Abstract

The oblique electromagnetic scattering by a dielectric elliptical cylinder which is coated eccentrically by a nonconfocal dielectric elliptical cylinder is examined in this work. The problem is solved using the separation of variables in terms of Mathieu functions, in combination with the addition theorem for Mathieu functions, a complicated procedure due to the following three factors: the nonexistence of the orthogonality relations for Mathieu functions due to the different constitutive parameters between the two cylinders and the background medium, the complex expressions due to the oblique incidence that leads to hybrid waves for both the scattered and induced fields, and the use of the addition theorem, which introduces a cross relation between even and odd terms. The method described here is exact, its solution is validated compared with other published results from the literature, and the high accuracy is revealed. Both polarizations are examined and numerical results are given for the scattering cross sections, including lossless and lossy materials.

© 2013 Optical Society of America

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References

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  1. J. H. Richmond, “Scattering by a conducting elliptic cylinder with dielectric coating,” Radio Sci. 23, 1061–1066 (1988).
    [CrossRef]
  2. A. K. Hamid and M. I. Hussein, “Electromagnetic scattering by a lossy dielectric-coated elliptic cylinder,” Can. J. Phys. 81, 771–778 (2003).
    [CrossRef]
  3. J. A. Roumeliotis, H. K. Manthopoulos, and V. K. Manthopoulos, “Electromagnetic scattering from an infinite circular metallic cylinder coated by an elliptic dielectric one,” IEEE Trans. Microwave Theor. Tech. 41, 862–869 (1993).
    [CrossRef]
  4. P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, 1953).
  5. G. P. Zouros and J. A. Roumeliotis, “Scattering by an infinite dielectric cylinder having an elliptic metal core: asymptotic solutions,” IEEE Trans. Antennas Propag. 58, 3299–3309(2010).
    [CrossRef]
  6. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).
  7. J. A. Roumeliotis and S. P. Savaidis, “Scattering by an infinite circular dielectric cylinder coating eccentrically an elliptic metallic one,” IEEE Trans. Antennas Propag. 44, 757–763 (1996).
    [CrossRef]
  8. S. P. Savaidis and J. A. Roumeliotis, “Scattering by an infinite circular dielectric cylinder coating eccentrically an elliptic dielectric cylinder,” IEEE Trans. Antennas Propag. 52, 1180–1185 (2004).
    [CrossRef]
  9. S. P. Savaidis and J. A. Roumeliotis, “Scattering by an infinite elliptic dielectric cylinder coating eccentrically a circular metallic or dielectric cylinder,” IEEE Trans. Microwave Theor. Tech. 45, 1792–1800 (1997).
    [CrossRef]
  10. H. Ragheb, L. Shafai, and M. Hamid, “Plane-wave scattering by a conducting elliptic cylinder coated by a nonconfocal dielectric,” IEEE Trans. Antennas Propag. 39, 218–223 (1991).
    [CrossRef]
  11. A. Sebak, H. Ragheb, and L. Shafai, “Plane-wave scattering by dielectric elliptic cylinder coated with nonconfocal dielectric,” Radio Sci. 29, 1393–1401 (1994).
    [CrossRef]
  12. J. L. Tsalamengas, “Exponentially converging Nyström methods applied to the integral–integrodifferential equations of oblique scattering/hybrid wave propagation in presence of composite dielectric cylinders of arbitrary cross section,” IEEE Trans. Antennas Propag. 55, 3239–3250 (2007).
    [CrossRef]
  13. C. S. Kim, “Scattering of an obliquely incident wave by a coated elliptical conducting cylinder,” J. Electromagn. Waves Appl. 5, 1169–1186 (1991).
    [CrossRef]
  14. C. S. Kim and C. Yeh, “Scattering of an obliquely incident wave by a multilayered elliptical lossy dielectric cylinder,” Radio Sci. 26, 1165–1176 (1991).
    [CrossRef]
  15. S. C. Mao, Z. S. Wu, and H. Y. Li, “Three-dimensional scattering by an infinite homogeneous anisotropic elliptic cylinder in terms of Mathieu functions,” J. Opt. Soc. Am. A 26, 2282–2291 (2009).
    [CrossRef]
  16. G. P. Zouros, “Electromagnetic plane wave scattering by arbitrarily oriented elliptical dielectric cylinders,” J. Opt. Soc. Am. A 28, 2376–2384 (2011).
    [CrossRef]
  17. G. P. Zouros and J. A. Roumeliotis, “Exact and closed-form cutoff wavenumbers of elliptical dielectric waveguides,” IEEE Trans. Microwave Theor. Tech. 60, 2741–2751 (2012).
    [CrossRef]
  18. C. H. Ziener, M. Rückl, T. Kampf, W. R. Bauer, and H. P. Schlemmer, “Mathieu functions for purely imaginary parameters,” J. Comput. Appl. Math. 236, 4513–4524 (2012).
    [CrossRef]
  19. A. M. Berezman, M. K. Kerimov, S. L. Skorokhodov, and G. A. Shadrin, “Calculation of the eigenvalues of Mathieu’s equation with a complex parameter,” Comput. Math. Math. Phys. 26, 48–55 (1986).
    [CrossRef]
  20. S. P. Savaidis, “Propagation and scattering of electromagnetic waves in eccentric circular-elliptic cylindrical conductor-dielectric configurations,” Ph.D. thesis (National Technical University of Athens, 1996) (in greek). Available online at http://phdtheses.ekt.gr/eadd/handle/10442/8872 .
  21. J. Meixner and F. W. Schäfke, Mathieusche Funktionen und Sphäroidfunktionen (Springer-Verlag, 1954).
  22. K. Særmark, “A note on addition theorems for Mathieu functions,” Z. angew. Math. Phys. 10, 426–428 (1959).
    [CrossRef]
  23. K. Særmark, “Scattering of a plane monochromatic wave by a system of strips,” Appl. Sci. Res. B 7, 417–440 (1959).
    [CrossRef]
  24. The Computation Laboratory of the National Applied Mathematics Laboratories, Tables Relating to Mathieu Functions (Columbia University, 1951).

