Abstract

Within the generalized Lorenz–Mie theory framework, an analytic solution to the scattering of an on-axis Gaussian beam by a chiral spheroid is presented by expanding the incident Gaussian beam, scattered fields as well as internal fields in terms of appropriate spheroidal vector wave functions. The unknown expansion coefficients are determined by a system of linear equations derived from the boundary conditions. Numerical results of the normalized differential scattering cross section are shown, and the scattering characteristics are discussed concisely.

© 2012 Optical Society of America

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  1. T. G. Mackay and A. Lakhtakia, “Simultaneous negative-and-positive-phase-velocity propagation in an isotropic chiral medium,” Microw. Opt. Technol. Lett. 49, 1245–1246 (2007).
    [CrossRef]
  2. J. Dong, “Exotic characteristics of power propagation in the chiral nihility fiber,” Prog. Electromagn. Res. 99, 163–178 (2009).
    [CrossRef]
  3. N. Wongkasem and A. Akyurtlu, “Light splitting effects in chiral metamaterials,” J. Opt. 12, 035101 (2010).
    [CrossRef]
  4. M. S. Kluskens and E. H. Newman, “Scattering by a multilayer chiral cylinder,” IEEE Trans. Antennas Propag. 39, 91–96 (1991).
    [CrossRef]
  5. B. N. Khatir, M. Al-Kanhal, and A. Sebak, “Electromagnetic wave scattering by elliptic chiral cylinder,” J. Electromagn. Waves Appl. 20, 1377–1390 (2006).
    [CrossRef]
  6. V. Demir, A. Elsherbeni, D. Worasawate, and E. Arvas, “A graphical user interface (GUI) for plane-wave scattering from a conducting, dielectric, or chiral sphere,” IEEE Trans. Antennas Propag. Mag. 46, 94–99 (2004).
    [CrossRef]
  7. D. Worasawate, J. R. Mautz, and E. Arvas, “Electromagnetic scattering from an arbitrarily shaped three-dimensional homogeneous chiral body,” IEEE Trans. Antennas Propag. 51, 1077–1084 (2003).
    [CrossRef]
  8. A. Semichaevsky, A. Akyurtlu, D. Kern, D. H. Werner, and M. G. Bray, “Novel BI-FDTD approach for the analysis of chiral cylinders and spheres,” IEEE Trans. Antennas Propag. 54, 925–932 (2006).
    [CrossRef]
  9. M. Yokota, S. He, and T. Takenaka, “Scattering of a Hermite–Gaussian beam field by a chiral sphere,” J. Opt. Soc. Am. A 18, 1681–1689 (2001).
    [CrossRef]
  10. 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]
  11. B. Maheu, G. Gouesbet, and G. Gréhan, “A concise presentation of the generalized Lorenz–Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt. 19, 59–67 (1988).
    [CrossRef]
  12. 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, a review,” J. Quant. Spectrosc. Radiat. Transfer 112, 1–27 (2011).
    [CrossRef]
  13. G. Gouesbet, K. F. Ren, L. Mees, and G. Gréhan, “Cylindrical localized approximation to speed up computations for Gaussian beams in the generalized Lorenz–Mie theory for cylinders, with arbitrary location and orientation of the scatterer,” Appl. Opt. 38, 2647–2665 (1999).
    [CrossRef]
  14. L. Mees, 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]
  15. Z. S. Wu, L. X. Guo, K. F. Ren, G. Gouesbet, and G. Gréhan, “Improved algorithm for electromagnetic scattering of plane waves and shaped beams by multilayered spheres,” Appl. Opt. 36, 5188–5198 (1997).
    [CrossRef]
  16. Y. P. Han and Z. S. Wu, “Scattering of a spheroidal particle illuminated by a Gaussian beam,” Appl. Opt. 40, 2501–2509 (2001).
    [CrossRef]
  17. F. Xu, K. F. Ren, G. Gouesbet, G. Gréhan, and X. Cai, “Generalized Lorenz–Mie theory for an arbitrarily oriented, located, and shaped beam scattered by homogeneous spheroid,” J. Opt. Soc. Am. A 24, 119–131 (2007).
    [CrossRef]
  18. G. Gouesbet, F. Xu, and Y. P. Han, “Expanded description of electromagnetic arbitrary shaped beams in spheroidal coordinates, for use in light scattering theories: a review,” J. Quant. Spectrosc. Radiat. Transfer 112, 2249–2267 (2011).
    [CrossRef]
  19. H. Y. Zhang and Y. P. Han, “Scattering of shaped beam by an infinite cylinder of arbitrary orientation,” J. Opt. Soc. Am. B 25, 131–135 (2008).
    [CrossRef]
  20. A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton University, 1957), Chap. 4.
  21. Y. P. Han, H. Y. Zhang, and G. X. Han, “The expansion coefficients of arbitrarily shaped beam in oblique illumination,” Opt. Express 15, 735–746 (2007).
    [CrossRef]
  22. C. Flammer, Spheroidal Wave Functions (Stanford University, 1957).
  23. L. W. Davis, “Theory of electromagnetic beam,” Phys. Rev. A 19, 1177–1179 (1979).
    [CrossRef]
  24. J. J. Wang and G. Gouesbet, “Note on the use of localized beam models for light scattering theories in spherical coordinates,” Appl. Opt. 51, 3832–3836 (2012).
    [CrossRef]
  25. S. Asano and G. Yamamoto, “Light scattering by a spheroid particle,” Appl. Opt. 14, 29–49 (1975).

2012

2011

G. Gouesbet, F. Xu, and Y. P. Han, “Expanded description of electromagnetic arbitrary shaped beams in spheroidal coordinates, for use in light scattering theories: a review,” J. Quant. Spectrosc. Radiat. Transfer 112, 2249–2267 (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, a review,” J. Quant. Spectrosc. Radiat. Transfer 112, 1–27 (2011).
[CrossRef]

2010

N. Wongkasem and A. Akyurtlu, “Light splitting effects in chiral metamaterials,” J. Opt. 12, 035101 (2010).
[CrossRef]

2009

J. Dong, “Exotic characteristics of power propagation in the chiral nihility fiber,” Prog. Electromagn. Res. 99, 163–178 (2009).
[CrossRef]

2008

2007

2006

B. N. Khatir, M. Al-Kanhal, and A. Sebak, “Electromagnetic wave scattering by elliptic chiral cylinder,” J. Electromagn. Waves Appl. 20, 1377–1390 (2006).
[CrossRef]

A. Semichaevsky, A. Akyurtlu, D. Kern, D. H. Werner, and M. G. Bray, “Novel BI-FDTD approach for the analysis of chiral cylinders and spheres,” IEEE Trans. Antennas Propag. 54, 925–932 (2006).
[CrossRef]

2004

V. Demir, A. Elsherbeni, D. Worasawate, and E. Arvas, “A graphical user interface (GUI) for plane-wave scattering from a conducting, dielectric, or chiral sphere,” IEEE Trans. Antennas Propag. Mag. 46, 94–99 (2004).
[CrossRef]

2003

D. Worasawate, J. R. Mautz, and E. Arvas, “Electromagnetic scattering from an arbitrarily shaped three-dimensional homogeneous chiral body,” IEEE Trans. Antennas Propag. 51, 1077–1084 (2003).
[CrossRef]

2001

1999

1997

1991

M. S. Kluskens and E. H. Newman, “Scattering by a multilayer chiral cylinder,” IEEE Trans. Antennas Propag. 39, 91–96 (1991).
[CrossRef]

1988

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 scatterer in an arbitrary incident profile,” J. Opt. 19, 59–67 (1988).
[CrossRef]

1979

L. W. Davis, “Theory of electromagnetic beam,” Phys. Rev. A 19, 1177–1179 (1979).
[CrossRef]

1975

Akyurtlu, A.

N. Wongkasem and A. Akyurtlu, “Light splitting effects in chiral metamaterials,” J. Opt. 12, 035101 (2010).
[CrossRef]

A. Semichaevsky, A. Akyurtlu, D. Kern, D. H. Werner, and M. G. Bray, “Novel BI-FDTD approach for the analysis of chiral cylinders and spheres,” IEEE Trans. Antennas Propag. 54, 925–932 (2006).
[CrossRef]

Al-Kanhal, M.

