Skip to main content
SpringerLink
Log in

Competition mechanism of multiple four-wave mixing in highly nonlinear fiber: spatial instability and satellite characteristics

  • Research Article
  • Published:
Frontiers of Optoelectronics Aims and scope Submit manuscript

Abstract

Competition mechanism in multiple four-wave mixing (MFWM) processes is demonstrated theoretically. Provided considering only two waves injected into a highly nonlinear fiber (HNLF), there are three modes displaying comprehensive dynamic behaviors, such as fixed points, periodic motion, and chaotic motion. Especially, Mode C of MFWM is emphasized by analyzing its phase-space trajectory to demonstrate nonlinear wave-wave interactions. The study shows that, when the phase-space trajectory approaches or gets through a saddle point, a dramatic power depletion for the injected wave can be realized, with the representative point moving chaotically, but when phase-space trajectories are distributed around a center point, the power for the injected wave is retained almost invariable, with the representative point moving periodically. Finally, the evolvement of satellite wave over an optical fiber is investigated by comparing it with the interference pattern in Young’s double-slit experiment.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Islam M N, Boyraz Ö. Fiber parametric amplifiers for wavelength band conversion. IEEE Journal of Quantum Electronics, 2002, 8(3): 527–537

    Article  Google Scholar 

  2. Geraghty D F, Lee R B, Verdiell M, Ziari M, Mathur A, Vahala K J. Wavelength conversion for WDM communication systems using four-wave mixing in semiconductor optical amplifiers. IEEE Journal of Quantum Electronics, 1997, 3(5): 1146–1155

    Article  Google Scholar 

  3. Hansryd J, Andrekson PA, Westlund M, Li J, Hedekvist P O. Fiberbased optical parametric amplifiers and their applications. IEEE Journal of Quantum Electronics, 2002, 8(3): 506–520

    Article  Google Scholar 

  4. Hedekvist P O, Karlsson M, Andrekson P A. Fiber four-wave mixing demultiplexing with inherent parametric amplification. Journal of Lightwave Technology, 1997, 15(11): 2051–2058

    Article  Google Scholar 

  5. Zhao Y. All-optical power-controlled switching in four-wave mixing. Optics Letters, 1989, 14(19): 1085–1087

    Article  Google Scholar 

  6. Nie Z Q, Zheng H B, Zhang Y, Zhao Y, Zuo C, Li C, Chang H, Xiao M. Experimental demonstration of optical switching and routing via four-wave mixing spatial shift. Optics Express, 2010, 18(2): 899–905

    Article  Google Scholar 

  7. Ciaramella E, Trillo S. All-optical signal reshaping via four-wave mixing in optical fibers. IEEE Photonics Technology Letters, 2000, 12(7): 849–851

    Article  Google Scholar 

  8. Ciaramella E, Curti F, Trillo S. All-optical signal reshaping by means of four-wave mixing in optical fibers. IEEE Photonics Technology Letters, 2001, 13(2): 142–144

    Article  Google Scholar 

  9. Liu X M, Zhou X Q, Lu C. Multiple four-wave mixing self-stability in optical fibers. Physical Review A, 2005, 72(1): 013811

    Article  Google Scholar 

  10. Liu X M, Zhou X Q, Lu C. Four-wave mixing assisted stability enhancement: theory, experiment, and application. Optics Letters, 2005, 30(17): 2257–2259

    Article  Google Scholar 

  11. Cappellini G, Trillo S. Third-order three-wave mixing in singlemode fibers: exact solutions and spatial instability effects. Journal of the Optical Society of America. B, Optical Physics, 1991, 8(4): 824–838

    Article  Google Scholar 

  12. Trillo S, Wabnitz S, Kennedy T A. Nonlinear dynamics of dualfrequency-pumped multiwave mixing in optical fibers. Physical Review A, 1994, 50(2): 1732–1747

    Article  Google Scholar 

  13. Cappellini G, Trillo S. Energy conversion in degenerate four-photon mixing in birefringent fibers. Optics Letters, 1991, 16(12): 895–897

    Article  Google Scholar 

  14. Trillo S, Wabnitz S. Dynamics of the nonlinear modulational instability in optical fibers. Optics Letters, 1991, 16(13): 986–988

    Article  Google Scholar 

  15. Zhao L, Sun J Q. Investigation of tunable trap filter utilizing intense signal four wave mixing model in highly non-linear fiber. Optics Communications, 2009, 282(14): 2975–2982

    Article  Google Scholar 

  16. Marhic M E, Wong K K Y, Ho M C, Kazovsky L G. 92% pump depletion in a continuous-wave one-pump fiber optical parametric amplifier. Optics Letters, 2001, 26(9): 620–622

    Article  Google Scholar 

  17. Gachet D, Brustlein S, Rigneault H. Revisiting the Young’s double slit experiment for background-free nonlinear Raman spectroscopy and microscopy. Physical Review Letters, 2010, 104(21): 213905

    Article  Google Scholar 

  18. Intonti F, Riboli F, Caselli N, Abbarchi M, Vignolini S, Wiersma D S, Vinattieri A, Gerace D, Balet L, Li L H, Francardi M, Gerardino A, Fiore A, Gurioli M. Young’s type interference for probing the mode symmetry in photonic structures. Physical Review Letters, 2011, 106(14): 143901

    Article  Google Scholar 

  19. Liu X M. Theory and experiments for multiple four-wave-mixing processes with multifrequency pumps in optical fibers. Physical Review A, 2008, 77: 043818

    Article  Google Scholar 

  20. Hart D L, Judy A F, Roy R, Beletic J. Dynamical evolution of multiple four-wave-mixing processes in an optical fiber. Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 1998, 57(4): 4757–4774

    Article  Google Scholar 

  21. Wu B B, Fu S N, Wu J, Shum P, Ngo N Q, Xu K, Hong X, Lin J. Simultaneous implementation of all-optical OR and AND logic gates for NRZ/RZ/CSRZ ON-OFF-keying signals. Optics Communications, 2010, 283(3): 349–354

    Article  Google Scholar 

  22. Zhao L, Sun J Q, Huang D. Photonic generation of ultrawideband signals by exploiting gain saturation of dark pump pulse with double undershoots in a highly nonlinear fiber. Optics Communications, 2011, 284(6): 1669–1676

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Wuhan Foreign Languages School, Wuhan, 430022, China

    Liang Zhao

  2. Wuhan National Laboratory for Optoelectronics, School of Optoelectronic Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China

    Junqiang Sun & Xinliang Zhang

  3. Naval University of Engineering, Wuhan, 430033, China

    Cong Chen

Authors
  1. Liang Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Junqiang Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xinliang Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Cong Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Liang Zhao.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhao, L., Sun, J., Zhang, X. et al. Competition mechanism of multiple four-wave mixing in highly nonlinear fiber: spatial instability and satellite characteristics. Front. Optoelectron. 5, 414–428 (2012). https://doi.org/10.1007/s12200-012-0280-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12200-012-0280-z

Keywords

Search

Navigation