OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 17, Iss. 6 — Jun. 1, 2000
  • pp: 959–965

Nonlinear phase shift resulting from two-color multistep cascading

Solomon Saltiel, Kaloian Koynov, Yana Deyanova, and Yuri S. Kivshar  »View Author Affiliations

JOSA B, Vol. 17, Issue 6, pp. 959-965 (2000)

View Full Text Article

Enhanced HTML    Acrobat PDF (246 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We propose a novel type of cascading parametric interaction for generating a nonlinear phase shift in dielectric media with a quadratic nonlinear response based on two-frequency wave mixing of the fundamental and second-harmonic waves. Self-phase modulation of the fundamental wave results from a cascading process consisting of four second-order subprocesses, the direct and reverse subprocesses of Type I second-harmonic generation (SHG) and the direct and reverse subprocesses of Type II SHG. It is found analytically and numerically that the fundamental wave passing through a quadratic medium, tuned for simultaneous near phase matching for these two processes, collects 60% more nonlinear phase shift than does the corresponding two-step cascading. We also obtain the conditions for stationary waves (nonlinear modes) supported by such multistep cascading processes.

© 2000 Optical Society of America

OCIS Codes
(190.0190) Nonlinear optics : Nonlinear optics
(190.4360) Nonlinear optics : Nonlinear optics, devices
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing
(190.5940) Nonlinear optics : Self-action effects
(200.4740) Optics in computing : Optical processing