2012 (2)

G. P. Zouros and J. A. Roumeliotis, “Exact and closed-form cutoff wavenumbers of elliptical dielectric waveguides,” IEEE Trans. Microwave Theor. Tech. 60, 2741–2751 (2012).
[CrossRef]

C. H. Ziener, M. Rückl, T. Kampf, W. R. Bauer, and H. P. Schlemmer, “Mathieu functions for purely imaginary parameters,” J. Comput. Appl. Math. 236, 4513–4524 (2012).
[CrossRef]

2011 (1)

2010 (1)

G. P. Zouros and J. A. Roumeliotis, “Scattering by an infinite dielectric cylinder having an elliptic metal core: asymptotic solutions,” IEEE Trans. Antennas Propag. 58, 3299–3309(2010).
[CrossRef]

2009 (1)

2007 (1)

J. L. Tsalamengas, “Exponentially converging Nyström methods applied to the integral–integrodifferential equations of oblique scattering/hybrid wave propagation in presence of composite dielectric cylinders of arbitrary cross section,” IEEE Trans. Antennas Propag. 55, 3239–3250 (2007).
[CrossRef]

2004 (1)

S. P. Savaidis and J. A. Roumeliotis, “Scattering by an infinite circular dielectric cylinder coating eccentrically an elliptic dielectric cylinder,” IEEE Trans. Antennas Propag. 52, 1180–1185 (2004).
[CrossRef]

2003 (1)

A. K. Hamid and M. I. Hussein, “Electromagnetic scattering by a lossy dielectric-coated elliptic cylinder,” Can. J. Phys. 81, 771–778 (2003).
[CrossRef]

1997 (1)

S. P. Savaidis and J. A. Roumeliotis, “Scattering by an infinite elliptic dielectric cylinder coating eccentrically a circular metallic or dielectric cylinder,” IEEE Trans. Microwave Theor. Tech. 45, 1792–1800 (1997).
[CrossRef]

1996 (1)

J. A. Roumeliotis and S. P. Savaidis, “Scattering by an infinite circular dielectric cylinder coating eccentrically an elliptic metallic one,” IEEE Trans. Antennas Propag. 44, 757–763 (1996).
[CrossRef]

1994 (1)

A. Sebak, H. Ragheb, and L. Shafai, “Plane-wave scattering by dielectric elliptic cylinder coated with nonconfocal dielectric,” Radio Sci. 29, 1393–1401 (1994).
[CrossRef]

1993 (1)

J. A. Roumeliotis, H. K. Manthopoulos, and V. K. Manthopoulos, “Electromagnetic scattering from an infinite circular metallic cylinder coated by an elliptic dielectric one,” IEEE Trans. Microwave Theor. Tech. 41, 862–869 (1993).
[CrossRef]

1991 (3)

H. Ragheb, L. Shafai, and M. Hamid, “Plane-wave scattering by a conducting elliptic cylinder coated by a nonconfocal dielectric,” IEEE Trans. Antennas Propag. 39, 218–223 (1991).
[CrossRef]

