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We obtain analytical conditions for the occurrence of numerical instability (NI) of a split-step method when the simulated solution of the nonlinear Schrödinger equation is close to a plane wave with nonzero carrier frequency. We also numerically study such an instability when the solution is a sequence of pulses rather than a plane wave. The plane-wave-based analysis gives reasonable predictions for the frequencies of the numerically unstable Fourier modes but overestimates the instability growth rate. The latter is found to be strongly influenced by the randomness of the signal’s profile: The more randomly it varies during the propagation, the weaker is the NI. Using an example of a realistic transmission system, we demonstrate that our single-channel results can be used to predict occurrences of NI in multichannel simulations. We also give an estimate for the integration step size for which NI, while present, will not affect simulation results for such systems. Using that estimate may lead to a significant saving of computational time.

We derive an analytic expression for the evolution of the differential group delay (DGD) in a fiber-optic circulating loop. We distill a simple analytic solution for the average DGD and show that it accumulates approximately linearly with transmission distance. The scaling of this linear function is confirmed experimentally using a long-haul fiber-optic transmission test-bed. This result is contrasted with DGD accumulation in a long straight-line transmission system, where the average DGD accumulates as a square root of the system’s length.

We present a comprehensive study of the effects of third-order dispersion (TOD) on dispersion-managed (DM) solitons. The two main effects of TOD are creation of asymmetry of the DM soliton’s profile and generation of continuum radiation. Considering these two effects, we derive a conservative bound on the magnitude of TOD below which it will not have a significant detrimental effect on DM solitons over transoceanic distances. We also calculate the shifts in the DM soliton’s position and central frequency that are due to TOD. Finally, we discuss a novel possibility of observing a nonradiating soliton in DM systems with TOD.

The multiple-scale expansion is used to derive averaged equations governing the slow evolution of a pulse in a randomly birefringent, non-polarization-preserving fiber. It is shown that, in the limit when the average beat length is much less than the correlation length of random variations of the fiber’s parameters, these equations are two nonlinearly coupled nonlinear Schrödinger equations, with the cross-coupling coefficient being, in general, different from 1. The effect of perturbations of the averaged equations that result from randomness of the fiber parameters is estimated.

We consider soliton solutions to equations describing a pair of tunnel-coupled nonlinear optical fibers with a phase-velocity mismatch between them. The analysis is based on the variational approximation, which is checked (with quite favorable results) against direct numerical solutions at selected values of the parameters. The results are presented in the form of curves demonstrating evolution of the energy in one of the soliton's components with increase of the mismatch, with the total energy of the soliton being fixed. Two bifurcations are found. One of them, which to our knowledge has not been observed in any form earlier, involves a termination, occurring at a finite value of the mismatch parameter, of the branch whose solitons have components of the opposite sign; this branch corresponds to the antisymmetric soliton in the model with no mismatch. The other, more important, bifurcation is perceived as the occurrence of a hysteresis-type behavior of another branch, whose solitons have the same signs of their components; this branch corresponds to both the symmetric and the asymmetric solitons in the model with no mismatch. The implications of this second bifurcation for the propagation of a subpicosecond soliton in a real-world dual-core fiber are also discussed.

The variational method is used to derive correlation equations that model phase jitter in dispersion-managed soliton systems. The predictions of these correlation equations are consistent with numerical solutions of the nonlinear Schrödinger equation on which they are based.

We present an analytic theory of timing jitter in dispersion-managed light-wave systems that is based on the moment method and the assumption of a chirped Gaussian pulse. We apply the theory to a soliton system and show that 50% postcompensation of the accumulated dispersion can reduce the jitter by a factor of 2. We also apply the theory to a low-power light-wave system employing the return-to-zero format and find that timing jitter can be minimized along the fiber link for an optimal choice of precompensation and postcompensation.

Polarization mode dispersion causes solitons to emit background radiation, which degrades transmission quality. It is shown theoretically and confirmed by numerical simulations that dispersion-managed solitons can trap part of that radiation into localized eigenmodes, thus yielding improvement in transmission quality compared with that of conventional solitons.

We calculate the self-frequency shift experienced by a soliton in a dispersion-managed fiber that is due to the Raman effect, as well as the energy and frequency shifts that result from a collision of such solitons with different wavelengths. We find that dispersion management suppresses both types of frequency shift but does not significantly affect the energy shift that is accumulated over a large propagation distance. The latter shift may represent a potential problem for wavelength-division-multiplexed systems with several gigabits per second in a single channel.