Abstract

An exact analytical solution to the transmission of a Gaussian beam through a gyrotropic cylinder is formulated in terms of a cylindrical vector wave function expansion form. By applying the continuous boundary conditions of electromagnetic fields, the unknown expansion coefficients of the scattered and internal fields are determined. For a localized beam model, numerical results are presented for the normalized near-surface and internal field intensity distributions, and the propagation characteristics are discussed concisely.

© 2014 Optical Society of America

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  1. W. Ren, “Contributions to the electromagnetic wave theory of bounded homogeneous anisotropic media,” Phys. Rev. E 47, 664–673 (1993).
    [CrossRef]
  2. X. B. Wu and K. Yasumoto, “Three-dimensional scattering by an infinite homogeneous anisotropic circular cylinder: an analytical solution,” J. Appl. Phys. 82, 1996–2003 (1997).
    [CrossRef]
  3. Y. L. Geng, X. B. Wu, L. W. Li, and B. R. Guan, “Mie scattering by a uniaxial anisotropic sphere,” Phys. Rev. E 70, 056609 (2004).
    [CrossRef]
  4. Y. L. Geng and C. W. Qiu, “Extended Mie theory for a gyrotropic-coated conducting sphere: an analytical approach,” IEEE Trans. Antennas Propag. 59, 4364–4368 (2011).
    [CrossRef]
  5. R. D. Graglia, P. L. E. Uslenghi, and R. S. Zich, “Moment method with isoparametric elements for three dimensional anisotropic scatterers,” Proc. IEEE 77, 750–760 (1989).
    [CrossRef]
  6. V. V. Varadan, A. Lakhtakia, and V. K. Varadan, “Scattering by three-dimensional anisotropic scatterers,” IEEE Trans. Antennas Propag. 37, 800–802 (1989).
    [CrossRef]
  7. S. N. Papadakis, N. K. Uzunoglu, and C. N. Capsalis, “Scattering of a plane wave by a general anisotropic dielectric ellipsoid,” J. Opt. Soc. Am. A 7, 991–997 (1990).
    [CrossRef]
  8. C. M. Rappaport and B. J. McCartin, “FDFD analysis of electromagnetic scattering in anisotropic media using unconstrained triangular meshes,” IEEE Trans. Antennas Propag. 39, 345–349 (1991).
    [CrossRef]
  9. Z. S. Wu, Q. K. Yuan, Y. Peng, and Z. J. Li, “Internal and external electromagnetic fields for on-axis Gaussian beam scattering from a uniaxial anisotropic sphere,” J. Opt. Soc. Am. A 26, 1778–1787 (2009).
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  10. Q. K. Yuan, Z. S. Wu, and Z. J. Li, “Electromagnetic scattering for a uniaxial anisotropic sphere in an off-axis obliquely incident Gaussian beam,” J. Opt. Soc. Am. A 27, 1457–1465 (2010).
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  11. G. Gouesbet, “Interaction between Gaussian beams and infinite cylinders, by using the theory of distributions,” J. Opt. 26, 225–239 (1995).
    [CrossRef]
  12. 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]
  13. H. Y. Zhang, Y. P. Han, and G. X. Han, “Expansion of the electromagnetic fields of a shaped beam in terms of cylindrical vector wave functions,” J. Opt. Soc. Am. B 24, 1383–1391 (2007).
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  14. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941), Chap. VII.
  15. L. W. Davis, “Theory of electromagnetic beam,” Phys. Rev. A 19, 1177–1179 (1979).
    [CrossRef]
  16. G. Gouesbet, “Validity of the localized approximation for arbitrary shaped beam in the generalized Lorenz–Mie theory for spheres,” J. Opt. Soc. Am. A 16, 1641–1650 (1999).
    [CrossRef]
  17. 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]
  18. H. Y. Zhang, Z. X. Huang, and Y. Shi, “Internal and near-surface electromagnetic fields for a uniaxial anisotropic cylinder illuminated with a Gaussian beam,” Opt. Express 21, 15645–15653 (2013).
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  19. Y. L. Geng and C. W. Qiu, “Analytical spectral-domain scattering theory of a general gyrotropic sphere,” arXiv:1102.4057 (2011).

