Abstract

The use of an adaptive step size selection significantly reduces the computational effort for the numerical solution of the generalized nonlinear Schrödinger 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 Schrödinger 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 ${\sim 50}\%$ relative to the local error method.

© 2009 IEEE

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2008 (2)

2007 (2)

G. Genty, S. Coen, J. M. Dudley, "Fiber supercontinuum sources (invited)," J. Opt. Soc. Am. B 24, 1771-1785 (2007).

J. Laegsgaard, "Mode profile dispersion in the generalised nonlinear Schrödinger equation," Opt. Express 15, 16110-16123 (2007).

2006 (1)

J. M. Dudley, G. Genty, S. Coen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78, 1135-1184 (2006).

2005 (2)

B. Kibler, J. Dudley, S. Coen, "Supercontinuum generation and nonlinear pulse propagation in photonic crystal fiber: Influence of the frequency-dependent effective mode area," Appl. Phys. B 81, 337-342 (2005).

M. Frosz, P. Falk, O. Bang, "The role of the second zero-dispersion wavelength in generation of supercontinua and bright-bright soliton-pairs across the zero-dispersion wavelength," Opt. Express 13, 6181-6192 (2005).

2004 (2)

2003 (1)

O. V. Sinkin, R. Holzlöhner, J. Zweck, C. R. Menyuk, "Optimization of the split-step Fourier method in modeling optical-fiber communications systems," J. Lightw. Technol. 21, 61-68 (2003).

2000 (1)

G. Bosco, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, S. Benedetto, "Suppression of spurious tones induced by the split-step method in fiber systems simulation," IEEE Photon. Technol. Lett. 12, 489-491 (2000).

1991 (1)

1989 (2)

K. Blow, D. Wood, "Theoretical description of transient stimulated raman scattering in optical fibers," IEEE J. Quantum Electron. 25, 2665-2673 (1989).

R. H. Stolen, J. P. Gordon, W. J. Tomlinson, H. A. Haus, "Raman response function of silica-core fibers," J. Opt. Soc. Am. B 6, 1159-1166 (1989).

Appl. Phys. B (1)

B. Kibler, J. Dudley, S. Coen, "Supercontinuum generation and nonlinear pulse propagation in photonic crystal fiber: Influence of the frequency-dependent effective mode area," Appl. Phys. B 81, 337-342 (2005).

IEEE Photon. Technol. Lett. (1)

G. Bosco, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, S. Benedetto, "Suppression of spurious tones induced by the split-step method in fiber systems simulation," IEEE Photon. Technol. Lett. 12, 489-491 (2000).

IEEE J. Quantum Electron. (1)

K. Blow, D. Wood, "Theoretical description of transient stimulated raman scattering in optical fibers," IEEE J. Quantum Electron. 25, 2665-2673 (1989).

J. Lightw. Technol. (1)

O. V. Sinkin, R. Holzlöhner, J. Zweck, C. R. Menyuk, "Optimization of the split-step Fourier method in modeling optical-fiber communications systems," J. Lightw. Technol. 21, 61-68 (2003).

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (3)

Opt. Express (2)

I. Cristiani, R. Tediosi, L. Tartara, V. Degiorgio, "Dispersive wave generation by solitons in microstructured optical fibers," Opt. Express 12, 124-135 (2004).

J. Laegsgaard, "Mode profile dispersion in the generalised nonlinear Schrödinger equation," Opt. Express 15, 16110-16123 (2007).

Opt. Express (3)

Rev. Mod. Phys. (1)

J. M. Dudley, G. Genty, S. Coen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78, 1135-1184 (2006).

Other (2)

B. M. Caradoc-Davies, Vortex dynamics in Bose–Einstein condensates Ph.D. dissertation Univ. OtagoDunedinNew Zealand (2000).

G. Agrawal, Nonlinear Fiber Optics (Academic Press, 2001).

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