Solomon Saltiel, Kaloian Koynov, Yana Deyanova, and Yuri S. Kivshar, "Nonlinear phase shift resulting from two-color multistep cascading," J. Opt. Soc. Am. B 17, 959-965 (2000)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. G. Stegeman, D. 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]
  2. G. Stegeman, R. Scheik, L. Torner, W. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. Van Stryland, D. Hagan, and G. Assanto, “Cascading: a promising approach to nonlinear optical phenomena,” in Novel Optical Materials and Applications, I.-C. Khoo, F. Simoni, and C. Umeton, eds. (Wiley, New York, 1997), pp. 49–76.
  3. S. Saltiel, I. Buchvarov, and K. Koynov, “Control of laser light parameters by χ(2)(2) cascading,” in Advanced Photonics with Second-Order Nonlinear Processes, A. Boardman, L. Pavlov, and S. Tanev, eds. (Kluwer Academic, Dordrecht, The Netherlands, 1998), pp. 89–112.
  4. R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, and H. Vanherzeele, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17, 28–31 (1992). [CrossRef] [PubMed]
  5. K. Koynov, S. Saltiel, and I. Buchvarov, “All-optical switching by means of an interferometer with nonlinear frequency doubling mirrors,” J. Opt. Soc. Am. B 14, 834–838 (1997). [CrossRef]
  6. M. Cha, “Casaded phase shift and intensity phase modulation in aperiodic quasi-phase matched gratings,” Opt. Lett. 23, 250–252 (1998). [CrossRef]
  7. S. Saltiel, K. Koynov, and M. Fejer, “Aperiodic quasi-phase-matching as a method to reduce switching intensity in de-vices based on second-order cascading,” in Conference on Lasers and Electro-Optics (CLEO Europe) (Optical Society of America, Washington, D.C., 1998), paper CWF68, p. 193.
  8. K. Koynov and S. Saltiel, “Nonlinear phase shift via multistep cascading,” Opt. Commun. 152, 96–100 (1998). [CrossRef]
  9. G. Assanto, I. Torelli, and S. Trillo, “All-optical processing by means of vectorial interactions in second-order cascading: novel approaches,” Opt. Lett. 19, 1720–1722 (1994). [CrossRef] [PubMed]
  10. A. L. Belostotsky, A. S. Leonov, and A. V. Meleshko, “Nonlinear phase change in type II second-harmonic generation under exact phase-matched conditions,” Opt. Lett. 19, 856–858 (1994). [CrossRef] [PubMed]
  11. G. Assanto, G. Stegeman, M. Sheik-Bahae, and E. W. Van Stryland, “Coherent interactions for all optical signal processing via quadratic nonlinearities,” IEEE J. Quantum Electron. 31, 673–681 (1995). [CrossRef]
  12. S. Saltiel and Y. Deyanova, “Polarization switching as a result of cascading of two simultaneously phase-matched processes,” Opt. Lett. 24, 1296–1298 (1999). [CrossRef]
  13. 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]
  14. O. Pfister, J. S. Wells, L. Hollberg, L. Zink, D. A. Van Baak, M. D. Levenson, and W. R. Bosenberg, “Continuous-wave frequency tripling and quadrupoling by simultaneous three-wave mixing in periodically poled crystals: application to a two-step 1.19–10.71-mm frequency bridge,” Opt. Lett. 22, 1211–1213 (1997). [CrossRef] [PubMed]
  15. Yu. S. Kivshar, A. A. Sukhorukov, and S. Saltiel, “Two-colour multistep cascading and parametric soliton-induced waveguides,” Phys. Rev. E 60, R5056–R5059 (1999). [CrossRef]
  16. Kh. I. Pushkarov, D. I. Pushkarov, and I. V. Tomov, “Self-action of light beams in nonlinear media: soliton solutions,” Opt. Quantum Electron. 11, 471–478 (1979). [CrossRef]
  17. R. W. Micalef, V. V. Afanasjev, Yu. S. Kivshar, and J. D. Love, “Optical solitons with power-law asymptotics,” Phys. Rev. E 54, 2936–2942 (1996). [CrossRef]
  18. S. Saltiel, S. Tanev, and A. Boardman, “High-order nonlinear phase shift due to cascaded third-order processes,” Opt. Lett. 22, 148–150 (1997). [CrossRef] [PubMed]
  19. S. Saltiel, K. Koynov, P. Tzankov, A. Boardman, and S. Tanev, “Nonlinear phase shift as a result of cascaded third-order processes,” Phys. Rev. A 57, 3028–3035 (1998). [CrossRef]
  20. R. A. Sammut, A. V. Buryak, and Yu. S. Kivshar, “Modification of solitary waves by third-harmonic generation,” Opt. Lett. 22, 1385–1387 (1997). [CrossRef]
  21. G. Cerullo, S. De Silvestri, A. Monduzzi, D. Segala, and V. Magni, “Self-starting mode-locking of a cw Nd:YAG laser using cascaded second-order nonlinearities,” Opt. Lett. 20, 746–748 (1995). [CrossRef] [PubMed]
  22. V. Couderc, O. Guy, E. Roisse, and A. Barthelemy, “Mode locking of cw Nd:YAG laser using nonlinear polarization evolution in Type II frequency doubling crystal,” Electron. Lett. 34, 672–677 (1998). [CrossRef]
  23. S. Zhu, Y. Zhu, Y. Qin, H. Wang, C. Ge, and N. Ming, “Experimental realisation of second-harmonic generation in a Fibonacci optical superlattices of LiTaO3,” Phys. Rev. Lett. 78, 2752–2755 (1997). [CrossRef]
  24. C. B. Clausen, Yu. S. Kivshar, O. Bang, and P. L. Christiansen, “Quasiperiodic envelope solitons,” Phys. Rev. Lett. 83, 4740–4743 (1999). [CrossRef]
  25. Yu. S. Kivshar, T. J. Alexander, and S. Saltiel, “Spatial optical solitons resulting from multistep cascading,” Opt. Lett. 24, 759–761 (1999). [CrossRef]
  26. I. Towers, R. Sammut, A. V. Buryak, and B. A. Malomed, “Soliton multistability as a result of double-resonance wave mixing in χ(2) media,” Opt. Lett. 24, 1738–1740 (1999). [CrossRef]
  27. A. V. Buryak and Yu. S. Kivshar, “Multistability of three-wave parametric self-trapping,” Phys. Rev. Lett. 78, 3286–3290 (1997). [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.


Fig. 1 Fig. 2 Fig. 3
Fig. 4 Fig. 5

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited