ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Polyakov S. V., Sukhorukov A. P. Gap solitons. Izvestiya VUZ. Applied Nonlinear Dynamics, 1998, vol. 6, iss. 4, pp. 45-56.

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(En):
PDF icon 1998no4p045.pdf
(downloads: 3)
Language: 
Russian
Heading: 
Nonlinear Waves. Solitons
Article type: 
Article
UDC: 
621.3.09:621.373.1

Gap solitons

Autors: 
Polyakov Sergey V., Lomonosov Moscow State University
Sukhorukov Anatoly Petrovich, Lomonosov Moscow State University
Abstract: 

In this paper we present the studies of the problem of slow and immobile solitons which are excited inside the stop bands of inhomogeneous media with either quadratic or cubic nonlinearity. We found an integral criterion of slow soliton formation, determined the main properties of gар solitons. The dynamics of parametric gap soliton formation and propagation in quadratic media is illustrated by means of computer simulations and compared with such solitons due to cubic nonlinearity.

Key words: 
-
Acknowledgments: 
The research is supported by RFBR, Program «Russian Scientific Schools» and INTAS (grant 97-0581).
Reference: 
  1. Vinogradova MV, Rudenko OV, Sukhorukov AP. Theory of Waves. Moscow: Nauka; 1990. 432 p. (in Russian).
  2. Newell АС. Nonlinear tunneling. J. Math. Phys. 1978;19(5):1126-1133.
  3. Voloshchenko YuI, Rizhov YuN, Sotin VЕ. Stationary waves in non-linear, periodically modulated media with higher group deceleration. Tech. Phys. 1981;51(5):902-907. (in Russian).
  4. Chen W, Mills DL. Gар solitons and the nonlinear optical response оf superlattices. Phys. Rev. Lett. 1987;58(2):160-163. DOI: 10.1103/PhysRevLett.58.160.
  5. Eggleton ВJ, Slusher RE, dе Sterke СM, Krug PА, Sipe JЕ. Bragg grating solitons. Phys. Rev. Lett. 1996;76(10):1627-1630. DOI: 10.1103/PhysRevLett.76.1627.
  6. Karamzin YuN, Sukhorukov AP. Nonlinear-interaction of diffracted light beams in а medium with quadratic nonlinearity: mutual focusing of beams and limitation of the efficiency of optical frequency converters. JETP Lett. 1974;20(11):339-342.
  7. Torruellas WE, Wang Z, Hagan DJ, Van Stryland EW, Stegeman GI, Torner L, Menyuk CR. Observation of two-dimensional spatial solitary waves in quadratic medium. Phys. Rev. Lett. 1995;74(25):5036-5039. DOI: 10.1103/PhysRevLett.74.5036.
  8. Stegeman GI, Hagan DJ, Torner L. X(2) cascading phenomena and their applications to all-optical signal processing, mode locking, pulse compression and solitons. Opt. Quant. Electron. 1996;28(12):1691-1740. DOI: 10.1007/BF00698538.
  9. Sukhorukov АP. Nonlinear Wave Interactions in Optics and Radiophysics. Moscow: Nauka; 1988. 230 p. (in Russian).
  10. Steblina VV, Kivshar YuS, Lisak M, Malomed ВА. Self-guided beams in diffractive x^2 medium: variational approach. Opt. Comm. 1995;118(3-4):345-352. DOI: 10.1016/0030-4018(95)00308-U.
  11. Karamzin YuN, Sukhorukov АР, Trofimov VА. Mathematical modeling in nonlinear optics. Moscow: Moscow University Press; 1989. 153 p. (in Russian).
  12. Kivshar YuS. Gар solitons due to cascading. Phys. Rev. E. 1995;51(2):1613-1615. DOI: 10.1103/physreve.51.1613.
  13. Conti C, Trillo S, Assanto G. Bloch function approach for parametric gap solitons. Opt. Lett. 1997;22(7):445-447. DOI: 10.1364/ol.22.000445.
  14. Polyakov SV, Sukhorukov AP. Formation and Properties of Bicolored Gap Solitons. Bull. Russ. Acad. Sci. Phys. 1998;62(12):2327-2337.
  15. Akhmanov SА, Visloukh VА, Chirkin АS. Optics оf Femtosecond Laser Pulses. NY: American Institute of Physics; 1992. 366 p.
  16. Karamzin YuN, Polyakov SV, Sukhorukov АP. Nonlinear tunneling in waveguids. Moscow University Phys. Bull. 1996;5:70.
  17. Polyakov SV, Sukhorukov AP. Slow and immovable parametric solitons in periodically inhomogeneous media. Bull. Russ. Acad. Sci. Phys. 1997;61(12):2353-2358.
  18. Conti C, Trillo S, Assanto G. Trapping оf slowly moving оr stationary two-color gар solitons. Opt. Lett. 1998;23(5):334-336. DOI: 10.1364/ol.23.000334.
Received: 
13.07.1998
Accepted: 
26.10.1998
Published: 
10.12.1998
  • 36 reads