C. S. Kim, “Scattering of an obliquely incident wave by a coated elliptical conducting cylinder,” J. Electromagn. Waves Appl. 5, 1169–1186 (1991).
[CrossRef]

C. S. Kim and C. Yeh, “Scattering of an obliquely incident wave by a multilayered elliptical lossy dielectric cylinder,” Radio Sci. 26, 1165–1176 (1991).
[CrossRef]

1988 (1)

J. H. Richmond, “Scattering by a conducting elliptic cylinder with dielectric coating,” Radio Sci. 23, 1061–1066 (1988).
[CrossRef]

1986 (1)

A. M. Berezman, M. K. Kerimov, S. L. Skorokhodov, and G. A. Shadrin, “Calculation of the eigenvalues of Mathieu’s equation with a complex parameter,” Comput. Math. Math. Phys. 26, 48–55 (1986).
[CrossRef]

1959 (2)

K. Særmark, “A note on addition theorems for Mathieu functions,” Z. angew. Math. Phys. 10, 426–428 (1959).
[CrossRef]

K. Særmark, “Scattering of a plane monochromatic wave by a system of strips,” Appl. Sci. Res. B 7, 417–440 (1959).
[CrossRef]

Bauer, W. R.

C. H. Ziener, M. Rückl, T. Kampf, W. R. Bauer, and H. P. Schlemmer, “Mathieu functions for purely imaginary parameters,” J. Comput. Appl. Math. 236, 4513–4524 (2012).
[CrossRef]

Berezman, A. M.

A. M. Berezman, M. K. Kerimov, S. L. Skorokhodov, and G. A. Shadrin, “Calculation of the eigenvalues of Mathieu’s equation with a complex parameter,” Comput. Math. Math. Phys. 26, 48–55 (1986).
[CrossRef]

Feshbach, H.

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

Hamid, A. K.

A. K. Hamid and M. I. Hussein, “Electromagnetic scattering by a lossy dielectric-coated elliptic cylinder,” Can. J. Phys. 81, 771–778 (2003).
[CrossRef]

Hamid, M.

H. Ragheb, L. Shafai, and M. Hamid, “Plane-wave scattering by a conducting elliptic cylinder coated by a nonconfocal dielectric,” IEEE Trans. Antennas Propag. 39, 218–223 (1991).
[CrossRef]

Hussein, M. I.

A. K. Hamid and M. I. Hussein, “Electromagnetic scattering by a lossy dielectric-coated elliptic cylinder,” Can. J. Phys. 81, 771–778 (2003).
[CrossRef]

Kampf, T.

C. H. Ziener, M. Rückl, T. Kampf, W. R. Bauer, and H. P. Schlemmer, “Mathieu functions for purely imaginary parameters,” J. Comput. Appl. Math. 236, 4513–4524 (2012).
[CrossRef]

Kerimov, M. K.

A. M. Berezman, M. K. Kerimov, S. L. Skorokhodov, and G. A. Shadrin, “Calculation of the eigenvalues of Mathieu’s equation with a complex parameter,” Comput. Math. Math. Phys. 26, 48–55 (1986).
[CrossRef]

Kim, C. S.

C. S. Kim, “Scattering of an obliquely incident wave by a coated elliptical conducting cylinder,” J. Electromagn. Waves Appl. 5, 1169–1186 (1991).
[CrossRef]

C. S. Kim and C. Yeh, “Scattering of an obliquely incident wave by a multilayered elliptical lossy dielectric cylinder,” Radio Sci. 26, 1165–1176 (1991).
[CrossRef]

Li, H. Y.

Manthopoulos, H. K.

J. A. Roumeliotis, H. K. Manthopoulos, and V. K. Manthopoulos, “Electromagnetic scattering from an infinite circular metallic cylinder coated by an elliptic dielectric one,” IEEE Trans. Microwave Theor. Tech. 41, 862–869 (1993).
[CrossRef]

Manthopoulos, V. K.

J. A. Roumeliotis, H. K. Manthopoulos, and V. K. Manthopoulos, “Electromagnetic scattering from an infinite circular metallic cylinder coated by an elliptic dielectric one,” IEEE Trans. Microwave Theor. Tech. 41, 862–869 (1993).
[CrossRef]

Mao, S. C.

Meixner, J.

J. Meixner and F. W. Schäfke, Mathieusche Funktionen und Sphäroidfunktionen (Springer-Verlag, 1954).

Morse, P. M.

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

Ragheb, H.

