Normal Average Dispersion Research Articles

MoS2/graphene heterostructure incorporated passively mode-locked fiber laser: from anomalous to normal average dispersion

Two-dimensional (2D) nanomaterials for ultrafast photonic applications have attracted significant attention in recent years. 2D nanocomposites are of great interest because of their capability to combine the merits of each nanomaterial. In this work, we have demonstrated erbium-doped mode-locked fiber lasers that incorporate MoS2/graphene heterostructure based saturable absorbers (SAs) from anomalous to normal average dispersion for the first time. The modulation depth, the saturation intensity, and the non-saturable absorption of the MoS2/graphene heterostructure are measured to be 12.4%, 12.7 MW/cm2 and 28%, respectively. By incorporating this particular MoS2/graphene heterostructure based SA, the mode-locked fiber lasers can produce stable pulse trains at anomalous, near-zero, and normal average dispersion. At an anomalous average dispersion of -0.181 ps2, the Kelly sidebands are found to be superimposed on the optical spectrum, and a stable soliton pulse train has been measured with a signal-to-noise ratio of ∼73 dB in the radio frequency spectrum. At a near-zero average dispersion of -0.082 ps2, a Gaussian-like optical spectrum has been observed where the narrowest pulse width is ∼837 fs. At normal average dispersion of + 0.041 ps2, the steep-edge optical spectrum has been produced, indicating that dissipative solitons have been generated. The obtained results prove that a MoS2/graphene heterostructure is an ideal SA in mode-locked fiber lasers for ultrashort pulse generation from anomalous to normal average dispersion.

Energy diagram and stability range of families of soliton molecules in fibers

Following an analytically predicted energy diagram, we numerically investigate the behavior of a soliton molecule in terms of its energy with respect to the breathing factor and average-dispersion of dispersion managed optical fiber lines. We demonstrate the stable families of soliton molecules in anomalous, normal and zero average dispersion regimes. For normal average dispersion, it is showed that each stable family of SM is distributed over a lower and an upper branches. Further, the stability range is limited by a threshold value and a higher value of the breathing factor.

Competing four-wave mixing processes in dispersion oscillating telecom fiber

We experimentally study the dynamics of the generation of multiple sidebands by means of a quasi-phase-matched four-wave mixing (FWM) process occurring in a dispersion-oscillating, highly nonlinear optical fiber. The fiber under test is pumped by a ns microchip laser operating in the normal average group-velocity dispersion regime and in the telecom C band. We reveal that the growth of higher-order sidebands is strongly influenced by the competition with cascade FWM between the pump and the first-order quasi-phase matched sidebands. The properties of these competing FWM processes are substantially affected when a partially coherent pump source is used, leading to a drastic reduction of the average power needed for sideband generation.

Nonperiodic quasi-stable nonlinear optical carrier pulses with sliding chirp-free points for transmission at 40 Gbit/s rate

We present a novel nonlinear transmission regime at 40Gbit/s using nonperiodic carrier pulses with 50% duty cycle and sliding (with propagation) chirp-free points. Quasi-stable transmission of such carrier pulses is supported by a large normal span average dispersion and misbalanced optical amplification. The possibility of applying this new nonlinear carrier pulse to WDM transmission systems is illustrated with two examples.

Soliton pairs in a fiber laser: from anomalous to normal average dispersion regime

We report the observation of self phase-locked pulse pairs in a stretched-pulse fiber laser operating in the normal path-averaged dispersion regime. Numerical simulations agree with our experimental results. More insight is provided with a numerical comparison between intracavity profiles of pulse pairs in anomalous and in normal dispersion regimes.

Tolerance of dispersion-managed soliton transmission to the shape of the input pulses

We showed that long-distance transmission is affected by the source pulse tails. Fast tail dropoff dramatically improves the transmission. We found that the tails must be at least 20 dB down 50 ps from the peak in order to successfully transmit signals over 20 000 km at 20 Gbit/s with anomalous path average dispersion. While tails that are 15 dB down 50 ps from the peak are sufficient to transmit data at 10 Gbit/s over 20 000 km with anomalous path average dispersion, the tails must be down at least 25 dB 50 ps from the peak to transmit data with slightly normal path average dispersion.

