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Local polarization of tightly focused unpolarized light

Abstract

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.

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Figure 1: Distribution of P3D in the focal plane of a high-NA lens.
Figure 2: Experimental set-up for mapping the degree of polarization.
Figure 3: Polarization by focusing.
Figure 4: Measured P2D for different values of the degree of polarization of the incident beam Pinc2D.
Figure 5: Influence of the axial electric-field component on P2D.

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References

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

    Article  MathSciNet  Google Scholar 

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

    Google Scholar 

  3. Berry, M. V., Dennis, M. R. & Lee R. L. Jr. Polarization singularities in the clear sky. New J. Phys. 6, 162 (2004).

    Article  ADS  Google Scholar 

  4. Kovac, J. M. et al. Detection of polarization in the cosmic microwave background using DASI. Nature 420, 772–787 (2002).

    Article  ADS  Google Scholar 

  5. 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).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  8. 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).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  11. Ellis, J. & Dogariu, A. Optical polarimetry of random fields. Phys. Rev. Lett. 95, 203905 (2005).

    Article  ADS  Google Scholar 

  12. 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).

    Article  ADS  Google Scholar 

  13. Mandel, L. & Wolf, E. Optical Coherence and Quantum Optics (Cambridge Univ. Press, Cambridge, 1995).

    Book  Google Scholar 

  14. Brosseau, C. Fundamentals of Polarized Light. A Statistical Optics Approach (Wiley, New York, 1998).

    Google Scholar 

  15. 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).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  17. 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).

    Google Scholar 

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

    Article  ADS  Google Scholar 

  19. 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).

    Article  MathSciNet  Google Scholar 

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

    Google Scholar 

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

    Article  ADS  Google Scholar 

Download references

Acknowledgements

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.

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Correspondence to Klas Lindfors.

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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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