Manifestation of the Gouy phase in strongly focused, radially polarized beams.dvi

The Gouy phase, sometimes called the focal phase anomaly, is the curious effect that in the vicinity of its focus a diffracted field, compared to a non-diffracted, converging spherical wave of the same frequency, undergoes a rapid phase change by an amount of π . We theoretically investigate the phase behavior and the polarization ellipse of a strongly focused, radially polarized beam. We find that the significant variation of the state of polarization in the focal region, is a manifestation of the different Gouy phases that the two electric field components undergo. © 2013 Optical Society of America OCIS codes: (050.1960) Diffraction theory; (260.1960) Diffraction theory; (260.2110) Electromagnetic optics; (260.5430) Polarization. References and links 1. L. G. Gouy, “Sur une propriété nouvelle des ondes lumineuses,” Comptes Rendus hebdomadaires des Séances de l’Académie des Sciences 110, 1251–1253 (1890). 2. L. G. Gouy, “Sur la propagation anomale des ondes,” Annales des Chimie et de Physique 6e 24, 145–213 (1891). 3. S. M. Baumann, D. M. Kalb, and E. J. Galvez, “Propagation dynamics of optical vortices due to Gouy phase,” Opt. Express 17, 9818–9827 (2009). 4. G. M. Philip, V. Kumar, G. Milione, and N. K. Viswanathan, “Manifestation of the Gouy phase in vector-vortex beams,” Opt. Lett. 37, 2667–2669 (2012). 5. W. Zhu, A. Agrawal, A. Nahata, “Direct measurement of the Gouy phase shift for surface plasmon-polaritons,” Opt. Express 15, 9995–10001 (2007). 6. T. D. Visser and E. Wolf, “The origin of the Gouy phase anomaly and its generalization to astigmatic wavefields,” Opt. Commun. 283, 3371–3375 (2010). 7. M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993). 8. G. Lamouche, M. L. Dufour, B. Gauthier and J.-P. Monchalin, “Gouy phase anomaly in optical coherence tomography,” Opt. Commun. 239, 297–301 (2004). 9. T. Klaassen, A. Hoogeboom, M. P. van Exter and J. P. Woerdman, “Gouy phase of nonparaxial eigenmodes in a folded resonator,” J. Opt. Soc. Am. A 21, 1689–1693 (2004). 10. X. Pang, D. G. Fischer and T. D. Visser, “A generalized Gouy phase for focused partially coherent light and its implications for interferometry,” J. Opt. Soc. Am. A 29, 989–993. (2012). 11. X. Pang, T. D. Visser and E. Wolf, “Phase anomaly and phase singularities of the field in the focal region of high-numerical aperture systems,” Opt. Commun. 284, 5517–5522 (2011). 12. K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7, 77–87 (2000). 13. R. Martı́nez-Herrero and P. M. Mejı́as, “Propagation and parametric characterization of the polarization structure of paraxial radially and azimuthally polarized beams,” Opt. Laser Techn. 44, 482–485 (2012). 14. R. Dorn and S. Quabis and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003). #184950 $15.00 USD Received 5 Feb 2013; revised 19 Mar 2013; accepted 21 Mar 2013; published 28 Mar 2013 (C) 2013 OSA 8 April 2013 | Vol. 21, No. 7 | DOI:10.1364/OE.21.008331 | OPTICS EXPRESS 8331 15. L. Novotny, M. R. Beversluis, K. S. Youngworth and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254 (2001). 16. C. J. R. Sheppard and A. Choudhury, “Annular pupils, radial polarization, and superresolution,” Appl. Opt. 43, 4322–4327 (2004). 17. Q. Zhan, “Trapping metallic Rayleigh particles with radial polarization,” Opt. Express 12, 3377–3382 (2004). 18. T. A. Nieminen, N. R. Heckenberg and H. Rubinsztein-Dunlop, “Forces in optical tweezers with radially and azimuthally polarized trapping beams,” Opt. Lett. 33, 122–124 (2008). 19. D. P. Biss, K. S. Youngworth and T. G. Brown, “Dark-field imaging with cylindrical-vector beams,” Appl. Opt. 45, 470–479 (2006). 20. T. G. Brown “Unconventional polarization states: Beam propagation, focusing, and imaging,” in Progress in Optics, E. Wolf eds. (Elsevier, 2011), 56, pp. 81–129. 21. T. D. Visser and J. T. Foley, “On the wavefront spacing of focused, radially polarized beams,” J. Opt. Soc. Am. A 22, 2527–2531 (2005). 22. H. Chen, Q. Zhan, Y. Zhang, and Y.-P. Li, “The Gouy phase shift of the highly focused radially polarized beam,” Phys. Lett. A 371, 259–261 (2007). 23. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems, II. Structure of the image field in aplanatic systems,” Proc. R. Soc. London Ser. A 253, 358–379 (1959). 24. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, Seventh (expanded) edition (Cambridge University Press, 1999). 25. M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1965). 26. R.W. Schoonover and T.D. Visser, “Polarization singularities of focused, radially polarized fields,” Opt. Express 14, 5733–5745 (2006). 27. R. Martı́nez-Herrero and P.M. Mejı́as, “Stokes-parameters representation in terms of the radial and azimuthal field components: A proposal ,” Opt. Laser Techn. 42, 1099–1102 (2010). 28. G.J. Gbur, Mathematical Methods for Optical Physics and Engineering (Cambridge University Press, Cambridge, 2011), pp. 91–93. 29. D.W. Diehl, R.W. Schoonover and T.D. Visser, “The structure of focused, radially polarized fields,” Opt. Express 14, 3030–3038 (2006).