2013 (1)

2011 (2)

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]

Y. L. Geng and C. W. Qiu, “Extended Mie theory for a gyrotropic-coated conducting sphere: an analytical approach,” IEEE Trans. Antennas Propag. 59, 4364–4368 (2011).
[CrossRef]

2010 (1)

2009 (1)

2007 (1)

2004 (1)

Y. L. Geng, X. B. Wu, L. W. Li, and B. R. Guan, “Mie scattering by a uniaxial anisotropic sphere,” Phys. Rev. E 70, 056609 (2004).
[CrossRef]

1999 (1)

1997 (2)

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]

X. B. Wu and K. Yasumoto, “Three-dimensional scattering by an infinite homogeneous anisotropic circular cylinder: an analytical solution,” J. Appl. Phys. 82, 1996–2003 (1997).
[CrossRef]

1995 (1)

G. Gouesbet, “Interaction between Gaussian beams and infinite cylinders, by using the theory of distributions,” J. Opt. 26, 225–239 (1995).
[CrossRef]

1993 (1)

W. Ren, “Contributions to the electromagnetic wave theory of bounded homogeneous anisotropic media,” Phys. Rev. E 47, 664–673 (1993).
[CrossRef]

1991 (1)

C. M. Rappaport and B. J. McCartin, “FDFD analysis of electromagnetic scattering in anisotropic media using unconstrained triangular meshes,” IEEE Trans. Antennas Propag. 39, 345–349 (1991).
[CrossRef]

1990 (1)

1989 (2)

R. D. Graglia, P. L. E. Uslenghi, and R. S. Zich, “Moment method with isoparametric elements for three dimensional anisotropic scatterers,” Proc. IEEE 77, 750–760 (1989).
[CrossRef]

V. V. Varadan, A. Lakhtakia, and V. K. Varadan, “Scattering by three-dimensional anisotropic scatterers,” IEEE Trans. Antennas Propag. 37, 800–802 (1989).
[CrossRef]

1979 (1)

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

Capsalis, C. N.

Davis, L. W.

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

Geng, Y. L.

Y. L. Geng and C. W. Qiu, “Extended Mie theory for a gyrotropic-coated conducting sphere: an analytical approach,” IEEE Trans. Antennas Propag. 59, 4364–4368 (2011).
[CrossRef]

Y. L. Geng, X. B. Wu, L. W. Li, and B. R. Guan, “Mie scattering by a uniaxial anisotropic sphere,” Phys. Rev. E 70, 056609 (2004).
[CrossRef]

Y. L. Geng and C. W. Qiu, “Analytical spectral-domain scattering theory of a general gyrotropic sphere,” arXiv:1102.4057 (2011).

Gouesbet, 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]

G. Gouesbet, “Validity of the localized approximation for arbitrary shaped beam in the generalized Lorenz–Mie theory for spheres,” J. Opt. Soc. Am. A 16, 1641–1650 (1999).
[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]

G. Gouesbet, “Interaction between Gaussian beams and infinite cylinders, by using the theory of distributions,” J. Opt. 26, 225–239 (1995).
[CrossRef]

Graglia, R. D.

R. D. Graglia, P. L. E. Uslenghi, and R. S. Zich, “Moment method with isoparametric elements for three dimensional anisotropic scatterers,” Proc. IEEE 77, 750–760 (1989).
[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]

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]

Guan, B. R.

Y. L. Geng, X. B. Wu, L. W. Li, and B. R. Guan, “Mie scattering by a uniaxial anisotropic sphere,” Phys. Rev. E 70, 056609 (2004).
[CrossRef]

Han, G. X.

Han, Y. P.

Huang, Z. X.

Lakhtakia, A.

V. V. Varadan, A. Lakhtakia, and V. K. Varadan, “Scattering by three-dimensional anisotropic scatterers,” IEEE Trans. Antennas Propag. 37, 800–802 (1989).
[CrossRef]

Li, L. W.

Y. L. Geng, X. B. Wu, L. W. Li, and B. R. Guan, “Mie scattering by a uniaxial anisotropic sphere,” Phys. Rev. E 70, 056609 (2004).
[CrossRef]

Li, Z. J.

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]

McCartin, B. J.

C. M. Rappaport and B. J. McCartin, “FDFD analysis of electromagnetic scattering in anisotropic media using unconstrained triangular meshes,” IEEE Trans. Antennas Propag. 39, 345–349 (1991).
[CrossRef]

Papadakis, S. N.

Peng, Y.

Qiu, C. W.

Y. L. Geng and C. W. Qiu, “Extended Mie theory for a gyrotropic-coated conducting sphere: an analytical approach,” IEEE Trans. Antennas Propag. 59, 4364–4368 (2011).
[CrossRef]

Y. L. Geng and C. W. Qiu, “Analytical spectral-domain scattering theory of a general gyrotropic sphere,” arXiv:1102.4057 (2011).

Rappaport, C. M.

C. M. Rappaport and B. J. McCartin, “FDFD analysis of electromagnetic scattering in anisotropic media using unconstrained triangular meshes,” IEEE Trans. Antennas Propag. 39, 345–349 (1991).
[CrossRef]

Ren, K. F.

Ren, W.

W. Ren, “Contributions to the electromagnetic wave theory of bounded homogeneous anisotropic media,” Phys. Rev. E 47, 664–673 (1993).
[CrossRef]

Shi, Y.

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941), Chap. VII.

Uslenghi, P. L. E.

R. D. Graglia, P. L. E. Uslenghi, and R. S. Zich, “Moment method with isoparametric elements for three dimensional anisotropic scatterers,” Proc. IEEE 77, 750–760 (1989).
[CrossRef]

Uzunoglu, N. K.

Varadan, V. K.

V. V. Varadan, A. Lakhtakia, and V. K. Varadan, “Scattering by three-dimensional anisotropic scatterers,” IEEE Trans. Antennas Propag. 37, 800–802 (1989).
[CrossRef]

Varadan, V. V.

V. V. Varadan, A. Lakhtakia, and V. K. Varadan, “Scattering by three-dimensional anisotropic scatterers,” IEEE Trans. Antennas Propag. 37, 800–802 (1989).
[CrossRef]

Wu, X. B.

Y. L. Geng, X. B. Wu, L. W. Li, and B. R. Guan, “Mie scattering by a uniaxial anisotropic sphere,” Phys. Rev. E 70, 056609 (2004).
[CrossRef]

X. B. Wu and K. Yasumoto, “Three-dimensional scattering by an infinite homogeneous anisotropic circular cylinder: an analytical solution,” J. Appl. Phys. 82, 1996–2003 (1997).
[CrossRef]

Wu, Z. S.

Yasumoto, K.

X. B. Wu and K. Yasumoto, “Three-dimensional scattering by an infinite homogeneous anisotropic circular cylinder: an analytical solution,” J. Appl. Phys. 82, 1996–2003 (1997).
[CrossRef]

Yuan, Q. K.

Zhang, H. Y.

Zich, R. S.

R. D. Graglia, P. L. E. Uslenghi, and R. S. Zich, “Moment method with isoparametric elements for three dimensional anisotropic scatterers,” Proc. IEEE 77, 750–760 (1989).
[CrossRef]

IEEE Trans. Antennas Propag. (3)

Y. L. Geng and C. W. Qiu, “Extended Mie theory for a gyrotropic-coated conducting sphere: an analytical approach,” IEEE Trans. Antennas Propag. 59, 4364–4368 (2011).
[CrossRef]

V. V. Varadan, A. Lakhtakia, and V. K. Varadan, “Scattering by three-dimensional anisotropic scatterers,” IEEE Trans. Antennas Propag. 37, 800–802 (1989).
[CrossRef]

C. M. Rappaport and B. J. McCartin, “FDFD analysis of electromagnetic scattering in anisotropic media using unconstrained triangular meshes,” IEEE Trans. Antennas Propag. 39, 345–349 (1991).
[CrossRef]

J. Appl. Phys. (1)

X. B. Wu and K. Yasumoto, “Three-dimensional scattering by an infinite homogeneous anisotropic circular cylinder: an analytical solution,” J. Appl. Phys. 82, 1996–2003 (1997).
[CrossRef]

