Abstract

This paper presents a theoretical treatment of scattering by a radially stratified infinite cylinder buried in an absorbing, i.e., lossy, half-space. The permeability and refractive index of the host medium and cylinder layers are generally complex. The half-space is irradiated by an arbitrarily polarized plane wave that propagates in the plane perpendicular to the axis of the cylinder. The theoretical formulation rigorously accounts for the Fresnel effect at the half-space interface, interaction of the cylinder with scattered waves that are reflected from the interface, and attenuation of the propagating waves by the host medium. Analytical formulas are derived for the electric and magnetic fields and Poynting vector of the scattered waves emerging from the half-space. Numerical results on backscattering are shown for the cases of a homogeneous and a hollow cylinder buried at various depths in an absorbing half-space.

© 2013 Optical Society of America

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References

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  1. H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).
  2. B. J. Davis, P. S. Carney, and R. Bhargava, “Theory of infrared microspectroscopy for intact fibers,” Anal. Chem. 83, 525–532 (2011).
    [CrossRef]
  3. S. C. Lee and G. R. Cunnington, “Theoretical models for radiative transfer in fibrous media,” in Annual Review of Heat Transfer, C. L. Tien, ed., (Begell House, 1998), Vol. 9, pp. 159–212.
  4. R. Ruppin, “Extinction by a circular cylinder in an absorbing medium,” Opt. Commun. 211, 335–340 (2002).
    [CrossRef]
  5. W. Sun, N. G. Loeb, and B. Lin, “Light scattering by an infinite circular cylinder immersed in an absorbing medium,” Appl. Opt. 44, 2338–2342 (2005).
    [CrossRef]
  6. W. Sun, N. G. Loeb, S. Tanev, and G. Videen, “Finite-difference time-domain solution of light scattering by an infinite dielectric column immersed in an absorbing medium,” Appl. Opt. 44, 1977–1983 (2005).
    [CrossRef]
  7. S. C. Lee, “Light scattering by a coated infinite cylinder in an absorbing medium,” J. Opt. Soc. Am. A 28, 1067–1075(2011).
    [CrossRef]
  8. T. C. Rao and R. Barakat, “Plane-wave scattering by a conducting cylinder partially buried in a ground plane. I: TM case,” J. Opt. Soc. Am. A 6, 1270–1280 (1989).
    [CrossRef]
  9. T. C. Rao and R. Barakat, “Plane-wave scattering by a conducting cylinder partially buried in a ground plane. II: TE case,” J. Opt. Soc. Am. A 8, 1986–1990 (1991).
    [CrossRef]
  10. T. C. Rao and R. Barakat, “Plane wave scattering by a finite array of conducting cylinders partially buried in a ground plane: TM polarization,” Appl. Opt. 3, 1023–1047 (1994).
    [CrossRef]
  11. R. Borghi, F. Gori, M. Santarsiero, F. Frezza, and G. Schettini, “Plane-wave scattering by a set of perfectly conducting circular cylinder in the presence of a plane surface,” J. Opt. Soc. Am. A 13, 2441–2456 (1996).
    [CrossRef]
  12. S. C. Lee and J. A. Grzesik, “Light scattering by closely spaced parallel cylinders embedded in a semi-infinite dielectric medium,” J. Opt. Soc. Am. A 15, 163–173 (1998).
    [CrossRef]
  13. S. C. Lee, “Light scattering by closely spaced parallel cylinders embedded in a finite dielectric slab,” J. Opt. Soc. Am. A 16, 1350–1361 (1999).
    [CrossRef]
  14. S. J. Radzevocois and J. L. Daniels, “Ground penetrating radar polarization and scattering from cylinders,” J. Appl. Geophys. 45, 111–125 (2000).
    [CrossRef]
  15. M. Di Vico, F. Frezza, L. Pajewski, and G. Schettini, “Scattering by a finite set of perfectly conducting cylinders buried in a dielectric half-space: a spectral-domain solution,” IEEE Trans. Antennas Propag. 53, 719–727 (2005).
    [CrossRef]
  16. H. Jia and K. Yasumoto, “Scattering and absorption characteristics of multilayered gratings embedded in a dielectric slab,” Int. J. Infrared Millim. Waves 26, 1111–1126 (2005).
    [CrossRef]
  17. S. C. Lee, “Optical extinction by closely spaced parallel cylinders inside a finite dielectric slab,” J. Opt. Soc. Am. A 23, 2219–2232 (2006).
    [CrossRef]
  18. F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by perfectly conducting circular cylinders buried in a dielectric slab through the cylindrical wave approach,” IEEE Trans. Antennas Propag. 57, 1208–1217 (2009).
    [CrossRef]
  19. F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by dielectric circular cylinders in a dielectric slab,” J. Opt. Soc. Am. A 27, 687–695 (2010).
    [CrossRef]
  20. J. R. Parry and S. H. Ward, “Electromagnetic scattering from cylinders of arbitrary cross-section in a conductive half-space,” Geophysics 36, 67–100 (1971).
    [CrossRef]
  21. M. K. Moaveni, A. A. Rizvi, and B. A. Kamran, “Plane-wave scattering by gratings of conducting cylinders in an inhomogeneous and lossy dielectric,” J. Opt. Soc. Am. A 5, 834–843 (1988).
    [CrossRef]
  22. S. F. Mahmoud, S. M. Ali, and J. R. Wait, “Electromagnetic scattering from buried cylindrical inhomogeneity inside a lossy earth,” Radio Sci. 16, 1285–1298 (1981).
    [CrossRef]
  23. J. D. Kanellopoulos and N. E. Buris, “Scattering from conducting cylinders embedded in a lossy medium,” Int. J. Electron. 57, 391–401 (1984).
    [CrossRef]
  24. F. Frezza, G. Schettini, L. Pajewski, C. Ponti, and N. Tedeschi, “Electromagnetic scattering by a metallic cylinder buried in a lossy medium with the cylindrical-wave approach,” IEEE Geosci. Remote Sens. Lett. 10, 179–183(2013).
    [CrossRef]
  25. F. Frezza, G. Schettini, and N. Tedeschi, “Generalized plane-wave expansion of cylindrical functions in lossy media convergent in the whole complex plane,” Opt. Commun. 284, 3867–3871 (2011).
    [CrossRef]
  26. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).
  27. S. C. Lee, “Scattering by closely spaced parallel nonhomogeneous cylinders in an absorbing medium,” J. Opt. Soc. Am. A 28, 1812–1819 (2011).
    [CrossRef]

