Abstract

Based on the eigenfunction expansion of electromagnetic waves in a reciprocal uniaxial bianisotropic medium, an extended mode-matching method is proposed to study the scattering of an infinitely long reciprocal uniaxial bianisotropic cylinder with arbitrary cross section. Excellent convergence of the echo width is numerically verified, which establishes the reliability and applicability of the present extended mode-matching method for the two-dimensional single-body problem in which the reciprocal uniaxial bianisotropic medium has a curved surface.

© 1999 Optical Society of America

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  1. W. W. Hansen, “A new type of expansion in radiation problems,” Phys. Rev. 47, 139–143 (1935).
    [CrossRef]
  2. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  3. P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).
  4. C. T. Tai, Dyadic Green’s Functions in Electromagnetic Theory (Intertext, New York, 1971).
  5. R. D. Graglia, P. L. E. Uslenghi, R. S. Zich, “Moment method with isoparameteric elements for three-dimensional anisotropic scatterers,” Proc. IEEE 77, 750–760 (1989).
    [CrossRef]
  6. V. V. Varadan, A. Lakhtakia, V. K. Varadan, “Scattering by a three dimensional anisotropic scatterers,” IEEE Trans. Antennas Propag. 37, 800–802 (1989).
    [CrossRef]
  7. S. N. Papadakis, N. K. Uzunoglu, N. Christos, “Scattering of a plane wave by a general anisotropic dielectric ellipsoid,” J. Opt. Soc. Am. A 7, 991–997 (1990).
    [CrossRef]
  8. J. A. Kong, Theory of Electromagnetic Waves (Wiley, New York, 1975).
  9. C. Yeh, “Perturbation method in the diffraction of electromagnetic waves by arbitrarily shaped penetrable obstacles,” J. Math. Phys. 6, 2008–2013 (1965).
    [CrossRef]
  10. V. K. Varadan, V. V. Varadan, eds., Acoustic, Electromagnetic and Elastic Wave Scattering—Focus on the T-Matrix Approach (Pergamon, New York, 1980).
  11. E. J. Rothwell, L. L. Frasch, “Propagation characteristics of dielectric-rod-loaded waveguides,” IEEE Trans. Microwave Theory Tech. 36, 594–600 (1988).
    [CrossRef]
  12. C. Hafner, The Generalized Multipole Technique for Computational Electromagnetics (Artech House, London, 1990).
  13. I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, A. J. Viitanen, Electromagnetic Waves in Chiral and Bianisotropic Media (Artech House, Norwood, 1994).
  14. A. Priou, ed., Bianisotropic and Biisotropic Media and Applications (EMW, Boston, 1994).
  15. N. Engheta, ed., Special issue, “Wave interaction with chiral and complex media,” J. Electromagn. Waves Appl. 6, 537–793 (1992).
  16. S. A. Tretyakov, A. A. Sochava, “Plane electromagnetic waves in uniaxial bianisotropic media,” in Proceedings of the Second International Conference and Workshop on Electromagnetics of Complex Media (Helsinki University of Technology, Helsinki, 1993), pp. 46–49.
  17. D. Cheng, “Field representations in reciprocal uniaxial bianisotropic media by cylindrical vector wave functions,” Microwave Opt. Technol. Lett. 13, 358–363 (1996).
    [CrossRef]
  18. D. Cheng, W. Ren, “Green dyadics in reciprocal uniaxial bianisotropic medium by cylindrical vector wave functions,” Phys. Rev. E 54, 2917–2924 (1996).
    [CrossRef]
  19. I. V. Lindell, A. J. Viitanen, P. K. Koivisto, “Plane-wave propagation in a transversely bianisotropic uniaxial medium,” Microwave Opt. Technol. Lett. 6, 478–481 (1993).
    [CrossRef]
  20. S. A. Tretyakov, A. A. Sochava, “Proposed composite material for non-reflecting shields and antenna redomes,” Electron. Lett. 29, 1048–1049 (1993).
    [CrossRef]
  21. A. J. Viitanen, I. V. Lindell, “Uniaxial chiral quarter-wave polarization transformer,” Electron. Lett. 29, 1074–1075 (1993).
    [CrossRef]
  22. I. V. Lindell, S. A. Tretyakov, A. J. Viitanen, “Plane-wave propagation in a uniaxial chiro-omega medium,” Microwave Opt. Technol. Lett. 6, 517–520 (1993).
    [CrossRef]
  23. N. K. Uzunoglu, P. G. Cottis, J. G. Fikioris, “Excitation of electromagnetic wave in a greoelectric cylinder,” IEEE Trans. Antennas Propag. 33, 90–98 (1985).
    [CrossRef]
  24. W. H. Eggiman, “Scattering of a plane wave on a ferrite cylinder at normal incidence,” IEEE Trans. Microwave Theory Tech. 8, 440–445 (1960).
    [CrossRef]
  25. N. Okamoto, “Matrix formulation of scattering by a homogeneous gyrotropic cylinder,” IEEE Trans. Antennas Propag. 18, 642–649 (1970).
    [CrossRef]
  26. R. D. Graglia, P. L. E. Uslenghi, “Electromagnetic scattering from anisotropic materials, part II: computer code and numerical results in two dimensions,” IEEE Trans. Antennas Propag. 35, 225–232 (1987).
    [CrossRef]
  27. L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1985).
  28. R. J. Pogorzelski, E. Lun, “On the expansion of cylindrical vector waves in terms of spherical vector waves,” Radio Sci. 11, 753–761 (1976).
    [CrossRef]

