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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Bibliographic Details
Published in:Journal of lightwave technology Vol. 27; no. 18; pp. 3984 - 3991
Main Author: Heidt, A.M.
Format: Journal Article
Language:English
Published: New York, NY IEEE 15.09.2009
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
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
Online Access:Get full text
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Description
Summary: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.
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ISSN:0733-8724
1558-2213
DOI:10.1109/JLT.2009.2021538