2013 (1)

F. Frezza, G. Schettini, L. Pajewski, C. Ponti, and N. Tedeschi, “Electromagnetic scattering by a metallic cylinder buried in a lossy medium with the cylindrical-wave approach,” IEEE Geosci. Remote Sens. Lett. 10, 179–183(2013).
[CrossRef]

2011 (4)

F. Frezza, G. Schettini, and N. Tedeschi, “Generalized plane-wave expansion of cylindrical functions in lossy media convergent in the whole complex plane,” Opt. Commun. 284, 3867–3871 (2011).
[CrossRef]

B. J. Davis, P. S. Carney, and R. Bhargava, “Theory of infrared microspectroscopy for intact fibers,” Anal. Chem. 83, 525–532 (2011).
[CrossRef]

S. C. Lee, “Light scattering by a coated infinite cylinder in an absorbing medium,” J. Opt. Soc. Am. A 28, 1067–1075(2011).
[CrossRef]

S. C. Lee, “Scattering by closely spaced parallel nonhomogeneous cylinders in an absorbing medium,” J. Opt. Soc. Am. A 28, 1812–1819 (2011).
[CrossRef]

2010 (1)

2009 (1)

F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by perfectly conducting circular cylinders buried in a dielectric slab through the cylindrical wave approach,” IEEE Trans. Antennas Propag. 57, 1208–1217 (2009).
[CrossRef]

2006 (1)

2005 (4)

M. Di Vico, F. Frezza, L. Pajewski, and G. Schettini, “Scattering by a finite set of perfectly conducting cylinders buried in a dielectric half-space: a spectral-domain solution,” IEEE Trans. Antennas Propag. 53, 719–727 (2005).
[CrossRef]

H. Jia and K. Yasumoto, “Scattering and absorption characteristics of multilayered gratings embedded in a dielectric slab,” Int. J. Infrared Millim. Waves 26, 1111–1126 (2005).
[CrossRef]

W. Sun, N. G. Loeb, S. Tanev, and G. Videen, “Finite-difference time-domain solution of light scattering by an infinite dielectric column immersed in an absorbing medium,” Appl. Opt. 44, 1977–1983 (2005).
[CrossRef]

W. Sun, N. G. Loeb, and B. Lin, “Light scattering by an infinite circular cylinder immersed in an absorbing medium,” Appl. Opt. 44, 2338–2342 (2005).
[CrossRef]

2002 (1)

