Lindfors, K., Setälä, T., Kaivola, M. & Friberg, A. T. Degree of polarization in tightly focused optical fields. J. Opt. Soc. Am. A. 22, 561–568 (2005).

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Royal Institute of Technology (KTH), School of Information and Communication Technology, Electrum 229, Kista, SE-164 40, Sweden

Sick, B., Hecht, B. & Novotny, L. Orientational imaging of single molecules by annular illumination. Phys. Rev. Lett. 85, 4482–4485 (2000).

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Setälä, T., Shevchenko, A., Kaivola, M. & Friberg, A. T. Degree of polarization for optical near fields. Phys. Rev. E 66, 016615 (2002).

Setälä, T., Kaivola, M. & Friberg, A. T. Degree of polarization in near fields of thermal sources: effects of surface waves. Phys. Rev. Lett. 88, 123902 (2002).

Novotny, L., Beversluis, M. R., Youngworth, K. S. & Brown, T. G. Longitudinal field modes probed by single molecules. Phys. Rev. Lett. 86, 5251–5254 (2001).

The authors from TKK acknowledge financial support from the Academy of Finland, project numbers 201293 and 118074, and A.T.F. acknowledges the support of the Swedish Foundation for Strategic Research. J. Pekola and O. Hahtela are thanked for loans of equipment.

Ellis, J., Dogariu, A., Ponomarenko, S. & Wolf, E. Correlation matrix of a completely polarized, statistically stationary electromagnetic field. Opt. Lett. 29, 1536–1538 (2004).

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The polarization of light is important in a great variety of optical phenomena, ranging from transmission, reflection and scattering to polarimetric imaging of scenes and quantum-mechanical selection rules of atomic and molecular transitions. Among some less-well-known phenomena that illustrate the vectorial nature of light are the Pancharatnam1 (or geometric2) phase, singularities in the polarization pattern of clear sky3 and polarization of microwave background radiation4. Here, we examine the partial polarization of focused light. We experimentally demonstrate a rather surprising phenomenon, where the focusing of unpolarized light results in rings of full polarization in the focal plane of the focusing optics. The polarization rings are imaged with a resolution of <100 nm by probing the focal region using a gold nanoparticle.

Brosseau, C. & Dogariu, A. Symmetry properties and polarization descriptors for an arbitrary electromagnetic wavefield. In Prog. Opt., vol. 49 (ed. Wolf, E.) 315–380 (Elsevier, Amsterdam, The Netherlands, 2006).

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I have bought many over the years. They are very good. Hint: Drive them through a power resistor of fx 5 ohms to prolong life.

Department of Engineering Physics and Mathematics and Center for New Materials, Helsinki University of Technology (TKK), PO Box 3500, FI-02015 TKK, Finland

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Lindfors, K., Priimagi, A., Setälä, T. et al. Local polarization of tightly focused unpolarized light. Nature Photon 1, 228–231 (2007). https://doi.org/10.1038/nphoton.2007.30

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Hariharan, P. The geometric phase. In Prog. Opt., vol. 48 (ed. Wolf, E.) 149–201 (Elsevier, Amsterdam, The Netherlands, 2005).