A. Sebak, H. Ragheb, and L. Shafai, “Plane-wave scattering by dielectric elliptic cylinder coated with nonconfocal dielectric,” Radio Sci. 29, 1393–1401 (1994).
[CrossRef]

H. Ragheb, L. Shafai, and M. Hamid, “Plane-wave scattering by a conducting elliptic cylinder coated by a nonconfocal dielectric,” IEEE Trans. Antennas Propag. 39, 218–223 (1991).
[CrossRef]

Richmond, J. H.

J. H. Richmond, “Scattering by a conducting elliptic cylinder with dielectric coating,” Radio Sci. 23, 1061–1066 (1988).
[CrossRef]

Roumeliotis, J. A.

G. P. Zouros and J. A. Roumeliotis, “Exact and closed-form cutoff wavenumbers of elliptical dielectric waveguides,” IEEE Trans. Microwave Theor. Tech. 60, 2741–2751 (2012).
[CrossRef]

G. P. Zouros and J. A. Roumeliotis, “Scattering by an infinite dielectric cylinder having an elliptic metal core: asymptotic solutions,” IEEE Trans. Antennas Propag. 58, 3299–3309(2010).
[CrossRef]

S. P. Savaidis and J. A. Roumeliotis, “Scattering by an infinite circular dielectric cylinder coating eccentrically an elliptic dielectric cylinder,” IEEE Trans. Antennas Propag. 52, 1180–1185 (2004).
[CrossRef]

S. P. Savaidis and J. A. Roumeliotis, “Scattering by an infinite elliptic dielectric cylinder coating eccentrically a circular metallic or dielectric cylinder,” IEEE Trans. Microwave Theor. Tech. 45, 1792–1800 (1997).
[CrossRef]

J. A. Roumeliotis and S. P. Savaidis, “Scattering by an infinite circular dielectric cylinder coating eccentrically an elliptic metallic one,” IEEE Trans. Antennas Propag. 44, 757–763 (1996).
[CrossRef]

J. A. Roumeliotis, H. K. Manthopoulos, and V. K. Manthopoulos, “Electromagnetic scattering from an infinite circular metallic cylinder coated by an elliptic dielectric one,” IEEE Trans. Microwave Theor. Tech. 41, 862–869 (1993).
[CrossRef]

Rückl, M.

C. H. Ziener, M. Rückl, T. Kampf, W. R. Bauer, and H. P. Schlemmer, “Mathieu functions for purely imaginary parameters,” J. Comput. Appl. Math. 236, 4513–4524 (2012).
[CrossRef]

Særmark, K.

K. Særmark, “A note on addition theorems for Mathieu functions,” Z. angew. Math. Phys. 10, 426–428 (1959).
[CrossRef]

K. Særmark, “Scattering of a plane monochromatic wave by a system of strips,” Appl. Sci. Res. B 7, 417–440 (1959).
[CrossRef]

Savaidis, S. P.

S. P. Savaidis and J. A. Roumeliotis, “Scattering by an infinite circular dielectric cylinder coating eccentrically an elliptic dielectric cylinder,” IEEE Trans. Antennas Propag. 52, 1180–1185 (2004).
[CrossRef]

S. P. Savaidis and J. A. Roumeliotis, “Scattering by an infinite elliptic dielectric cylinder coating eccentrically a circular metallic or dielectric cylinder,” IEEE Trans. Microwave Theor. Tech. 45, 1792–1800 (1997).
[CrossRef]

J. A. Roumeliotis and S. P. Savaidis, “Scattering by an infinite circular dielectric cylinder coating eccentrically an elliptic metallic one,” IEEE Trans. Antennas Propag. 44, 757–763 (1996).
[CrossRef]

S. P. Savaidis, “Propagation and scattering of electromagnetic waves in eccentric circular-elliptic cylindrical conductor-dielectric configurations,” Ph.D. thesis (National Technical University of Athens, 1996) (in greek). Available online at http://phdtheses.ekt.gr/eadd/handle/10442/8872 .

Schäfke, F. W.

J. Meixner and F. W. Schäfke, Mathieusche Funktionen und Sphäroidfunktionen (Springer-Verlag, 1954).

Schlemmer, H. P.

C. H. Ziener, M. Rückl, T. Kampf, W. R. Bauer, and H. P. Schlemmer, “Mathieu functions for purely imaginary parameters,” J. Comput. Appl. Math. 236, 4513–4524 (2012).
[CrossRef]

Sebak, A.

A. Sebak, H. Ragheb, and L. Shafai, “Plane-wave scattering by dielectric elliptic cylinder coated with nonconfocal dielectric,” Radio Sci. 29, 1393–1401 (1994).
[CrossRef]

Shadrin, G. A.