R. Ruppin, “Extinction by a circular cylinder in an absorbing medium,” Opt. Commun. 211, 335–340 (2002).
[CrossRef]

2000 (1)

S. J. Radzevocois and J. L. Daniels, “Ground penetrating radar polarization and scattering from cylinders,” J. Appl. Geophys. 45, 111–125 (2000).
[CrossRef]

1999 (1)

1998 (1)

1996 (1)

1994 (1)

1991 (1)

1989 (1)

1988 (1)

1984 (1)

J. D. Kanellopoulos and N. E. Buris, “Scattering from conducting cylinders embedded in a lossy medium,” Int. J. Electron. 57, 391–401 (1984).
[CrossRef]

1981 (1)

S. F. Mahmoud, S. M. Ali, and J. R. Wait, “Electromagnetic scattering from buried cylindrical inhomogeneity inside a lossy earth,” Radio Sci. 16, 1285–1298 (1981).
[CrossRef]

1971 (1)

J. R. Parry and S. H. Ward, “Electromagnetic scattering from cylinders of arbitrary cross-section in a conductive half-space,” Geophysics 36, 67–100 (1971).
[CrossRef]

Ali, S. M.

S. F. Mahmoud, S. M. Ali, and J. R. Wait, “Electromagnetic scattering from buried cylindrical inhomogeneity inside a lossy earth,” Radio Sci. 16, 1285–1298 (1981).
[CrossRef]

Barakat, R.

Bhargava, R.

B. J. Davis, P. S. Carney, and R. Bhargava, “Theory of infrared microspectroscopy for intact fibers,” Anal. Chem. 83, 525–532 (2011).
[CrossRef]

Borghi, R.

Buris, N. E.

J. D. Kanellopoulos and N. E. Buris, “Scattering from conducting cylinders embedded in a lossy medium,” Int. J. Electron. 57, 391–401 (1984).
[CrossRef]

Carney, P. S.

B. J. Davis, P. S. Carney, and R. Bhargava, “Theory of infrared microspectroscopy for intact fibers,” Anal. Chem. 83, 525–532 (2011).
[CrossRef]

Cunnington, G. R.

S. C. Lee and G. R. Cunnington, “Theoretical models for radiative transfer in fibrous media,” in Annual Review of Heat Transfer, C. L. Tien, ed., (Begell House, 1998), Vol. 9, pp. 159–212.

Daniels, J. L.

S. J. Radzevocois and J. L. Daniels, “Ground penetrating radar polarization and scattering from cylinders,” J. Appl. Geophys. 45, 111–125 (2000).
[CrossRef]

Davis, B. J.

B. J. Davis, P. S. Carney, and R. Bhargava, “Theory of infrared microspectroscopy for intact fibers,” Anal. Chem. 83, 525–532 (2011).
[CrossRef]

Di Vico, M.

M. Di Vico, F. Frezza, L. Pajewski, and G. Schettini, “Scattering by a finite set of perfectly conducting cylinders buried in a dielectric half-space: a spectral-domain solution,” IEEE Trans. Antennas Propag. 53, 719–727 (2005).
[CrossRef]

Frezza, F.

F. Frezza, G. Schettini, L. Pajewski, C. Ponti, and N. Tedeschi, “Electromagnetic scattering by a metallic cylinder buried in a lossy medium with the cylindrical-wave approach,” IEEE Geosci. Remote Sens. Lett. 10, 179–183(2013).
[CrossRef]

F. Frezza, G. Schettini, and N. Tedeschi, “Generalized plane-wave expansion of cylindrical functions in lossy media convergent in the whole complex plane,” Opt. Commun. 284, 3867–3871 (2011).
[CrossRef]

F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by dielectric circular cylinders in a dielectric slab,” J. Opt. Soc. Am. A 27, 687–695 (2010).
[CrossRef]

F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by perfectly conducting circular cylinders buried in a dielectric slab through the cylindrical wave approach,” IEEE Trans. Antennas Propag. 57, 1208–1217 (2009).
[CrossRef]

M. Di Vico, F. Frezza, L. Pajewski, and G. Schettini, “Scattering by a finite set of perfectly conducting cylinders buried in a dielectric half-space: a spectral-domain solution,” IEEE Trans. Antennas Propag. 53, 719–727 (2005).
[CrossRef]

R. Borghi, F. Gori, M. Santarsiero, F. Frezza, and G. Schettini, “Plane-wave scattering by a set of perfectly conducting circular cylinder in the presence of a plane surface,” J. Opt. Soc. Am. A 13, 2441–2456 (1996).
[CrossRef]

Gori, F.

