OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 10 — May. 9, 2011
  • pp: 9848–9862

Systematic approach to complex periodic vortex and helix lattices

Julian Becker, Patrick Rose, Martin Boguslawski, and Cornelia Denz  »View Author Affiliations


Optics Express, Vol. 19, Issue 10, pp. 9848-9862 (2011)
http://dx.doi.org/10.1364/OE.19.009848


View Full Text Article

Enhanced HTML    Acrobat PDF (4659 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We present a general comprehensive framework for the description of symmetries of complex light fields, facilitating the construction of sophisticated periodic structures carrying phase dislocations. In particular, we demonstrate the derivation of all three fundamental two-dimensional vortex lattices based on vortices of triangular, quadratic, and hexagonal shape, respectively. We show that these patterns represent the foundation of complex three-dimensional lattices with outstanding helical intensity distributions which suggest valuable applications in holographic lithography. This systematic approach is substantiated by a comparative study of corresponding numerically calculated and experimentally realized complex intensity and phase distributions.

© 2011 OSA

OCIS Codes
(090.0090) Holography : Holography
(220.4000) Optical design and fabrication : Microstructure fabrication
(160.1585) Materials : Chiral media
(050.4865) Diffraction and gratings : Optical vortices

ToC Category:
Physical Optics

History
Original Manuscript: February 22, 2011
Revised Manuscript: March 29, 2011
Manuscript Accepted: March 29, 2011
Published: May 5, 2011

Citation
Julian Becker, Patrick Rose, Martin Boguslawski, and Cornelia Denz, "Systematic approach to complex periodic vortex and helix lattices," Opt. Express 19, 9848-9862 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-10-9848


