OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Henry Van Driel
  • Vol. 26, Iss. 1 — Jan. 1, 2009
  • pp: 42–49

Radially symmetric nonlinear photonic crystals

Noa Voloch, Tal Ellenbogen, and Ady Arie  »View Author Affiliations

JOSA B, Vol. 26, Issue 1, pp. 42-49 (2009)

View Full Text Article

Enhanced HTML    Acrobat PDF (1158 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Different types of quadratic, radially symmetric, nonlinear photonic crystals are presented. The modulation of the nonlinear coefficient may be a periodic or an aperiodic function of the radial coordinate, whereas the azimuthal symmetry of the crystal may be either continuous or discrete. Nonlinear interactions within these structures are studied in two orientations, transverse and longitudinal, for which the interacting beams propagate either perpendicularly or in the plane of modulation. We show that radially symmetric structures can phase match multiple arbitrary processes in any direction. We study multiple wavelength three-wave mixing interactions and multiple direction interactions and analyze spatially dependent polarization states of the generated harmonics.

© 2008 Optical Society of America

OCIS Codes
(190.2620) Nonlinear optics : Harmonic generation and mixing
(190.4160) Nonlinear optics : Multiharmonic generation
(190.4360) Nonlinear optics : Nonlinear optics, devices

ToC Category:
Photonic Crystals

Original Manuscript: July 23, 2008
Manuscript Accepted: September 23, 2008
Published: December 15, 2008

Noa Voloch, Tal Ellenbogen, and Ady Arie, "Radially symmetric nonlinear photonic crystals," J. Opt. Soc. Am. B 26, 42-49 (2009)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation-tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631-2654 (1992). [CrossRef]
  2. M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, “First-order quasi-phase matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second-harmonic generation,” Appl. Phys. Lett. 62, 435-436 (1993). [CrossRef]
  3. N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, “Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal,” Phys. Rev. Lett. 84, 4345-4348 (2000). [CrossRef] [PubMed]
  4. I. Freund, “Nonlinear diffraction,” Phys. Rev. Lett. 21, 1404-1406 (1968). [CrossRef]
  5. V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett. 81, 4136-4139 (1998). [CrossRef]
  6. S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278, 843-846 (1997). [CrossRef]
  7. H. Liu, S. N. Zhu, Y. Y. Zhu, N. B. Ming, X. C. Lin, W. J. Ling, A. Y. Yao, and Z. Y. Xu, “Multiple-wavelength second-harmonic generation in aperiodic optical superlattices,” Appl. Phys. Lett. 81, 3326-3328 (2002). [CrossRef]
  8. K. Fradkin, A. Arie, P. Urenski, and G. Rosenman, “Multiple nonlinear optical interactions with arbitrary wave vector differences,” Phys. Rev. Lett. 88, 023903 (2001). [CrossRef]
  9. J. Liao, J. L. He, H. Liu, J. Du, F. Xu, H. T. Wang, S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Red, yellow, green and blue four-color light from a single, aperiodically poled LiTaO3 crystal,” Appl. Phys. B 78, 265-267 (2004). [CrossRef]
  10. R. Lifshitz, A. Arie, and A. Bahabad, “Photonic quasi-crystals for nonlinear optical frequency conversion,” Phys. Rev. Lett. 95, 133901 (2005). [CrossRef] [PubMed]
  11. R. T. Bratfalean, A. C. Peacock, N. G. R. Broderick, K. Gallo, and R. Lewen, “Harmonic generation in a two-dimensional nonlinear quasi-crystal,” Opt. Lett. 30, 424-426 (2005). [CrossRef] [PubMed]
  12. M. H. Chou, K. R. Parameswaran, M. M. Fejer, and I. Brener, “Multiple-channel wavelength conversion by use of engineered quasi-phase-matching,” Opt. Lett. 24, 1157-1159 (1999). [CrossRef]
  13. M. Baudrier-Raybaut, R. Haïdar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, “Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials,” Nature (London) 432, 374-376 (2004). [CrossRef]
  14. G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691-1740 (1996). [CrossRef]
  15. Y. S. Kivshar, A. A. Sukhorukov, and S. M. Saltiel, “Two-color multistep cascading and parametric soliton-induced waveguides,” Phys. Rev. E 60, R5056-R5059 (1999). [CrossRef]
  16. D. Kasimov, A. Arie, E. Winebrand, G. Rosenman, A. Bruner, P. Shaier, and D. Eger, “Annular symmetry nonlinear frequency converters,” Opt. Express 14, 9371-9376 (2006). [CrossRef] [PubMed]
  17. T. Wang, B. Ma, Y. Sheng, P. Ni, B. Cheng, and D. Zhang, “Large-angle acceptance of quasi-phase-matched second-harmonic generation in homocentrically poled LiNbO3,” Opt. Commun. 252, 397-401 (2005). [CrossRef]
  18. Y. Sheng, J. Dou, J. Li, D. Ma, B. Cheng, and D. Zhang, “Broadband efficient second harmonic generation in media with a short-range order,” Appl. Phys. Lett. 91, 101109 (2007). [CrossRef]
  19. S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski1, A. Arie, and Y. S. Kivshar, “Spatiotemporal toroidal waves from the transverse second-harmonic generation,” Opt. Lett. 33, 527-529 (2008). [CrossRef] [PubMed]
  20. S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski1, A. Arie, and Y. S. Kivshar, “Generation of the second-harmonic conical waves via nonlinear Bragg diffraction,” Phys. Rev. Lett. 100, 103902 (2008). [CrossRef] [PubMed]
  21. A. Arie, N. Habshoosh, and A. Bahabad, “Quasi phase matching in two-dimensional nonlinear photonic crystals,” Opt. Quantum Electron. 39, 361-375 (2007). [CrossRef]
  22. T. Ellenbogen, A. Arie, and S. M. Saltiel, “Noncollinear double quasi-phase matching in one-dimensional poled crystals,” Opt. Lett. 32, 262-264 (2007). [CrossRef] [PubMed]
  23. I. Amidror, “Fourier spectrum of radially periodic images,” J. Opt. Soc. Am. A 14, 816-826 (1997). [CrossRef]
  24. A. Bruner, D. Eger, M. B. Oron, P. Blau, M. Katz, and S. Ruschin, “Temperature-dependent Sellmeier equation for the refractive index of stoichiometric lithium tantalate,” Opt. Lett. 28, 194-196 (2003). [CrossRef] [PubMed]
  25. A. Bahabad, A. Ganany-Padowicz, and A. Arie, “Engineering two-dimensional nonlinear photonic quasi-crystals,” Opt. Lett. 33, 1386-1388 (2008). [CrossRef] [PubMed]
  26. A. Bahabad, N. Voloch, A. Arie, and R. Lifshitz, “Experimental confirmation of the general solution to the multiple-phase-matching problem,” J. Opt. Soc. Am. B 24, 1916-1921 (2007). [CrossRef]
  27. T. Ellenbogen, A. Ganany, and A. Arie, “Nonlinear photonic structures for all-optical deflection,” Opt. Express 16, 3077-3082 (2008). [CrossRef] [PubMed]
  28. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics2nd ed. (Wiley, 2007), Chap. 6.

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