Grzesik, J. A.

Jia, H.

H. Jia and K. Yasumoto, “Scattering and absorption characteristics of multilayered gratings embedded in a dielectric slab,” Int. J. Infrared Millim. Waves 26, 1111–1126 (2005).
[CrossRef]

Kamran, B. A.

Kanellopoulos, J. D.

J. D. Kanellopoulos and N. E. Buris, “Scattering from conducting cylinders embedded in a lossy medium,” Int. J. Electron. 57, 391–401 (1984).
[CrossRef]

Lee, S. C.

Lin, B.

Loeb, N. G.

Mahmoud, S. F.

S. F. Mahmoud, S. M. Ali, and J. R. Wait, “Electromagnetic scattering from buried cylindrical inhomogeneity inside a lossy earth,” Radio Sci. 16, 1285–1298 (1981).
[CrossRef]

Moaveni, M. K.

Pajewski, L.

F. Frezza, G. Schettini, L. Pajewski, C. Ponti, and N. Tedeschi, “Electromagnetic scattering by a metallic cylinder buried in a lossy medium with the cylindrical-wave approach,” IEEE Geosci. Remote Sens. Lett. 10, 179–183(2013).
[CrossRef]

F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by dielectric circular cylinders in a dielectric slab,” J. Opt. Soc. Am. A 27, 687–695 (2010).
[CrossRef]

F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by perfectly conducting circular cylinders buried in a dielectric slab through the cylindrical wave approach,” IEEE Trans. Antennas Propag. 57, 1208–1217 (2009).
[CrossRef]

M. Di Vico, F. Frezza, L. Pajewski, and G. Schettini, “Scattering by a finite set of perfectly conducting cylinders buried in a dielectric half-space: a spectral-domain solution,” IEEE Trans. Antennas Propag. 53, 719–727 (2005).
[CrossRef]

Parry, J. R.

J. R. Parry and S. H. Ward, “Electromagnetic scattering from cylinders of arbitrary cross-section in a conductive half-space,” Geophysics 36, 67–100 (1971).
[CrossRef]

Ponti, C.

F. Frezza, G. Schettini, L. Pajewski, C. Ponti, and N. Tedeschi, “Electromagnetic scattering by a metallic cylinder buried in a lossy medium with the cylindrical-wave approach,” IEEE Geosci. Remote Sens. Lett. 10, 179–183(2013).
[CrossRef]

F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by dielectric circular cylinders in a dielectric slab,” J. Opt. Soc. Am. A 27, 687–695 (2010).
[CrossRef]

F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by perfectly conducting circular cylinders buried in a dielectric slab through the cylindrical wave approach,” IEEE Trans. Antennas Propag. 57, 1208–1217 (2009).
[CrossRef]

Radzevocois, S. J.

S. J. Radzevocois and J. L. Daniels, “Ground penetrating radar polarization and scattering from cylinders,” J. Appl. Geophys. 45, 111–125 (2000).
[CrossRef]

Rao, T. C.

Rizvi, A. A.

Ruppin, R.

R. Ruppin, “Extinction by a circular cylinder in an absorbing medium,” Opt. Commun. 211, 335–340 (2002).
[CrossRef]

Santarsiero, M.

Schettini, G.

F. Frezza, G. Schettini, L. Pajewski, C. Ponti, and N. Tedeschi, “Electromagnetic scattering by a metallic cylinder buried in a lossy medium with the cylindrical-wave approach,” IEEE Geosci. Remote Sens. Lett. 10, 179–183(2013).
[CrossRef]

F. Frezza, G. Schettini, and N. Tedeschi, “Generalized plane-wave expansion of cylindrical functions in lossy media convergent in the whole complex plane,” Opt. Commun. 284, 3867–3871 (2011).
[CrossRef]

F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by dielectric circular cylinders in a dielectric slab,” J. Opt. Soc. Am. A 27, 687–695 (2010).
[CrossRef]

F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by perfectly conducting circular cylinders buried in a dielectric slab through the cylindrical wave approach,” IEEE Trans. Antennas Propag. 57, 1208–1217 (2009).
[CrossRef]

M. Di Vico, F. Frezza, L. Pajewski, and G. Schettini, “Scattering by a finite set of perfectly conducting cylinders buried in a dielectric half-space: a spectral-domain solution,” IEEE Trans. Antennas Propag. 53, 719–727 (2005).
[CrossRef]

R. Borghi, F. Gori, M. Santarsiero, F. Frezza, and G. Schettini, “Plane-wave scattering by a set of perfectly conducting circular cylinder in the presence of a plane surface,” J. Opt. Soc. Am. A 13, 2441–2456 (1996).
[CrossRef]

Stratton, J. A.

