OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Grover Swartzlander
  • Vol. 31, Iss. 6 — Jun. 1, 2014
  • pp: A46–A50

Engineering structured light with optical vortices

Jesús Rogel-Salazar, Juan Pablo Treviño, and Sabino Chávez-Cerda  »View Author Affiliations


JOSA B, Vol. 31, Issue 6, pp. A46-A50 (2014)
http://dx.doi.org/10.1364/JOSAB.31.000A46


View Full Text Article

Enhanced HTML    Acrobat PDF (376 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

In this work, we demonstrate the possibility of generating and controlling any given kind of structured radially symmetric intensity profile with an embedded optical vortex. This is achieved with the use of Sturm–Liouville theory on a circular domain with Bessel, Laguerre–Gauss, Zernike, and Fourier bases. We show that the core intensity profile can be constructed independently of the topological charge of the vortex.

© 2014 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(000.4430) General : Numerical approximation and analysis
(350.5500) Other areas of optics : Propagation
(350.4855) Other areas of optics : Optical tweezers or optical manipulation
(050.4865) Diffraction and gratings : Optical vortices

History
Original Manuscript: January 8, 2014
Revised Manuscript: March 25, 2014
Manuscript Accepted: April 12, 2014
Published: May 20, 2014

Citation
Jesús Rogel-Salazar, Juan Pablo Treviño, and Sabino Chávez-Cerda, "Engineering structured light with optical vortices," J. Opt. Soc. Am. B 31, A46-A50 (2014)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-31-6-A46


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photon. 3, 161–204 (2011). [CrossRef]
  2. J. Curtis and D. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90, 133901 (2003). [CrossRef]
  3. J. P. Treviño, O. López-Cruz, and S. Chávez-Cerda, “Segmented vortex telescope and its tolerance to diffraction effects and primary aberrations,” Opt. Eng. 52, 081605 (2013). [CrossRef]
  4. K. Dholakia and W. M. Lee, “Optical trapping takes shape: the use of structured light fields,” Adv. At. Mol. Opt. Phys. 56, 261–337 (2008).
  5. M. Hartrumpf and R. Munser, “Optical three-dimensional measurements by radially symmetric structured light projection,” Appl. Opt. 36, 2923–2928 (1997). [CrossRef]
  6. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992). [CrossRef]
  7. K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B 4, S82–S89 (2002).
  8. J. A. Hernández Nolasco, “Wave field families of the Helmholtz equation in eleven orthogonal coordinate systems,” Ph.D. thesis (INAOE, 2011).
  9. H. Feshbach and P. M. Morse, Methods of Theoretical Physics: Part II (Cambridge University, 1953).
  10. K. T. Tang, Mathematical Methods for Engineers and Scientists (Springer, 2007).
  11. H. F. Davis, Fourier Series and Orthogonal Functions (Dover, 1989).
  12. G. E. Andrews, R. Askey, and R. Roy, Special Functions (Cambridge University, 2000).
  13. M. A. Al-Gwaiz, Sturm-Liouville Theory and its Applications (Springer, 2008).
  14. H. F. Harmuth, Transmission of Information by Orthogonal Functions (Springer, 1970).
  15. G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010). [CrossRef]
  16. M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Courtial, N. K. Steinhoff, G. A. Tyler, A. E. Wilner, and M. J. Padgett, “Efficient measurement of an optical orbital- angular-momentum spectrum comprising more than 50 states,” New J. Phys. 15, 013024 (2013). [CrossRef]
  17. E. Karimi, D. Giovannini, E. Bolduc, N. Bent, F. M. Miatto, M. J. Padgett, and R. W. Boyd, “Exploring the quantum nature of the radial degree of freedom of a photon via Hong-Ou-Mandel interference,” Phys. Rev. A 89, 013829 (2014). [CrossRef]
  18. A. S. Ostrovsky, C. Rickenstorff-Parrao, and V. Arrizón, “Generation of the ‘perfect’ optical vortex using a liquid-crystal spatial light modulator,” Opt. Lett. 38, 534–536 (2013). [CrossRef]
  19. M. Chen, M. Mazilu, Y. Arita, E. M. Wright, and K. Dholakia, “Dynamics of microparticles trapped in a perfect vortex beam,” Opt. Lett. 38, 4919–4922 (2013). [CrossRef]
  20. A. M. Cormack, “Representation of a function by its line integrals, with some radiological applications,” J. Appl. Phys. 34, 2722–2727 (1963). [CrossRef]
  21. M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A 6, 259–268 (2004). [CrossRef]
  22. A. E. Siegman, Lasers (University Science Books, 1986).
  23. S. Ramo, J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communication Electronics (Wiley, 1984).
  24. B. G. Korenev, Bessel Functions and Their Applications (Taylor and Francis, 2002).
  25. G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge University, 1995).
  26. J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free Beams,” Phys. Rev. Lett. 58, 1499–1501 (1987). [CrossRef]
  27. S. Chávez-Cerda, “A new approach to Bessel beams,” J. Mod. Opt. 46, 923–930 (1999).
  28. S. Chávez-Cerda, M. A. Meneses-Nava, and J. M. Hickmann, “Interference of traveling nondiffracting beams,” Opt. Lett. 23, 1871–1873 (1998). [CrossRef]
  29. J. P. Treviño, J. E. Gómez-Correa, D. R. Iskander, and S. Chávez-Cerda, “Zernike vs. Bessel circular functions in visual optics,” Ophthalmic Physiolog. Opt. 33, 394–402 (2013). [CrossRef]
  30. B. R. A. Nijboer, “The diffraction theory of aberrations,” Ph.D. thesis (University of Groningen, 1942).
  31. F. Zernike, “Beugungstheorie des schneidenverfahrens und seiner verbesserten form, der phasenkontrastmethode,” Physica 1, 689–704 (1934). [CrossRef]
  32. V. Lakshminarayanan and A. Fleck, “Zernike polynomials: a guide,” J. Mod. Opt. 58, 545–561 (2011). [CrossRef]
  33. R. Navarro, R. Rivera, and J. Aporta, “Representation of wavefronts in free-form transmission pupils with Complex Zernike Polynomials,” J. Optom. 4, 41–48 (2011). [CrossRef]
  34. G. W. Forbes, “Robust and fast computation for the polynomials of optics,” Opt. Express 18, 13851–13862 (2010). [CrossRef]
  35. J. A. Murphy, “Examples of circularly symmetric diffraction using beam modes,” Eur. J. Phys. 14, 268–271 (1993). [CrossRef]
  36. J. A. Murphy and A. Egan, “Examples of Fresnel diffraction using Gaussian modes,” Eur. J. Phys. 14, 121–127 (1993). [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.

Figures

Fig. 1. Fig. 2. Fig. 3.
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited