Abstract

A spheroidal coordinate separation-of-variables solution has been developed for the determination of internal, near-surface, and scattered electromagnetic fields of a layered spheroid (either prolate or oblate) with arbitrary monochromatic illumination (e.g., plane wave or focused Gaussian beam). Calculated results are presented for layered 2:1 axis ratio prolate and oblate spheroids with an equivalent sphere size parameter of 20.

© 2001 Optical Society of America

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References

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  1. J. P. Barton, “Internal and near-surface electromagnetic fields for a spheroidal particle with arbitrary illumination,” Appl. Opt. 34, 5542–5551 (1995).
    [CrossRef] [PubMed]
  2. D.-S. Wang, P. W. Barber, “Scattering by inhomogeneous nonspherical objects,” Appl. Opt. 18, 1190–1197 (1979).
    [CrossRef] [PubMed]
  3. A. R. Sebak, B. P. Sinha, “Scattering by a conducting spheroidal object with dielectric coating at axial incidence,” IEEE Trans. Antennas Propag. 40, 268–274 (1992).
    [CrossRef]
  4. V. V. Somsikov, “Optical properties of two-layered spheroidal dust grains,” Astron. Lett. 22, 625–631 (1996).
  5. V. G. Farafonov, N. V. Voshchinnikov, V. V. Somsikov, “Light scattering by a core-mantle spheroidal particle,” Appl. Opt. 35, 5412–5426 (1996).
    [CrossRef] [PubMed]
  6. V. G. Farafonov, N. V. Voshchinnikov, “Light absorption by two-layer spheroidal particles,” Opt. Spectrosc. 81, 602–608 (1996).
  7. V. G. Farafonov, N. V. Voshchinnikov, “Extinction and scattering of light by two-layer spheroidal particles,” Opt. Spectrosc. 83, 899–906 (1997).
  8. J. P. Barton, “Electromagnetic field calculations for a sphere illuminated by a higher-order Gaussian beam. I. Internal and near-field effects,” Appl. Opt. 36, 1303–1311 (1997).
    [CrossRef] [PubMed]
  9. J. P. Barton, “Electromagnetic field calculations for a sphere illuminated by a higher-order Gaussian beam. II. Far-field scattering,” Appl. Opt. 37, 3339–3344 (1998).
    [CrossRef]
  10. J. P. Barton, W. Ma, S. A. Schaub, D. R. Alexander, “Electromagnetic field for a beam incident on two adjacent spherical particles,” Appl. Opt. 30, 4706–4715 (1991).
    [CrossRef] [PubMed]
  11. J. P. Barton, “Electromagnetic field calculations for irregularly shaped, axisymmetric layered particles with focused illumination,” Appl. Opt. 35, 532–541 (1996).
    [CrossRef] [PubMed]
  12. J. P. Barton, “Internal and near-surface electromagnetic fields for an absorbing spheroidal particle with arbitrary illumination,” Appl. Opt. 34, 8472–8473 (1995).
    [CrossRef] [PubMed]
  13. C. Flammer, Spheroidal Wave Functions (Stanford University, Stanford, Calif., 1957), Chaps. 3, 4, and 6.
  14. J. A. Stratton, Electromagnetic Theory, (McGraw-Hill, New York, 1941), pp. 349–354, 392–399, 414–420.
  15. J. P. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
    [CrossRef]

1998 (1)

1997 (2)

V. G. Farafonov, N. V. Voshchinnikov, “Extinction and scattering of light by two-layer spheroidal particles,” Opt. Spectrosc. 83, 899–906 (1997).

J. P. Barton, “Electromagnetic field calculations for a sphere illuminated by a higher-order Gaussian beam. I. Internal and near-field effects,” Appl. Opt. 36, 1303–1311 (1997).
[CrossRef] [PubMed]

1996 (4)

V. V. Somsikov, “Optical properties of two-layered spheroidal dust grains,” Astron. Lett. 22, 625–631 (1996).

V. G. Farafonov, N. V. Voshchinnikov, V. V. Somsikov, “Light scattering by a core-mantle spheroidal particle,” Appl. Opt. 35, 5412–5426 (1996).
[CrossRef] [PubMed]

V. G. Farafonov, N. V. Voshchinnikov, “Light absorption by two-layer spheroidal particles,” Opt. Spectrosc. 81, 602–608 (1996).

J. P. Barton, “Electromagnetic field calculations for irregularly shaped, axisymmetric layered particles with focused illumination,” Appl. Opt. 35, 532–541 (1996).
[CrossRef] [PubMed]

1995 (2)

1992 (1)

A. R. Sebak, B. P. Sinha, “Scattering by a conducting spheroidal object with dielectric coating at axial incidence,” IEEE Trans. Antennas Propag. 40, 268–274 (1992).
[CrossRef]

1991 (1)

1989 (1)

J. P. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
[CrossRef]

1979 (1)

Alexander, D. R.

J. P. Barton, W. Ma, S. A. Schaub, D. R. Alexander, “Electromagnetic field for a beam incident on two adjacent spherical particles,” Appl. Opt. 30, 4706–4715 (1991).
[CrossRef] [PubMed]

J. P. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
[CrossRef]

Barber, P. W.

Barton, J. P.

Farafonov, V. G.

V. G. Farafonov, N. V. Voshchinnikov, “Extinction and scattering of light by two-layer spheroidal particles,” Opt. Spectrosc. 83, 899–906 (1997).

V. G. Farafonov, N. V. Voshchinnikov, “Light absorption by two-layer spheroidal particles,” Opt. Spectrosc. 81, 602–608 (1996).

V. G. Farafonov, N. V. Voshchinnikov, V. V. Somsikov, “Light scattering by a core-mantle spheroidal particle,” Appl. Opt. 35, 5412–5426 (1996).
[CrossRef] [PubMed]

Flammer, C.

C. Flammer, Spheroidal Wave Functions (Stanford University, Stanford, Calif., 1957), Chaps. 3, 4, and 6.

Ma, W.

Schaub, S. A.

Sebak, A. R.

A. R. Sebak, B. P. Sinha, “Scattering by a conducting spheroidal object with dielectric coating at axial incidence,” IEEE Trans. Antennas Propag. 40, 268–274 (1992).
[CrossRef]

Sinha, B. P.

A. R. Sebak, B. P. Sinha, “Scattering by a conducting spheroidal object with dielectric coating at axial incidence,” IEEE Trans. Antennas Propag. 40, 268–274 (1992).
[CrossRef]

Somsikov, V. V.

V. V. Somsikov, “Optical properties of two-layered spheroidal dust grains,” Astron. Lett. 22, 625–631 (1996).

V. G. Farafonov, N. V. Voshchinnikov, V. V. Somsikov, “Light scattering by a core-mantle spheroidal particle,” Appl. Opt. 35, 5412–5426 (1996).
[CrossRef] [PubMed]

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory, (McGraw-Hill, New York, 1941), pp. 349–354, 392–399, 414–420.

Voshchinnikov, N. V.

V. G. Farafonov, N. V. Voshchinnikov, “Extinction and scattering of light by two-layer spheroidal particles,” Opt. Spectrosc. 83, 899–906 (1997).

V. G. Farafonov, N. V. Voshchinnikov, “Light absorption by two-layer spheroidal particles,” Opt. Spectrosc. 81, 602–608 (1996).

V. G. Farafonov, N. V. Voshchinnikov, V. V. Somsikov, “Light scattering by a core-mantle spheroidal particle,” Appl. Opt. 35, 5412–5426 (1996).
[CrossRef] [PubMed]

Wang, D.-S.

Appl. Opt. (8)

Astron. Lett. (1)

V. V. Somsikov, “Optical properties of two-layered spheroidal dust grains,” Astron. Lett. 22, 625–631 (1996).

IEEE Trans. Antennas Propag. (1)

A. R. Sebak, B. P. Sinha, “Scattering by a conducting spheroidal object with dielectric coating at axial incidence,” IEEE Trans. Antennas Propag. 40, 268–274 (1992).
[CrossRef]

J. Appl. Phys. (1)

J. P. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
[CrossRef]

Opt. Spectrosc. (2)

V. G. Farafonov, N. V. Voshchinnikov, “Light absorption by two-layer spheroidal particles,” Opt. Spectrosc. 81, 602–608 (1996).

V. G. Farafonov, N. V. Voshchinnikov, “Extinction and scattering of light by two-layer spheroidal particles,” Opt. Spectrosc. 83, 899–906 (1997).

Other (2)

C. Flammer, Spheroidal Wave Functions (Stanford University, Stanford, Calif., 1957), Chaps. 3, 4, and 6.

J. A. Stratton, Electromagnetic Theory, (McGraw-Hill, New York, 1941), pp. 349–354, 392–399, 414–420.

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Figures (15)

Fig. 1
Fig. 1

Schematic of the geometric arrangement. The boundary of the spheroid rotates about the z axis. For the prolate spheroid (as shown), the major axis of the spheroid is along the z axis. For the oblate spheroid, the major axis of the spheroid is along the x axis. The outer surface of the spheroid (the layer–external interface) is located at ξ = ξ0 and the core–layer interface is located at ξ = ξ c < ξ0.

Fig. 2
Fig. 2

Surface grid plot of the electric field magnitude in the xz plane for a plane wave incident upon a 2:1 axis ratio prolate spheroid with a 2.5:1 axis ratio core. Incident propagation angle θbd = 30°, incident electric field polarization angle ϕbd = 90°, spheroid size parameter h ext = 27.494593, relative index of refraction of core n c = 1.33, and relative index of refraction of layer n l = 1.50.

Fig. 3
Fig. 3

Contour and gray-level (white implies low, black implies high) plots of the electric field magnitude in the xz plane for a plane wave incident upon a 2:1 axis ratio layered prolate spheroid with a 2.5:1 axis ratio core. Same conditions as Fig. 2.

Fig. 4
Fig. 4

Surface grid plot of the electric field magnitude in the xz plane for a plane wave incident upon a 2:1 axis ratio prolate spheroid with a 2.5:1 axis ratio core. θbd = 30°, ϕbd = 90°, h ext = 27.494593, n c = 1.50, n l = 1.33.

Fig. 5
Fig. 5

Surface grid plot of the electric field magnitude in the xz plane for a plane wave incident upon a 2:1 axis ratio homogeneous prolate spheroid. θbd = 30°, ϕbd = 90°, h ext = 27.494593, n c = n l = 1.33.

Fig. 6
Fig. 6

Polar plots (log scale, range from 0.001 to 10.0) of the far-field scattering in the xz plane for a plane wave incident upon a 2:1 axis ratio prolate spheroid with a 2.5:1 axis ratio core. θbd = 30°, ϕbd = 90°, h ext = 27.494593. For the plot on the left, n c = 1.33 and n l = 1.50 (S r,max = 18.77495); for the plot on the right, n c = 1.50 and n l = 1.33 (S r,max = 14.79815).

Fig. 7
Fig. 7

Polar plots (log scale, range from 0.001 to 10.0) of the far-field scattering in the xz plane for a plane wave incident upon a 2:1 axis ratio homogeneous prolate spheroid. θbd = 30°, ϕbd = 90°, h ext = 27.494593. For the plot on the left, n c = n l = 1.33 (S r,max = 12.18744); for the plot on the right, n c = n l = 1.50 (S r,max = 14.48922).

Fig. 8
Fig. 8

Surface grid plot of the electric field magnitude in the xz plane for a plane wave incident upon a 2:1 axis ratio oblate spheroid with a 2.5:1 axis ratio core. θbd = 30°, ϕbd = 90°, h ext = 21.822473, n c = 1.33, n l = 1.50.

Fig. 9
Fig. 9

Contour and gray-level (white implies low, black implies high) plots of the electric field magnitude in the xz plane for a plane wave incident upon a 2:1 axis ratio layered oblate spheroid with a 2.5:1 axis ratio core. Same conditions as Fig. 8.

Fig. 10
Fig. 10

Surface grid plot of the electric field magnitude in the xz plane for a plane wave incident upon a 2:1 axis ratio oblate spheroid with a 2.5:1 axis ratio core. θbd = 30°, ϕbd = 90°, h ext = 21.822473, n c = 1.50, n l = 1.33.

Fig. 11
Fig. 11

Surface grid plot of the electric field magnitude in the xz plane for a plane wave incident upon a 2:1 axis ratio homogeneous oblate spheroid. θbd = 30°, ϕbd = 90°, h ext = 21.822473, n c = n l = 1.33.

Fig. 12
Fig. 12

Polar plots (log scale, range from 0.001 to 10.0) of the far-field scattering in the xz plane for a plane wave incident upon a 2:1 axis ratio oblate spheroid with a 2.5:1 axis ratio core. θbd = 30°, ϕbd = 90°, h ext = 21.822473. For the plot on the left, n c = 1.33 and n l = 1.50 (S r,max = 84.95962); for the plot on the right, n c = 1.50 and n l = 1.33 (S r,max = 64.08979).

Fig. 13
Fig. 13

Polar plots (log scale, range from 0.001 to 10.00) of the far-field scattering in the xz plane for a plane wave incident upon a 2:1 axis ratio homogeneous oblate spheroid. θbd = 30°, ϕbd = 90°, h ext = 21.822473. For the plot on the left, n c = n l = 1.33 (S r,max = 60.93952); for the plot on the right, n c = n l = 1.50 (S r,max = 51.01663).

Fig. 14
Fig. 14

Surface grid plot of the electric field magnitude in the xz plane for a focused beam incident upon a 2:1 axis ratio oblate spheroid with a 2.5:1 axis ratio core. θbd = 30°, ϕbd = 90°, h ext = 21.822473, n c = 1.33, n l = 1.50, w 0 = 0.50, (x 0, y 0, z 0) = (0.0, 0.0, 0.75).

Fig. 15
Fig. 15

Contour and gray-level (white implies low, black implies high) plots of the electric field magnitude in the xz plane for a focused beam incident upon a 2:1 axis ratio layered oblate spheroid with a 2.5:1 axis ratio core. Same conditions as Fig. 14.

Equations (74)

