Abstract

The field lines of energy flow of the radiation emitted by a linear dipole in free space are straight lines, running radially outward from the source. When the dipole is embedded in a medium, the field lines are curves when the imaginary part of the relative permittivity is finite. It is shown that due to the damping in the material all radiation is emitted in directions perpendicular to the dipole axis, whereas for a dipole in free space the radiation is emitted in all directions except along the dipole axis. It is also shown that some field lines in the near field form semiloops. Energy flowing along these semiloops is absorbed by the material and does not contribute to the radiative power in the far field.

© 2011 Optical Society of America

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References

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  1. M. W. McCall, A. Lakhtakia, and W. S. Weiglhofer, Eur. J. Phys. 23, 353 (2002).
    [CrossRef]
  2. J. D. Jackson, Classical Electrodynamics, 3rd. ed. (Wiley, 1999).
  3. J. Shu, X. Li, and H. F. Arnoldus, J. Mod. Opt. 55, 2457 (2008).
    [CrossRef]

2008 (1)

J. Shu, X. Li, and H. F. Arnoldus, J. Mod. Opt. 55, 2457 (2008).
[CrossRef]

2002 (1)

M. W. McCall, A. Lakhtakia, and W. S. Weiglhofer, Eur. J. Phys. 23, 353 (2002).
[CrossRef]

Arnoldus, H. F.

J. Shu, X. Li, and H. F. Arnoldus, J. Mod. Opt. 55, 2457 (2008).
[CrossRef]

Jackson, J. D.

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

Lakhtakia, A.

M. W. McCall, A. Lakhtakia, and W. S. Weiglhofer, Eur. J. Phys. 23, 353 (2002).
[CrossRef]

Li, X.

J. Shu, X. Li, and H. F. Arnoldus, J. Mod. Opt. 55, 2457 (2008).
[CrossRef]

McCall, M. W.

M. W. McCall, A. Lakhtakia, and W. S. Weiglhofer, Eur. J. Phys. 23, 353 (2002).
[CrossRef]

Shu, J.

J. Shu, X. Li, and H. F. Arnoldus, J. Mod. Opt. 55, 2457 (2008).
[CrossRef]

Weiglhofer, W. S.

M. W. McCall, A. Lakhtakia, and W. S. Weiglhofer, Eur. J. Phys. 23, 353 (2002).
[CrossRef]

Eur. J. Phys. (1)

M. W. McCall, A. Lakhtakia, and W. S. Weiglhofer, Eur. J. Phys. 23, 353 (2002).
[CrossRef]

J. Mod. Opt. (1)

J. Shu, X. Li, and H. F. Arnoldus, J. Mod. Opt. 55, 2457 (2008).
[CrossRef]

Other (1)

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

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Figures (3)

Fig. 1
Fig. 1

Field lines of the Poynting vector of the radiation emitted by a dipole in free space, oscillating along the z axis, are straight lines in a radially outward direction.

Fig. 2
Fig. 2

Field lines of the Poynting vector for a dipole oscillating along the z axis and embedded in a material with ε r = 1.7 + 0.06 i and μ r = 1 . These are the values for water at 3 μm . The index of refraction is n = 1.3 + 0.023 i .

Fig. 3
Fig. 3

Larger view of the field lines in Fig. 2. Far away from the dipole the field lines run approximately in a radial direction, except near the z axis. The curving close to the z axis is a near-field effect that persists in the far field.

Equations (10)

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S ( r ) = 1 2 μ o Re [ 1 μ r E ( r ) * × B ( r ) ] .
E ( r ) = E o e i n k o z , B ( r ) = n c ( e z × E o ) e i n k o z ,
S ( r ) = 1 2 μ o c ( E o * · E o ) e 2 k o z Im n e z Re ( n / μ r ) .
E ( r ) = μ r d o k o 2 4 π ε o r [ e θ sin θ + ( 3 r ^ cos θ e z ) i n q ( 1 + i n q ) ] e i n q ,
B ( r ) = n μ r c d o k o 2 4 π ε o r e ϕ sin θ ( 1 + i n q ) e i n q ,
S ( r ) = 3 P o 8 π r 2 | μ r | 2 e 2 q Im n σ ( q ) ,
σ ( q ) = r ^ sin 2 θ Re [ n μ r ( 1 + i n q ) ] + 1 | n | 2 q | 1 + i n q | 2 [ r ^ ( 1 3 cos 2 θ ) + 2 e z cos θ ] Im ε r .
r ^ ( 1 3 cos 2 θ ) + 2 e z cos θ = sin θ [ e y ( 1 3 cos 2 θ ) + 3 e z sin θ cos θ ] .
d z ¯ d y ¯ = σ ( q ) z σ ( q ) y
d z ¯ d y ¯ = 3 y ¯ z ¯ y ¯ 2 2 z ¯ 2 .

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