A. M. Berezman, M. K. Kerimov, S. L. Skorokhodov, and G. A. Shadrin, “Calculation of the eigenvalues of Mathieu’s equation with a complex parameter,” Comput. Math. Math. Phys. 26, 48–55 (1986).
[CrossRef]

Shafai, L.

A. Sebak, H. Ragheb, and L. Shafai, “Plane-wave scattering by dielectric elliptic cylinder coated with nonconfocal dielectric,” Radio Sci. 29, 1393–1401 (1994).
[CrossRef]

H. Ragheb, L. Shafai, and M. Hamid, “Plane-wave scattering by a conducting elliptic cylinder coated by a nonconfocal dielectric,” IEEE Trans. Antennas Propag. 39, 218–223 (1991).
[CrossRef]

Skorokhodov, S. L.

A. M. Berezman, M. K. Kerimov, S. L. Skorokhodov, and G. A. Shadrin, “Calculation of the eigenvalues of Mathieu’s equation with a complex parameter,” Comput. Math. Math. Phys. 26, 48–55 (1986).
[CrossRef]

Stratton, J. A.

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

Tsalamengas, J. L.

J. L. Tsalamengas, “Exponentially converging Nyström methods applied to the integral–integrodifferential equations of oblique scattering/hybrid wave propagation in presence of composite dielectric cylinders of arbitrary cross section,” IEEE Trans. Antennas Propag. 55, 3239–3250 (2007).
[CrossRef]

Wu, Z. S.

Yeh, C.

C. S. Kim and C. Yeh, “Scattering of an obliquely incident wave by a multilayered elliptical lossy dielectric cylinder,” Radio Sci. 26, 1165–1176 (1991).
[CrossRef]

Ziener, C. H.

C. H. Ziener, M. Rückl, T. Kampf, W. R. Bauer, and H. P. Schlemmer, “Mathieu functions for purely imaginary parameters,” J. Comput. Appl. Math. 236, 4513–4524 (2012).
[CrossRef]

Zouros, G. P.

G. P. Zouros and J. A. Roumeliotis, “Exact and closed-form cutoff wavenumbers of elliptical dielectric waveguides,” IEEE Trans. Microwave Theor. Tech. 60, 2741–2751 (2012).
[CrossRef]

G. P. Zouros, “Electromagnetic plane wave scattering by arbitrarily oriented elliptical dielectric cylinders,” J. Opt. Soc. Am. A 28, 2376–2384 (2011).
[CrossRef]

G. P. Zouros and J. A. Roumeliotis, “Scattering by an infinite dielectric cylinder having an elliptic metal core: asymptotic solutions,” IEEE Trans. Antennas Propag. 58, 3299–3309(2010).
[CrossRef]

Appl. Sci. Res. B (1)

K. Særmark, “Scattering of a plane monochromatic wave by a system of strips,” Appl. Sci. Res. B 7, 417–440 (1959).
[CrossRef]

Can. J. Phys. (1)

A. K. Hamid and M. I. Hussein, “Electromagnetic scattering by a lossy dielectric-coated elliptic cylinder,” Can. J. Phys. 81, 771–778 (2003).
[CrossRef]

Comput. Math. Math. Phys. (1)

A. M. Berezman, M. K. Kerimov, S. L. Skorokhodov, and G. A. Shadrin, “Calculation of the eigenvalues of Mathieu’s equation with a complex parameter,” Comput. Math. Math. Phys. 26, 48–55 (1986).
[CrossRef]

IEEE Trans. Antennas Propag. (5)

J. L. Tsalamengas, “Exponentially converging Nyström methods applied to the integral–integrodifferential equations of oblique scattering/hybrid wave propagation in presence of composite dielectric cylinders of arbitrary cross section,” IEEE Trans. Antennas Propag. 55, 3239–3250 (2007).
[CrossRef]

G. P. Zouros and J. A. Roumeliotis, “Scattering by an infinite dielectric cylinder having an elliptic metal core: asymptotic solutions,” IEEE Trans. Antennas Propag. 58, 3299–3309(2010).
[CrossRef]

J. A. Roumeliotis and S. P. Savaidis, “Scattering by an infinite circular dielectric cylinder coating eccentrically an elliptic metallic one,” IEEE Trans. Antennas Propag. 44, 757–763 (1996).
[CrossRef]

S. P. Savaidis and J. A. Roumeliotis, “Scattering by an infinite circular dielectric cylinder coating eccentrically an elliptic dielectric cylinder,” IEEE Trans. Antennas Propag. 52, 1180–1185 (2004).
[CrossRef]