B. N. Khatir, M. Al-Kanhal, and A. Sebak, “Electromagnetic wave scattering by elliptic chiral cylinder,” J. Electromagn. Waves Appl. 20, 1377–1390 (2006).
[CrossRef]

Arvas, E.

V. Demir, A. Elsherbeni, D. Worasawate, and E. Arvas, “A graphical user interface (GUI) for plane-wave scattering from a conducting, dielectric, or chiral sphere,” IEEE Trans. Antennas Propag. Mag. 46, 94–99 (2004).
[CrossRef]

D. Worasawate, J. R. Mautz, and E. Arvas, “Electromagnetic scattering from an arbitrarily shaped three-dimensional homogeneous chiral body,” IEEE Trans. Antennas Propag. 51, 1077–1084 (2003).
[CrossRef]

Asano, S.

Bray, M. G.

A. Semichaevsky, A. Akyurtlu, D. Kern, D. H. Werner, and M. G. Bray, “Novel BI-FDTD approach for the analysis of chiral cylinders and spheres,” IEEE Trans. Antennas Propag. 54, 925–932 (2006).
[CrossRef]

Cai, X.

Davis, L. W.

L. W. Davis, “Theory of electromagnetic beam,” Phys. Rev. A 19, 1177–1179 (1979).
[CrossRef]

Demir, V.

V. Demir, A. Elsherbeni, D. Worasawate, and E. Arvas, “A graphical user interface (GUI) for plane-wave scattering from a conducting, dielectric, or chiral sphere,” IEEE Trans. Antennas Propag. Mag. 46, 94–99 (2004).
[CrossRef]

Dong, J.

J. Dong, “Exotic characteristics of power propagation in the chiral nihility fiber,” Prog. Electromagn. Res. 99, 163–178 (2009).
[CrossRef]

Edmonds, A. R.

A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton University, 1957), Chap. 4.

Elsherbeni, A.

V. Demir, A. Elsherbeni, D. Worasawate, and E. Arvas, “A graphical user interface (GUI) for plane-wave scattering from a conducting, dielectric, or chiral sphere,” IEEE Trans. Antennas Propag. Mag. 46, 94–99 (2004).
[CrossRef]

Flammer, C.

C. Flammer, Spheroidal Wave Functions (Stanford University, 1957).

Gouesbet, G.

J. J. Wang and G. Gouesbet, “Note on the use of localized beam models for light scattering theories in spherical coordinates,” Appl. Opt. 51, 3832–3836 (2012).
[CrossRef]

G. Gouesbet, F. Xu, and Y. P. Han, “Expanded description of electromagnetic arbitrary shaped beams in spheroidal coordinates, for use in light scattering theories: a review,” J. Quant. Spectrosc. Radiat. Transfer 112, 2249–2267 (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, a review,” J. Quant. Spectrosc. Radiat. Transfer 112, 1–27 (2011).
[CrossRef]

F. Xu, K. F. Ren, G. Gouesbet, G. Gréhan, and X. Cai, “Generalized Lorenz–Mie theory for an arbitrarily oriented, located, and shaped beam scattered by homogeneous spheroid,” J. Opt. Soc. Am. A 24, 119–131 (2007).
[CrossRef]

L. Mees, 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, K. F. Ren, L. Mees, and G. Gréhan, “Cylindrical localized approximation to speed up computations for Gaussian beams in the generalized Lorenz–Mie theory for cylinders, with arbitrary location and orientation of the scatterer,” Appl. Opt. 38, 2647–2665 (1999).
[CrossRef]

Z. S. Wu, L. X. Guo, K. F. Ren, G. Gouesbet, and G. Gréhan, “Improved algorithm for electromagnetic scattering of plane waves and shaped beams by multilayered spheres,” Appl. Opt. 36, 5188–5198 (1997).
[CrossRef]

B. Maheu, G. Gouesbet, and G. Gréhan, “A concise presentation of the generalized Lorenz–Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt. 19, 59–67 (1988).
[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]

Gréhan, G.

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, a review,” J. Quant. Spectrosc. Radiat. Transfer 112, 1–27 (2011).
[CrossRef]

F. Xu, K. F. Ren, G. Gouesbet, G. Gréhan, and X. Cai, “Generalized Lorenz–Mie theory for an arbitrarily oriented, located, and shaped beam scattered by homogeneous spheroid,” J. Opt. Soc. Am. A 24, 119–131 (2007).
[CrossRef]

L. Mees, 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, K. F. Ren, L. Mees, and G. Gréhan, “Cylindrical localized approximation to speed up computations for Gaussian beams in the generalized Lorenz–Mie theory for cylinders, with arbitrary location and orientation of the scatterer,” Appl. Opt. 38, 2647–2665 (1999).
[CrossRef]

Z. S. Wu, L. X. Guo, K. F. Ren, G. Gouesbet, and G. Gréhan, “Improved algorithm for electromagnetic scattering of plane waves and shaped beams by multilayered spheres,” Appl. Opt. 36, 5188–5198 (1997).
[CrossRef]

B. Maheu, G. Gouesbet, and G. Gréhan, “A concise presentation of the generalized Lorenz–Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt. 19, 59–67 (1988).
[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]

Guo, L. X.

Han, G. X.

Han, Y. P.

He, S.

Kern, D.

A. Semichaevsky, A. Akyurtlu, D. Kern, D. H. Werner, and M. G. Bray, “Novel BI-FDTD approach for the analysis of chiral cylinders and spheres,” IEEE Trans. Antennas Propag. 54, 925–932 (2006).
[CrossRef]

Khatir, B. N.

B. N. Khatir, M. Al-Kanhal, and A. Sebak, “Electromagnetic wave scattering by elliptic chiral cylinder,” J. Electromagn. Waves Appl. 20, 1377–1390 (2006).
[CrossRef]

Kluskens, M. S.

M. S. Kluskens and E. H. Newman, “Scattering by a multilayer chiral cylinder,” IEEE Trans. Antennas Propag. 39, 91–96 (1991).
[CrossRef]

Lakhtakia, A.

T. G. Mackay and A. Lakhtakia, “Simultaneous negative-and-positive-phase-velocity propagation in an isotropic chiral medium,” Microw. Opt. Technol. Lett. 49, 1245–1246 (2007).
[CrossRef]

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, a review,” J. Quant. Spectrosc. Radiat. Transfer 112, 1–27 (2011).
[CrossRef]

Mackay, T. G.

T. G. Mackay and A. Lakhtakia, “Simultaneous negative-and-positive-phase-velocity propagation in an isotropic chiral medium,” Microw. Opt. Technol. Lett. 49, 1245–1246 (2007).
[CrossRef]

Maheu, B.

B. Maheu, G. Gouesbet, and G. Gréhan, “A concise presentation of the generalized Lorenz–Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt. 19, 59–67 (1988).
[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]

Mautz, J. R.

D. Worasawate, J. R. Mautz, and E. Arvas, “Electromagnetic scattering from an arbitrarily shaped three-dimensional homogeneous chiral body,” IEEE Trans. Antennas Propag. 51, 1077–1084 (2003).
[CrossRef]

Mees, L.

Newman, E. H.

M. S. Kluskens and E. H. Newman, “Scattering by a multilayer chiral cylinder,” IEEE Trans. Antennas Propag. 39, 91–96 (1991).
[CrossRef]

Ren, K. F.

Sebak, A.

B. N. Khatir, M. Al-Kanhal, and A. Sebak, “Electromagnetic wave scattering by elliptic chiral cylinder,” J. Electromagn. Waves Appl. 20, 1377–1390 (2006).
[CrossRef]

Semichaevsky, A.

A. Semichaevsky, A. Akyurtlu, D. Kern, D. H. Werner, and M. G. Bray, “Novel BI-FDTD approach for the analysis of chiral cylinders and spheres,” IEEE Trans. Antennas Propag. 54, 925–932 (2006).
[CrossRef]

Takenaka, T.

Wang, J. J.

Werner, D. H.

A. Semichaevsky, A. Akyurtlu, D. Kern, D. H. Werner, and M. G. Bray, “Novel BI-FDTD approach for the analysis of chiral cylinders and spheres,” IEEE Trans. Antennas Propag. 54, 925–932 (2006).
[CrossRef]

Wongkasem, N.

N. Wongkasem and A. Akyurtlu, “Light splitting effects in chiral metamaterials,” J. Opt. 12, 035101 (2010).
[CrossRef]

Worasawate, D.

V. Demir, A. Elsherbeni, D. Worasawate, and E. Arvas, “A graphical user interface (GUI) for plane-wave scattering from a conducting, dielectric, or chiral sphere,” IEEE Trans. Antennas Propag. Mag. 46, 94–99 (2004).
[CrossRef]

D. Worasawate, J. R. Mautz, and E. Arvas, “Electromagnetic scattering from an arbitrarily shaped three-dimensional homogeneous chiral body,” IEEE Trans. Antennas Propag. 51, 1077–1084 (2003).
[CrossRef]

Wu, Z. S.

Xu, F.

G. Gouesbet, F. Xu, and Y. P. Han, “Expanded description of electromagnetic arbitrary shaped beams in spheroidal coordinates, for use in light scattering theories: a review,” J. Quant. Spectrosc. Radiat. Transfer 112, 2249–2267 (2011).
[CrossRef]

F. Xu, K. F. Ren, G. Gouesbet, G. Gréhan, and X. Cai, “Generalized Lorenz–Mie theory for an arbitrarily oriented, located, and shaped beam scattered by homogeneous spheroid,” J. Opt. Soc. Am. A 24, 119–131 (2007).
[CrossRef]

Yamamoto, G.

Yokota, M.

Zhang, H. Y.

Appl. Opt.

IEEE Trans. Antennas Propag.

M. S. Kluskens and E. H. Newman, “Scattering by a multilayer chiral cylinder,” IEEE Trans. Antennas Propag. 39, 91–96 (1991).
[CrossRef]

D. Worasawate, J. R. Mautz, and E. Arvas, “Electromagnetic scattering from an arbitrarily shaped three-dimensional homogeneous chiral body,” IEEE Trans. Antennas Propag. 51, 1077–1084 (2003).
[CrossRef]

A. Semichaevsky, A. Akyurtlu, D. Kern, D. H. Werner, and M. G. Bray, “Novel BI-FDTD approach for the analysis of chiral cylinders and spheres,” IEEE Trans. Antennas Propag. 54, 925–932 (2006).
[CrossRef]

IEEE Trans. Antennas Propag. Mag.

V. Demir, A. Elsherbeni, D. Worasawate, and E. Arvas, “A graphical user interface (GUI) for plane-wave scattering from a conducting, dielectric, or chiral sphere,” IEEE Trans. Antennas Propag. Mag. 46, 94–99 (2004).
[CrossRef]

J. Electromagn. Waves Appl.

B. N. Khatir, M. Al-Kanhal, and A. Sebak, “Electromagnetic wave scattering by elliptic chiral cylinder,” J. Electromagn. Waves Appl. 20, 1377–1390 (2006).
[CrossRef]

J. Opt.

N. Wongkasem and A. Akyurtlu, “Light splitting effects in chiral metamaterials,” J. Opt. 12, 035101 (2010).
[CrossRef]

B. Maheu, G. Gouesbet, and G. Gréhan, “A concise presentation of the generalized Lorenz–Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt. 19, 59–67 (1988).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

J. Quant. Spectrosc. Radiat. Transfer

G. Gouesbet, F. Xu, and Y. P. Han, “Expanded description of electromagnetic arbitrary shaped beams in spheroidal coordinates, for use in light scattering theories: a review,” J. Quant. Spectrosc. Radiat. Transfer 112, 2249–2267 (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, a review,” J. Quant. Spectrosc. Radiat. Transfer 112, 1–27 (2011).
[CrossRef]

Microw. Opt. Technol. Lett.

T. G. Mackay and A. Lakhtakia, “Simultaneous negative-and-positive-phase-velocity propagation in an isotropic chiral medium,” Microw. Opt. Technol. Lett. 49, 1245–1246 (2007).
[CrossRef]

Opt. Express

Phys. Rev. A

L. W. Davis, “Theory of electromagnetic beam,” Phys. Rev. A 19, 1177–1179 (1979).
[CrossRef]

Prog. Electromagn. Res.