1996

D. Cheng, “Field representations in reciprocal uniaxial bianisotropic media by cylindrical vector wave functions,” Microwave Opt. Technol. Lett. 13, 358–363 (1996).
[CrossRef]

D. Cheng, W. Ren, “Green dyadics in reciprocal uniaxial bianisotropic medium by cylindrical vector wave functions,” Phys. Rev. E 54, 2917–2924 (1996).
[CrossRef]

1993

I. V. Lindell, A. J. Viitanen, P. K. Koivisto, “Plane-wave propagation in a transversely bianisotropic uniaxial medium,” Microwave Opt. Technol. Lett. 6, 478–481 (1993).
[CrossRef]

S. A. Tretyakov, A. A. Sochava, “Proposed composite material for non-reflecting shields and antenna redomes,” Electron. Lett. 29, 1048–1049 (1993).
[CrossRef]

A. J. Viitanen, I. V. Lindell, “Uniaxial chiral quarter-wave polarization transformer,” Electron. Lett. 29, 1074–1075 (1993).
[CrossRef]

I. V. Lindell, S. A. Tretyakov, A. J. Viitanen, “Plane-wave propagation in a uniaxial chiro-omega medium,” Microwave Opt. Technol. Lett. 6, 517–520 (1993).
[CrossRef]

1992

N. Engheta, ed., Special issue, “Wave interaction with chiral and complex media,” J. Electromagn. Waves Appl. 6, 537–793 (1992).

1990

1989

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

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

1988

E. J. Rothwell, L. L. Frasch, “Propagation characteristics of dielectric-rod-loaded waveguides,” IEEE Trans. Microwave Theory Tech. 36, 594–600 (1988).
[CrossRef]

1987

R. D. Graglia, P. L. E. Uslenghi, “Electromagnetic scattering from anisotropic materials, part II: computer code and numerical results in two dimensions,” IEEE Trans. Antennas Propag. 35, 225–232 (1987).
[CrossRef]

1985

N. K. Uzunoglu, P. G. Cottis, J. G. Fikioris, “Excitation of electromagnetic wave in a greoelectric cylinder,” IEEE Trans. Antennas Propag. 33, 90–98 (1985).
[CrossRef]

