221
Views
6
CrossRef citations to date
0
Altmetric
Original Articles

Numerical method for 2d soliton solution at SHG in media with time‐dependent combined nonlinearity

&
Pages 123-133 | Received 28 Sep 2007, Published online: 14 Oct 2010

References

  • Agrawal , G. 1993 . Nonlinear fiber optics , New York : Academic Press .
  • Akhmediev , N. N. and Ankiewicz , A. 1997 . Solitons: Nonlinear pulses and beams , London : Kluwer Academic Publishers .
  • Ashihara , S. , Nishina , J. , Shimura , T. and Kuroda , K. 2002 . Soliton compression of femtosecond pulses in quadratic media . JOSA B , 19 (10) : 2505 – 2510 .
  • Brull , L. and Lange , H. 1986 . Stationary, oscillatory and solitary wave type solution of singular nonlinear Schrodinger equations . Math. Meth. in the Appl. Sci , 8 (4) : 559 – 575 .
  • Buryak , A. V. and Kivshar , Yu. S. 1994 . Spatial optical solitons governed by quadratic nonlinearity . Opt. Lett , 19 (20) : 1612 – 1615 .
  • Buryak , A. V. , Trapani , P. D. , Skryabi , D. V. and Trillo , S. 2002 . Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications . Phys. Rep , 370 (2) : 63 – 235 .
  • Demmel , J. W. 1997 . Applied numerical linear algebra , Cambridge : Cambridge University Press .
  • Golub , G. and van Loan , C. 1996 . Matrix computations , London : The Johns Hopkins University Press .
  • Grimshaw , R. , Kuznetso , E. A. and Shapiro , E. G. 2001 . The two‐parameter soliton family for the interaction of a fundamental and its second harmonic . Phys. D. , : 152 – 153 .
  • He , H. , Werne , M. J. and Drummond , P. D. 1996 . Simultaneous solitary‐wave solutions in nonlinear parametric waveguide . Phys. Rev. E , 54 (1) : 896 – 911 .
  • Kapitula , T. and Sandstede , B. 1998 . Stability of bright and dark solitary‐wave solutions to perturbed nonlinear Schrodinger equations . Phys. D. , 124 (1–3) : 58 – 103 .
  • Karamzin , Yu. N. and Sukhorukov , A. P. 1974 . Nonlinear interaction of diffracted light beams in a medium with quadratic nonlinearity: mutual focusing of beams and limitation on the efficiency of optical frequency convertors . JETP , 20 (11) : 339 – 342 .
  • Kivshar , Yu. S. and Agrawal , G. P. 2003 . Optical Solitons: From fibers to photonic crystals , San Diego : Academic Press .
  • Liu , X. , Beckwitt , K. and Wise , F. W. 2000 . Two‐dimensional optical spatiotemporal solitons in quadratic media . Phys. Rev. E , 62 (1) : 1328 – 1340 .
  • Malomed , B. A. , Mihalache , D. , Wise , F. and Torner , L. 2005 . Spatiotemporal optical solitons . J. Opt. B , 7 (5) : 53 – 72 .
  • Stegeman , G. , Haga , D. J. and Torner , L. 1996 . Xi(2) cascading phenomena and their applications to all‐optical signal processing . Opt. Quantum electron , 28 (12) : 1691 – 1740 .
  • Trofimov , V. A. and Matusevich , O. V. 2005 . “ Bistable regime of SHG of femtosecond laser pulse in optical fiber ” . In Proceedings of SPIE, volume 5949 of Photonics Applications in Industry and Research IV Edited by: Romaniuk , R. S. , Simrock , S. and Lutkovski , V.M . 300 – 306 .
  • Trofimov , V. A. and Matusevich , O. V. 2008 . Iterative method for finding of eigen‐functions for system of 2 Schrödinger equations with combined nonlinearity . Computational Mathematics and Mathematical Physics ,

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.