OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 2 — Jan. 28, 2013
  • pp: 1623–1632

Complete energy conversion by autoresonant three-wave mixing in nonuniform media

O. Yaakobi, L. Caspani, M. Clerici, F. Vidal, and R. Morandotti  »View Author Affiliations

Optics Express, Vol. 21, Issue 2, pp. 1623-1632 (2013)

View Full Text Article

Enhanced HTML    Acrobat PDF (883 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Resonant three-wave interactions appear in many fields of physics e.g. nonlinear optics, plasma physics, acoustics and hydrodynamics. A general theory of autoresonant three-wave mixing in a nonuniform media is derived analytically and demonstrated numerically. It is shown that due to the medium nonuniformity, a stable phase-locked evolution is automatically established. For a weak nonuniformity, the efficiency of the energy conversion between the interacting waves can reach almost 100%. One of the potential applications of our theory is the design of highly-efficient optical parametric amplifiers.

© 2013 OSA

OCIS Codes
(190.4410) Nonlinear optics : Nonlinear optics, parametric processes
(190.4970) Nonlinear optics : Parametric oscillators and amplifiers
(350.5500) Other areas of optics : Propagation
(350.7420) Other areas of optics : Waves
(190.4223) Nonlinear optics : Nonlinear wave mixing
(190.4975) Nonlinear optics : Parametric processes

ToC Category:
Nonlinear Optics

Original Manuscript: November 12, 2012
Revised Manuscript: December 20, 2012
Manuscript Accepted: December 21, 2012
Published: January 15, 2013

O. Yaakobi, L. Caspani, M. Clerici, F. Vidal, and R. Morandotti, "Complete energy conversion by autoresonant three-wave mixing in nonuniform media," Opt. Express 21, 1623-1632 (2013)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. L. Friedland, “Autoresonance in nonlinear systems,” Scholarpedia4, 5473 (2009). [CrossRef]
  2. V. I. Veksler, “A new method of acceleration of relativistic particles,” J. Phys. USSR9, 153–158 (1945).
  3. E. M. McMillan, “The synchrotron - a proposed high energy particle accelerator,” Phys. Rev.68, 143–144 (1945). [CrossRef]
  4. G. B. Andresen, M. D. Ashkezari, M. Baquero-Ruiz, W. Bertsche, P. D. Bowe, E. Butler, C. L. Cesar, S. Chapman, M. Charlton, A. Deller, S. Eriksson, J. Fajans, T. Friesen, M. C. Fujiwara, D. R. Gill, A. Gutierrez, J. S. Hangst, W. N. Hardy, M. E. Hayden, A. J. Humphries, R. Hydomako, M. J. Jenkins, S. Jonsell, L. V. Jorgensen, L. Kurchaninov, N. Madsen, S. Menary, P. Nolan, K. Olchanski, A. Olin, A. Povilus, P. Pusa, F. Robicheaux, E. Sarid, S. Seif el Nasr, D. M. Silveira, C. So, J. W. Storey, R. I. Thompson, D. P. van der Werf, J. S. Wurtele, and Y. Yamazaki, “Trapped antihydrogen,” Nature468, 673–676 (2010). [CrossRef] [PubMed]
  5. T. Suhara and H. Nishihara, “Theoretical analysis of waveguide second-harmonic generation phase matched with uniform and chirped gratings,” IEEE J. Quantum Electron.26, 1265–1276 (1990). [CrossRef]
  6. K. Mizuuchi, K. Yamamoto, M. Kato, and H. Sato, “Broadening of the phase-matching bandwidth in quasi-phase-matched second-harmonic generation,” IEEE J. Quantum Electron.30, 1596–1604 (1994). [CrossRef]
  7. G. Imeshev, M. M. Fejer, A. Galvanauskas, and D. Harter, “Pulse shaping by difference-frequency mixing with quasi-phase-matching gratings,” J. Opt. Soc. Am. B,18, 534–539 (2001). [CrossRef]
  8. H. Suchowski, D. Oron, A. Arie, and Y. Silberberg, “Geometrical representation of sum frequency generation and adiabatic frequency conversion,” Phys. Rev. A78, 063821 (2008). [CrossRef]
  9. H. Suchowski, V. Prabhudesai, D. Oron, A. Arie, and Y. Silberberg, “Robust adiabatic sum frequency conversion,” Optics Express17, 12731–12740 (2009). [CrossRef] [PubMed]
  10. A. Barak, Y. Lamhot, L. Friedland, and M. Segev, “Autoresonant dynamics of optical guided waves,” Phys. Rev. Lett.103, 123901 (2009). [CrossRef] [PubMed]
  11. A. Barak, Y. Lamhot, L. Friedland, and M. Segev, “Autoresonant propagation of incoherent light-waves,” Optics Express, 18, 17709–17718 (2010). [CrossRef] [PubMed]
  12. S. Trendafilov, V. Khudik, M. Tokman, and G. Shvets, “Hamiltonian description of non-reciprocal light propagation in nonlinear chiral fibers,” Physica B405, 3003–3006 (2010). [CrossRef]
  13. S. Richard, “Second-harmonic generation in tapered optical fibers,” J. Opt. Soc. Am. B27, 1504–1512 (2010). [CrossRef]
  14. L. Friedland, “Autoresonant three-wave interactions,” Phys. Rev. Lett.69, 1749–1752 (1992). [CrossRef] [PubMed]
  15. S. Longhi, “Third-harmonic generation in quasi-phase-matched χ(2) media with missing second harmonic,” Optics Letters32, 1791–1793 (2007). [CrossRef] [PubMed]
  16. M. Charbonneau-Lefort, B. Afeyan, and M. M. Fejer, “Competing collinear and noncollinear interactions in chirped quasi-phase-matched optical parametric amplifiers,” J. Opt. Soc. Am. B,25, 1402–1413 (2008). [CrossRef]
  17. I. Y. Dodin, G. M. Fraiman, V. M. Malkin, and N. J. Fisch, “Amplification of short laser pulses by Raman backscattering in capillary plasmas,” JETP95, 625–638 (2002). [CrossRef]
  18. O. Yaakobi, L. Friedland, R. R. Lindberg, A. E. Charman, G. Penn, and J. S. Wurtele, “Spatially autoresonant stimulated Raman scattering in nonuniform plasmas,” Phys. Plasmas15, 032105 (2008). [CrossRef]
  19. T. Chapman, S. Huller, P. E. Masson-Laborde, W. Rozmus, and D. Pesme, “Spatially autoresonant stimulated Raman scattering in inhomogeneous plasmas in the kinetic regime,” Phys. Plasmas17, 122317 (2010). [CrossRef]
  20. O. Yaakobi and L. Friedland, “Multidimensional, autoresonant three-wave interactions,” Phys. Plasmas15, 102104 (2008). [CrossRef]
  21. O. Yaakobi and L. Friedland, “Autoresonant four-wave mixing in optical fibers,” Phys. Rev. A82, 023820 (2010). [CrossRef]
  22. W. L. Kruer, The Physics of Laser Plasma Interactions (reprint ed.Westview Press, Boulder, CO, 2001).
  23. A. P. Mayer, “Surface acoustic waves in nonlinear elastic media,” Phys. Rep.256, 237–366 (1995). [CrossRef]
  24. K. Trulsen and C. C. Mei, “Modulation of three resonating gravity-capillary waves by a long gravity wave,” J. Fluid Mech.290, 345–376 (1995). [CrossRef]
  25. R. B. Boyd, Nonlinear Optics (Third Edition, AP2007).

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 Fig. 3

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited