## 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 $\lambda \u2215\pi $, where *λ* is the wavelength of the light.

© 2008 Optical Society of America

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### Equations (8)

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(1)
$$\mathbf{d}\left(t\right)={d}_{o}\phantom{\rule{0.2em}{0ex}}\mathrm{Re}\left[\mathit{\epsilon}{e}^{-i\omega t}\right],$$
(2)
$$\mathbf{S}\left(\mathbf{r}\right)=\frac{1}{2{\mu}_{o}}\phantom{\rule{0.2em}{0ex}}\mathrm{Re}[\mathbf{E}\left(\mathbf{r}\right)\times \mathbf{B}{\left(\mathbf{r}\right)}^{*}]$$
(3)
$$\mathbf{S}\left(\mathbf{r}\right)=\frac{3}{8\pi}\frac{{P}_{o}}{{r}^{2}}\{[1-(\widehat{\mathbf{r}}\cdot \mathit{\epsilon})(\widehat{\mathbf{r}}\cdot {\mathit{\epsilon}}^{*})]\widehat{\mathbf{r}}-\frac{2}{q}(1+\frac{1}{{q}^{2}})\mathrm{Im}[\widehat{\mathbf{r}}\cdot \mathit{\epsilon}]{\mathit{\epsilon}}^{*}\},$$
(4)
$$\mathbf{S}\left(\mathbf{r}\right)=\frac{3}{8\pi}\frac{{P}_{o}}{{r}^{2}}\widehat{\mathbf{r}}\phantom{\rule{0.2em}{0ex}}{\mathrm{sin}}^{2}\alpha ,$$
(5)
$$\mathbf{S}\left(\mathbf{r}\right)=\frac{3}{8\pi}\frac{{P}_{o}}{{r}^{2}}\{[1-\frac{1}{2}\phantom{\rule{0.2em}{0ex}}{\mathrm{sin}}^{2}\theta ]\widehat{\mathbf{r}}+\frac{\tau}{q}(1+\frac{1}{{q}^{2}})\mathrm{sin}\phantom{\rule{0.2em}{0ex}}\theta {\mathbf{e}}_{\varphi}\}.$$
(6)
$$\theta ={\theta}_{o},\phantom{\rule{1em}{0ex}}\varphi \left(q\right)={\varphi}_{o}-\tau Z\left({\theta}_{o}\right)\frac{1}{q}(1+\frac{1}{3{q}^{2}}),$$
(7)
$${\mathbf{q}}_{d}=\tau \phantom{\rule{0.2em}{0ex}}\mathrm{sin}\phantom{\rule{0.2em}{0ex}}{\theta}_{o}Z\left({\theta}_{o}\right)({\mathbf{e}}_{x}\phantom{\rule{0.2em}{0ex}}\mathrm{sin}\phantom{\rule{0.2em}{0ex}}{\varphi}_{o}-{e}_{y}\phantom{\rule{0.2em}{0ex}}\mathrm{cos}\phantom{\rule{0.2em}{0ex}}{\varphi}_{o}).$$
(8)
$${\mathbf{q}}_{f}=-\tau \phantom{\rule{0.2em}{0ex}}\mathrm{sin}\phantom{\rule{0.2em}{0ex}}{\theta}_{o}Z\left({\theta}_{o}\right){\mathbf{e}}_{{\varphi}_{o}}.$$