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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 21 — Oct. 10, 2011
  • pp: 20616–20621

Engineering a square truncated lattice with light's orbital angular momentum

Pedro H. F. Mesquita, Alcenísio J. Jesus-Silva, Eduardo J. S. Fonseca, and Jandir M. Hickmann  »View Author Affiliations

Optics Express, Vol. 19, Issue 21, pp. 20616-20621 (2011)

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We engineer an intensity square lattice using the Fraunhofer diffraction of a Laguerre-Gauss beam by a square aperture. We verify numerically and experimentally that a perfect optical intensity lattice takes place only for even values of the topological charge. We explain the origin of this behavior based on the decomposition of the patterns. We also study the evolution of the lattice formation by observing the transition from one order to the next of the orbital angular momentum varying the topological charge in fractional steps.

© 2011 OSA

OCIS Codes
(050.1220) Diffraction and gratings : Apertures
(050.1940) Diffraction and gratings : Diffraction
(050.4865) Diffraction and gratings : Optical vortices

ToC Category:
Diffraction and Gratings

Original Manuscript: August 11, 2011
Revised Manuscript: September 19, 2011
Manuscript Accepted: September 19, 2011
Published: October 3, 2011

Pedro H. F. Mesquita, Alcenísio J. Jesus-Silva, Eduardo J. S. Fonseca, and Jandir M. Hickmann, "Engineering a square truncated lattice with light's orbital angular momentum," Opt. Express 19, 20616-20621 (2011)

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  1. L. M. Pismen, Vortices in Nonlinear Fields: From Liquid Crystals to Superfluids, from Non-Equilibrium Patterns to Cosmic Strings (Oxford University Press, Oxford, 1999).
  2. Y. S. Kivshar, and G. P. Agrawal, Optical solitons: from fibers to photonic crystals (Academic Press, Amsterdam; Boston, 2003).
  3. V. Tikhonenko, J. Christou, and B. Lutherdaves, “Spiraling bright spatial solitons formed by the breakup of an optical vortex in a saturable self-focusing medium,” J. Opt. Soc. Am. B 12(11), 2046–2052 (1995). [CrossRef]
  4. V. Tikhonenko, J. Christou, and B. Luther-Davies, “Three dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett. 76(15), 2698–2701 (1996). [CrossRef] [PubMed]
  5. D. V. Petrov, L. Torner, J. Martorell, R. Vilaseca, J. P. Torres, and C. Cojocaru, “Observation of azimuthal modulational instability and formation of patterns of optical solitons in a quadratic nonlinear crystal,” Opt. Lett. 23(18), 1444–1446 (1998). [CrossRef] [PubMed]
  6. J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W. Ketterle, “Observation of vortex lattices in Bose-Einstein condensates,” Science 292(5516), 476–479 (2001). [CrossRef] [PubMed]
  7. J. Masajada, A. Popiolek-Masajada, and M. Leniec, “Creation of vortex lattices by a wavefront division,” Opt. Express 15(8), 5196–5207 (2007). [CrossRef] [PubMed]
  8. J. Masajada and B. Dubik, “Optical vortex generation by three plane wave interference,” Opt. Commun. 198(1-3), 21–27 (2001). [CrossRef]
  9. J. Masajada, A. Popiolek-Masajada, and D. M. Wieliczka, “The interferometric system using optical vortices as phase markers,” Opt. Commun. 207(1-6), 85–93 (2002). [CrossRef]
  10. J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett. 105(5), 053904 (2010). [CrossRef] [PubMed]
  11. R. W. Schoonover and T. D. Visser, “Creating polarization singularities with an N-pinhole interferometer,” Phys. Rev. A 79(4), 043809 (2009). [CrossRef]
  12. G. C. G. Berkhout and M. W. Beijersbergen, “Method for probing the orbital angular momentum of optical vortices in electromagnetic waves from astronomical objects,” Phys. Rev. Lett. 101(10), 100801 (2008). [CrossRef] [PubMed]
  13. G. C. G. Berkhout and M. W. Beijersbergen, “Using a multipoint interferometer to measure the orbital angular momentum of light in astrophysics,” J. Opt. A, Pure Appl. Opt. 11(9), 094021 (2009). [CrossRef]
  14. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).
  15. J. P. Kirk and A. L. Jones, “Phase-only complex-valued spatial filter,”, J. Opt. Soc. Am. B 61, 1023–1028 (1971).
  16. J. Leach, M. Dennis, J. Courtial, and M. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005). [CrossRef]
  17. U. Sinha, C. Couteau, T. Jennewein, R. Laflamme, and G. Weihs, “Ruling out multi-order interference in quantum mechanics,” Science 329(5990), 418–421 (2010). [CrossRef] [PubMed]
  18. Q. S. Ferreira, A. J. Jesus-Silva, E. J. S. Fonseca, and J. M. Hickmann, “Fraunhofer diffraction of light with orbital angular momentum by a slit,” Opt. Lett. 36(16), 3106–3108 (2011). [CrossRef] [PubMed]

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