Abstract

The incidence of an inhomogeneous plane wave on the interface between two lossy media is analyzed. The analytical expressions of the incidence angle of the phase vector, for which the transmitted wave has the phase or the attenuation vector parallel to the interface, are obtained. The transmitted wave with the attenuation vector parallel to the interface is physically interpreted, finding a wave in a lossy medium without attenuation away from the interface. The same effect appears at the interface between a lossless medium and a lossy one.

© 2012 Optical Society of America

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References

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  1. J. E. Roy, IEEE Trans. Antennas Propag. 51, 1206 (2003).
    [CrossRef]
  2. R. B. Adler, L. J. Chu, and R. M. Fano, Electromagnetic Transmission and Radiation (Wiley, 1972).
  3. T. Tamir and A. A. Oliner, Proc. Inst. Electr. Eng. 110, 310 (1963).
    [CrossRef]
  4. T. Tamir, Optik 38, 269 (1973).
  5. D. R. Jackson and A. A. Oliner, Modern Antenna Handbook, C. A. Balanis, ed. (Wiley, 2008), Chap. 7.
  6. Y. Wang, A. S. Helmy, and G. V. Eleftheriades, Opt. Express 19, 12392 (2011).
    [CrossRef]

2011

2003

J. E. Roy, IEEE Trans. Antennas Propag. 51, 1206 (2003).
[CrossRef]

1973

T. Tamir, Optik 38, 269 (1973).

1963

T. Tamir and A. A. Oliner, Proc. Inst. Electr. Eng. 110, 310 (1963).
[CrossRef]

Adler, R. B.

R. B. Adler, L. J. Chu, and R. M. Fano, Electromagnetic Transmission and Radiation (Wiley, 1972).

Chu, L. J.

R. B. Adler, L. J. Chu, and R. M. Fano, Electromagnetic Transmission and Radiation (Wiley, 1972).

Eleftheriades, G. V.

Fano, R. M.

R. B. Adler, L. J. Chu, and R. M. Fano, Electromagnetic Transmission and Radiation (Wiley, 1972).

Helmy, A. S.

Jackson, D. R.

D. R. Jackson and A. A. Oliner, Modern Antenna Handbook, C. A. Balanis, ed. (Wiley, 2008), Chap. 7.

Oliner, A. A.

T. Tamir and A. A. Oliner, Proc. Inst. Electr. Eng. 110, 310 (1963).
[CrossRef]

D. R. Jackson and A. A. Oliner, Modern Antenna Handbook, C. A. Balanis, ed. (Wiley, 2008), Chap. 7.

Roy, J. E.

J. E. Roy, IEEE Trans. Antennas Propag. 51, 1206 (2003).
[CrossRef]

Tamir, T.

T. Tamir, Optik 38, 269 (1973).

T. Tamir and A. A. Oliner, Proc. Inst. Electr. Eng. 110, 310 (1963).
[CrossRef]

Wang, Y.

IEEE Trans. Antennas Propag.

J. E. Roy, IEEE Trans. Antennas Propag. 51, 1206 (2003).
[CrossRef]

Opt. Express

Optik

T. Tamir, Optik 38, 269 (1973).

Proc. Inst. Electr. Eng.

T. Tamir and A. A. Oliner, Proc. Inst. Electr. Eng. 110, 310 (1963).
[CrossRef]

Other

D. R. Jackson and A. A. Oliner, Modern Antenna Handbook, C. A. Balanis, ed. (Wiley, 2008), Chap. 7.

R. B. Adler, L. J. Chu, and R. M. Fano, Electromagnetic Transmission and Radiation (Wiley, 1972).

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Figures (4)

Fig. 1.
Fig. 1.

Geometry of the problem.

Fig. 2.
Fig. 2.

Amplitude of the Poynting vector as a function of x/λ0, for an incident wave impinging at ξ1=ξ1ζ, for different values of η1.

Fig. 3.
Fig. 3.

Amplitude of the Poynting vector as a function of x/λ0, in y=0, for an inhomogeneous wave incident at the critical angle ξc (solid line) and for a homogeneous plane wave (dashed line) impinging at the same angle, at the interface between a vacuum and a lossy medium.

Fig. 4.
Fig. 4.

Real part of the electric field as a function of x/λ0 and y/λ0 for an inhomogeneous plane wave incident at the critical angle ξc=5.91°.

Equations (13)

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β1sinξ1=β2sinξ2,
α1sinζ1=α2sinζ2,
β22α22=Re(k22),
2β2α2cosη2=Im(k22).
2β1α1sinξ1sinζ1=Im(k22).
(χ1)tan2ξ1tanη1tanξ1+χ=0,
χ=Im(k22)Im(k12).
tanξ±=tanη1±tan2η14χ(χ1)2(χ1).
tanξ±=1tanη1.
ξ±={ξ1ξifRe(kiτ2)Re(k22)ξ1ζifRe(kiτ2)<Re(k22).
β1α1sin(2ξ1)=Im(k22).
ξc=12arcsin[Im(k22)β1α1].
β1k121+1+[2Im(k22)k12]2.

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