J. Dong, “Exotic characteristics of power propagation in the chiral nihility fiber,” Prog. Electromagn. Res. 99, 163–178 (2009).
[CrossRef]

Other

C. Flammer, Spheroidal Wave Functions (Stanford University, 1957).

A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton University, 1957), Chap. 4.

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Figures (3)

Fig. 1.
Fig. 1.

System Oxyz is obtained first by a translation of the Gaussian beam coordinate system Oxyz along the z axis and then by a rigid-body rotation through Euler angles α and β. A chiral spheroid is natural to Oxyz.

Fig. 2.
Fig. 2.

Normalized differential scattering cross sections πσ(θ,0)/λ2, πσ(θ,π/4)/λ2, and πσ(θ,π/2)/λ2 for a chiral spheroid (k0a=6, a/b=2, εr=4, μr=1, κ=0.5, α=0, β=π/4) illuminated by a Gaussian beam with w0=2λ.

Fig. 3.
Fig. 3.

Comparison between the normalized differential scattering cross section πσ(θ,0)/λ2 for a chiral spheroid (k0a=9.42, a/b=2, εr=4, μr=1, κ=0.5, and that for a dielectric one (k0a=9.42, a/b=2, εr=4, μr=1, κ=0), both with α=π/4, β=π/3 and illuminated by a Gaussian beam of w0=2λ.

Equations (28)

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

Ei=E0m=0n=min[Gn,TEmMemnr(1)(c,ζ,η,ϕ)+Gn,TEmMomnr(1)(c,ζ,η,ϕ)iGn,TMmNemnr(1)(c,ζ,η,ϕ)+iGn,TMmNomnr(1)(c,ζ,η,ϕ)],
Hi=E01η0m=0n=min[iGn,TEmNemnr(1)(c,ζ,η,ϕ)iGn,TEmNomnr(1)(c,ζ,η,ϕ)Gn,TMmMemnr(1)(c,ζ,η,ϕ)+Gn,TMmMomnr(1)(c,ζ,η,ϕ)],
[Gn,TEmGn,TEmGn,TMmGn,TMm]=2(1)m1Nmn(c)r=2,1drmn(c)(r+m)(r+m+1)gr+m[21+δm0dPr+mm(cosβ)dβsinα2mPr+mm(cosβ)sinβcosα21+δm0dPr+mm(cosβ)dβcosα2mPr+mm(cosβ)sinβsinα],
gr+m=11+2isz0/w0exp(ikz0)exp[s2(r+m+1/2)21+2isz0/w0],
Es=E0m=0n=min[βmnMemnr(3)(c,ζ,η,ϕ)+βmnMomnr(3)(c,ζ,η,ϕ)iαmnNemnr(3)(c,ζ,η,ϕ)+iαmnNomnr(3)(c,ζ,η,ϕ)],
Hs=E01η0m=0n=min[iβmnNemnr(3)(c,ζ,η,ϕ)iβmnNomnr(3)(c,ζ,η,ϕ)αmnMemnr(3)(c,ζ,η,ϕ)+αmnMomnr(3)(c,ζ,η,ϕ)],
D=ϵ0ϵrE+iκμ0ϵ0H,
B=μ0μrHiκμ0ϵ0E,
[EH]=[E+H+]+[EH],
E±=±iη0μrϵrH±=±iηH±.
2[E+E]+[k+2E+k2E]=[00],
k±=k0(μrϵr±κ).
×[E+E]=[k+E+kE],
·[E+E]=[00].
Ew=E0m=0n=min{δmn[Memnr(1)(c+,ζ,η,ϕ)+Nemnr(1)(c+,ζ,η,ϕ)]+χmn[Momnr(1)(c+,ζ,η,ϕ)+Nomnr(1)(c+,ζ,η,ϕ)]+τmn[Memnr(1)(c,ζ,η,ϕ)Nemnr(1)(c,ζ,η,ϕ)]+γmn[Momnr(1)(c,ζ,η,ϕ)Nomnr(1)(c,ζ,η,ϕ)]},
Hw=E0iηm=0n=min{δmn[Memnr(1)(c+,ζ,η,ϕ)+Nemnr(1)(c+,ζ,η,ϕ)]χmn[Momnr(1)(c+,ζ,η,ϕ)+Nomnr(1)(c+,ζ,η,ϕ)]+τmn[Memnr(1)(c,ζ,η,ϕ)Nemnr(1)(c,ζ,η,ϕ)]+γmn[Momnr(1)(c,ζ,η,ϕ)Nomnr(1)(c,ζ,η,ϕ)]},
Eηi+Eηs=Eηw,Eϕi+Eϕs=EϕwHηi+Hηs=Hηw,Hϕi+Hϕs=Hϕw}atζ=ζ0,
n=minδmnUmn(1),t(c+)n=miniχmnVmn(1),t(c+)+n=minτmnUmn(1),t(c)+n=miniγmnVmn(1),t(c)=n=min[Gn,TEmUmn(1),t(c)+Gn,TMmVmn(1),t(c)]+n=min[βmnUmn(3),t(c)+αmnVmn(3),t(c)],
n=miniδmnVmn(1),t(c+)+n=minχmnUmn(1),t(c+)n=miniτmnVmn(1),t(c)+n=minγmnUmn(1),t(c)=n=min[Gn,TEmUmn(1),t(c)+Gn,TMmVmn(1),t(c)]+n=min[βmnUmn(3),t(c)+αmnVmn(3),t(c)],
n=minδmnXmn(1),t(c+)n=miniχmnYmn(1),t(c+)+n=minτmnXmn(1),t(c)+n=miniγmnYmn(1),t(c)=n=min[Gn,TEmXmn(1),t(c)+Gn,TMmYmn(1),t(c)]+n=min[βmnXmn(3),t(c)+αmnYmn(3),t(c)],
n=miniδmnYmn(1),t(c+)+n=minχmnXmn(1),t(c+)n=miniτmnYmn(1),t(c)+n=minγmnXmn(1),t(c)=n=min[Gn,TEmXmn(1),t(c)+Gn,TMmYmn(1),t(c)]+n=min[βmnXmn(3),t(c)+αmnYmn(3),t(c)],
n=minδmnVmn(1),t(c+)n=miniχmnUmn(1),t(c+)+n=minτmnVmn(1),t(c)+n=miniγmnUmn(1),t(c)=ηη0n=min[Gn,TEmVmn(1),t(c)+Gn,TMmUmn(1),t(c)]+ηη0n=min[βmnVmn(3),t(c)+αmnUmn(3),t(c)],
n=miniδmnUmn(1),t(c+)+n=minχmnVmn(1),t(c+)n=miniτmnUmn(1),t(c)+n=minγmnVmn(1),t(c)=ηη0n=min[Gn,TEmVmn(1),t(c)+Gn,TMmUmn(1),t(c)]+ηη0n=min[βmnVmn(3),t(c)+αmnUmn(3),t(c)],
n=minδmnYmn(1),t(c+)n=miniχmnXmn(1),t(c+)+n=minτmnYmn(1),t(c)+n=miniγmnXmn(1),t(c)=ηη0n=min[Gn,TEmYmn(1),t(c)+Gn,TMmXmn(1),t(c)]+ηη0n=min[βmnYmn(3),t(c)+αmnXmn(3),t(c)],
n=miniδmnXmn(1),t(c+)+n=minχmnYmn(1),t(c+)n=miniτmnXmn(1),t(c)+n=minγmnYmn(1),t(c)=ηη0n=min[Gn,TEmYmn(1),t(c)+Gn,TMmXmn(1),t(c)]+ηη0n=min[βmnYmn(3),t(c)+αmnXmn(3),t(c)],
σ(θ,ϕ)=4πr2|EsE0|2=λ2π(|T1(θ,ϕ)|2+|T2(θ,ϕ)|2),
T1(θ,ϕ)=m=0n=m{[αmndSmn(c,cosθ)dθ+βmnmSmn(c,cosθ)sinθ]sinmϕ[αmndSmn(c,cosθ)dθ+βmnmSmn(c,cosθ)sinθ]cosmϕ},
T2(θ,ϕ)=m=0n=m{[αmnmSmn(c,cosθ)sinθ+βmndSmn(c,cosθ)dθ]cosmϕ+[αmnmSmn(c,cosθ)sinθ+βmndSmn(c,cosθ)dθ]sinmϕ},

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