Conservative finite-difference scheme for the problem of propagation of a femtosecond pulse in a nonlinear photonic crystal with nonreflecting boundary conditions

Computational Mathematics and Mathematical Physics

Volumn 46, Issue 1, 2006, Pages 154-164

  Tereshin, E B ^a   Trofimov, V A ^a   Fedotov, M V ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

Conservative finite difference scheme; Nonlinear Schr dinger equation; Nonreflecting boundary conditions; Photonic crystal

Indexed keywords

EID: 33746034109     PISSN: 09655425     EISSN: 15556662     Source Type: Journal    
DOI: 10.1134/S0965542506010155     Document Type: Article

References (19)

1. J. Hait, US Patent No. 367443.
2. P. P. Markowicz, H. Tiryaki, and P. N. Prasad, "Dramatic Enhancement of Third-Hannonic Generation in Three-Dimensional Photonic Crystals," Phys. Rev. Lett 92, 083903 (2004).
3. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton, New York, 1995).
4. M. Scalora, F. P. Dawling, C. M. Bowden, and M. J. Blomer, "Optical Limiting and Switching of Ultrashort Pulses in Nonlinear Photonic Bandgap Materials," Phys. Rev. Lett. 73, 1368-1371 (1994).
5. V. A. Trofimov, E. B. Tereshin, and M. V. Fedotov, "On the Possibility of Light Energy Localization in a Nonlinear Photonic Crystal," Opt. Spektrosk. 95, 106 (2003)
6. [Opt. Spectrosc. 95, 106-109 (2003)].
7. B. Alpert, L. Greengard, and T. Hagstrom, "Nonreflecting Boundary Conditions for the Time-Dependent Wave Equation," J. Comput. Phys. 180, 270-296 (2002).
8. G. Fibich and S. Tsynkov, "High-Order Two-Way Artificial Boundary Conditions for Nonlinear Wave Propagation with Backscattering," J. Comput. Phys. 171, 632-677 (2001).
9. T. Hagstorm and S. I. Hariharan, "A Formulation of Asymptotic and Exact Boundary Conditions Using Local Operators," Appl. Numer. Math. 27, 403-416 (1998).
10. C. W. Rowley and T. Colonius, "Discretely Nonreflecting Boundary Conditions for Linear Hyperbolic Systems," J. Comput. Phys. 157, 500-538 (2000).
11. T. M. Lysak and V. A. Trofimov, "Second Harmonic Generation by Femtosecond Pulses under the Condition of Nonzero Amplitude of the Double-Frequency Wave," Opt. Spektrosk. 93, 861-874 (2002)
12. [Opt. Spectrosc. 93, 797-809 (2002)].
13. E. B. Tereshin, V. A. Trofimov, and M. V. Fedotov, "A Conservative Difference Scheme for the Problem of Two-Wave Interaction between Femtosecond Pulses in a Photonic Crystal," Zh. Vychisl. Mat. Mat. Fiz. 43, 1530-1535 (2003)
14. [Comput. Math. Math. Phys. 43, 1472-1477 (2003)].
15. V. A. Trofimov, "Invariance of Femtosecond Light Pulse Propagation in Photonic Crystals," Zh. Vychisl. Mat. Mat. Fiz. 41, 1429-1433 (2001)
16. [Comput. Math. Math. Phys. 41, 1358-1362 (2001)].
17. V. A. Trofimov, "New Approach to Numerical Simulation of Femtosecond Pulse Propagation in Photonic Crystal," Laser Phys. Spectrosc. (Proc. of SPIE, Bellingham) 4002, 28-36 (2000).
18. V. A. Trofimov and E. B. Tereshin, "Comparison of Various Difference Schemes for the Problem of Femtosecond Pulse Propagation in Nonlinear Layered Medium," Proceedings of CMMSE-2004 (Uppsala, Sweden, 2004), pp. 281-287.
19. V. A. Trofimov, E. B. Tereshin, and M. V. Fedotov, "Analysis of Difference Schemes for the Problem of Self-Action of a Femtosecond Pulse in Photonic Crystal," Vestn. Mosk. Gos. Univ., Ser. 15: Vychisl. Mat. Kibern., No. 2, 20-26 (2003).