Asian Journal of Physics Vol. 33, Nos 3 & 4 (2024) 197-204

Geometric phase in dual-beam interference

Ari T Friberg
Center for Photonics Sciences, University of Eastern Finland (UEF), P.O. Box 111, FI-80101 Joensuu, Finland

Dedicated to Professor Anna Consortini for her significant contributions and pioneering works in the field of atmospheric turbulence and her continuous commitment to promote optics at global level 


Geometric phase is a fundamental and universal concept in physics. Its most famous realization in optics is the Pancharatnam–Berry phase, which is an extra phase a beam of light acquires when its state of polarization is varied. We consider several aspects of the geometric and dynamical phases in three circumstances. A widely encountered situation is Mach–Zehnder interferometry, in which the polarization is typically changed in discrete steps. When beating two optical waves of slightly different frequencies, the polarization state of the superposition field varies continuously. Finally, in Young’s dual-beam interference, a cornerstone of optical physics, the field exhibits periodic polarization state changes along a line perpendicular to the fringes. New far-zone geometric-phase results in Young’s interference are provided. © Anita Publications. All rights reserved.
Doi: 10.54955/AJP.33.3-4.2024.197-204
Keywords: Polarizaion state, Pancharatnam–Berry phase, Dynamical phase, Young’s setup.


Peer Review Information
Method: Single- anonymous; Screened for Plagiarism? Yes
Buy this Article in Print © Anita Publications. All rights reserve

References

  1. Arteaga O, Fresnel–Arago fifth law of interference; the first descripton of a geometric phase in optics, J Mod Opt, 68(2021)350–356.
  2. Pancahratnam S, Generalized theory of interference and its applications – Part Coherent pencils, Proc Indian Acad Sci A, 44(1956)247–262.
  3. Berry M V, Quantal phase factors accompanying adiabatic changes, Proc Royal Soc (London) A, 392(1984)45–54.
  4. Berry M V, The adiabatic phase and Pancharatnam’s phase for polarized light, J Mod Opt, 34(1987)1401–1407.
  5. Garza-Soto L, Hagen N, Lopez-Mago D, Deciphering Pancharatnam’s discovery of geometric phase: trospective, J Opt Soc Am A, 40(2023)925–931.
  6. Hariharan P, The geometric phase, in Progress in Optics, (ed) Wolf E, (Elsevier, 2006), vol 48, pp.149–201.
  7. Kim J, Li Y, Miskiewicz M N, Oh C, Kudenov M W, Escuti M J, Fabrication of ideal geometric-phase holograms with arbitrary waveforms, Optica, 2(2015)958–964.
  8. Maguid E, Yelevich I, Yannai M, Kleiner V, Bongersma M L, Hasman E, Multifuntional interleaved geometric-phase dielectric metasurfaces, Light Sci Appl, 6(2017)e17027; doi.org/10.1038/lsa.2017.27.
  9. Minovich A E, Zayats A V, Geometric-phase metasurfaces based on anisotropic reflection: generalized design rules, ACS Photonics, 8(2018)1755–1761.
  10. Daniel S, Saastamoinen K, Saastamoinen T, Vartiainen I, Friberg A T, Visser T D, Surface plasmons carry the Pancharatnam–Berry geometric phase, Phys Rev Lett, 119 (2017)253901;doi. org/10.1103/PhysRevLett.119.253901.
  11. Kwiat P G, Chiao R Y, Observation of nonclassical Berry’s phase for the photon, Phys Rev Lett, 66(1991)588–591.
  12. Alonso M A, Geometric descriptions for the polarization of nonparaxial light: a tutorial, Adv Opt Photonics, 15(2023)176–235.
  13. Zela F D, The Pancharatnam–Berry phase: theoretical and experimental aspects, in Theoretical Concepts of Quantum Mechanics, (ed) Pahlavani M R, (IntechOpen), Chapt 14, 2012.
  14. Hannonen A, Saastamoinen K, Leppänen L.-P, Koivurova M, Shevchenko A, Friberg A T, Setälä T, Geometric phase in beating of light waves, New J Phys, 21(2019)083030; 10.1088/1367-2630/ab3740.
  15. Hannonen A, Partanen H, Tervo J,Setälä T, Friberg A T, Pancharatnam-Berry phase in electromagnetic double-pinhole interference, Phys Rev A, 99(2019)053826; doi.org/10.1103/PhysRevA.99.053826.
  16. Brosseau C, Fundamentals of Polarized A Statistical Optics Approach, (Wiley), 1998.
  17. Setälä T, Tervo J, Friberg A T, Stokes parameters and polarization contrasts in Young’s interference experiment, Opt Lett, 31(2006)2208–2210.
  18. Hannonen A, Partanen H, Leinonen A, Heikkinen J, Hakala T K, Friberg A T, Setälä T, Measurement of the Pancharatnam–Berry phase in two-beam interference, Optica, 7(2020)1435–1439.
  19. Zhou Z, Margalit Y, Moukouri S, Meir Y, Folman R, An experimental test of the geodesic rule proposition for the noncyclic geometric phase, Sci Adv, 6(2020)eaay8345; doi. 10.1126/sciadv.aay83.
  20. Leinonen A, Hannonen A, Partanen H, Heikkinen J, Setälä T, Friberg A T, Hakala T K, Noncyclic continuous Pancharatnam–Berry phase in dual-beam interference, Commun Phys, 6(2023)132; doi.org/10.1038/s42005-023-01249-2.