Stabilized scheme for dispersion management

We introduce a model in which completely stable propagation of dispersion-managed (DM) solitons is provided by periodic coupling of the system fiber’s core to short segments of a parallel lossy core. Considering the model in the distributed approximation, we identified a vast stability domain in its parameter space. We also obtained a set of DM-strength–power characteristics for stable solitons at fixed values of the DM period. We found that, as for the filtered single-core DM model, stable transmission of the solitons is possible at virtually all the values of the DM strength, whereas the normalized peak power of the pulse must exceed a certain minimum value. Close to this minimum, we found a stable transmission regime with moderate values of the DM strength, S∼3, and a DM period of approximately 1.5–2 soliton periods (defined as for the homogeneous fiber), which may be promising for reducing soliton–soliton interactions. We also found cases in which the soliton transmission remained stable in the corresponding strongly discrete (lumped) model as well as at normal average dispersion.

Experimental demonstration of long-distance dispersion-managed soliton propagation at zero average dispersion

We observed for the first time stable propagation of dispersion-managed solitons with zero or slightly below normal average dispersion over 28000 km in a recirculating fiber loop. Comparison between theory and experiment provides a highly sensitive estimate of the average dispersion.

Dispersion-managed solitons in the normal dispersion regime: a physical interpretation

We present an analytic description of dispersion-managed soliton propagation based on split-step and variational models. Using these models, we derive the threshold map strength for the existence of dispersion-managed solitons in the normal dispersion regime and obtain a bound on the maximum normal average dispersion.

Power dependence and accessible bandwidth for dispersion-managedsolitons in asymmetric dispersion maps

The authors investigate how the parameters of dispersion managed solitons depend on the asymmetry of the dispersion map. Using the variational approach and numerical simulations it is shown that asymmetric maps can increase the accessible bandwidth in the normal average dispersion regime and equalise the power in adjacent WDM channels.

Variational approach to optical pulse propagation in dispersion compensated transmission systems

Within the area of optical pulse propagation in long-haul transmission systems various designs for dispersion compensation are investigated. On the basis of variational procedures with collective coordinates, a very effective method is presented which allows to determine quite accurately the possible operation points. We have obtained an analytical formula for the soliton power enhancement. This analytical expression is in good agreement with numerical results, in the (practical) limit when residual dispersion and nonlinearity only slightly affect the pulse dynamics over one compensation period. The procedure is suitable to analyze the proper design of dispersion compensating elements. The results allow also to describe the shape of the dispersion-managed soliton. We discuss also a qualitative physical explanation of the possibility to transmit a soliton at zero or normal average dispersion. Analytical predictions are confirmed by direct numerical simulations.

Dispersion-managed solitons in optical amplifier transmission systems with zero average dispersion

Soliton propagation in a cascaded dispersion-managed optical amplifier system with zero net dispersion is examined. We present a qualitative physical explanation for the recently discovered fact that a soliton with finite energy can propagate down a fiber line with zero or normal average dispersion. We describe a specific practical system for the main properties of such a soliton, namely, the dependence of the soliton power on the pulse width at chirp-free points and the soliton average energy and width at chirp-free points as functions of the dispersion-allocation (strength of the map) parameter.

Dispersion-managed solitons at normal average dispersion

We find that in a dispersion-managed fiber, in which the strength of the dispersion management is above some threshold, solitons can exist with normal average dispersion. When the normal average dispersion is below some limiting value there exist two soliton solutions with the same pulse duration and different pulse energies. When the normal average dispersion is above this limiting value, no soliton exists. Both higher-energy and lower-energy solitons are dynamically stable in the parameter range that we considered.

Modulational instability in optical fibers with variable dispersion

We study modulational instability in optical fibres whose dispersion varies with the propagation distance. We distinguish between two cases, viz. periodic and random dispersion variation. In the former case it is found that due to the parametric resonance between the dispersion modulation and the modes of the linearized system new domains of modulational instability arise for anomalous as well as normal average dispersion. In the latter case stochastic parametric resonances again lead to the occurrence of modulational instability for normal dispersion. If the dispersion is anomalous the region of modulational instability increases and the respective gain decreases in comparison with a fibre with constant dispersion.