J. Opt. (1)

G. Gouesbet, “Interaction between Gaussian beams and infinite cylinders, by using the theory of distributions,” J. Opt. 26, 225–239 (1995).
[CrossRef]

J. Opt. Soc. Am. A (5)

J. Opt. Soc. Am. B (1)

J. Quant. Spectrosc. Radiat. Transfer (1)

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]

Opt. Express (1)

Phys. Rev. A (1)

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

Phys. Rev. E (2)

W. Ren, “Contributions to the electromagnetic wave theory of bounded homogeneous anisotropic media,” Phys. Rev. E 47, 664–673 (1993).
[CrossRef]

Y. L. Geng, X. B. Wu, L. W. Li, and B. R. Guan, “Mie scattering by a uniaxial anisotropic sphere,” Phys. Rev. E 70, 056609 (2004).
[CrossRef]

Proc. IEEE (1)

R. D. Graglia, P. L. E. Uslenghi, and R. S. Zich, “Moment method with isoparametric elements for three dimensional anisotropic scatterers,” Proc. IEEE 77, 750–760 (1989).
[CrossRef]

Other (2)

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941), Chap. VII.

Y. L. Geng and C. W. Qiu, “Analytical spectral-domain scattering theory of a general gyrotropic sphere,” arXiv:1102.4057 (2011).

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Figures (3)

Fig. 1.
Fig. 1.

Gyrotropic cylinder illuminated by an on-axis incident Gaussian beam.

Fig. 2.
Fig. 2.

|(Ei+Es)/E0|2 and |Ew/E0|2 for a gyrotropic cylinder illuminated by a TE-polarized Gaussian beam.

Fig. 3.
Fig. 3.

|(Ei+Es)/E0|2 and |Ew/E0|2 for the same model as in Fig. 2, but illuminated by a TM-polarized Gaussian beam.

Equations (44)

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

Ei=E0m=0π[Im,TE(ζ)mmλ(1)(h)+Im,TM(ζ)nmλ(1)(h)]eihzdζ,
Im,TE=(i)m+1k0n=|m|(nm)!(n+m)!2n+12n(n+1)gn[m2Pnm(cosβ)sinβPnm(cosζ)sinζ+dPnm(cosβ)dβdPnm(cosζ)dζ],
Im,TM=(i)m+1k0mn=|m|(nm)!(n+m)!2n+12n(n+1)gn[Pnm(cosβ)sinβdPnm(cosζ)dζ+dPnm(cosβ)dβPnm(cosζ)sinζ],
gn=11+2isz0/w0exp(ikz0)exp[s2(n+1/2)21+2isz0/w0],
Es=E0m=0π[αm(ζ)mmλ(3)+βm(ζ)nmλ(3)]eihzdζ,
Ew=E0q=12m=0πFmq(ζ)[αqe(ζ)mmλq(1)+βqe(ζ)nmλq(1)+γqe(ζ)lmλq(1)]eihzdζ,
k1=(2Lh2M+M24LN)12,λ1=(2LMM24LNM+M24LNh2)12,
k2=(2Lh2MM24LN)12,λ2=(2LM+M24LNMM24LNh2)12,
L=a32(a14a24)+(a14a24a12a32)h2,
M=(a14a24+a12a32)h2+(a12a32)h4,N=a12h4,
αqe(ζ)=ia22ha24(h2a12)(kq2a12),
βqe(ζ)=ikqa24+a12(kq2a12)a24(h2a12)(kq2a12),
γqe(ζ)=hkq2a24(kq2a12)2a24(h2a12)(kq2a12).
H=1iωμ0×E,[mmλnmλ]eihz=1k×[nmλmmλ]eihz,×lmλeihz=0.
Eϕi+Eϕs=Eϕw,Ezi+Ezs=EzwHϕi+Hϕs=Hϕw,Hzi+Hzs=Hzw}atr=r0.
ξddξJm(ξ)Im,TE+hmk0Jm(ξ)Im,TM+ξddξHm(1)(ξ)αm(ζ)+hmk0Hm(1)(ξ)βm(ζ)=Fm1(ζ)[α1e(ζ)ξ1ddξ1Jm(ξ1)+β1e(ζ)hmk1Jm(ξ1)γ1e(ζ)imJm(ξ1)]+Fm2(ζ)[α2e(ζ)ξ2ddξ2Jm(ξ2)+β2e(ζ)hmk2Jm(ξ2)γ2e(ζ)imJm(ξ2)],
ξ2[Jm(ξ)Im,TM+Hm(1)(ξ)βm(ζ)]=Fm1(ζ)k0k1ξ12Jm(ξ1)[β1e(ζ)+γ1e(ζ)ihk1λ12]+Fm2(ζ)k0k2ξ22Jm(ξ2)[β2e(ζ)+γ2e(ζ)ihk2λ22],
hmk0Jm(ξ)Im,TE+ξddξJm(ξ)Im,TM+hmk0Hm(1)(ξ)αm(ζ)+ξddξHm(1)(ξ)βm(ζ)=Fm1(ζ)[hmk0α1e(ζ)Jm(ξ1)+k1k0β1e(ζ)ξ1ddξ1Jm(ξ1)]+Fm2(ζ)[hmk0α2e(ζ)Jm(ξ2)+k2k0β2e(ζ)ξ2ddξ2Jm(ξ2)],
ξ2[Jm(ξ)Im,TE+Hm(1)(ξ)αm(ζ)]=Fm1(ζ)α1e(ζ)ξ12Jm(ξ1)+Fm2(ζ)α2e(ζ)ξ22Jm(ξ2),
|(Ei+Es)/E0|2=|Eri+Ers|2+|Eϕi+Eϕs|2+|Ezi+Ezs|2,
|Ew/E0|2=|Erw|2+|Eϕw|2+|Ezw|2.
Ew=E0q=12kq2sinθkdθk02πfq(θk,ϕk)Fqe(θk,ϕk)eikq·rdϕk,
Fqe(θk,ϕk)eikq·r=(Δ1Δsinϕk+Δ2Δcosϕk)x^eikq·r+(Δ1Δcosϕk+Δ2Δsinϕk)y^eikq·r+z^eikq·r,
k12=B+B24AC2A,k22=BB24AC2A,
A=a12sin2θk+a32cos2θk,
B=(a14a24)sin2θk+a12a32(1+cos2θk),
C=a32(a14a24),
a12=ω2μ0ε1,a22=ω2μ0ε2,a32=ω2μ0ε3,
Δ1=ia22kq2sinθkcosθk,
Δ2=(kq2a12)kq2sinθkcosθk,
Δ=a24+(kq2cos2θka12)(kq2a12).
fq(θk,ϕk)=n=Gnq(θk)einϕk.
Ew=E0q=12n=Gnq(θk)kq2sinθkdθk02πFqe(θk,ϕk)eikq·reinϕkdϕk.
x^eik·r=m=(amxmmλ(1)+bmxnmλ(1)+cmxlmλ(1))eihz,
y^eik·r=m=(amymmλ(1)+bmynmλ(1)+cmylmλ(1))eihz,
z^eik·r=m=(amzmmλ(1)+bmznmλ(1)+cmzlmλ(1))eihz,
[amxbmxcmx]=im1eimϕkk[1sinθksinϕkicosθksinθkcosϕksinθkcosϕk],
[amybmycmy]=im1eimϕkk[1sinθkcosϕkicosθksinθksinϕksinθksinϕk],
[amzbmzcmz]=im1eimϕkk[0icosθk].
Fqe(θk,ϕk)eikq·r=m=im1eimϕk[Aqe(θk)mmλq(1)+Bqe(θk)nmλq(1)+Cqe(θk)lmλq(1)]eihqz,
Aqe(θk)=1kqsinθkΔ1Δ,
Bqe(θk)=ikqsinθk(sinθkΔ2Δcosθk),
Cqe(θk)=1kq(Δ2Δsinθk+cosθk).
Ew=E0q=12m=Gmq(θk)[Aqe(θk)mmλq(1)+Bqe(θk)nmλq(1)+Cqe(θk)lmλq(1)]eihqzdθk,

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