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

Sun, W.

Tanev, S.

Tedeschi, N.

F. Frezza, G. Schettini, L. Pajewski, C. Ponti, and N. Tedeschi, “Electromagnetic scattering by a metallic cylinder buried in a lossy medium with the cylindrical-wave approach,” IEEE Geosci. Remote Sens. Lett. 10, 179–183(2013).
[CrossRef]

F. Frezza, G. Schettini, and N. Tedeschi, “Generalized plane-wave expansion of cylindrical functions in lossy media convergent in the whole complex plane,” Opt. Commun. 284, 3867–3871 (2011).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

Videen, G.

Wait, J. R.

S. F. Mahmoud, S. M. Ali, and J. R. Wait, “Electromagnetic scattering from buried cylindrical inhomogeneity inside a lossy earth,” Radio Sci. 16, 1285–1298 (1981).
[CrossRef]

Ward, S. H.

J. R. Parry and S. H. Ward, “Electromagnetic scattering from cylinders of arbitrary cross-section in a conductive half-space,” Geophysics 36, 67–100 (1971).
[CrossRef]

Yasumoto, K.

H. Jia and K. Yasumoto, “Scattering and absorption characteristics of multilayered gratings embedded in a dielectric slab,” Int. J. Infrared Millim. Waves 26, 1111–1126 (2005).
[CrossRef]

Anal. Chem. (1)

B. J. Davis, P. S. Carney, and R. Bhargava, “Theory of infrared microspectroscopy for intact fibers,” Anal. Chem. 83, 525–532 (2011).
[CrossRef]

Appl. Opt. (3)

Geophysics (1)

J. R. Parry and S. H. Ward, “Electromagnetic scattering from cylinders of arbitrary cross-section in a conductive half-space,” Geophysics 36, 67–100 (1971).
[CrossRef]

IEEE Geosci. Remote Sens. Lett. (1)

F. Frezza, G. Schettini, L. Pajewski, C. Ponti, and N. Tedeschi, “Electromagnetic scattering by a metallic cylinder buried in a lossy medium with the cylindrical-wave approach,” IEEE Geosci. Remote Sens. Lett. 10, 179–183(2013).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

M. Di Vico, F. Frezza, L. Pajewski, and G. Schettini, “Scattering by a finite set of perfectly conducting cylinders buried in a dielectric half-space: a spectral-domain solution,” IEEE Trans. Antennas Propag. 53, 719–727 (2005).
[CrossRef]

F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by perfectly conducting circular cylinders buried in a dielectric slab through the cylindrical wave approach,” IEEE Trans. Antennas Propag. 57, 1208–1217 (2009).
[CrossRef]

Int. J. Electron. (1)

J. D. Kanellopoulos and N. E. Buris, “Scattering from conducting cylinders embedded in a lossy medium,” Int. J. Electron. 57, 391–401 (1984).
[CrossRef]

Int. J. Infrared Millim. Waves (1)

H. Jia and K. Yasumoto, “Scattering and absorption characteristics of multilayered gratings embedded in a dielectric slab,” Int. J. Infrared Millim. Waves 26, 1111–1126 (2005).
[CrossRef]

J. Appl. Geophys. (1)

S. J. Radzevocois and J. L. Daniels, “Ground penetrating radar polarization and scattering from cylinders,” J. Appl. Geophys. 45, 111–125 (2000).
[CrossRef]

J. Opt. Soc. Am. A (10)

M. K. Moaveni, A. A. Rizvi, and B. A. Kamran, “Plane-wave scattering by gratings of conducting cylinders in an inhomogeneous and lossy dielectric,” J. Opt. Soc. Am. A 5, 834–843 (1988).
[CrossRef]

S. C. Lee, “Scattering by closely spaced parallel nonhomogeneous cylinders in an absorbing medium,” J. Opt. Soc. Am. A 28, 1812–1819 (2011).
[CrossRef]

S. C. Lee, “Optical extinction by closely spaced parallel cylinders inside a finite dielectric slab,” J. Opt. Soc. Am. A 23, 2219–2232 (2006).
[CrossRef]

F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by dielectric circular cylinders in a dielectric slab,” J. Opt. Soc. Am. A 27, 687–695 (2010).
[CrossRef]

