Opt. 34, 7113–7124 (1995).
[CrossRef] [PubMed]

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]

G. Gouesbet, G. Gréhan, and B. Maheu, “Localized interpretation to compute all the coefficients gnm in the generalized Lorenz–Mie theory,” J. Opt. Soc. Am. A 7, 998–1007 (1990).
[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]

G. Gouesbet and G. Gréhan, Generalized Lorenz–Mie Theories (Springer, 2011).
[CrossRef]

Gréhan, G.

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. 284, 411–417 (2011).
[CrossRef]

G. Gouesbet, J. A. Lock, and G. Gréhan, “Generalized Lorenz–Mie theories and description of electromagnetic arbitrary shaped beams: localized approximations and localized beam models,” J. Quant. Spectrosc. Radiat. Transfer 112, 1–27 (2011).
[CrossRef]

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).
[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]

Y. P. Han, L. Méès, G. Gouesbet, Z. S. Wu, and G. Gréhan, “Resonant spectra of a deformed spherical microcavity,” J. Opt. Soc. Am. B 23, 1390–1397 (2006).
[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, “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 and G. Gréhan, “Generalized Lorenz–Mie theory for a sphere with an eccentrically located spherical inclusion,” J. Mod. Opt. 47, 821–837 (2000).

F. Onofri, G. Gréhan, and G. Gouesbet, “Electromagnetic scattering from a multilayered sphere located in an arbitrary beam,” Appl. Opt. 34, 7113–7124 (1995).
[CrossRef] [PubMed]

G. Gouesbet, G. Gréhan, and B. Maheu, “Localized interpretation to compute all the coefficients gnm in the generalized Lorenz–Mie theory,” J. Opt. Soc. Am. A 7, 998–1007 (1990).
[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]

G. Gouesbet and G. Gréhan, Generalized Lorenz–Mie Theories (Springer, 2011).
[CrossRef]

Gupta, S. D.

V. S. C. M. Rao and S. D. Gupta, “Broken azimuthal degeneracy with whispering gallery modes of microspheres,” J. Opt. A 7, 279–285 (2005).
[CrossRef]

Han, G. X.

Han, X.

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 11, 015705, 2009.
[CrossRef]

Han, Y. P.

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).
[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]

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. I. General formulation,” Opt. Commun. 283, 3218–3225 (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]

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. 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]

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, L. Méès, G. Gouesbet, Z. S. Wu, and G. Gréhan, “Resonant spectra of a deformed spherical microcavity,” J. Opt. Soc. Am. B 23, 1390–1397 (2006).
[CrossRef]

Hentschel, M.

M. Hentschel and K. Richter, “Quantum chaos in optical systems: the annular billiard,” Phys. Rev. E 66, 056207 (2002).
[CrossRef]

Hill, S. C.

Khaled, E. E. M.

Kiehl, J. T.

P. Chýlek, J. T. Kiehl, and M. K. W. Ko, “Optical levitation and partial-wave resonance,” Phys. Rev. A 18, 2229–2233 (1978).
[CrossRef]

Kippenberg, T. J.

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415, 621–623 (2002).
[CrossRef] [PubMed]

Ko, M. K. W.

P. Chýlek, J. T. Kiehl, and M. K. W. Ko, “Optical levitation and partial-wave resonance,” Phys. Rev. A 18, 2229–2233 (1978).
[CrossRef]

Lacis, A. A.

Leung, P. T.

Liu, J. Y.

Lock, J. A.

G. Gouesbet, J. A. Lock, and G. Gréhan, “Generalized Lorenz–Mie theories and description of electromagnetic arbitrary shaped beams: localized approximations and localized beam models,” J. Quant. Spectrosc. Radiat. Transfer 112, 1–27 (2011).
[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. 284, 411–417 (2011).
[CrossRef]

J. A. Lock, “An improved Gaussian beam scattering algorithm,” Appl. Opt. 34, 559–570 (1995).
[CrossRef] [PubMed]

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]

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]

Long, M. B.

Maheu, B.

Mazumder, M. M.

G. Chen, M. M. Mazumder, R. K. Chang, J. C. Swindal, and W. P. Acker, “Laser diagnostics for droplet characterization: application of morphology dependent resonances,” Progr. Energy Combust. Sci. 22, 163–188 (1996).
[CrossRef]

M. M. Mazumder, S. C. Hill, and P. W. Barber, “Morphology-dependent resonances in inhomogeneous spheres: comparison of the layered T-matrix method and the time-independent perturbation method,” J. Opt. Soc. Am. A 9, 1844–1853 (1992).
[CrossRef]

Méès, L.

Meunier-Guttin-Cluzel, S.

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]

Mishchenko, M. I.

Ng, S. W.

Ngo, D.

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]

D. Ngo and R. G. Pinnick, “Suppression of scattering resonances in inhomogeneous microdroplets,” J. Opt. Soc. Am. A 11, 1352–1359 (1994).
[CrossRef]

Onofri, F.

Pang, K. M.

Pinnick, R. G.

Ramaswamy, B.

Rao, V. S. C. M.

V. S. C. M. Rao and S. D. Gupta, “Broken azimuthal degeneracy with whispering gallery modes of microspheres,” J. Opt. A 7, 279–285 (2005).
[CrossRef]

Ren, K. F.

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 11, 015705, 2009.
[CrossRef]

Richter, K.

M. Hentschel and K. Richter, “Quantum chaos in optical systems: the annular billiard,” Phys. Rev. E 66, 056207 (2002).
[CrossRef]

Schaub, S. A.

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
[CrossRef]

Spillane, S. M.

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415, 621–623 (2002).
[CrossRef] [PubMed]

Swindal, J. C.

G. Chen, M. M. Mazumder, R. K. Chang, J. C. Swindal, and W. P. Acker, “Laser diagnostics for droplet characterization: application of morphology dependent resonances,” Progr. Energy Combust. Sci. 22, 163–188 (1996).
[CrossRef]

Tzeng, H.-M.

Vahala, K. J.

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415, 621–623 (2002).
[CrossRef] [PubMed]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Peter Smith, 1982).

Videen, G.

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]

Wall, K. F.

Wang, J. J.

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. 284, 411–417 (2011).
[CrossRef]

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).
[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, 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. 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, 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]

Wu, Z. S.

Yan, B.

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 11, 015705, 2009.
[CrossRef]

Zhang, H. Y.

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]

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]

Zhang, Y.

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. 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]

Appl. Opt. (7)

Comput. Phys. Commun. (1)

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]

J. Appl. Phys. (1)

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
[CrossRef]

J. Mod. Opt. (1)

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).

J. Opt. A (2)

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 11, 015705, 2009.
[CrossRef]

V. S. C. M. Rao and S. D. Gupta, “Broken azimuthal degeneracy with whispering gallery modes of microspheres,” J. Opt. A 7, 279–285 (2005).
[CrossRef]

J. Opt. Soc. Am. A (8)

M. M. Mazumder, S. C. Hill, and P. W. Barber, “Morphology-dependent resonances in inhomogeneous spheres: comparison of the layered T-matrix method and the time-independent perturbation method,” J. Opt. Soc. Am. A 9, 1844–1853 (1992).
[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]

G. Gouesbet, G. Gréhan, and B. Maheu, “Localized interpretation to compute all the coefficients gnm in the generalized Lorenz–Mie theory,” J. Opt. Soc. Am. A 7, 998–1007 (1990).
[CrossRef]

D. Ngo and R. G. Pinnick, “Suppression of scattering resonances in inhomogeneous microdroplets,” J. Opt. Soc. Am. A 11, 1352–1359 (1994).
[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]

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]

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).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Quant. Spectrosc. Radiat. Transfer (2)

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. A. Lock, and G. Gréhan, “Generalized Lorenz–Mie theories and description of electromagnetic arbitrary shaped beams: localized approximations and localized beam models,” J. Quant. Spectrosc. Radiat. Transfer 112, 1–27 (2011).
[CrossRef]

Nature (1)

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415, 621–623 (2002).
[CrossRef] [PubMed]

Opt. Commun. (6)

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. 284, 411–417 (2011).
[CrossRef]

G. Gouesbet, “T-matrix formulation and generalized Lorenz–Mie theories in spherical coordinates,” Opt. Commun. 283, 517–521(2010).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Part. Part. Syst. Charact. (1)

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]

Phys. Rev. A (1)

P. Chýlek, J. T. Kiehl, and M. K. W. Ko, “Optical levitation and partial-wave resonance,” Phys. Rev. A 18, 2229–2233 (1978).
[CrossRef]

Phys. Rev. E (2)

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]

M. Hentschel and K. Richter, “Quantum chaos in optical systems: the annular billiard,” Phys. Rev. E 66, 056207 (2002).
[CrossRef]

Phys. Rev. Lett. (1)

A. Ashkin and J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351–1354 (1977).
[CrossRef]

Progr. Energy Combust. Sci. (1)

G. Chen, M. M. Mazumder, R. K. Chang, J. C. Swindal, and W. P. Acker, “Laser diagnostics for droplet characterization: application of morphology dependent resonances,” Progr. Energy Combust. Sci. 22, 163–188 (1996).
[CrossRef]

Other (4)

J. Ducastel, “Etude des résonances morphologiquement dépendantes et application à la caractérisation de microparticules en milieu diphasique,” Ph.D. thesis (Institut National des Sciences Appliquées de Rouen, 2007).