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. M. Decker, M. Ruther, C. E. Kriegler, J. Zhou, C. M. Soukoulis, S. Linden, and M. Wegener, “Strong optical activity from twisted-cross photonic metamaterials,” Opt. Lett. 34, 2501–2503 (2009). [CrossRef] [PubMed]
  2. S. T. Chui, “Giant wave rotation for small helical structures,” J. Appl. Phys. 104, 013904 (2008). [CrossRef]
  3. K. Konishi, B. Bai, X. Meng, P. Karvinen, J. Turunen, Y. P. Svirko, and M. Kuwata-Gonokami, “Observation of extraordinary optical activity in planar chiral photonic crystals,” Opt. Express 16, 7189–7196 (2008). [CrossRef] [PubMed]
  4. F. Miyamaru and M. Hangyo, “Strong optical activity in chiral metamaterials of metal screw hole arrays,” Appl. Phys. Lett. 89, 211105 (2006). [CrossRef]
  5. M. Thiel, G. von Freymann, and M. Wegener, “Layer-by-layer three-dimensional chiral photonic crystals,” Opt. Lett. 32, 2547–2549 (2007). [CrossRef] [PubMed]
  6. D.-H. Kwon, P. L. Werner, and D. H. Werner, “Optical planar chiral metamaterial designs for strong circular dichroism and polarization rotation,” Opt. Express 16, 11802–11807 (2008). [CrossRef] [PubMed]
  7. M. Decker, R. Zhao, C. M. Soukoulis, S. Linden, and M. Wegener, “Twisted split-ring-resonator photonic meta-material with huge optical activity,” Opt. Lett. 35, 1593–1595 (2010). [CrossRef] [PubMed]
  8. M. Thiel, M. Decker, M. Deubel, M. Wegener, S. Linden, and G. von Freymann, “Polarization Stop Bands in Chiral Polymeric Three-Dimensional Photonic Crystals,” Adv. Mater. 19, 207–210 (2007). [CrossRef]
  9. J. B. Pendry, “A chiral route to negative refraction,” Science 306, 1353–1355 (2004). [CrossRef] [PubMed]
  10. C. Zhang and T. J. Cui, “Negative reflections of electromagnetic waves in a strong chiral medium,” Applied Physics Letters 91, 194101 (2007). [CrossRef]
  11. E. Plum, J. Zhou, J. Dong, V. Fedotov, T. Koschny, C. Soukoulis, and N. Zheludev, “Metamaterial with negative index due to chirality,” Physical Review B 79, 035407 (2009). [CrossRef]
  12. S. Zhang, Y.-S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative Refractive Index in Chiral Metamaterials,” Phys. Rev. Lett. 102, 023901 (2009). [CrossRef] [PubMed]
  13. M. Matuszewski, I. L. Garanovich, and A. A. Sukhorukov, “Light bullets in nonlinear periodically curved waveguide arrays,” Phys. Rev. A 81, 043833 (2010). [CrossRef]
  14. M. Thiel, M. Decker, M. Deubel, M. Wegener, S. Linden, and G. von Freymann, “Polarization Stop Bands in Chiral Polymeric Three-Dimensional Photonic Crystals,” Adv. Mater. 19, 207–210 (2007). [CrossRef]
  15. M. Thiel, H. Fischer, G. von Freymann, and M. Wegener, “Three-dimensional chiral photonic superlattices,” Opt. Lett. 35, 166–168 (2010). [CrossRef] [PubMed]
  16. C. Lu and R. Lipson, “Interference lithography: a powerful tool for fabricating periodic structures,” Laser Photon. Rev. 4, 568–580 (2009). [CrossRef]
  17. J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987). [CrossRef]
  18. E. Betzig, “Sparse and composite coherent lattices,” Phys. Rev. A 71, 063406 (2005). [CrossRef]
  19. A. Schinzel, “Sur l’existence d’un cercle passant par un nombre donné de points aux coordonnées entières,” Enseign. Math. 4, 71–72 (1958).
  20. D. S. Rokhsar, D. C. Wright, and N. D. Mermin, “The two-dimensional quasicrystallographic space groups with rotational symmetries less than 23-fold,” Acta Crystallogr. 44, 197–211 (1988). [CrossRef]
  21. D. Rokhsar, D. Wright, and N. Mermin, “Scale equivalence of quasicrystallographic space groups,” Phys. Rev. B 37, 8145–8149 (1988). [CrossRef]
  22. D. Rabson, N. Mermin, D. Rokhsar, and D. Wright, “The space groups of axial crystals and quasicrystals,” Rev. Mod. Phys. 63, 699–733 (1991). [CrossRef]
  23. N. Mermin, “The space groups of icosahedral quasicrystals and cubic, orthorhombic, monoclinic, and triclinic crystals,” Rev. Mod. Phys. 64, 3–49 (1992). [CrossRef]
  24. R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, 2000), chap. 6, pp. 105–135, 3rd ed.
  25. A. König and N. D. Mermin, “Symmetry, extinctions, and band sticking,” Am. J. Phys. 68, 525–530 (2000). [CrossRef]
  26. C. Guo, Y. Zhang, Y. Han, J. Ding, and H. Wang, “Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering,” Opt. Commun. 259, 449–454 (2006). [CrossRef]
  27. B. Terhalle, D. Göries, T. Richter, P. Rose, A. S. Desyatnikov, F. Kaiser, and C. Denz, “Anisotropy-controlled topological stability of discrete vortex solitons in optically induced photonic lattices,” Opt. Lett. 35, 604–606 (2010). [CrossRef] [PubMed]
  28. M. Petrović, M. Belić, C. Denz, and Y. Kivshar, “Counterpropagating optical beams and solitons,” Laser Photon. Rev. 5, 214–233 (2011). [CrossRef]
  29. G. Juzeliu̅nas and P. Öhberg, “Optical Manipulation of Ultracold Atoms,” in Structured Light and Its Applications, D. Andrews, ed., (Elsevier, 2008), chap. 12, pp. 259–333.
  30. J. Curtis, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002). [CrossRef]
  31. D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003). [CrossRef] [PubMed]
  32. C. H. J. Schmitz, K. Uhrig, J. P. Spatz, and J. E. Curtis, “Tuning the orbital angular momentum in optical vortex beams,” Opt. Express 14, 6604–6612 (2006). [CrossRef] [PubMed]
  33. J. E. Curtis and D. G. Grier, “Modulated optical vortices,” Opt. Lett. 28, 872–874 (2003). [CrossRef] [PubMed]
  34. J. Lin, X.-C. Yuan, S. H. Tao, X. Peng, and H. B. Niu, “Deterministic approach to the generation of modified helical beams for optical manipulation,” Opt. Express 13, 3862–3867 (2005). [CrossRef] [PubMed]
  35. M. Mazilu, D. Stevenson, F. Gunn-Moore, and K. Dholakia, “Light beats the spread: non-diffracting beams,” Laser Photon. Rev. 4, 529–547 (2009). [CrossRef]
  36. F. Courvoisier, P.-A. Lacourt, M. Jacquot, M. K. Bhuyan, L. Furfaro, and J. M. Dudley, “Surface nanoprocessing with nondiffracting femtosecond Bessel beams,” Opt. Lett. 34, 3163–3165 (2009). [CrossRef] [PubMed]
  37. F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780–785 (2010). [CrossRef]
  38. A. König and N. D. Mermin, “Screw rotations and glide mirrors: crystallography in Fourier space,” Proc. Natl. Acad. Sci. U.S.A. 96, 3502–3506 (1999). [CrossRef] [PubMed]
  39. B. Schaefer, E. Collett, R. Smyth, D. Barrett, and B. Fraher, “Measuring the Stokes polarization parameters,” Am. J. Phys. 75, 163–168 (2007). [CrossRef]
  40. J. Xavier, M. Boguslawski, P. Rose, J. Joseph, and C. Denz, “Reconfigurable optically induced quasicrystallographic three-dimensional complex nonlinear photonic lattice structures,” Adv. Mater. 22, 356–360 (2010). [CrossRef] [PubMed]
  41. X. Xiong, X. Chen, M. Wang, R. Peng, and D. Shu, “Optically nonactive assorted helix array with interchangeable magnetic / electric resonance,” Appl. Phys. Lett. 98, 071901 (2011). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited