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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 53, Iss. 10 — Apr. 1, 2014
  • pp: 2040–2050

Arithmetic of focused vortex beams in three-dimensional optical lattice arrays

Jeffrey A. Davis, Don M. Cottrell, Kyle R. McCormick, Jorge Albero, and Ignacio Moreno  »View Author Affiliations

Applied Optics, Vol. 53, Issue 10, pp. 2040-2050 (2014)

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In this work, we present a method to generate a 3D lattice of vortex beams. We apply phase look-up tables (LUTs) designed to generate gratings having an arbitrary content of diffraction orders. This phase LUT can be applied to a variety of diffraction optical elements, such as linear phase gratings, blazed diffractive lenses, and spiral phase patterns. We concentrate on combinations of all of these to create 3D structures of vortex beams. In particular, we generate all of these elements in the first output quadrant and eliminate the zero-order diffraction that often unavoidably accompanies these patterns. We discuss different ways of producing these 3D vortex gratings, and how the various output beams are related to the arithmetic of the 3D distribution of topological charges. Experimental results are provided by means of a liquid crystal spatial light modulator.

© 2014 Optical Society of America

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(050.1965) Diffraction and gratings : Diffractive lenses
(050.4865) Diffraction and gratings : Optical vortices
(070.6120) Fourier optics and signal processing : Spatial light modulators

ToC Category:
Diffraction and Gratings

Original Manuscript: December 13, 2013
Revised Manuscript: February 7, 2014
Manuscript Accepted: February 14, 2014
Published: March 25, 2014

Jeffrey A. Davis, Don M. Cottrell, Kyle R. McCormick, Jorge Albero, and Ignacio Moreno, "Arithmetic of focused vortex beams in three-dimensional optical lattice arrays," Appl. Opt. 53, 2040-2050 (2014)

