Perturbation Theory for the Assessment of Soliton Transmission Control

Non-Gaussian statistics of soliton timing jitter induced by amplifier noise

“…All noise terms of n A (ζ), n Ω (ζ), and n T (ζ) are independent Gaussian processes with autocorrelation of 6,9 E{n A (ζ 1 )n A (ζ 2 )} = Aσ…”

“…The inclusion of amplitude jitter in (4) to (6) is still within the equations of the first-order soliton perturbation theory 4,5,6 . The nonlinear first-order perturbation can be interpreted the repeated usage of the linearized first-order perturbation 3 .…”

“…The second-order soliton perturbation also includes noise and noise interaction 20,21 . However, the equations of (1) to (3) with noise variances of (4) to (5) are directly from the first-order perturbation of soliton 4,5,6 . Similarly, the non-Gaussian timing jitter of (9) is induced by the term of The probability density functions of frequency and Gordon-Haus timing jitter are the inverse Fourier transforms of the corresponding characteristic functions of (10) and (11) is normalized with respect to the standard deviation of frequency σ Ω (ζ) and timing σ T (ζ) jitter [see (21)] for Figs.…”

Influence of Filter Frequency Dispersion on Soliton Arrival Time Jitter

“…Soliton transmission over transoceanic distances has become mature since the advent of the path-averaged soliton [1][2][3] and of soliton in-line control [4][5][6][7][8][9][10][11][12][13][14]. The first one allows large amplifier spacing and a robustness against the imperfections of the transmission line.…”

Efficient and accurate computation of eye diagrams and bit-error rates in a single-channel CRZ system

“…However, these nonlinear equations are also phase and time invariant, which implies that phase and timing jitter can be removed from the standard Fourier basis without affecting the subsequent evolution, in which case the coefficients of the modified Fourier basis, along with the phase and timing jitter, remain multivariate-Gaussian distributed far longer than the original Fourier coefficients [4]. 1 This result is well known in the theory of solitons, where it is standard to use a basis set that consists of discrete as well as continuous components, rather than the usual Fourier basis, when studying the effects of perturbations and noise [5]- [7].…”