- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review A

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Spin of random stationary light

José J. Gil1,*, Andreas Norrman2, Ari T. Friberg2, and Tero Setälä2

  • 1Department of Applied Physics, University of Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain
  • 2Center for Photonics Sciences, University of Eastern Finland, P. O. Box 111, FI-80101 Joensuu, Finland

  • *ppgil@unizar.es
PDF

Phys. Rev. A 107, 053518 – Published 22 May, 2023

DOI: https://doi.org/10.1103/PhysRevA.107.053518

Abstract

We develop a theoretical foundation for the spin angular momentum (SAM) of random, statistically stationary polychromatic light fields within the framework of classical optical coherence theory. The formulation is valid for fields of arbitrary frequency bandwidth and dimensionality. Both temporal and spectral representations are given, and we further elucidate the relationship between the SAM and the polarization characteristics of such fields as compared to monochromatic light. The special cases of quasimonochromatic light and planar fields are analyzed separately. Generally, our paper offers deeper insights into the SAM and polarization structures as well as their interlinked connections in random stationary light, which could be beneficial in exploiting SAM in stochastic optical near fields and tightly focused beams exhibiting complex polarization character.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (55)

  1. S. M. Barnett, Rotation of electromagnetic fields and the nature of optical angular momentum, J. Mod. Opt. 57, 1339 (2010).
  2. M. Masuripur, Spin and orbital angular momenta of electromagnetic waves in free space, Phys. Rev. A 84, 033838 (2011).
  3. K. Y. Bliokh, J. Dressel, and F. Nori, Conservation of spin and orbital angular momenta in electromagnetism, New J. Phys. 16, 093037 (2014).
  4. K. Y. Bliokh and F. Nori, Transverse and longitudinal angular momenta of light, Phys. Rep. 592, 1 (2015).
  5. A. Aiello, P. Banzer, M. Neugebauer, and G. Leuch, From transverse angular momentum to photonic wheels, Nat. Photonics 9, 789 (2015).
  6. S. M. Barnett, L. Allen, R. P. Cameron, C. R. Gilson, M. J. Padgett, F. C. Speirits, and A. M. Yao, On the natures of the spin and orbital parts of optical angular momentum, J. Opt. 18, 064004 (2016).
  7. A. I. Arbab, New derivation of the spin of the electromagnetic field, Optik 184, 436 (2019).
  8. A. Aiello, Helicity, chirality, and spin of optical fields without vector potentials, Phys. Rev. A 106, 043519 (2022).
  9. C. Brosseau, Fundamentals of Polarized Light: A Statistical Approach (Wiley, New York, 1998).
  10. J. J. Gil and R. Ossikovski, Polarized Light and the Mueller Matrix Approach (CRC, Boca Raton, FL, 2022).
  11. J. H. Poynting, The wave-motion of a revolving shaft, and a suggestion as to the angular momentum in a beam of circularly polarised light, Proc. R. Soc. London, Ser. A 82, 560 (1909).
  12. R. A. Beth, Mechanical detection and measurement of the angular momentum of light, Phys. Rev. 50, 115 (1936).
  13. K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, Extraordinary momentum and spin in evanescent waves, Nat. Commun. 5, 3300 (2014).
  14. M. Neugebauer, T. Bauer, A. Aiello, and P. Banzer, Measuring the Transverse Spin Density of Light, Phys. Rev. Lett. 114, 063901 (2015).
  15. M. Neugebauer, J. S. Eismann, T. Bauer, and P. Banzer, Magnetic and Electric Transverse Spin Density of Spatially Confined Light, Phys. Rev. X 8, 021042 (2018).
  16. J. S. Eismann, P. Banzer, and M. Neugebauer, Spin-orbit coupling affecting the evolution of transverse spin, Phys. Rev. Res. 1, 033143 (2019).
  17. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, UK, 1995).
  18. M. Dennis, Geometric interpretation of the three-dimensional coherence matrix for nonparaxial polarization, J. Opt. A: Pure Appl. Opt. 6, S26 (2004).
  19. J. J. Gil, A. T. Friberg, A. Norrman, and T. Setälä, Effect of polarimetric nonregularity on the spin of three-dimensional polarization states, New J. Phys. 23, 063059 (2021).
  20. Y. Chen, F. Wang, Z. Dong, Y. Cai, A. Norrman, J. J. Gil, A. T. Friberg, and T. Setälä, Structure of transverse spin in focused random light, Phys. Rev. A 104, 013516 (2021).
  21. J. S. Eismann, L. H. Nicholls, D. J. Roth, M. A. Alonso, P. Banzer, F. J. Rodríguez-Fortuno, A. V. Zayats, F. Nori, and K. Y. Bliokh, Transverse spinning of unpolarized light, Nat. Photonics 15, 156 (2021).
  22. J. J. Gil, A. Norrman, A. T. Friberg, and T. Setälä, Intensity and spin anisotropy of three-dimensional polarization states, Opt. Lett. 44, 3578 (2019).
  23. Y. Chen, A. Norrman, S. A. Ponomarenko, and A. T. Friberg, Spin density in partially coherent surface-plasmon-polariton vortex fields, Phys. Rev. A 103, 063511 (2021).
  24. Z. Wang, C. Yan, F. Wang, Y. Chen, and Y. Cai, Effect of optical spatial coherence on localized spin angular momentum density in tightly focused light [Invited], J. Opt. Soc. Am. A 39, C58 (2022).
  25. K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, Dual electromagnetism: Helicity, spin, momentum and angular momentum, New J. Phys. 15, 033026 (2013).
  26. V. B. Berestetskii, E. M. Lifshitz, and L. P. Pitaevskii, Quantum Electrodynamics, 2nd ed. (Pergamon, New York, 1982).
  27. J. J. Gil, Interpretation of the coherency matrix for three-dimensional polarization states, Phys. Rev. A 90, 043858 (2014).
  28. J. J. Gil, Components of purity of a three-dimensional polarization state, J. Opt. Soc. Am. A 33, 40 (2016).
  29. R. M. A. Azzam, Three-dimensional polarization states of monochromatic light fields, J. Opt. Soc. Am. A 28, 2279 (2011).
  30. C. J. R. Sheppard, Jones and Stokes parameters for polarization in three dimensions, Phys. Rev. A 90, 023809 (2014).
  31. J. J. Gil, I. San José, A. Norrman, A. T. Friberg, and T. Setälä, Sets of orthogonal three-dimensional polarization states and their physical interpretation, Phys. Rev. A 100, 033824 (2019).
  32. A. Norrman, A. T. Friberg, J. J. Gil, and T. Setälä, Dimensionality of random light fields, J. Eur. Opt. Soc.-Rapid Publ. 13, 36 (2017).
  33. J. J. Gil, Geometric interpretation and general classification of three-dimensional polarization states through the intrinsic Stokes parameters, Photonics 8, 315 (2021).
  34. L. Mandel, Intensity fluctuations of partially polarized light, Proc. Phys. Soc. 81, 1104 (1963).
  35. T. Setälä, K. Lindfors, M. Kaivola, J. Tervo, and A. T. Friberg, Intensity fluctuations and degree of polarization in three-dimensional thermal light fields, Opt. Lett. 29, 2587 (2004).
  36. G. G. Stokes, On the composition and resolution of streams of polarized light from different sources, Trans. Cambridge Philos. Soc. 9, 399 (1852).
  37. P. Roman, Generalized Stokes parameters for waves with arbitrary form, Nuovo Cimento 13, 974 (1959).
  38. U. Fano, Description of states in quantum mechanics by density matrix and operator techniques, Rev. Mod. Phys. 29, 74 (1957).
  39. R. Barakat, Degree of polarization and the principal idempotents of the coherency matrix, Opt. Commun. 23, 147 (1077).
  40. T. Carozzi, R. Karlsson, and J. Bergman, Parameters characterizing electromagnetic wave polarization, Phys. Rev. E 61, 2024 (2000).
  41. T. Setälä, Degree of polarization for optical near fields, Phys. Rev. E 66, 016615 (2002).
  42. J. J. Gil, J. M. Correas, P. Melero, and C. Ferreira, Generalized polarization algebra, Monog. Sem. Mat. G. Galdeano 31, 161 (2004).
  43. N. I. Petrov, Vector and tensor polarizations of light beams, Laser Phys. 18, 522 (2008).
  44. C. J. R. Sheppard, M. Castello, and A. Diaspro, Three-dimensional polarization algebra, J. Opt. Soc Am. A 33, 1938 (2016).
  45. J. J. Gil, Intrinsic Stokes parameters for 2D and 3D polarization states, J. Eur. Opt. Soc.-Rapid Publ. 10, 15054 (2015).
  46. E. Wolf, Coherence properties of partially polarized electromagnetic radiation, Nuovo Cimento 13, 1165 (1959).
  47. J. Tervo, T. Setälä, and A. T. Friberg, Theory of partially coherent electromagnetic fields in the space-frequency domain, J. Opt. Soc. Am. A 21, 2205 (2004).
  48. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University Press, Cambridge, UK, 2007).
  49. M. A. Alonso, Geometric descriptions for the polarization of nonparaxial light: A tutorial, Adv. Opt. Photon. 15, 176 (2023).
  50. T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, Polarization time and length for random optical beams, Phys. Rev. A 78, 033817 (2008).
  51. T. Voipio, T. Setälä, A. Shevchenko, and A. T. Friberg, Polarization dynamics and polarization time of random three-dimensional electromagnetic fields, Phys. Rev. A 82, 063807 (2010).
  52. A. Shevchenko, M. Roussey, A. T. Friberg, and T. Setälä, Polarization time of unpolarized light, Optica 4, 64 (2017).
  53. T. Setälä, F. Nunziata, and A. T. Friberg, Differences between partial polarizations in the space–time and space–frequency domains, Opt. Lett. 34, 2924 (2009).
  54. H. Partanen, B. J. Hoenders, A. T. Friberg, and T. Setälä, Young's interference experiment with electromagnetic narrowband light, J. Opt. Soc. Am. A 35, 1379 (2018).
  55. M. Lahiri and E. Wolf, Does a light beam of very narrow bandwidth always behave as a monochromatic beam? Phys. Lett. A 374, 997 (2010).

Outline

Information

Phys. Rev. A 107, 053518– Published 22 May, 2023
  • Received 1 March 2023
  • Accepted 28 April 2023
Crossmark - Check for updates button

©2023 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation