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).

Polarization oflightnotes PDF

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

Youngworth, K. S. & Brown, T. G. Focusing of high numerical aperture cylindrical-vector beams. Opt. Express 7, 77–87 (2000).

Plane polarizedlight

Kalkbrenner, T., Ramstein, M., Mlynek, J. & Sandoghdar, V. A single gold particle as a probe for apertureless scanning near-field optical microscopy. J. Microsc. 202, 72–76 (2001).

Pancharatnam, S. Generalized theory of interference and its applications. Part I. Coherent pencils. Proc. Ind. Acad. Sci. A. 44, 247–262 (1956).

Circularly polarizedlight

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

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).

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.

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

Wilson, T., Juškaitis, R. & Higdon, P. The imaging of dielectric point scatterers in conventional and confocal polarisation microscopes. Opt. Commun. 141, 298–313 (1997).

Polarized and unpolarizedlight

Light waves are transverse: that is, the vibrating electric vector associated with each wave is perpendicular to the direction of propagation. A beam of unpolarized light consists of waves moving in the same direction with their electric vectors pointed in random orientations about the axis of propagation. Plane polarized light consists of waves in which the direction of vibration is the same for all waves. In circular polarization the electric vector rotates about the direction of propagation as the wave progresses. Light may be polarized by reflection or by passing it through filters, such as certain crystals, that transmit vibration in one plane but not in others.

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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).

Unpolarizedlight

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.

polarization, property of certain electromagnetic radiations in which the direction and magnitude of the vibrating electric field are related in a specified way.

Empedocles, S. A., Neuhauser, R. & Bawendi, M. G. Three-dimensional orientation measurements of symmetric single chromophores using polarization microscopy. Nature 399, 126–130 (1999).

Polarised lightin physics

Friese, M. E. J., Nieminen, T. A., Heckenberg, N. R. & Rubinsztein-Dunlop, H. Optical alignment and spinning of laser-trapped microscopic particles. Nature 394, 348–350 (1998).

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

Polarised lightmeaning

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

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

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

Dorn, R., Quabis, S. & Leuchs, G. Sharper focus for a radially polarized light beam. Phys. Rev. Lett. 91, 233901 (2003).

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

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).