H. Ragheb, L. Shafai, and M. Hamid, “Plane-wave scattering by a conducting elliptic cylinder coated by a nonconfocal dielectric,” IEEE Trans. Antennas Propag. 39, 218–223 (1991).
[CrossRef]

IEEE Trans. Microwave Theor. Tech. (3)

S. P. Savaidis and J. A. Roumeliotis, “Scattering by an infinite elliptic dielectric cylinder coating eccentrically a circular metallic or dielectric cylinder,” IEEE Trans. Microwave Theor. Tech. 45, 1792–1800 (1997).
[CrossRef]

J. A. Roumeliotis, H. K. Manthopoulos, and V. K. Manthopoulos, “Electromagnetic scattering from an infinite circular metallic cylinder coated by an elliptic dielectric one,” IEEE Trans. Microwave Theor. Tech. 41, 862–869 (1993).
[CrossRef]

G. P. Zouros and J. A. Roumeliotis, “Exact and closed-form cutoff wavenumbers of elliptical dielectric waveguides,” IEEE Trans. Microwave Theor. Tech. 60, 2741–2751 (2012).
[CrossRef]

J. Comput. Appl. Math. (1)

C. H. Ziener, M. Rückl, T. Kampf, W. R. Bauer, and H. P. Schlemmer, “Mathieu functions for purely imaginary parameters,” J. Comput. Appl. Math. 236, 4513–4524 (2012).
[CrossRef]

J. Electromagn. Waves Appl. (1)

C. S. Kim, “Scattering of an obliquely incident wave by a coated elliptical conducting cylinder,” J. Electromagn. Waves Appl. 5, 1169–1186 (1991).
[CrossRef]

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

Radio Sci. (3)

C. S. Kim and C. Yeh, “Scattering of an obliquely incident wave by a multilayered elliptical lossy dielectric cylinder,” Radio Sci. 26, 1165–1176 (1991).
[CrossRef]

J. H. Richmond, “Scattering by a conducting elliptic cylinder with dielectric coating,” Radio Sci. 23, 1061–1066 (1988).
[CrossRef]

A. Sebak, H. Ragheb, and L. Shafai, “Plane-wave scattering by dielectric elliptic cylinder coated with nonconfocal dielectric,” Radio Sci. 29, 1393–1401 (1994).
[CrossRef]

Z. angew. Math. Phys. (1)

K. Særmark, “A note on addition theorems for Mathieu functions,” Z. angew. Math. Phys. 10, 426–428 (1959).
[CrossRef]

Other (5)

S. P. Savaidis, “Propagation and scattering of electromagnetic waves in eccentric circular-elliptic cylindrical conductor-dielectric configurations,” Ph.D. thesis (National Technical University of Athens, 1996) (in greek). Available online at http://phdtheses.ekt.gr/eadd/handle/10442/8872 .

J. Meixner and F. W. Schäfke, Mathieusche Funktionen und Sphäroidfunktionen (Springer-Verlag, 1954).

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

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

The Computation Laboratory of the National Applied Mathematics Laboratories, Tables Relating to Mathieu Functions (Columbia University, 1951).

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Figures (9)

Fig. 1.
Fig. 1.

Geometry of the configuration.

Fig. 2.
Fig. 2.

Back scattering cross section versus incident angle ψ for the concentric configuration depicted in the figure. Solid curves, ϵ 2 / ϵ 1 = 2.54 ; dashed curves, ϵ 2 / ϵ 1 = 2.54 j 0.5 ; dash-dotted curves, ϵ 2 / ϵ 1 = 2.54 j 1 . Red curves, E -wave; blue curves, H -wave. The rest parameters are ϵ 3 / ϵ 1 = 4 , μ 2 / μ 1 = 1 , μ 3 / μ 1 = 1 , k 1 c 0 = 2 π , k 1 c 0 = π , k 1 d 0 = 0 , d = 0.6 , d = 0.8 , θ = 45 ° , α = 0 ° , and γ = 0 ° .

Fig. 3.
Fig. 3.

Forward scattering cross section versus incident angle ψ for the concentric configuration depicted in the figure. The graph legends and the values of the parameters are the same as in Fig. 2.

Fig. 4.
Fig. 4.

Total scattering cross section versus incident angle ψ for the concentric configuration depicted in the figure. The graph legends and the values of the parameters are the same as in Fig. 2.

Fig. 5.
Fig. 5.