R. Borghi, F. Gori, M. Santarsiero, F. Frezza, and G. Schettini, “Plane-wave scattering by a set of perfectly conducting circular cylinder in the presence of a plane surface,” J. Opt. Soc. Am. A 13, 2441–2456 (1996).
[CrossRef]

S. C. Lee and J. A. Grzesik, “Light scattering by closely spaced parallel cylinders embedded in a semi-infinite dielectric medium,” J. Opt. Soc. Am. A 15, 163–173 (1998).
[CrossRef]

S. C. Lee, “Light scattering by closely spaced parallel cylinders embedded in a finite dielectric slab,” J. Opt. Soc. Am. A 16, 1350–1361 (1999).
[CrossRef]

S. C. Lee, “Light scattering by a coated infinite cylinder in an absorbing medium,” J. Opt. Soc. Am. A 28, 1067–1075(2011).
[CrossRef]

T. C. Rao and R. Barakat, “Plane-wave scattering by a conducting cylinder partially buried in a ground plane. I: TM case,” J. Opt. Soc. Am. A 6, 1270–1280 (1989).
[CrossRef]

T. C. Rao and R. Barakat, “Plane-wave scattering by a conducting cylinder partially buried in a ground plane. II: TE case,” J. Opt. Soc. Am. A 8, 1986–1990 (1991).
[CrossRef]

Opt. Commun. (2)

R. Ruppin, “Extinction by a circular cylinder in an absorbing medium,” Opt. Commun. 211, 335–340 (2002).
[CrossRef]

F. Frezza, G. Schettini, and N. Tedeschi, “Generalized plane-wave expansion of cylindrical functions in lossy media convergent in the whole complex plane,” Opt. Commun. 284, 3867–3871 (2011).
[CrossRef]

Radio Sci. (1)

S. F. Mahmoud, S. M. Ali, and J. R. Wait, “Electromagnetic scattering from buried cylindrical inhomogeneity inside a lossy earth,” Radio Sci. 16, 1285–1298 (1981).
[CrossRef]

Other (3)

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

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

S. C. Lee and G. R. Cunnington, “Theoretical models for radiative transfer in fibrous media,” in Annual Review of Heat Transfer, C. L. Tien, ed., (Begell House, 1998), Vol. 9, pp. 159–212.

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Figures (7)

Fig. 1.
Fig. 1.

Schematic diagram depicting the present problem.

Fig. 2.
Fig. 2.

Scattered-incident, -reflected, and -transmitted waves at the half-space interface.

Fig. 3.
Fig. 3.

Comparison of the present results with published data for a perfectly conducting cylinder buried in lossy ground.

Fig. 4.
Fig. 4.

Backscattering from a homogeneous cylinder buried at xo=6ro in a lossy half-space for several values of absorption index (m˜2=1.2m2ii, m2i=0, 0.01, 0.05).

Fig. 5.
Fig. 5.

Backscattering from a homogeneous cylinder buried at different depths (xo=2ro, 6ro, 10ro) in a lossy half-space (m˜2=1.20.01i).

Fig. 6.
Fig. 6.

Backscattering from a homogeneous cylinder buried at xo=6ro in a lossy half-space (m˜2=1.20.05i) for several incidence angles (θ1=0, 30°, 60°).

Fig. 7.
Fig. 7.

Backscattering from a hollow magnetic cylinder (ri=1.15μm, ro=1.59μm, m˜shell=1.0510.0255i, μshell=0.70.1i) buried at different depths in a lossy and magnetic medium (m˜2=1.20.05i, μ2=1.50.5i).

Equations (71)

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

E⃗=×(e⃗zv)+ik××(e⃗zu),
H⃗=m˜μ×(e⃗zu)+iμko××(e⃗zv),
(m˜,μ,k)={(m˜1,μ1,k1=m˜1ko),x<0(m˜2,μ2,k2=m˜2ko),x>0(m˜q,μq,kq=m˜qko),rq1<RoP<rq,q=1,Q,
(E⃗2H⃗2)=(E⃗2+H⃗2+)+(E⃗2r+H⃗2r+)+(E⃗2scaH⃗2sca).
ψoσ=αψσexp(ik⃗σ·R⃗P),
k⃗i=k1(cosθ1e⃗xsinθ1e⃗y),
k⃗r=k1(cosθ1e⃗x+sinθ1e⃗y),
k⃗+=k2xe⃗x+k2ye⃗y,
[E⃗1iH⃗1i/m¯1]=ik1[αvi(sinθ1e⃗x+cosθ1e⃗y)+αuie⃗zαui(sinθ1e⃗x+cosθ1e⃗y)+αvie⃗z]exp(ik⃗i·R⃗P),
[E⃗1rH⃗1r/m¯1]=ik1[αvr(sinθ1e⃗xcosθ1e⃗y)+αure⃗zαur(sinθ1e⃗xcosθ1e⃗y)+αvre⃗z]exp(ik⃗r·R⃗P),
[E⃗2+H⃗2+/m¯2]=i[αv+(k2ye⃗x+k2xe⃗y)+αu+e⃗zαu+(k2ye⃗xk2xe⃗y)+αv+e⃗z]exp(ik⃗+·R⃗P),
e⃗x×(E⃗1i+E⃗1r,H⃗1i+H⃗1r)xP=0=e⃗x×(E⃗2+,H⃗2+)xP=0+.
k2y=k1sinθ1,
(r12u,r12v)=(m¯1cosθ1m¯2k2x/k2m¯1cosθ1+m¯2k2x/k2,m¯2cosθ1m¯1k2x/k2m¯2cosθ1+m¯1k2x/k2),
(t12u,t12v)=(2m¯1cosθ1m¯1cosθ1+m¯2k2x/k2,2m¯1cosθ1m¯1k2x/k2+m¯2cosθ1).
k2x=k22(k1sinθ1)2,
k2x=k2x,rik2x,i={ρoexp(iϑo/2),Re(k22)k1sinθ1iρoexp(iϑo/2),Re(k22)<k1sinθ1,
ρo=[Re(k22)k12sin2θ1]2+(2k2rk2i)2,
ϑo=tan1[2k2rk2i/|Re(k22)k12sin2θ1|].
k⃗+=k2(cosθ2e⃗xsinθ2e⃗y).
sinθ2=k1sinθ1/k2,
(E⃗2+H⃗2+/m¯2)=ik2εon=(i)nexp[in(γoP+θ2)](nk2RoPαv+Jne⃗R+iαv+Jne⃗γ+αu+Jne⃗znk2RoPαu+Jne⃗Riαu+Jne⃗γ+αv+Jne⃗z),
(uscavsca)=n=(i)nexp(inγoP)Hn(k2RoP)(bnan).
(E⃗2scaH⃗2sca/m¯2)=ik2n=(i)nexp(inγoP)(nk2RoPanHne⃗RianHne⃗γbnHne⃗znk2RoPbnHne⃗R+ibnHne⃗γanHne⃗z),
exp(inγoP)Hn(k2RoP)=(i)nπ(βiη)nβexp[ik2(βxoPηyoP)]dη,
lim|η||yoP|/xoPk2r/k2i,
(usvs)=exp(ik⃗s·R⃗oP)(XY)dη,
(ur+vr+)=exp(ik⃗s+·R⃗P+ik⃗s·R⃗o)(Xr+Yr+)dη,
(utvt)=exp(ik⃗t·R⃗P+ik⃗s·R⃗o)(XtYt)dη,
(XY)=1πn=(1)n(βiη)nβ(bnan).
k⃗s±=k2(±βe⃗x+ηe⃗y),
k⃗t=γ1e⃗x+kye⃗y,
[E⃗sH⃗s/m¯2]=ik2[Y(ηe⃗x+βe⃗y)Xe⃗zX(ηe⃗x+βe⃗y)Ye⃗z]exp[ik2β(xPxo)ik2ηyoP]dη,
[E⃗r+H⃗r+/m¯2]=ik2[Yr+(ηe⃗xβe⃗y)Xr+e⃗zXr+(ηe⃗xβe⃗y)Yr+e⃗z]exp[ik2β(xP+xo)ik2ηyoP]dη,
[E⃗tH⃗t/m¯1]=ik1[Yt(kye⃗x+γ1e⃗y)/k1Xte⃗zXt(kye⃗x+γ1e⃗y)/k1Yte⃗z]exp(iγ1xPik2βxoikyyoP)dη.
e⃗x×(E⃗s+E⃗r+,H⃗s+H⃗r+)xP=0+=e⃗x×(E⃗t,H⃗t)xP=0.
ky=k2η,
exp(inγoP)Hn(k2RoP)=(i)nπexp[insin1(ky/k2)]k22ky2exp(ik22ky2|xoP|ikyyoP)dky,
sin1(ky/k2)=iln[(iky+k22ky2)/k2].
exp(ik22ky2|xoP|)={exp[iρ|xoP|exp(iϑ/2)],Re(k22)|ky|exp[ρ|xoP|exp(iϑ/2)],Re(k22)<|ky|,
ρ=[Re(k22)ky2]2+(2k2rk2i)2,
ϑ=tan1[2k2rk2i/|Re(k22)ky2|].
r21u=Xr+X=k22ky2γ1μ2/μ1k22ky2+γ1μ2/μ1,
r21v=Yr+Y=k22ky2γ1(μ1/μ2)(k2/k1)2k22ky2+γ1(μ1/μ2)(k2/k1)2,
t21u=k1Xtk2X=2k22ky2k22ky2+γ1μ2/μ1,
t21v=k1Ytk2Y=2k22ky2k2γ1/k1+k1μ2/(k2μ1)k22ky2.
E⃗r+=ik2n=s=(i)nexp(inγoP)(nk2RoPJnRnsvase⃗R+iJnRnsvase⃗γ+JnRnsubse⃗z),
H⃗r+=im¯2k2n=s=(i)nexp(inγoP)(nk2RoPJnRnsubse⃗R+iJnRnsubse⃗γJnRnsvase⃗z),
Rnsψ=(1)sπr21ψexp[i(n+s)sin1(ky/k2)]k22ky2exp(i2xok22ky2)dky,
(E⃗qincH⃗qinc/m¯q)=ikqn=(i)nexp(inγoP)(nkqRoPJnAn(q)e⃗R+iJnAn(q)e⃗γ+JnBn(q)e⃗znkqRoPJnBn(q)e⃗RiJnBn(q)e⃗γ+JnAn(q)e⃗z),
(E⃗qscaH⃗qsca/m¯q)=ikqn=(i)nexp(inγoP)(nkqRoPHnan(q)e⃗RiHnan(q)e⃗γHnbn(q)e⃗znkqRoPHnbn(q)e⃗R+iHnbn(q)e⃗γHnan(q)e⃗z),
(CnuCnv)=εo(αu+Cno,uαv+Cno,v)exp(inθ2)s=(RnsuCno,ubsRnsvCno,vas),
Cnu=[bnbn(Q)Bn(Q)bn(2)Bn(2)Bn(1)]T,
Cnv=[anan(Q)An(Q)an(2)An(2)An(1)]T,
s=(δns+bno,IRnsu)bs=εoαu+bno,Iexp(inθ2),
s=(δns+ano,IIRnsv)as=εoαv+ano,IIexp(inθ2),
E⃗t=iπk1[(kye⃗x+γ1e⃗y)Tvk1Tue⃗z]exp[iRP(γ1cosγPkysinγP)]dky,
H⃗t=m¯1iπk1[Tu(kye⃗x+γ1e⃗y)+Tvk1e⃗z]exp[iRP(γ1cosγPkysinγP)]dky,
(TuTv)=k2exp(ixok22ky2+ikyyo)k22ky2n=(1)nexp[insin1(ky/k2)](t21ubnt21van),
γ1={k12ky2k1|ky|iky2k12k1<|ky|.
ky=k1sinγP,γ1=k1cosγP,
[E⃗tH⃗t/m¯1]=2k1iπRPexp(ik1RP)[Tvo(sinγPe⃗x+cosγPe⃗y)+Tuoe⃗zTuo(sinγPe⃗xcosγPe⃗y)+Tvoe⃗z],
Tuo=2k2cosγPexp(ixok22k12sin2γP+ik1yosinγP)k22k12sin2γP(μ2/μ1)k1cosγP·n=(1)nexp[insin1(k1k2sinγP)]bn,
Tvo=2k2cosγPexp(ixok22k12sin2γP+ik1yosinγP)k1μ2/(k2μ1)k22k12sin2γPk2cosγPn=(1)nexp[insin1(k1k2sinγP)]an,
k22k12sin2γP={ρ1exp(iϑ1/2)Re(k22)k12sin2γPiρ1exp(iϑ1/2)Re(k22)<k12sin2γP,
ρ1=[Re(k22)k12sin2γP]2+(2k2rk2i)2,
ϑ1=tan1(2k2rk2i/|Re(k22)k12sin2γP|).
S⃗t=2Soπk1RP|Tuo|2+|Tvo|2|αui|2+|αvi|2(cosγPe⃗x+sinγPe⃗y),
So=cok128πm¯1(|αui|2+|αvi|2).
bno,I=Jn(k2ro)/Hn(k2ro),
ano,II=Jn(k2ro)/Hn(k2ro).

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