Abstract

Electromagnetic radiation incident upon a perfect mirror induces a current density on the surface of the conducting material of the mirror. It is shown that this surface current density can be expressed directly in terms of the source current density, which generates the incident field, without evaluating the electric and magnetic fields first.

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References

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  1. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  2. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999), p. 18.
  3. A. F. Peterson, S. L. Ray, and R. Mittra, Computational Methods for Electromagnetics (IEEE, 1998), Chap. 1.
  4. J. J. Bowman, T. B. A. Senior, and P. L. E. Uslenghi, Electromagnetic and Acoustic Scattering by Simple Shapes (Hemisphere, 1987), p. 16.
  5. A. W. Maue, Z. Phys. A 126, 601 (1949).
  6. P. K. Murthy, K. C. Hill, and G. A. Thiele, IEEE Trans. Antennas Propag. 34, 1173 (1986).
    [CrossRef]
  7. D. Torrungrueng, H.-T. Chou, and J. T. Johnson, IEEE Trans. Geosci. Remote Sens. 38, 1656 (2000).
    [CrossRef]
  8. H. F. Arnoldus and J. T. Foley, Opt. Commun. 231, 115 (2004).
    [CrossRef]
  9. H. F. Arnoldus, Surf. Sci. 601, 450 (2007).
    [CrossRef]
  10. H. F. Arnoldus, J. Opt. Soc. Am. A 23, 3063 (2006).
    [CrossRef]
  11. H. F. Arnoldus, J. Mod. Opt. 54, 45 (2007).
    [CrossRef]

2007

H. F. Arnoldus, Surf. Sci. 601, 450 (2007).
[CrossRef]

H. F. Arnoldus, J. Mod. Opt. 54, 45 (2007).
[CrossRef]

2006

2004

H. F. Arnoldus and J. T. Foley, Opt. Commun. 231, 115 (2004).
[CrossRef]

2000

D. Torrungrueng, H.-T. Chou, and J. T. Johnson, IEEE Trans. Geosci. Remote Sens. 38, 1656 (2000).
[CrossRef]

1986

P. K. Murthy, K. C. Hill, and G. A. Thiele, IEEE Trans. Antennas Propag. 34, 1173 (1986).
[CrossRef]

1949

A. W. Maue, Z. Phys. A 126, 601 (1949).

IEEE Trans. Antennas Propag.

P. K. Murthy, K. C. Hill, and G. A. Thiele, IEEE Trans. Antennas Propag. 34, 1173 (1986).
[CrossRef]

IEEE Trans. Geosci. Remote Sens.

D. Torrungrueng, H.-T. Chou, and J. T. Johnson, IEEE Trans. Geosci. Remote Sens. 38, 1656 (2000).
[CrossRef]

J. Mod. Opt.

H. F. Arnoldus, J. Mod. Opt. 54, 45 (2007).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

H. F. Arnoldus and J. T. Foley, Opt. Commun. 231, 115 (2004).
[CrossRef]

Surf. Sci.

H. F. Arnoldus, Surf. Sci. 601, 450 (2007).
[CrossRef]

Z. Phys. A

A. W. Maue, Z. Phys. A 126, 601 (1949).

Other

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999), p. 18.

A. F. Peterson, S. L. Ray, and R. Mittra, Computational Methods for Electromagnetics (IEEE, 1998), Chap. 1.

J. J. Bowman, T. B. A. Senior, and P. L. E. Uslenghi, Electromagnetic and Acoustic Scattering by Simple Shapes (Hemisphere, 1987), p. 16.

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Figures (3)

Fig. 1
Fig. 1

A volume current density j ( r ) represents a source of radiation in front of a mirror. The surface of the mirror is the x y plane, and the z axis is directed towards the source. A surface current density i ( r ) is induced on the surface of the mirror, and this vector field can be represented by a pattern of field lines.

Fig. 2
Fig. 2

An electric dipole d is located at position r o in front of the mirror. The current density at point r of the surface depends on vector r r o , which is the field-point vector r, relative to the position of the dipole.

Fig. 3
Fig. 3

Field lines of the current density in the mirror induced by a dipole oscillating along the z axis. The current is in the radial direction, and it reverses its orientation across each of the thin circles. There is an infinite set of these circles, which are spaced by about half an optical wavelength. As time progresses these circles expand, and new circles emanate from the origin of coordinates.

Equations (9)

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i ( r ) = 1 μ o n ̂ ( r ) × B ( r ) ,
i ( r , t ) = Re [ i ( r ) e i ω t ] ,
i ( r ) = 2 μ o e z × B ( r ) inc .
B ( r ) inc = μ o 4 π × d 3 r g ( r r ) j ( r ) ,
i ( r ) = 1 2 π e z × d 3 r f ( r r ) ( r r ) × j ( r ) ,
f ( r ) = 1 r 2 [ i k 1 r ] e i k r .
j ( r ) = i ω d δ ( r r o ) ,
i ( r ) = i ω 2 π f ( r r o ) e z × [ d × ( r r o ) ]
i ( r , t ) = c k 3 d o 2 π q q 1 2 [ cos ( q 1 ω t ) 1 q 1 sin ( q 1 ω t ) ] e ρ .

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