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f=a1-b/a21/2.
2+h2Π=0,
Πlm=Slmh, ηRlmh, ξexpimϕ,
2+h2E=0,
2+h2H=0.
Mlm=×rΠlm,
Nlm=1h ×Mlm.
Es=l,malmNlms+blmMlms,
Hs=-iextl,malmMlms+blmNlms,
Πlms=Slmhext, ηRlm3hext, ξexpimϕ.
Ec=l,mclmNlmc+dlmMlmc,
Hc=-iext ncl,mclmMlmc+dlmNlmc,
Πlmc=Slmhc, ηRlm1hc, ξexpimϕ.
El=l,melmNlml,1+flmMlml,1+glmNlml,2+hlmMlml,2,
Hl=-iext nll,melmMlml,1+flmNlml,1+glmMlml,2+hlmNlml,2,
Πlml,1=Slmhl, ηRlm1hl, ξexpimϕ,
Πlml,2=Slmhl, ηRlm2hl, ξexpimϕ.
Eηl-Eηs=Eηi,
Eϕl-Eϕs=Eϕi,
Hηl-Hηs=Hηi,
Hϕl-Hϕs=Hϕi;
Eηl-Eηc=0,
Eϕl-Eϕc=0,
Hηl-Hηc=0,
Hϕl-Hϕc=0.
l=|m|L-Ilml1alm-Ilml2blm+Ilml3elm+Ilml4flm+Ilml5glm+Ilml6hlm=12π Almη,
l=|m|L-Ilml7alm-Ilml8blm+Ilml9elm+Ilml10flm+Ilml11glm+Ilml12hlm=12π Almϕ,
l=|m|L-Ilml2alm-Ilml1blm+nlIlml4elm+nlIlml3flm+nlIlml6glm+nlIlml5hlm=i2πext Blmη,
l=|m|L-Ilml8alm-Ilml7blm+nlIlml10elm+nlIlml9flm+nlIlml12glm+nlIlml11hlm=i2πext Blmϕ,
l=|m|L-Ilml13clm-Ilml14dlm+Ilml15elm+Ilml16flm+Ilml17glm+Ilml18hlm=0,
l=|m|L-Ilml19clm-Ilml20dlm+Ilml21elm+Ilml22flm+Ilml23glm+Ilml24hlm=0,
l=|m|L-ncIlml14clm-ncIlml13dlm+nlIlml16elm+nlIlml15flm+nlIlml18glm+nlIlml17hlm=0,
l=|m|L-ncIlml20clm-ncIlml19dlm+nlIlml22elm+nlIlml21flm+nlIlml24glm+nlIlml23hlm=0,
Almη=02π-11 Eηiξ0, η, ϕSlmhext, η×exp-imϕdηdϕ,
Almϕ=02π-11 Eϕiξ0, η, ϕSlmhext, η×exp-imϕdηdϕ,
Blmη=02π-11 Hηiξ0, η, ϕSlmhext, η×exp-imϕdηdϕ,
Blmϕ=02π-11 Hϕiξ0, η, ϕSlmhext, η×exp-imϕdηdϕ,
x=ξ2-11-η21/2 cos ϕ,
y=ξ2-11-η21/2 sin ϕ,
z=ξη.
a/b=ξ0ξ02-11/2.
x=ξ2+11-η21/2 cos ϕ,
y=ξ2+11-η21/2 sin ϕ,
z=ξη.
a/b=1+1/ξ021/2.
Eξi+Eξs=nl2Eξl,
Hξi+Hξs=Hξl;
nl2Eξl=nc2Eξc,
Hξl=Hξc.
Srθ, ϕ=limrr2Src8π E02πf2=limξξ2πReEϕsHηs*-EηsHϕs*.
Ilml1=2 01 Nlm,ηsξ0, η, 0Sl,mhext, ηdη,
Ilml2=2 01 Mlm,ηsξ0, η, 0Sl,mhext, ηdη,
Ilml3=2 01 Nlm,ηl,1ξ0, η, 0Sl,mhext, ηdη,
Ilml4=2 01 Mlm,ηl,1ξ0, η, 0Sl,mhext, ηdη,
Ilml5=2 01 Nlm,ηl,2ξ0, η, 0Sl,mhext, ηdη,
Ilml6=2 01 Mlm,ηl,2ξ0, η, 0Sl,mhext, ηdη,
Ilml7=2 01 Nlm,ϕsξ0, η, 0Sl,mhext, ηdη,
Ilml8=2 01 Mlm,ϕsξ0, η, 0Sl,mhext, ηdη,
Ilml9=2 01 Nlm,ϕl,1ξ0, η, 0Sl,mhext, ηdη,
Ilml10=2 01 Mlm,ϕl,1ξ0, η, 0Sl,mhext, ηdη,
Ilml11=2 01 Nlm,ϕl,2ξ0, η, 0Sl,mhext, ηdη,
Ilml12=2 01 Mlm,ϕl,2ξ0, η, 0Sl,mhext, ηdη,
Ilml13=2 01 Nlm,ηcξc, η, 0Sl,mhl, ηdη,
Ilml14=2 01 Mlm,ηcξc, η, 0Sl,mhl, ηdη,
Ilml15=2 01 Nlm,ηl,1ξc, η, 0Sl,mhl, ηdη,
Ilml16=2 01 Mlm,ηl,1ξc, η, 0Sl,mhl, ηdη,
Ilml17=2 01 Nlm,ηl,2ξc, η, 0Sl,mhl, ηdη,
Ilml18=2 01 Mlm,ηl,2ξc, η, 0Sl,mhl, ηdη,
Ilml19=2 01 Nlm,ϕcξc, η, 0Sl,mhl, ηdη,
Ilml20=2 01 Mlm,ϕcξc, η, 0Sl,mhl, ηdη,
Ilml21=2 01 Nlm,ϕl,1ξc, η, 0Sl,mhl, ηdη,
Ilml22=2 01 Mlm,ϕl,1ξc, η, 0Sl,mhl, ηdη,
Ilml23=2 01 Nlm,ϕl,2ξc, η, 0Sl,mhl, ηdη,
Ilml24=2 01 Mlm,ϕl,2ξc, η, 0Sl,mhl, ηdη,

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