H. C. van de Hulst, Light Scattering by Small Particles (Peter Smith, 1982).

P. W. Barber and S. C. Hill, Light Scattering by Particles: Computational Methods, Vol.  2 of Advanced Series in Applied Physics (World Scientific, 1990).
[CrossRef]

G. Gouesbet and G. Gréhan, Generalized Lorenz–Mie Theories (Springer, 2011).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Scattering geometry of the problem under study.

Fig. 2
Fig. 2

Extinction efficiency spectrum and backward intensity spectrum for a concentric sphere. The radius of the inclusion is r = 0.7 R , plane-wave illumination with incidence angle 0.0 ° .

Fig. 3
Fig. 3

Comparison of extinction efficiency spectra and of backward intensity spectra for a concentric sphere and an eccentric sphere ( d = 0.1 R ), respectively. The radius of the inclusion is r = 0.7 R , Gaussian beam illumination with incidence angle 0.0 ° .

Fig. 4
Fig. 4

Comparison of extinction efficiency spectra and of backward intensity spectra for a concentric sphere and an eccentric sphere ( d = 0.04 R ), respectively. The radius of the inclusion is r = 0.92 R , Gaussian beam illumination with incidence angle 0.0 ° .

Fig. 5
Fig. 5

Comparison of extinction efficiency spectra and of backward intensity spectra for concentric spheres of r = 0.7 R and of r = 0.92 R , respectively. Gaussian beam illumination with incidence angle 0.0 ° .

Fig. 6
Fig. 6

Comparison of extinction efficiency spectra for a concentric sphere and eccentric spheres ( d = 0.04 R , d = 0.04 R ). The radius of the inclusion is r = 0.92 R , plane-wave illumination with incidence angle 90.0 ° .

Fig. 7
Fig. 7

Comparison of extinction efficiency spectra for eccentric spheres of r = 0.7 R with different center–center separation distances illuminated by a Gaussian beam.

Fig. 8
Fig. 8

Comparison of extinction efficiency spectra for eccentric spheres of r = 0.92 R with different center–center separation distances illuminated by a Gaussian beam.

Fig. 9
Fig. 9

Distributions of internal field for an eccentric sphere illuminated by (a), (b), (c) plane wave and (d), (e), (f) Gaussian beam. (a), (d) off-resonance case with d = 0.04 R ; (b), (e) complete resonance case with d = 0.0 R , and (c), (f) broken-resonance case with d = 0.04 R . The radius of the inclusion is r = 0.92 R . The incident wave propagates along the x axis from negative to positive.

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

x 2 = x 1 , y 2 = y 1 , z 2 = z 1 d .
E inc = n = 1 m = n + n a n m M n m ( 1 ) ( k 0 r 1 ) + b n m N n m ( 1 ) ( k 0 r 1 ) ,
E sca = n = 1 m = n + n c n m M n m ( 4 ) ( k 0 r 1 ) + d n m N n m ( 4 ) ( k 0 r 1 ) .
E int 1 = n = 1 m = n + n e n m M n m ( 3 ) ( k 1 r 1 ) + f n m N n m ( 3 ) ( k 1 r 1 ) + v n m M n m ( 4 ) ( k 1 r 1 ) + h n m N n m ( 4 ) ( k 1 r 1 ) .
E int 1 = n = 1 m = n + n r n m M n m ( 3 ) ( k 1 r 2 ) + s n m N n m ( 3 ) ( k 1 r 2 ) + t n m M n m ( 4 ) ( k 1 r 2 ) + u n m N n m ( 4 ) ( k 1 r 2 ) ,
E int 2 = n = 1 m = n + n p n m M n m ( 1 ) ( k 2 r 2 ) + q n m N n m ( 1 ) ( k 2 r 2 ) .
C ext = λ 2 π Re [ n = 1 m = n + n 2 n + 1 n ( n + 1 ) n + | m | ! n | m | ! × ( c n m a n m * + d n m b n m * ) ] .
σ sca = | E sca | 2 π a 2 .
a n m = i k c n p w ( 1 ) m ( 1 ) m | m | 2 ( n m ) ! ( n | m | ) ! g ˜ n , TE m c n m ,
b n m = k c n p w ( 1 ) m ( 1 ) m | m | 2 ( n m ) ! ( n | m | ) ! g ˜ n , TM m c n m ,
c n p w = 1 k ( i ) n + 1 2 n + 1 n ( n + 1 ) .
g ˜ n , X m = μ n m s = n n H s n m μ n s g n , X s ,
μ n m = ( 1 ) m ( 1 ) m | m | 2 ( n | m | ) ! ( n m ) ! ,
H s n m = ( 1 ) n + s ( n m ) ! ( n s ) ! e i m γ e i s α σ ( 1 ) σ ( n + s n m σ ) ( n s σ ) ( cos β 2 ) 2 σ + m + s ( sin β 2 ) 2 n 2 σ m s ,
S = | E | 2 / | E 0 | 2 ,

Metrics