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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 27 — Dec. 17, 2012
  • pp: 28929–28940

Phase anomalies in Bessel-Gauss beams

Myun-Sik Kim, Toralf Scharf, Alberto da Costa Assafrao, Carsten Rockstuhl, Silvania F. Pereira, H. Paul Urbach, and Hans Peter Herzig  »View Author Affiliations


Optics Express, Vol. 20, Issue 27, pp. 28929-28940 (2012)
http://dx.doi.org/10.1364/OE.20.028929


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Abstract

Bessel-Gauss beams are known as non-diffracting beams. They can be obtained by focusing an annularly shaped collimated laser beam. Here, we report for the first time on the direct measurement of the phase evolution of such beams by relying on longitudinal-differential interferometry. We found that the characteristics of Bessel-Gauss beams cause a continuously increasing phase anomaly in the spatial domain where such beams do not diverge, i.e. there is a larger phase advance of the beam when compared to a referential plane wave. Simulations are in excellent agreement with measurements. We also provide an analytical treatment of the problem that matches both experimental and numerical results and provides an intuitive explanation.

© 2012 OSA

OCIS Codes
(050.5080) Diffraction and gratings : Phase shift
(180.3170) Microscopy : Interference microscopy
(260.0260) Physical optics : Physical optics
(100.5088) Image processing : Phase unwrapping
(260.6042) Physical optics : Singular optics

ToC Category:
Physical Optics

History
Original Manuscript: October 16, 2012
Revised Manuscript: November 30, 2012
Manuscript Accepted: November 30, 2012
Published: December 12, 2012

Citation
Myun-Sik Kim, Toralf Scharf, Alberto da Costa Assafrao, Carsten Rockstuhl, Silvania F. Pereira, H. Paul Urbach, and Hans Peter Herzig, "Phase anomalies in Bessel-Gauss beams," Opt. Express 20, 28929-28940 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-27-28929


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References

  1. L. G. Gouy, “Sur une propriété nouvelle des ondes lumineuses,” C. R. Acad. Sci.110, 1251–1253 (1890).
  2. A. E. Siegman, Lasers (University Science Books, 1986).
  3. M. Born and E. Wolf, Principles of Optics, 7th ed (Cambridge University Press, 1999).
  4. F. Gittes and C. F. Schmidt, “Interference model for back-focal-plane displacement detection in optical tweezers,” Opt. Lett.23(1), 7–9 (1998). [CrossRef] [PubMed]
  5. B. Roy, S. B. Pal, A. Haldar, R. K. Gupta, N. Ghosh, and A. Banerjee, “Probing the dynamics of an optically trapped particle by phase sensitive back focal plane interferometry,” Opt. Express20(8), 8317–8328 (2012). [CrossRef] [PubMed]
  6. L. Friedrich and A. Rohrbach, “Tuning the detection sensitivity: a model for axial backfocal plane interferometric tracking,” Opt. Lett.37(11), 2109–2111 (2012). [CrossRef] [PubMed]
  7. R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic Press, San Diego, 1992)
  8. S. Carrasco, B. E. A. Saleh, M. C. Teich, and J. T. Fourkas, “Second- and third-harmonic generation with vector Gaussian beams,” J. Opt. Soc. Am. B23(10), 2134–2141 (2006). [CrossRef]
  9. C. Zhang, Y.-Q. Qin, and Y.-Y. Zhu, “Perfect quasi-phase matching for the third-harmonic generation using focused Gaussian beams,” Opt. Lett.33(7), 720–722 (2008). [CrossRef] [PubMed]
  10. T. Popmintchev, M.-C. Chen, P. Arpin, M. M. Murnane, and H. C. Kapteyn, “The attosecond nonlinear optics of bright coherent X-ray generation,” Nat. Photonics4(12), 822–832 (2010). [CrossRef]
  11. J. T. Foley and E. Wolf, “Wave-front spacing in the focal region of high-numerical-aperture systems,” Opt. Lett.30(11), 1312–1314 (2005). [CrossRef] [PubMed]
  12. H. Chen, Q. Zhan, Y. Zhang, and Y.-P. Li, “The Gouy phase shift of the highly focused radially polarized beam,” Phys. Lett. A371(3), 259–261 (2007). [CrossRef]
  13. T. Tyc, “Gouy phase for full-aperture spherical and cylindrical waves,” Opt. Lett.37(5), 924–926 (2012). [CrossRef] [PubMed]
  14. R. W. Boyd, “Intuitive explanation of the phase anomaly of focused light beams,” J. Opt. Soc. Am.70(7), 877–880 (1980). [CrossRef]
  15. D. Subbarao, “Topological phase in Gaussian beam optics,” Opt. Lett.20(21), 2162–2164 (1995). [CrossRef] [PubMed]
  16. R. Simon and N. Mukunda, “Bargmann invariant and the geometry of the Güoy effect,” Phys. Rev. Lett.70(7), 880–883 (1993). [CrossRef] [PubMed]
  17. S. J. M. Habraken and G. Nienhuis, “Geometric phases in astigmatic optical modes of arbitrary order,” J. Math. Phys.51(8), 082702 (2010). [CrossRef]
  18. G. F. Brand, “A new millimeter wave geometric phase demonstration,” Int. J. Infrared Millim. Waves21(4), 505–518 (2000). [CrossRef]
  19. P. Hariharan and P. A. Robinson, “The Gouy phase shift as a geometrical quantum effect,” J. Mod. Opt.43, 219–221 (1996).
  20. S. Feng and H. G. Winful, “Physical origin of the Gouy phase shift,” Opt. Lett.26(8), 485–487 (2001). [CrossRef] [PubMed]
  21. I. G. da Paz, P. L. Saldanha, M. C. Nemes, and J. G. Peixoto de Faria, “Experimental proposal for measuring the Gouy phase of matter waves,” New J. Phys.13(12), 125005 (2011). [CrossRef]
  22. T. D. Visser and E. Wolf, “The origin of the Gouy phase anomaly and its generalization to astigmatic wavefields,” Opt. Commun.283(18), 3371–3375 (2010). [CrossRef]
  23. J. P. Rolland, K. P. Thompson, K.-S. Lee, J. Tamkin, T. Schmid, and E. Wolf, “Observation of the Gouy phase anomaly in astigmatic beams,” Appl. Opt.51(15), 2902–2908 (2012). [CrossRef] [PubMed]
  24. N. C. R. Holme, B. C. Daly, M. T. Myaing, and T. B. Norris, “Gouy phase shift of single-cycle picosecond acoustic pulses,” Appl. Phys. Lett.83(2), 392–394 (2003). [CrossRef]
  25. C. R. Carpenter, “Gouy phase advance with microwaves,” Am. J. Phys.27, 98–100 (1959).
  26. J. F. Federici, R. L. Wample, D. Rodriguez, and S. Mukherjee, “Application of terahertz Gouy phase shift from curved surfaces for estimation of crop yield,” Appl. Opt.48(7), 1382–1388 (2009). [CrossRef] [PubMed]
  27. A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, “Direct observation of the Gouy phase shift with single-cycle terahertz pulse,” Phys. Rev. Lett.83(17), 3410–3413 (1999). [CrossRef]
  28. H. He and X.-C. Zhang, “Analysis of Gouy phase shift for optimizing terahertz air-biased-coherent-detection,” Appl. Phys. Lett.100(6), 061105 (2012). [CrossRef]
  29. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
  30. H. Kogelnik and T. Li, “Laser beams and resonators,” Appl. Opt.5(10), 1550–1567 (1966). [CrossRef] [PubMed]
  31. T. Ackemanna, W. Grosse-Nobis, and G. L. Lippia, “The Gouy phase shift, the average phase lag of Fourier components of Hermite-Gaussian modes and their application to resonance conditions in optical cavities,” Opt. Commun.189(1-3), 5–14 (2001). [CrossRef]
  32. J. Courtial, “Self-imaging beams and the Guoy effect,” Opt. Commun.151(1-3), 1–4 (1998). [CrossRef]
  33. J. Hamazaki, Y. Mineta, K. Oka, and R. Morita, “Direct observation of Gouy phase shift in a propagating optical vortex,” Opt. Express14(18), 8382–8392 (2006). [CrossRef] [PubMed]
  34. H. X. Cui, X. L. Wang, B. Gu, Y. N. Li, J. Chen, and H. T. Wang, “Angular diffraction of an optical vortex induced by the Gouy phase,” J. Opt.14(5), 055707 (2012). [CrossRef]
  35. X. Pang, G. Gbur, and T. D. Visser, “The Gouy phase of Airy beams,” Opt. Lett.36(13), 2492–2494 (2011). [CrossRef] [PubMed]
  36. R. Gadonas, V. Jarutis, R. Paškauskas, V. Smilgevičius, A. Stabinis, and V. Vaičaitis, “Self-action of Bessel beam in nonlinear medium,” Opt. Commun.196(1-6), 309–316 (2001). [CrossRef]
  37. P. Martelli, M. Tacca, A. Gatto, G. Moneta, and M. Martinelli, “Gouy phase shift in nondiffracting Bessel beams,” Opt. Express18(7), 7108–7120 (2010). [CrossRef] [PubMed]
  38. W. Zhu, A. Agrawal, and A. Nahata, “Direct measurement of the Gouy phase shift for surface plasmon-polaritons,” Opt. Express15(16), 9995–10001 (2007). [CrossRef] [PubMed]
  39. M.-S. Kim, T. Scharf, S. Mühlig, C. Rockstuhl, and H. P. Herzig, “Gouy phase anomaly in photonic nanojets,” Appl. Phys. Lett.98(19), 191114 (2011). [CrossRef]
  40. M.-S. Kim, T. Scharf, C. Etrich, C. Rockstuhl, and H. H. Peter, “Longitudinal-differential interferometry: Direct imaging of axial superluminal phase propagation,” Opt. Lett.37(3), 305–307 (2012). [CrossRef] [PubMed]
  41. D. Chauvat, O. Emile, M. Brunel, and A. Le Floch, “Direct measurement of the central fringe velocity in Young-type experiments,” Phys. Lett. A295(2-3), 78–80 (2002). [CrossRef]
  42. M. Vasnetsov, V. Pas’ko, A. Khoroshun, V. Slyusar, and M. Soskin, “Observation of superluminal wave-front propagation at the shadow area behind an opaque disk,” Opt. Lett.32(13), 1830–1832 (2007). [CrossRef] [PubMed]
  43. Q. Zhan, “Second-order tilted wave interpretation of the Gouy phase shift under high numerical aperture uniform illumination,” Opt. Commun.242(4-6), 351–360 (2004). [CrossRef]
  44. F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics4(11), 780–785 (2010). [CrossRef]
  45. F. O. Fahrbach and A. Rohrbach, “Propagation stability of self-reconstructing Bessel beams enables contrast-enhanced imaging in thick media,” Nat Commun3, 632 (2012). [CrossRef] [PubMed]
  46. T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods8(5), 417–423 (2011). [CrossRef] [PubMed]
  47. B. Sick, B. Hecht, and L. Novotny, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett.85(21), 4482–4485 (2000). [CrossRef] [PubMed]
  48. V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature419(6903), 145–147 (2002). [CrossRef] [PubMed]
  49. E. Mcleod and C. B. Arnold, “Subwavelength direct-write nanopatterning using optically trapped microspheres,” Nat. Nanotechnol.3(7), 413–417 (2008). [CrossRef] [PubMed]
  50. J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun.197(4-6), 239–245 (2001). [CrossRef]
  51. V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett.91(9), 093602 (2003). [CrossRef] [PubMed]
  52. M. K. Bhuyan, F. Courvoisier, P.-A. Lacourt, M. Jacquot, L. Furfaro, M. J. Withford, and J. M. Dudley, “High aspect ratio taper-free microchannel fabrication using femtosecond Bessel beams,” Opt. Express18(2), 566–574 (2010). [CrossRef] [PubMed]
  53. X.-F. Li, R. J. Winfield, S. O’Brien, and G. M. Crean, “Application of Bessel beams to 2D microfabrication,” Appl. Surf. Sci.255(10), 5146–5149 (2009). [CrossRef]
  54. H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics2(8), 501–505 (2008). [CrossRef]
  55. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci.253(1274), 358–379 (1959). [CrossRef]
  56. J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58(15), 1499–1501 (1987). [CrossRef] [PubMed]
  57. F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun.64(6), 491–495 (1987). [CrossRef]
  58. J. H. McLeod, “The axicon: A new type of optical element,” J. Opt. Soc. Am.44(8), 592–597 (1954). [CrossRef]
  59. G. Indebetouw, “Nondiffracting optical fields: some remarks in their analysis and synthesis,” J. Opt. Soc. Am. A6(1), 150–152 (1989). [CrossRef]
  60. A. Vasara, J. Turunen, and A. T. Friberg, “Realization of general nondiffracting beams with computer-generated holograms,” J. Opt. Soc. Am. A6(11), 1748–1754 (1989). [CrossRef] [PubMed]
  61. Q. Huang, S. Coetmellec, F. Duval, A. Louis, H. Leblond, and M. Brunel, “Analytical expressions for diffraction-free beams through an opaque disk,” J. Europ. Opt. Soc. Rap. Public.6, 11031 (2011). [CrossRef]
  62. C. J. R. Sheppard and T. Wilson, “Gaussian-beam theory of lenses with annular aperture,” IEE J. Microwaves, Opt. Acoust.2(4), 105–112 (1978). [CrossRef]
  63. M.-S. Kim, T. Scharf, S. Mühlig, C. Rockstuhl, and H. P. Herzig, “Engineering photonic nanojets,” Opt. Express19(11), 10206–10220 (2011). [CrossRef] [PubMed]
  64. M.-S. Kim, T. Scharf, and H. P. Herzig, “Small-size microlens characterization by multiwavelength high-resolution interference microscopy,” Opt. Express18(14), 14319–14329 (2010). [CrossRef] [PubMed]
  65. X. Pang, D. G. Fischer, and T. D. Visser, “Generalized Gouy phase for focused partially coherent light and its implications for interferometry,” J. Opt. Soc. Am. A29(6), 989–993 (2012). [CrossRef] [PubMed]
  66. E. H. Linfoot and E. Wolf, “Phase distribution near focus in an aberration-free diffraction image,” Proc. Phys. Soc. Lond.69(8), 823–832 (1956). [CrossRef]

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