|
Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2006, Volume 46, Number 12, Pages 2254–2264
(Mi zvmmf371)
|
|
|
|
This article is cited in 4 scientific papers (total in 4 papers)
Conservative finite-difference scheme for the problem of propagation of a femtosecond pulse in a photonic crystal with combined nonlinearity
E. B. Terëshin, V. A. Trofimov Faculty of Computational Mathematics and Cybernetics, Moscow State University, Leninskie gory, Moscow, 119992, Russia
Abstract:
A conservative finite-difference scheme is constructed for the problem of propagation of a light pulse in a one-dimensional nonlinear photonic crystal with combined nonlinearity. The invariants of the corresponding differential problem and their difference analogues are given. The scheme is compared with those based on the widespread splitting method. For combined cubic and quadratic nonlinearity in photonic crystal layers, it is shown that the classical splitting method is ineffective, since it requires time steps that are smaller by one or more orders of magnitude. The finite-difference scheme proposed conserves the propagation invariants, which cannot be achieved for splitting schemes even on considerably finer grids. Nonreflecting conditions substantially improve the efficiency of conservative finite-difference schemes as applied to the simulation of complex nonlinear effects in photonic crystals, which require much smaller steps in space and time than those used in the case of linear propagation. The simulation is based on the approach proposed by the authors for the given class of problems.
Key words:
propagation of femtosecond pulses, conservative finite-difference scheme, propagation invariants, splitting method.
Received: 19.01.2006
Citation:
E. B. Terëshin, V. A. Trofimov, “Conservative finite-difference scheme for the problem of propagation of a femtosecond pulse in a photonic crystal with combined nonlinearity”, Zh. Vychisl. Mat. Mat. Fiz., 46:12 (2006), 2254–2264; Comput. Math. Math. Phys., 46:12 (2006), 2154–2163
Linking options:
https://www.mathnet.ru/eng/zvmmf371 https://www.mathnet.ru/eng/zvmmf/v46/i12/p2254
|
|