Efficient Adaptive Step Size Method for the Simulation of Supercontinuum Generation in Optical Fibers

The use of an adaptive step size selection significantly reduces the computational effort for the numerical solution of the generalized nonlinear SchrOumldinger equation (GNLSE). The most commonly employed adaptive step size method is based on the estimation of the local error by applying step size...

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Vydáno v:	Journal of lightwave technology Ročník 27; číslo 18; s. 3984 - 3991
Hlavní autor:	Heidt, A.M.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York, NY IEEE 15.09.2009 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	Applied sciences Circuit properties Computation Computational modeling Electric, optical and optoelectronic circuits Electronics Errors Exact sciences and technology Extrapolation Integrated optics. Optical fibers and wave guides Mathematical models Nonlinear equations Nonlinear optics Nonlinearity Optical and optoelectronic circuits Optical fibers Optical losses Optical propagation optical propagation in nonlinear media Optical pulses Runge-Kutta method Schrodinger equation Schroedinger equation solitons Supercontinuum generation Integrated optics Supercontinuum generation Second order optical propagation in nonlinear media optical fibers Step method Soliton Numerical method Runge Kutta method Computational complexity Modeling Adaptive method Schrödinger equation Non linear equation Pulse propagation Ultrashort pulse Algorithm performance Simulation Nonlinear optics solitons Optical fiber
ISSN:	0733-8724, 1558-2213
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Popis
Shrnutí:	The use of an adaptive step size selection significantly reduces the computational effort for the numerical solution of the generalized nonlinear SchrOumldinger equation (GNLSE). The most commonly employed adaptive step size method is based on the estimation of the local error by applying step size doubling and local extrapolation. While this method works well in combination with the globally second-order split-step Fourier (SSF) integration scheme, it can be significantly improved when the highly accurate fourth-order Runge-Kutta in the interaction picture (RK4IP) method is used for integration, which was recently introduced into the nonlinear optics field. It is demonstrated that the local error can then be estimated using a conservation quantity error (CQE) without the necessity of step size doubling. The CQE method for solving the GNLSE is explained in detail, and in addition the concept is transferred to the normal nonlinear Schrodinger equation and extended to include linear loss. The RK4IP-CQE combination proves to be the most efficient algorithm for the modeling of ultrashort pulse propagation in optical fiber, reducing the computational effort by up to ~50% relative to the local error method.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 ObjectType-Article-2 ObjectType-Feature-1 content type line 23
ISSN:	0733-8724 1558-2213
DOI:	10.1109/JLT.2009.2021538