Asian Journal of Physics Vol. 30 Nos 8 & 9 (2021) 1307-1314

On three-dimensional polarization states of light
José J Gil1, Andreas Norrman2,3, Tero Setälä3 and Ari T Friberg3


As the electric field vector of a monochromatic optical field oscillates in a plane, truly three-dimensional polarization states of light necessitate polychromatic fields. We consider random three-dimensional polarization states, and employing the characteristic decomposition of the spectral polarization matrix we assess various physical properties of such light states. These properties include polarimetric purity (degree of polarization), the concept and measure of nonregularity, apparent dimensionality, spin angular momentum, and various anisotropies of the state. Polarization states endowed with these features are typically encountered in connection with fluctuating vectorial evanescent waves and highly focused random fields. © Anita Publications. All rights reserved.
Keywords: Polarized light, Degree of polarization, Nonregularity, Dimensionality.

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  1. Mandel L, Wolf E, Optical Coherence and Quantum Optics, (Cambridge University Press), 1995.
  2. Friberg A T, Setälä T, Electromagnetic theory of optical coherence (invited), J Opt Soc Am A, 33(2016)2431–2442.
  3. Setälä T, Shevchenko A, Kaivola M, Friberg A T, Degree of polarization for optical near fields, Phys Rev E, 66(2002)016615;
  4. Gil J J, Polarimetric characterization of light and media, Eur Phys J: Appl Phys, 40(2007)1–47.
  5. Auñón J M, Nieto-Vesperinas M, On two definitions of the three-dimensional degree of polarization in the near field of statistically homogeneous partially coherent sources, Opt Lett, 38(2013)58–60.
  6. Gamel O, James D F V, Majorization and measures of classical polarization in three dimensions, J Opt Soc Am A, 31(2014)1620–1626.
  7. Sheppard C J R, Partial polarization in three dimensions, J Opt Soc Am A, 28(2011)2655–2659.
  8. Sheppard C J R, Geometric representation for partial polarization in three dimensions, Opt Lett, 37(2012)2772–2774.
  9. Sheppard C J R, Jones and Stokes parameters for polarization in three dimensions, Phys Rev A, 90(2014)023809;
  10. Born M, Wolf E, Principles of Optics, 7th (expanded) edition, (Cambridge University Press), 1999.
  11. Gil J J, Ossikovski R, Polarized Light and the Mueller Matrix Approach, (CRC Press), 2016.
  12. Gil J J, Friberg A T, Setälä T, José I S, Structure of polarimetric purity of three-dimensional polarization states,” Phys Rev A, 95(2017)053856;
  13. José I S, Gil J J, Invariant indices of polarimetric purity: generalized indices of purity for nxn covariance matrices, Opt Commun, 284(2011)38–47.
  14. Gil J J, Norrman A, Friberg A T, Setälä T, Polarimetric purity and the concept of degree of polarization, Phys Rev A, 97(2018)023838;
  15. Luis A, Degree of polarization for three-dimensional fields as a distance between correlation matrices, Opt Commun, 253(2005)10–14.
  16. Leppänen L.-P, Friberg A T, Setälä T, Partial polarization of optical beams and near fields probed with a nanoscatterer, J Opt Soc Am A, 31(2014)1627–1635.
  17. Gil J J, Norrman A, Friberg A T, Setälä T, Nonregularity of three-dimensional polarization states, Opt Lett, 43(2018)4611–4614.
  18. Norrman A, Friberg A T, Gil J J, Setälä T, Dimensionality of random light fields, J Eur Opt Soc, – Rapid Publ, 13 (2017)36;
  19. Dennis M R, Geometric interpretation of the three-dimensional coherence matrix for nonparaxial polarization, J Opt A: Pure Appl Opt, 6(2004)S26–S31.
  20. Gil J J, Interpretation of the coherency matrix for three-dimensional polarization states, Phys Rev A, 90(2014)043858; doi. org/10.1103/PhysRevA.90.043858.
  21. Gil J J, Norrman A, Friberg A T, Setälä T, Intensity and spin anisotropy of three-dimensional polarization states, Opt Lett, 44(2019)3578–3581.
  22. Bliokh K Y, Bekshaev A Y, Nori F, Extraordinary momentum and spin in evanescent waves, Nat Commun, 5(2014)1–8.
  23. Eismann J S, Nicholls L H, Roth D J, Alonso M A, Banzer P, Rodríguez-Fortuño F J, Zayats A V, Nori F, Bliokh K Y, Transverse spinning of unpolarized light, Nat Photonics, 15(2020)156–161.
  24. Gil J J, Friberg A T, Norrman A, Setälä T, Effect of polarimetric nonregularity on the spin of three-dimensional polarization states, New J Phys, 23(2021)063059; doi: 10.1088/1367-2630/abd9e5.
  25. Norrman A, Gil J J, Friberg A T, Setälä T, Polarimetric nonregularity of evanescent waves, Opt Lett, 44(2019)215–218 .
  26. Chen Y, Wang F, Dong Z, Cai Y, Norrman A, Gil J J, Friberg A T, Setälä T, Polarimetric dimension and nonregularity of tightly focused light beams, Phys Rev A, 101(2020)053825; doi. org/10.1103/PhysRevA.101.053825.