Numerical Algorithms for the Direct Spectral Transform with Applications to Nonlinear Schrödinger Type Systems

Burtsev, Sergey; Camassa, Roberto; Timofeyev, Ilya

doi:10.1006/jcph.1998.6087

Cited by 47 publications

(57 citation statements)

References 11 publications

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“…The discrete spectrum of the ZS operator is associated with solitons, whereas the continuous spectrum gives linearly dispersing waves (radiation). The total energy of a given pulse is proportional to the sum of two contributions: an integral over the continuous spectrum (radiation) and the sum of the imaginary parts of the discrete eigenvalues (solitons) of the ZS scattering problem [26]. We find that the field envelope of RR1 at z 12.1 m [ Fig.…”

Section: B Time Domain Analysismentioning

confidence: 97%

Dynamics of cascaded resonant radiations in a dispersion-varying optical fiber

Bendahmane¹,

Braud²,

Conforti³

et al. 2014

Optica

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Temporal solitons propagating in the vicinity of a zero-dispersion wavelength in an optical fiber emit phasematched resonant radiations (RRs) as a result of perturbations due to higher-order dispersion effects. These RRs propagate linearly and they usually rapidly spread out in time, thus having a very low peak power. Here, we show that the use of an engineered dispersion-varying optical fiber allows us to induce a completely new dynamics, in which a new physical mechanism-cascade of RRs-is discovered. It is explained by the fact that the RR is temporally recompressed thanks to the change of dispersion sign induced by the varying geometry along the fiber. In addition, we report the experimental evidence of physical processes that had remained unobserved experimentally so far, such as the emission of multiple RRs from a single soliton and the generation of a 500 nm continuum exclusively composed of polychromatic RRs.

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Section: B Time Domain Analysismentioning

confidence: 97%

Dynamics of cascaded resonant radiations in a dispersion-varying optical fiber

Bendahmane¹,

Braud²,

Conforti³

et al. 2014

Optica

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“…Given a solution u of the NLS equation at a particular value of z, one can discretize the Z-S eigenvalue problem and solve it numerically [27,31]. In the case of noisy solutions, which may not be smooth, it may be more robust to use a completely integrable discrete version, such as the Ablowitz-Ladik eigenvalue problem [27].…”

Section: Numerical Resultsmentioning

confidence: 99%

A Method to Compute Statistics of Large, Noise-Induced Perturbations of Nonlinear Schrödinger Solitons

Moore¹,

Biondini²,

Kath³

2008

SIAM Rev.

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Abstract. We show in detail how to apply importance sampling to the numerical simulation of large, noiseinduced perturbations in soliton-based optical transmission systems governed by the nonlinear Schrödinger equation. The method allows one to concentrate numerical Monte Carlo simulations around the noise realizations that are most likely to produce the large pulse deformations connected with errors, and yields computational speedups of several orders of magnitude over standard Monte Carlo simulations. We demonstrate the method by using it to calculate the probability density functions associated with pulse amplitude, frequency and timing fluctuations in a prototypical soliton-based communication system.

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“…(4), utilizes the piecewise constant approximation of the input profile 26 used as a potential of the associated ZSSP. The sensitivity of the method (i.e., the lower threshold of the absolute values for the eigenvalues above which we were able to recognize the presence of a new soliton) was ͉ k ͉ ϳ 10 −3 .…”

Section: Multisoliton Decomposition Of a Chirped Gaussianmentioning

confidence: 99%

“…Note that the problem of conversion of the pulses having different shapes into NLSE solitons has already been studied in various contexts, both analytically and numerically, [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] including the study of chirped Gaussiantype input pulses. Let us recall some of these results, in order to clarify what is new in our studies.…”

Section: Introductionmentioning

confidence: 99%

“…When solving the direct ZSSP numerically, we use a well-documented piecewise constant approximation for the potential (see, e.g., Ref. 26 for the detailed description). Though for the systems far from integrable, the decomposition into soliton "modes" via ZSSP itself is not very meaningful; its application makes perfect sense when one considers a span of lossy fiber immediately followed by a span of quasi-lossless fiber.…”

Section: Introductionmentioning

confidence: 99%

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Conversion of a chirped Gaussian pulse to a soliton or a bound multisoliton state in quasi-lossless and lossy optical fiber spans

2007

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The formation of single-soliton or bound-multisoliton states from a single linearly chirped Gaussian pulse in quasi-lossless and lossy fiber spans is examined. The conversion of an input-chirped pulse into soliton states is carried out by virtue of the so-called direct Zakharov-Shabat spectral problem, the solution of which allows one to single out the radiative (dispersive) and soliton constituents of the beam and determine the parameters of the emerging bound state(s). We describe here how the emerging pulse characteristics (the number of bound solitons, the relative soliton power) depend on the input pulse chirp and amplitude.

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Numerical Algorithms for the Direct Spectral Transform with Applications to Nonlinear Schrödinger Type Systems

Cited by 47 publications

References 11 publications

Dynamics of cascaded resonant radiations in a dispersion-varying optical fiber

Dynamics of cascaded resonant radiations in a dispersion-varying optical fiber

A Method to Compute Statistics of Large, Noise-Induced Perturbations of Nonlinear Schrödinger Solitons

Conversion of a chirped Gaussian pulse to a soliton or a bound multisoliton state in quasi-lossless and lossy optical fiber spans

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