1976

R. J. Pogorzelski, E. Lun, “On the expansion of cylindrical vector waves in terms of spherical vector waves,” Radio Sci. 11, 753–761 (1976).
[CrossRef]

1970

N. Okamoto, “Matrix formulation of scattering by a homogeneous gyrotropic cylinder,” IEEE Trans. Antennas Propag. 18, 642–649 (1970).
[CrossRef]

1965

C. Yeh, “Perturbation method in the diffraction of electromagnetic waves by arbitrarily shaped penetrable obstacles,” J. Math. Phys. 6, 2008–2013 (1965).
[CrossRef]

1960

W. H. Eggiman, “Scattering of a plane wave on a ferrite cylinder at normal incidence,” IEEE Trans. Microwave Theory Tech. 8, 440–445 (1960).
[CrossRef]

1935

W. W. Hansen, “A new type of expansion in radiation problems,” Phys. Rev. 47, 139–143 (1935).
[CrossRef]

Cheng, D.

D. Cheng, “Field representations in reciprocal uniaxial bianisotropic media by cylindrical vector wave functions,” Microwave Opt. Technol. Lett. 13, 358–363 (1996).
[CrossRef]

D. Cheng, W. Ren, “Green dyadics in reciprocal uniaxial bianisotropic medium by cylindrical vector wave functions,” Phys. Rev. E 54, 2917–2924 (1996).
[CrossRef]

Christos, N.

Cottis, P. G.

N. K. Uzunoglu, P. G. Cottis, J. G. Fikioris, “Excitation of electromagnetic wave in a greoelectric cylinder,” IEEE Trans. Antennas Propag. 33, 90–98 (1985).
[CrossRef]

Eggiman, W. H.

W. H. Eggiman, “Scattering of a plane wave on a ferrite cylinder at normal incidence,” IEEE Trans. Microwave Theory Tech. 8, 440–445 (1960).
[CrossRef]

Feshbach, H.

P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).

Fikioris, J. G.

N. K. Uzunoglu, P. G. Cottis, J. G. Fikioris, “Excitation of electromagnetic wave in a greoelectric cylinder,” IEEE Trans. Antennas Propag. 33, 90–98 (1985).
[CrossRef]

Frasch, L. L.

E. J. Rothwell, L. L. Frasch, “Propagation characteristics of dielectric-rod-loaded waveguides,” IEEE Trans. Microwave Theory Tech. 36, 594–600 (1988).
[CrossRef]

Graglia, R. D.

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

R. D. Graglia, P. L. E. Uslenghi, “Electromagnetic scattering from anisotropic materials, part II: computer code and numerical results in two dimensions,” IEEE Trans. Antennas Propag. 35, 225–232 (1987).
[CrossRef]

Hafner, C.

C. Hafner, The Generalized Multipole Technique for Computational Electromagnetics (Artech House, London, 1990).

Hansen, W. W.

W. W. Hansen, “A new type of expansion in radiation problems,” Phys. Rev. 47, 139–143 (1935).
[CrossRef]

Koivisto, P. K.

I. V. Lindell, A. J. Viitanen, P. K. Koivisto, “Plane-wave propagation in a transversely bianisotropic uniaxial medium,” Microwave Opt. Technol. Lett. 6, 478–481 (1993).
[CrossRef]

Kong, J. A.

J. A. Kong, Theory of Electromagnetic Waves (Wiley, New York, 1975).

L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1985).

Lakhtakia, A.

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

Lindell, I. V.

I. V. Lindell, S. A. Tretyakov, A. J. Viitanen, “Plane-wave propagation in a uniaxial chiro-omega medium,” Microwave Opt. Technol. Lett. 6, 517–520 (1993).
[CrossRef]

I. V. Lindell, A. J. Viitanen, P. K. Koivisto, “Plane-wave propagation in a transversely bianisotropic uniaxial medium,” Microwave Opt. Technol. Lett. 6, 478–481 (1993).
[CrossRef]

A. J. Viitanen, I. V. Lindell, “Uniaxial chiral quarter-wave polarization transformer,” Electron. Lett. 29, 1074–1075 (1993).
[CrossRef]

I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, A. J. Viitanen, Electromagnetic Waves in Chiral and Bianisotropic Media (Artech House, Norwood, 1994).