Back scattering cross section versus incident angle ψ for the eccentric configuration depicted in the figure. Solid curves, θ = 10 ° ; dashed curves, θ = 30 ° ; dash-dotted curves, θ = 80 ° . Red curves, E -wave; blue curves, H -wave. The rest parameters are ϵ 2 / ϵ 1 = 2.54 , ϵ 3 / ϵ 1 = 4 , μ 2 / μ 1 = 1 , μ 3 / μ 1 = 1 , k 1 c 0 = 2 π , k 1 c 0 = π , k 1 d 0 = π , d = 0.6 , d = 0.8 , α = 0 ° , γ = 0 ° .

Fig. 6.
Fig. 6.

Forward scattering cross section versus incident angle ψ for the eccentric configuration depicted in the figure. The graph legends and the values of the parameters are the same as in Fig. 5.

Fig. 7.
Fig. 7.

Total scattering cross section versus incident angle ψ for the eccentric configuration depicted in the figure. The graph legends and the values of the parameters are the same as in Fig. 5.

Fig. 8.
Fig. 8.

Back scattering cross section in dB versus k 1 c 0 for the concentric configuration depicted in the figure. Solid curves, θ = 10 ° ; dashed curves, θ = 85 ° . Red curves, E -wave; blue curves, H -wave. The rest parameters are ϵ 2 / ϵ 1 = 2.54 , ϵ 3 / ϵ 1 = 4 , μ 2 / μ 1 = 1 , μ 3 / μ 1 = 1 , k 1 c 0 = k 1 c 0 / 2 , k 1 d 0 = 0 , d = 0.6 , d = 0.8 , ψ = 30 ° , α = 0 ° , and γ = 45 ° .

Fig. 9.
Fig. 9.

Back scattering cross section in dB versus k 1 c 0 for the concentric configuration depicted in the figure. Red curve, ϵ 2 / ϵ 1 = 2.54 j 0.5 ; blue curve, ϵ 2 / ϵ 1 = 2.54 j 1 ; green curve, ϵ 2 / ϵ 1 = 2.54 j 2 . The rest parameters are ϵ 3 / ϵ 1 = 4 , μ 2 / μ 1 = 1 , μ 3 / μ 1 = 1 , k 1 c 0 = k 1 c 0 / 2 , k 1 d 0 = 0 , d = 0.6 , d = 0.8 , ψ = 30 ° , θ = 10 ° , α = 0 ° , and γ = 45 ° .

Tables (4)

Tables Icon

Table 1. Comparison of the Current Work with Previously Published Results: E -Wave Polarization

Tables Icon

Table 2. Comparison of the Current Work with Previously Published Results: H -Wave Polarization

Tables Icon

Table 3. Comparison of the Current Work with Previously Published Results, under Oblique Incidence, with the Presence of a Perfectly Conducting Strip

Tables Icon

Table 4. Total Near Fields on the Elliptic Boundaries

Equations (15)

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E z i = 8 π [ m = 0 j m S e m ( q 1 , cos ψ ) M m e ( q 1 ) J e m ( q 1 , cosh η 1 ) × S e m ( q 1 , cos φ 1 ) + m = 1 j m S o m ( q 1 , cos ψ ) M m o ( q 1 ) × J o m ( q 1 , cosh η 1 ) S o m ( q 1 , cos φ 1 ) ] e j β z ,
[ E z sc H z sc ] = { m = 0 [ A m e R m e ] H e m ( q 1 , cosh η 1 ) S e m ( q 1 , cos φ 1 ) + m = 1 [ A m o R m o ] H o m ( q 1 , cosh η 1 ) S o m ( q 1 , cos φ 1 ) } e j β z ,
[ E z II H z II ] = ( m = 0 { [ D m e L m e ] J e m ( h 2 , cosh η 2 ) + [ F m e N m e ] Y e m ( h 2 , cosh η 2 ) } S e m ( h 2 , cos φ 2 ) + m = 1 { [ D m o L m o ] J o m ( h 2 , cosh η 2 ) + [ F m o N m o ] Y o m ( h 2 , cosh η 2 ) } S o m ( h 2 , cos φ 2 ) ) e j β z ,
[ E z III H z III ] = { m = 0 [ C m e G m e ] J e m ( h 3 , cosh η 2 ) S e m ( h 3 , cos φ 2 ) + m = 1 [ C m o G m o ] J o m ( h 3 , cosh η 2 ) S o m ( h 3 , cos φ 2 ) } e j β z ,
cos θ m = 1 A m o H o m ( q 1 , cosh η A ) M m s o e ( q 1 , q 2 ) μ 1 ϵ 1 m = 0 R m e H e m ( q 1 , cosh η A ) M m s e ( q 1 , q 2 ) ϵ 1 ϵ 2 μ 1 μ 2 cos θ m = 0 i = 1 [ D m e J o i ( q 2 , cosh η A ) + F m e Y o i ( q 2 , cosh η A ) ] W i m e M i s o e ( q 2 ) ϵ 1 ϵ 2 μ 1 μ 2 cos θ m = 1 i = 1 [ D m o J o i ( q 2 , cosh η A ) + F m o Y o i ( q 2 , cosh η A ) ] W i m o M i s o e ( q 2 ) + ϵ 1 ϵ 2 μ 1 ϵ 1 m = 0 [ L m e J e s ( q 2 , cosh η A ) + N m e Y e s ( q 2 , cosh η A ) ] V s m e M s e ( q 2 ) + ϵ 1 ϵ 2 μ 1 ϵ 1 m = 1 [ L m o J e s ( q 2 , cosh η A ) + N m o Y e s ( q 2 , cosh η A ) ] V s m o M s e ( q 2 ) = cos θ 8 π m = 1 j m S o m ( q 1 , cos ψ ) M m o ( q 1 ) J o m ( q 1 , cosh η A ) M m s o e ( q 1 , q 2 ) , s = 0 , 1 , 2 ,
M ν ( η 2 , t 2 ) m e ν ( φ 2 , t 2 2 ) = ξ = A ξ ν M ξ ( η 1 , t 1 ) × m e ξ ( φ 1 , t 1 2 ) , ν = , 2 , 1 , 0 , 1 , 2 , ,
A ξ ν = ( 1 ) ξ ν q = p = ( 1 ) p q c 2 p ν ( t 2 2 ) c 2 q ξ ( t 1 2 ) × e j ( ν + 2 p ) ( γ α ) J ( ν + 2 p ) ( ξ + 2 q ) ( k d 0 ) e j [ ( ξ + 2 q ) ] α , ξ , ν = , 2 , 1 , 0 , 1 , 2 ,
c r m m ( t 2 ) = c r m m ( t 2 ) = π 2 M m e ( h ) B r e ( h , m ) , r = 1 , 2 , , m = 0 , 1 ,
c m m ( t 2 ) = 2 π M m e ( h ) B r e ( h , m ) , r = 0 , m = 0 , 1 ,
c r + m m ( t 2 ) = c r + m m ( t 2 ) = π 2 M m o ( h ) B r o ( h , m ) , r , m = 1 , 2 ,
m e ν ν ( φ , t 2 ) = j 1 2 2 π M ν o e ( h ) S ν o e ( h , cos φ ) , ν 0 1 ,
M ν ν ( η , t ) = ( 1 ) q 2 2 π Z ν o e ( h , cosh η ) , ν 0 1 .
Z ν o e ( h 2 , cosh η 2 ) S ν o e ( h 2 , cos φ 2 ) = ξ = 0 V ξ ν o e Z e ξ ( h 1 , cosh η 1 ) S e ξ ( h 1 , cos φ 1 ) + ξ = 1 W ξ ν o e Z o ξ ( h 1 , cosh η 1 ) S o ξ ( h 1 , cos φ 1 ) , ν = 0 , 1 , ,
[ V ξ ν e V ξ ν o ] = [ ( 1 ) 3 ξ / 2 3 ν / 2 ( 1 ) 3 ξ / 2 + 5 ν / 2 ] π M ξ e ( h 1 ) × q = 0 [ p = 0 p = 1 ] ( 1 ) q / 2 p / 2 B q e ( h 1 , ξ ) [ B p e ( h 2 , ν ) B p o ( h 2 , ν ) ] × { J q p ( k d 0 ) [ cos [ p ( α γ ) q α ] sin [ p ( α γ ) q α ] ] + ( 1 ) p J p + q ( k d 0 ) [ cos [ p ( α γ ) + q α ] sin [ p ( α γ ) + q α ] ] } ,
[ W ξ ν e W ξ ν o ] = [ ( 1 ) ξ / 2 3 ν / 2 ( 1 ) ξ / 2 + 5 ν / 2 ] π M ξ o ( h 1 ) × q = 1 [ p = 0 p = 1 ] ( 1 ) q / 2 p / 2 B q o ( h 1 , ξ ) [ B p e ( h 2 , ν ) B p o ( h 2 , ν ) ] × { J q p ( k d 0 ) [ sin [ p ( α γ ) q α ] cos [ p ( α γ ) q α ] ] ( 1 ) p J p + q ( k d 0 ) [ sin [ p ( α γ ) + q α ] cos [ p ( α γ ) + q α ] ] } .

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