OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 10 — May. 20, 2013
  • pp: 12783–12789

Second harmonic generation in isotropic media: six-wave mixing of optical vortices

Matt M. Coles, Mathew D. Williams, and David L. Andrews  »View Author Affiliations

Optics Express, Vol. 21, Issue 10, pp. 12783-12789 (2013)

View Full Text Article

Enhanced HTML    Acrobat PDF (1064 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Optical vortex light can be up-converted into a second harmonic output in an isotropic medium, in which such conversion is normally forbidden, through six-wave mixing. The involvement of orbital angular momentum is tackled for the case of a Laguerre-Gaussian pump comprising l = 1 photons. By calculating quantum amplitudes for the emergent radiation states, utilizing a state-sequence method, the analysis identifies the characteristics of the emission and an entangled distribution of conserved orbital momentum. A distinctive conical spread affords a potential means of resolving the individual angular momentum content.

© 2013 OSA

OCIS Codes
(020.4180) Atomic and molecular physics : Multiphoton processes
(190.2620) Nonlinear optics : Harmonic generation and mixing
(190.4160) Nonlinear optics : Multiharmonic generation
(270.4180) Quantum optics : Multiphoton processes
(270.5580) Quantum optics : Quantum electrodynamics
(050.4865) Diffraction and gratings : Optical vortices

ToC Category:
Nonlinear Optics

Original Manuscript: February 22, 2013
Revised Manuscript: April 10, 2013
Manuscript Accepted: April 10, 2013
Published: May 16, 2013

Matt M. Coles, Mathew D. Williams, and David L. Andrews, "Second harmonic generation in isotropic media: six-wave mixing of optical vortices," Opt. Express 21, 12783-12789 (2013)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. D. L. Andrews, “Harmonic-generation in free molecules,” J. Phys. At. Mol. Opt. Phys.13(20), 4091–4099 (1980). [CrossRef]
  2. K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A54(5), R3742–R3745 (1996). [CrossRef] [PubMed]
  3. L. C. Dávila Romero, D. L. Andrews, and M. Babiker, “A quantum electrodynamics framework for the nonlinear optics of twisted beams,” J. Opt. B Quantum Semiclassical Opt.4(2), S66–S72 (2002). [CrossRef]
  4. P. Allcock and D. L. Andrews, “Six-wave mixing: secular resonances in a higher-order mechanism for second-harmonic generation,” J. Phys. At. Mol. Opt. Phys.30(16), 3731–3742 (1997). [CrossRef]
  5. I. D. Hands, S. J. Lin, S. R. Meech, and D. L. Andrews, “A quantum electrodynamical treatment of second harmonic generation through phase conjugate six-wave mixing: Polarization analysis,” J. Chem. Phys.109(24), 10580–10586 (1998). [CrossRef]
  6. K. D. Moll, D. Homoelle, A. L. Gaeta, and R. W. Boyd, “Conical Harmonic Generation in Isotropic Materials,” Phys. Rev. Lett.88(15), 153901 (2002). [CrossRef] [PubMed]
  7. R. M. Eisberg and R. Resnick, Quantum Physics Of Atoms, Molecules, Solids, Nuclei and Particles (Wiley, 1985), Appendix K.
  8. R. D. Jenkins, D. L. Andrews, and L. C. Dávila Romero, “A new diagrammatic methodology for non-relativistic quantum electrodynamics,” J. Phys. At. Mol. Opt. Phys.35(3), 445–468 (2002). [CrossRef]
  9. D. R. Mazur, Combinatorics: A Guided Tour (Mathematical Association of America, 2010).
  10. D. L. Andrews and M. Babiker, eds., The Angular Momentum of Light (Cambridge University Press, 2013), Chap. 9.
  11. D. L. Andrews and T. Thirunamachandran, “On three-dimensional rotational averages,” J. Chem. Phys.67(11), 5026–5033 (1977). [CrossRef]
  12. D. Flamm, C. Schulze, D. Naidoo, A. Forbes, and M. Duparré, “Mode analysis using the correlation filter method,” Proc. SPIE8637, 863717 (2013). [CrossRef]
  13. T. Kaiser, D. Flamm, S. Schröter, and M. Duparré, “Complete modal decomposition for optical fibers using CGH-based correlation filters,” Opt. Express17(11), 9347–9356 (2009). [CrossRef] [PubMed]
  14. S. Franke-Arnold, S. M. Barnett, M. J. Padgett, and L. Allen, “Two-photon entanglement of orbital angular momentum states,” Phys. Rev. A65(3), 033823 (2002). [CrossRef]
  15. J. Romero, D. Giovannini, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “Increasing the dimension in high-dimensional two-photon orbital angular momentum entanglement,” Phys. Rev. A86(1), 012334 (2012). [CrossRef]
  16. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature412(6844), 313–316 (2001). [CrossRef] [PubMed]
  17. G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express12(22), 5448–5456 (2004). [CrossRef] [PubMed]
  18. S. Franke and S. M. Barnett, “Angular momentum in spontaneous emission,” J. Phys. At. Mol. Opt. Phys.29(10), 2141–2150 (1996). [CrossRef]
  19. S. Franke-Arnold, S. M. Barnett, E. Yao, J. Leach, J. Courtial, and M. Padgett, “Uncertainty principle for angular position and angular momentum,” New J. Phys.6, 103 (2004). [CrossRef]
  20. H. H. Arnaut and G. A. Barbosa, “Orbital and intrinsic angular momentum of single photons and entangled pairs of photons generated by parametric down-conversion,” Phys. Rev. Lett.85(2), 286–289 (2000). [CrossRef] [PubMed]
  21. D. Shwa, E. Shtranvasser, Y. Shalibo, and N. Katz, “Controllable motion of optical vortex arrays using electromagnetically induced transparency,” Opt. Express20(22), 24835–24842 (2012). [CrossRef] [PubMed]
  22. N. Olivier, D. DéBarre, P. Mahou, and E. Beaurepaire, “Third-harmonic generation microscopy with Bessel beams: a numerical study,” Opt. Express20(22), 24886–24902 (2012). [CrossRef] [PubMed]
  23. M. T. Cao, L. Han, R. F. Liu, H. Liu, D. Wei, P. Zhang, Y. Zhou, W. G. Guo, S. G. Zhang, H. Gao, and F. L. Li, “Deutsch’s algorithm with topological charges of optical vortices via non-degenerate four-wave mixing,” Opt. Express20(22), 24263–24271 (2012). [CrossRef] [PubMed]
  24. M. N. O’Sullivan, M. Mirhosseini, M. Malik, and R. W. Boyd, “Near-perfect sorting of orbital angular momentum and angular position states of light,” Opt. Express20(22), 24444–24449 (2012). [CrossRef] [PubMed]
  25. M. P. J. Lavery, D. Robertson, M. Malik, B. Rodenburg, J. Courtial, R. W. Boyd, and M. J. Padgett, “The efficient sorting of light's orbital angular momentum for optical communications,” Proc. SPIE8542, 85421R, (2012). [CrossRef]
  26. J. Romero, D. Giovannini, S. Franke-Arnold, S. Barnett, and M. Padgett, “Increasing the dimension in high-dimensional two-photon orbital angular momentum entanglement,” Phys. Rev. A86(1), 012334 (2012). [CrossRef]
  27. S. Franke-Arnold, “Orbital angular momentum of photons, atoms, and electrons,” Proc. SPIE 8637, (in press).

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.


Fig. 1 Fig. 2

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited