Abstract

We describe a modified version of the split step Fourier transform algorithm used to analyze the propagation of multi-channel optical pulses. The modified algorithm divides the signal spectrum into separate envelopes, one for each channel, and computes the evolution of a set of nonlinear Schrödinger equations which accounts for the dispersion of both linear and nonlinear propagating parameters. We choose four exemplary cases for which the performances of the modified and standard split-step methods are compared in terms of computation cost versus global error of the solutions. We show that the modified technique is inferior when the spectrum is dense but it has a significant advantage for sparsely occupied spectra and for cases when the linear and nonlinear propagation parameters are dispersive.

© 2012 IEEE

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  1. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).
  2. R. A. Fisher, W. K. Bischel, "Numerical studies of the interplay between self-phase modulation and dispersion for intense plane-wave laser pulses," J. Appl. Phys. 46, 4921 (1975).
  3. J. A. Fleck, J. R. Morris, M. D. Feit, "Time-dependent propagation of high energy laser beams through the atmosphere," Appl. Phys. 10, 129 (1976).
  4. O. V. Sinkin, R. Holzlohner, 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).
  5. C. R. Menyuk, private communication.
  6. A. Gershikov, E. Shumakher, A. Willinger, G. Eisenstein, "Fiber parametric oscillator for the 2 μm wavelength range based on narrowband optical parametric amplification," Opt. Lett. 35, 3198-3200 (2010).
  7. E. Shumakher, A. Willinger, R. Blit, D. Dahan, G. Eisenstein, "Large tunable delay with low distortion of 10 Gbit/s data in a slow light system based on narrow band fiber parametric amplification," Opt. Exp. 14, 8540-8545 (2006).
  8. D. Dahan, G. Eisenstein, "Tunable all optical delay via slow and fast light propagation in a Raman assisted fiber optical parametric amplifier: A route to all optical buffering," Opt. Exp. 13, 6234-6249 (2005).
  9. J. Wang, C. Jiang, W. Hu, M. Gao, "Modified design of photonic crystal fibers with flattened dispersion," Opt. Laser Technol. 38, 169-172 (2006).
  10. M. Santagiustina, C. G. Someda, G. Vadala', S. Combrie', A. De Rossi, "Theory of slow light enhanced four-wave mixing in photonic crystal waveguides," Opt. Exp. 18, 21024-21029 (2010).
  11. I. Cestier, A. Willinger, P. Colman, S. Combrié, G. Lehoucq, A. De Rossi, G. Eisenstein, "Efficient parametric interactions in a low loss GaInP photonic crystal waveguide," Opt. Lett. 36, 3936-3938 (2011).
  12. C. E. Shannon, "Communication in the presence of noise," Proc. Inst. Radio Eng. (1949) pp. 10-21.
  13. J. Hansryd, P. A. Andrekson, M. Westlund, L. Jie, P. O. Hedekvist, "Fiber-based optical parametric amplifiers and their applications," IEEE J. Sel. Topics Quantum Electron. 8, 506-520 (2002).
  14. D. Marcuse, "Gaussian approximation of the fundamental modes of graded-index fibers," J. Opt. Soc. Amer. 68, 103-109 (1978).

2011 (1)

I. Cestier, A. Willinger, P. Colman, S. Combrié, G. Lehoucq, A. De Rossi, G. Eisenstein, "Efficient parametric interactions in a low loss GaInP photonic crystal waveguide," Opt. Lett. 36, 3936-3938 (2011).

2010 (2)

A. Gershikov, E. Shumakher, A. Willinger, G. Eisenstein, "Fiber parametric oscillator for the 2 μm wavelength range based on narrowband optical parametric amplification," Opt. Lett. 35, 3198-3200 (2010).

M. Santagiustina, C. G. Someda, G. Vadala', S. Combrie', A. De Rossi, "Theory of slow light enhanced four-wave mixing in photonic crystal waveguides," Opt. Exp. 18, 21024-21029 (2010).

2006 (2)

E. Shumakher, A. Willinger, R. Blit, D. Dahan, G. Eisenstein, "Large tunable delay with low distortion of 10 Gbit/s data in a slow light system based on narrow band fiber parametric amplification," Opt. Exp. 14, 8540-8545 (2006).

J. Wang, C. Jiang, W. Hu, M. Gao, "Modified design of photonic crystal fibers with flattened dispersion," Opt. Laser Technol. 38, 169-172 (2006).

2005 (1)

D. Dahan, G. Eisenstein, "Tunable all optical delay via slow and fast light propagation in a Raman assisted fiber optical parametric amplifier: A route to all optical buffering," Opt. Exp. 13, 6234-6249 (2005).

2003 (1)

O. V. Sinkin, R. Holzlohner, 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).

2002 (1)

J. Hansryd, P. A. Andrekson, M. Westlund, L. Jie, P. O. Hedekvist, "Fiber-based optical parametric amplifiers and their applications," IEEE J. Sel. Topics Quantum Electron. 8, 506-520 (2002).

1978 (1)

D. Marcuse, "Gaussian approximation of the fundamental modes of graded-index fibers," J. Opt. Soc. Amer. 68, 103-109 (1978).

1976 (1)

J. A. Fleck, J. R. Morris, M. D. Feit, "Time-dependent propagation of high energy laser beams through the atmosphere," Appl. Phys. 10, 129 (1976).

1975 (1)

R. A. Fisher, W. K. Bischel, "Numerical studies of the interplay between self-phase modulation and dispersion for intense plane-wave laser pulses," J. Appl. Phys. 46, 4921 (1975).

Appl. Phys. (1)

J. A. Fleck, J. R. Morris, M. D. Feit, "Time-dependent propagation of high energy laser beams through the atmosphere," Appl. Phys. 10, 129 (1976).

IEEE J. Sel. Topics Quantum Electron. (1)

J. Hansryd, P. A. Andrekson, M. Westlund, L. Jie, P. O. Hedekvist, "Fiber-based optical parametric amplifiers and their applications," IEEE J. Sel. Topics Quantum Electron. 8, 506-520 (2002).

J. Lightw. Technol. (1)

O. V. Sinkin, R. Holzlohner, 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. Opt. Soc. Amer. (1)

D. Marcuse, "Gaussian approximation of the fundamental modes of graded-index fibers," J. Opt. Soc. Amer. 68, 103-109 (1978).

J. Appl. Phys. (1)

R. A. Fisher, W. K. Bischel, "Numerical studies of the interplay between self-phase modulation and dispersion for intense plane-wave laser pulses," J. Appl. Phys. 46, 4921 (1975).

Opt. Exp. (2)

D. Dahan, G. Eisenstein, "Tunable all optical delay via slow and fast light propagation in a Raman assisted fiber optical parametric amplifier: A route to all optical buffering," Opt. Exp. 13, 6234-6249 (2005).

M. Santagiustina, C. G. Someda, G. Vadala', S. Combrie', A. De Rossi, "Theory of slow light enhanced four-wave mixing in photonic crystal waveguides," Opt. Exp. 18, 21024-21029 (2010).

Opt. Lett. (1)

I. Cestier, A. Willinger, P. Colman, S. Combrié, G. Lehoucq, A. De Rossi, G. Eisenstein, "Efficient parametric interactions in a low loss GaInP photonic crystal waveguide," Opt. Lett. 36, 3936-3938 (2011).

Opt. Exp. (1)

E. Shumakher, A. Willinger, R. Blit, D. Dahan, G. Eisenstein, "Large tunable delay with low distortion of 10 Gbit/s data in a slow light system based on narrow band fiber parametric amplification," Opt. Exp. 14, 8540-8545 (2006).

Opt. Laser Technol. (1)

J. Wang, C. Jiang, W. Hu, M. Gao, "Modified design of photonic crystal fibers with flattened dispersion," Opt. Laser Technol. 38, 169-172 (2006).

Opt. Lett. (1)

Other (3)

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

C. R. Menyuk, private communication.

C. E. Shannon, "Communication in the presence of noise," Proc. Inst. Radio Eng. (1949) pp. 10-21.

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