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  1. S. Jeon, J.-U. Park, R. Cirelli, S. Yang, C. E. Heitzman, P. V. Braun, P. J. A. Kenis, and J. A. Rogers, “Fabricating complex three-dimensional nanostructures with high-resolution conformable phase masks,” Proc. Natl. Acad. Sci. USA 101, 12428–12433 (2004). [CrossRef]
  2. E. Schonbrun, R. Piestun, P. Jordan, J. Cooper, K. D. Wulff, J. Courtial, and M. Padgett, “3D interferometric optical tweezers using a single spatial light modulator,” Opt. Express 13, 3777–3786 (2005). [CrossRef]
  3. V. G. Shvedov, C. Hnatovsky, N. Shostka, A. V. Rode, and W. Krolikowski, “Optical manipulation of particle ensembles in air,” Opt. Lett. 37, 1934–1936 (2012). [CrossRef]
  4. D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003). [CrossRef]
  5. S. Wong, M. Deubel, F. Pérez-Willard, S. John, G. A. Ozin, M. Wegener, and G. von Freymann, “Direct laser writing of three-dimensional photonic crystals with a complete photonic bandgap in chalcogenide glasses,” Adv. Mater. 18, 265–269 (2006). [CrossRef]
  6. T. Kondo, S. Matsuo, S. Juodkazis, and J. Misawa, “Femtosecond laser interference technique with diffractive beam splitter for fabrication of three-dimensional photonic crystals,” Appl. Phys. Lett. 79, 725–727 (2001). [CrossRef]
  7. Y. Kuroiwa, N. Takeshima, Y. Narita, S. Tanaka, and K. Hirao, “Arbitrary micropatterning method in femtosecond laser microprocessing using diffractive optical elements,” Opt. Express 12, 1908–1915 (2004). [CrossRef]
  8. J.-I. Kato, N. Takeyasu, Y. Adachi, H.-B. Sun, and S. Kawata, “Multiple-spot parallel processing for laser micronanofabrication,” Appl. Phys. Lett. 86, 044102 (2005). [CrossRef]
  9. S. Hasegawa, Y. Hayasaki, and N. Nishida, “Holographic femtosecond laser processing with multiplexed phase Fresnel lenses,” Opt. Lett. 31, 1705–1707 (2006). [CrossRef]
  10. Y. Hayasaki, T. Sugimoto, A. Takita, and N. Nishida, “Variable holographic femtosecond laser processing by use of a spatial light modulator,” Appl. Phys. Lett. 87, 031101 (2005). [CrossRef]
  11. H. Dammann and E. Klotz, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 24, 505–515 (1977). [CrossRef]
  12. D. Prongué, H. P. Herzig, R. Dändliker, and M. T. Gale, “Optimized kinoform structures for highly efficient fan-out elements,” Appl. Opt. 31, 5706–5711 (1992). [CrossRef]
  13. J. A. Davis, I. Moreno, J. L. Martínez, T. J. Hernandez, and D. M. Cottrell, “Creating 3D lattice patterns using programmable Dammann gratings,” Appl. Opt. 50, 3653–3657 (2011). [CrossRef]
  14. J. Yu, C. Zhou, W. Jia, W. Cao, S. Wang, J. Ma, and H. Cao, “Three-dimensional Dammann array,” Appl. Opt. 51, 1619–1630 (2012). [CrossRef]
  15. V. Yu. Bazhenov, V. Vasnetsov, and M. S. Soskin, “Laser-beams with screw dislocations in their wave-fronts,” JETP Lett. 52, 429–431 (1990).
  16. N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992). [CrossRef]
  17. S. H. Tao, X.-C. Yuan, J. Lin, and R. E. Burge, “Sequence of focused optical vortices generated by a spiral fractal zone plate,” Appl. Phys. Lett. 89, 031105 (2006). [CrossRef]
  18. J. Yu, C. Zhou, W. Jia, A. Hu, W. Cao, J. Wu, and S. Wang, “Three-dimensional Dammann vortex array with tunable topological charge,” Appl. Opt. 51, 2485–2490 (2012). [CrossRef]
  19. A. Calabuig, S. Sánchez-Ruiz, L. Martínez-León, E. Tajahuerce, M. Fernández-Alonso, W. D. Furlan, J. A. Monsoriu, and A. Pons-Martí, “Generation of programmable 3D optical vortex structures through devil’s vortex-lens arrays,” Appl. Opt. 52, 5822–5829 (2013). [CrossRef]
  20. I. Moreno, J. A. Davis, D. M. Cottrell, N. Zhang, and X. C. Yuan, “Encoding generalized phase functions on Dammann gratings,” Opt. Lett. 35, 1536–1538 (2010). [CrossRef]
  21. J. Yu, C. Zhou, W. Jia, A. Hu, W. Cao, J. Wu, and S. Wang, “Generation of dipole vortex array using spiral Dammann zone plates,” Appl. Opt. 51, 6799–6804 (2012). [CrossRef]
  22. L. A. Romero and F. M. Dickey, “Theory of optimal beam splitting by phase gratings. I. One-dimensional gratings,” J. Opt. Soc. Am. A 24, 2280–2295 (2007). [CrossRef]
  23. L. A. Romero and F. M. Dickey, “The mathematical theory of laser beam-splitting gratings,” Prog. Opt. 54, 319–386 (2010). [CrossRef]
  24. J. Albero, I. Moreno, J. A. Davis, D. M. Cottrell, and D. Sand, “Generalized phase diffraction gratings with tailored intensity,” Opt. Lett. 37, 4227–4229 (2012). [CrossRef]
  25. J. Albero, J. A. Davis, D. M. Cottrell, C. E. Granger, K. R. McCormick, and I. Moreno, “Generalized diffractive optical elements with asymmetric harmonic response and phase control,” Appl. Opt. 52, 3637–3644 (2013). [CrossRef]
  26. http://support.microsoft.com/kb/214115 .
  27. J. Albero, P. García-Martínez, J. L. Martínez, and I. Moreno, “Second order diffractive optical elements in a spatial light modulator with large phase dynamic range,” Opt. Lasers Eng. 51, 111–115 (2013). [CrossRef]
  28. J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, and J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38, 1051–1057 (1999). [CrossRef]
  29. I. Moreno, J. A. Davis, B. M. L. Pascoguin, M. J. Mitry, and D. M. Cottrell, “Vortex sensing diffraction gratings,” Opt. Lett. 34, 2927–2929 (2009). [CrossRef]
  30. K. Crabtree, J. A. Davis, and I. Moreno, “Optical processing with vortex producing lenses,” Appl. Opt. 43, 1360–1367 (2004). [CrossRef]

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