Abstract

The field lines of the Poynting vector for light emitted by a dipole with a rotating dipole moment show a vortex pattern near the location of the dipole. In the far field, each field line approaches a straight line, but this line does not appear to come exactly from the location of the dipole. As a result, the image of the dipole in its plane of rotation seems displaced. Secondly, the image in the far field is displaced as compared with the image of a source for which the field lines run radially outward. It turns out that both image displacements are the same. The displacements are of subwavelength scale, and they depend on the angles of observation. The maximum displacement occurs for observation in the plane of rotation and equals λπ, where λ is the wavelength of the light.

© 2008 Optical Society of America

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References

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  1. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980), Chap. 3.
  2. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999), Secs. 9.2 and 9.3.
  3. L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, 1975), p. 34.
  4. B. W. Shore, The Theory of Coherent Atomic Excitation (Wiley, 1990), Vol. 2, p. 821.
  5. H. F. Arnoldus and J. T. Foley, Opt. Commun. 231, 115 (2004).
    [CrossRef]

2004

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

Allen, L.

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, 1975), p. 34.

Arnoldus, H. F.

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

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980), Chap. 3.

Eberly, J. H.

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, 1975), p. 34.

Foley, J. T.

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

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999), Secs. 9.2 and 9.3.

Shore, B. W.

B. W. Shore, The Theory of Coherent Atomic Excitation (Wiley, 1990), Vol. 2, p. 821.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980), Chap. 3.

Opt. Commun.

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

Other

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980), Chap. 3.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999), Secs. 9.2 and 9.3.

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, 1975), p. 34.

B. W. Shore, The Theory of Coherent Atomic Excitation (Wiley, 1990), Vol. 2, p. 821.

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Figures (5)

Fig. 1
Fig. 1

Source at the origin of coordinates emits light, which is observed in the far field under angles ( θ o , ϕ o ) . Angle ϕ o is not shown in the figure.

Fig. 2
Fig. 2

For a rotating dipole moment at the origin of coordinates, a field line of the Poynting vector has a vortex structure close to the source. Far away from the dipole, the field line approaches a straight line. The dimensionless Cartesian coordinates are defined as x ¯ = k x , y ¯ = k y , and z ¯ = k z .

Fig. 3
Fig. 3

When a field line of the Poynting vector for a rotating dipole moment is observed in the far field, it appears that the image of the dipole in the xy plane is displaced over vector q d .

Fig. 4
Fig. 4

Field line of the Poynting vector for a rotating dipole moment at the origin of coordinates, which is observed along the x axis. For this case the image in the xy plane has its maximum displacement of λ π , which corresponds to q d = 2 in dimensionless units.

Fig. 5
Fig. 5

Image of the dipole in an observation plane in the far field is displaced over vector q f . It turns out that this displacement vector is the same as q d in Fig. 3.

Equations (8)

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d ( t ) = d o Re [ ε e i ω t ] ,
S ( r ) = 1 2 μ o Re [ E ( r ) × B ( r ) * ]
S ( r ) = 3 8 π P o r 2 { [ 1 ( r ̂ ε ) ( r ̂ ε * ) ] r ̂ 2 q ( 1 + 1 q 2 ) Im [ r ̂ ε ] ε * } ,
S ( r ) = 3 8 π P o r 2 r ̂ sin 2 α ,
S ( r ) = 3 8 π P o r 2 { [ 1 1 2 sin 2 θ ] r ̂ + τ q ( 1 + 1 q 2 ) sin θ e ϕ } .
θ = θ o , ϕ ( q ) = ϕ o τ Z ( θ o ) 1 q ( 1 + 1 3 q 2 ) ,
q d = τ sin θ o Z ( θ o ) ( e x sin ϕ o e y cos ϕ o ) .
q f = τ sin θ o Z ( θ o ) e ϕ o .

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