Lun, E.

R. J. Pogorzelski, E. Lun, “On the expansion of cylindrical vector waves in terms of spherical vector waves,” Radio Sci. 11, 753–761 (1976).
[CrossRef]

Morse, P. M.

P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).

Okamoto, N.

N. Okamoto, “Matrix formulation of scattering by a homogeneous gyrotropic cylinder,” IEEE Trans. Antennas Propag. 18, 642–649 (1970).
[CrossRef]

Papadakis, S. N.

Pogorzelski, R. J.

R. J. Pogorzelski, E. Lun, “On the expansion of cylindrical vector waves in terms of spherical vector waves,” Radio Sci. 11, 753–761 (1976).
[CrossRef]

Ren, W.

D. Cheng, W. Ren, “Green dyadics in reciprocal uniaxial bianisotropic medium by cylindrical vector wave functions,” Phys. Rev. E 54, 2917–2924 (1996).
[CrossRef]

Rothwell, E. J.

E. J. Rothwell, L. L. Frasch, “Propagation characteristics of dielectric-rod-loaded waveguides,” IEEE Trans. Microwave Theory Tech. 36, 594–600 (1988).
[CrossRef]

Shin, R. T.

L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1985).

Sihvola, A. H.

I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, A. J. Viitanen, Electromagnetic Waves in Chiral and Bianisotropic Media (Artech House, Norwood, 1994).

Sochava, A. A.

S. A. Tretyakov, A. A. Sochava, “Proposed composite material for non-reflecting shields and antenna redomes,” Electron. Lett. 29, 1048–1049 (1993).
[CrossRef]

S. A. Tretyakov, A. A. Sochava, “Plane electromagnetic waves in uniaxial bianisotropic media,” in Proceedings of the Second International Conference and Workshop on Electromagnetics of Complex Media (Helsinki University of Technology, Helsinki, 1993), pp. 46–49.

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

Tai, C. T.

C. T. Tai, Dyadic Green’s Functions in Electromagnetic Theory (Intertext, New York, 1971).

Tretyakov, S. A.

I. V. Lindell, S. A. Tretyakov, A. J. Viitanen, “Plane-wave propagation in a uniaxial chiro-omega medium,” Microwave Opt. Technol. Lett. 6, 517–520 (1993).
[CrossRef]

S. A. Tretyakov, A. A. Sochava, “Proposed composite material for non-reflecting shields and antenna redomes,” Electron. Lett. 29, 1048–1049 (1993).
[CrossRef]

I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, A. J. Viitanen, Electromagnetic Waves in Chiral and Bianisotropic Media (Artech House, Norwood, 1994).

S. A. Tretyakov, A. A. Sochava, “Plane electromagnetic waves in uniaxial bianisotropic media,” in Proceedings of the Second International Conference and Workshop on Electromagnetics of Complex Media (Helsinki University of Technology, Helsinki, 1993), pp. 46–49.

Tsang, L.

L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1985).

Uslenghi, P. L. E.

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

R. D. Graglia, P. L. E. Uslenghi, “Electromagnetic scattering from anisotropic materials, part II: computer code and numerical results in two dimensions,” IEEE Trans. Antennas Propag. 35, 225–232 (1987).
[CrossRef]

Uzunoglu, N. K.

S. N. Papadakis, N. K. Uzunoglu, N. Christos, “Scattering of a plane wave by a general anisotropic dielectric ellipsoid,” J. Opt. Soc. Am. A 7, 991–997 (1990).
[CrossRef]

N. K. Uzunoglu, P. G. Cottis, J. G. Fikioris, “Excitation of electromagnetic wave in a greoelectric cylinder,” IEEE Trans. Antennas Propag. 33, 90–98 (1985).
[CrossRef]

Varadan, V. K.

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

Varadan, V. V.

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

Viitanen, A. J.

A. J. Viitanen, I. V. Lindell, “Uniaxial chiral quarter-wave polarization transformer,” Electron. Lett. 29, 1074–1075 (1993).
[CrossRef]

I. V. Lindell, A. J. Viitanen, P. K. Koivisto, “Plane-wave propagation in a transversely bianisotropic uniaxial medium,” Microwave Opt. Technol. Lett. 6, 478–481 (1993).
[CrossRef]

I. V. Lindell, S. A. Tretyakov, A. J. Viitanen, “Plane-wave propagation in a uniaxial chiro-omega medium,” Microwave Opt. Technol. Lett. 6, 517–520 (1993).
[CrossRef]

I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, A. J. Viitanen, Electromagnetic Waves in Chiral and Bianisotropic Media (Artech House, Norwood, 1994).

Yeh, C.

C. Yeh, “Perturbation method in the diffraction of electromagnetic waves by arbitrarily shaped penetrable obstacles,” J. Math. Phys. 6, 2008–2013 (1965).
[CrossRef]

Zich, R. S.

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

Electron. Lett.

S. A. Tretyakov, A. A. Sochava, “Proposed composite material for non-reflecting shields and antenna redomes,” Electron. Lett. 29, 1048–1049 (1993).
[CrossRef]

A. J. Viitanen, I. V. Lindell, “Uniaxial chiral quarter-wave polarization transformer,” Electron. Lett. 29, 1074–1075 (1993).
[CrossRef]

IEEE Trans. Antennas Propag.

N. K. Uzunoglu, P. G. Cottis, J. G. Fikioris, “Excitation of electromagnetic wave in a greoelectric cylinder,” IEEE Trans. Antennas Propag. 33, 90–98 (1985).
[CrossRef]

N. Okamoto, “Matrix formulation of scattering by a homogeneous gyrotropic cylinder,” IEEE Trans. Antennas Propag. 18, 642–649 (1970).
[CrossRef]

R. D. Graglia, P. L. E. Uslenghi, “Electromagnetic scattering from anisotropic materials, part II: computer code and numerical results in two dimensions,” IEEE Trans. Antennas Propag. 35, 225–232 (1987).
[CrossRef]

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

IEEE Trans. Microwave Theory Tech.

W. H. Eggiman, “Scattering of a plane wave on a ferrite cylinder at normal incidence,” IEEE Trans. Microwave Theory Tech. 8, 440–445 (1960).
[CrossRef]

E. J. Rothwell, L. L. Frasch, “Propagation characteristics of dielectric-rod-loaded waveguides,” IEEE Trans. Microwave Theory Tech. 36, 594–600 (1988).
[CrossRef]

J. Electromagn. Waves Appl.

N. Engheta, ed., Special issue, “Wave interaction with chiral and complex media,” J. Electromagn. Waves Appl. 6, 537–793 (1992).

J. Math. Phys.

C. Yeh, “Perturbation method in the diffraction of electromagnetic waves by arbitrarily shaped penetrable obstacles,” J. Math. Phys. 6, 2008–2013 (1965).
[CrossRef]

J. Opt. Soc. Am. A

Microwave Opt. Technol. Lett.

I. V. Lindell, S. A. Tretyakov, A. J. Viitanen, “Plane-wave propagation in a uniaxial chiro-omega medium,” Microwave Opt. Technol. Lett. 6, 517–520 (1993).
[CrossRef]

D. Cheng, “Field representations in reciprocal uniaxial bianisotropic media by cylindrical vector wave functions,” Microwave Opt. Technol. Lett. 13, 358–363 (1996).
[CrossRef]

I. V. Lindell, A. J. Viitanen, P. K. Koivisto, “Plane-wave propagation in a transversely bianisotropic uniaxial medium,” Microwave Opt. Technol. Lett. 6, 478–481 (1993).
[CrossRef]

Phys. Rev.

W. W. Hansen, “A new type of expansion in radiation problems,” Phys. Rev. 47, 139–143 (1935).
[CrossRef]

Phys. Rev. E

D. Cheng, W. Ren, “Green dyadics in reciprocal uniaxial bianisotropic medium by cylindrical vector wave functions,” Phys. Rev. E 54, 2917–2924 (1996).
[CrossRef]

Proc. IEEE

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

Radio Sci.

R. J. Pogorzelski, E. Lun, “On the expansion of cylindrical vector waves in terms of spherical vector waves,” Radio Sci. 11, 753–761 (1976).
[CrossRef]

Other

L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1985).

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).

C. T. Tai, Dyadic Green’s Functions in Electromagnetic Theory (Intertext, New York, 1971).

J. A. Kong, Theory of Electromagnetic Waves (Wiley, New York, 1975).

V. K. Varadan, V. V. Varadan, eds., Acoustic, Electromagnetic and Elastic Wave Scattering—Focus on the T-Matrix Approach (Pergamon, New York, 1980).

S. A. Tretyakov, A. A. Sochava, “Plane electromagnetic waves in uniaxial bianisotropic media,” in Proceedings of the Second International Conference and Workshop on Electromagnetics of Complex Media (Helsinki University of Technology, Helsinki, 1993), pp. 46–49.

C. Hafner, The Generalized Multipole Technique for Computational Electromagnetics (Artech House, London, 1990).

I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, A. J. Viitanen, Electromagnetic Waves in Chiral and Bianisotropic Media (Artech House, Norwood, 1994).

A. Priou, ed., Bianisotropic and Biisotropic Media and Applications (EMW, Boston, 1994).

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Figures (1)

Fig. 1
Fig. 1

Scattering pattern of an infinitely long elliptical cylinder of a reciprocal uniaxial bianisotropic medium that is due to a normally incident TMz polarized wave. The constitutive parameters are taken to be μt/μ0=1.8, μz/μ0=1.2, t/0=2.5, z/0=2.1, α=0.3, β=0.4, and γ=0.7. The geometry parameters of the scatterer are taken to be with the semimajor axis=1.1λ0 and the semiminor axis=0.9λ0. The dotted curve corresponds to the case where the major axis of the scatterer is along the x axis, the dashed line for the major axis along the y axis, and the solid curve for the major axis taking an angle of 2π/9 with respect to the x axis.

Tables (1)

Tables Icon

Table 1 Convergence Test of an Infinitely Long Elliptical Cylinder of a Reciprocal Uniaxial Bianisotropic Medium That Is Due to a Normally Incident TMz-Polarized Wavea

Equations (39)

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

D=[]·E+[ξ]·H,
B=[μ]·H+[ζ]·E,
E(r)=q=12-dkzn=-(-i)neqn(kz)×[Aqe(kz)Mn(1)(kz, kρq)+Bqe(kz)Nn(1)(kz, kρq)+Cqe(kz)Ln(1)(kz, kρq)],
H(r)=q=12-dkzn=-(-i)neqn(kz)×[Aqh(kz)Mn(1)(kz, kρq)+Bqh(kz)Nn(1)(kz, kρq)+Cqh(kz)Ln(1)(kz, kρq)],
Mn(j)(kz, kρq)=×[Ψn(j)(kz, kρq)ez],
Nn(j)(kz, kρq)=1kq×Mn(j)(kz, kρq),
Ln(j)(kz, kρq)=Ψn(j)(kz, kρq),
Einc(r)=ez exp(-ik0x)=-dkzn=-(-i)nδ(kz)×Nn(1)(kz, kρ)/k0,
Hint(r)=-iey exp(-ik0x)/η0=-dkzn=-(-i)n-1δ(kz)×Mn(1)(kz, kρ)/(k0η0),
Esca(r)=-dkzn=-(-i)n[anMn(4)(kz, kρ)+bnNn(4)(kz, kρ)],
Hsca(r)=-dkzn=-(-i)n-1/η0[anNn(4)(kz, kρ)+bnMn(4)(kz, kρ)].
Eρint sin θ+Eϕint cos θ=(Eρinc+Eρsca)sin θ+(Eϕinc+Eϕsca)cos θ,
Ezint=Ezinc+Ezsca,
Hρint sin θ+Hϕint cos θ=(Hρinc+Hρsca)sin θ+(Hϕinc+Hϕsca)cos θ,
Hzint=Hzinc+Hzsca,
θ=tan-1f(ϕ)f(ϕ).
Vqnp(ρ)=-inρJn(kρqρ)Cqp(kz=0)-kρqJn(kρqρ)×Aqp(kz=0),
Xqnp(ρ)=kρqJn(kρqρ)Bqp(kz=0),
Yqnp(ρ)=-inρJn(kρqρ)Aqp(kz=0)+kρqJn(kρqρ)×Cqp(kz=0),
q=12[Iqe][eq]=[I(2)][a],
q=12[Iqh][eq]+k0iωμ0[I(2)][b]=[P][I],
q=12[Aqh][eq]=-k0iωμ0[I(5)][a],
q=12[Aqe][eq]-[I(5)][b]=[Q][I],
(Iqp)mn=ϕ=02π(-i)n exp[-i(n-m)ϕ]×[Yqnp(ρ)sin θ+Vqnp(ρ)cos θ]dϕ,
(I(2))mn=ϕ=02π(-i)n exp[-i(n-m)ϕ]×-inρHn(2)(k0ρ)×sin θ-k0Hn(2)(k0ρ)cos θdϕ,
(P)nm=1iωμ0ϕ=02π(-i)n exp[-i(n-m)ϕ]×inρJn(k0ρ)sin θ+k0Jn(k0ρ)cos θdϕ,
(Q)nm=ϕ=02π(-i)n exp[-i(n-m)ϕ]Jn(k0ρ)dϕ,
(Aqp)mn=ϕ=02π(-i)n exp[-i(n-m)ϕ]Xqnp(ρ)dϕ,
(I(5))mn=ϕ=02π(-i)n exp[-i(n-m)ϕ]k0×Hn(2)(k0ρ)dϕ,
[a]=iωμ0k0[I(2)]-1[D(1)]+[I(5)]-1[D(2)]-1·iωμ0k0[I(2)]-1[P]+[I(5)]-1[Q],
[b]=k0iωμ0[D(1)]-1[I(2)]+[D(2)]-1[I(5)]-1·{[D(1)]-1[P]-[D(2)]-1[Q]},
[D(1)]=[I1h][C(2)]+[I2h][C(1)],
[D(2)]=[A1e][C(2)]+[A2h][C(1)],
[C(1)]={[I1e]-1[I2e]-[A1h]-1[A2h]}-1·[I1e]-1[I(2)]+k0iωμ0[A1h]-1[I(5)],
[C(2)]={[I2e]-1[I1e]-[A2h]-1[A1h]}-1·[I2e]-1[I(2)]+k0iωμ0[A2h]-1[I(5)].
Aσ(ϕ)=limp 2πρRe{[Esca(r)]×[Hsca(r)]*}·eρRe{[Einc(r)]×[Hinc(r)]*}·ex,
Hn(2)(k0ρ)=2πk0ρ1/2 exp{-i[k0ρ-(2n+1)π/4]},
ρ,
Aσ(ϕ)=4k0n=-an exp(-inϕ)2+n=-bn exp(-inϕ)2.

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