Dispersion-managed Fiber Research Articles

Two regimes of widely tuneable noise-like pulses from a figure-eight fibre laser

In this paper we study a dispersion-managed figure-eight fibre laser generating noise-like pulses with adjustable characteristics. Non-self-starting mode locking leads to the formation of a single noise-like pulse circulating in the cavity. Both the duration of the pulse and its spectral width can be adjusted by tuning the angle of wave retarders, in particular a half-wave retarder that controls the switching power of the polarization-imbalanced nonlinear optical loop mirror that is used as mode locker. Wave retarder tuning also allows observing an abrupt transition between two clearly distinct noise-like pulse regimes, one characterized by a long (> 1 ns) rectangular pulse envelope with a narrow spectrum and the other characterized by shorter sub-ns bell-shaped pulses whose Raman-enhanced spectrum extends far beyond the doped fibre gain spectrum. The existence of two distinct noise-like pulsing modes can be understood in terms of the periodic variation of the pulse spectrum along the cavity, which is able to shift the effective dispersion regime of the laser. By joining the tuning ranges of each regime, the noise-like pulse duration can be adjusted between 57 ps and 6.3 ns, and its bandwidth between 3.5 and 59 nm.

280 GHz dark soliton fiber laser.

We report on an ultrahigh repetition rate dark soliton fiber laser. We show both numerically and experimentally that by taking advantage of the cavity self-induced modulation instability and the dark soliton formation in a net normal dispersion cavity fiber laser, stable ultrahigh repetition rate dark soliton trains can be formed in a dispersion-managed cavity fiber laser. Stable dark soliton trains with a repetition rate as high as ∼280 GHz have been generated in our experiment. Numerical simulations have shown that the effective gain bandwidth limitation plays an important role on the stabilization of the formed dark solitons in the laser.

Experimental observation of soliton molecule evolution in Yb-doped passively mode-locked fiber lasers

We have observed soliton molecules with variable modulation depth of spectra in a passively mode-locked dispersion-managed Yb-doped fiber laser. The soliton molecule we experimentally investigated presents diatomic and tetratomic types. With the enhancement of pump power, the laser alternately operates at solitons molecule, temporal-separation-oscillation solitons, and harmonic mode-locked states. Moreover, the phase of solitons molecule is only locked at low pump, and excess pump would cause phase vibration.

Averaged dynamics of soliton molecules in dispersion-managed optical fibers

The existence regimes and dynamics of soliton molecules in dispersion-managed (DM) optical fibers have been studied. Initially we develop a variational approximation (VA) for description of periodic dynamics of a soliton molecule within each unit cell of the dispersion map. The obtained system of coupled equations for the pulse width and chirp allows to find the parameters of DM soliton molecules for the given dispersion map and pulse energy. Then by means of a scaling transformation and averaging procedure we reduce the original nonlinear Schr\"odinger equation (NLSE) with piecewise-constant periodic dispersion to its counterpart with constant coefficients and additional parabolic potential. The obtained averaged NLSE with expulsive potential can explain the essential features of solitons and soliton molecules in DM fibers related to their energy loss during propagation. Also, the model of averaged NLSE predicts the instability of the temporal position of the soliton, which may lead to difficulty in holding the pulse in the middle of its time slot. All numerical simulations are performed using the parameters of the existing DM fiber setup, and illustrated via pertinent examples.

Pulse dynamics controlled by saturable absorber in a dispersion-managed normal dispersion Tm-doped mode-locked fiber laser

Based on the coupled Ginzburg-Landu equation, we numerically investigate the pulse dynamics in a dispersion-managed normal dispersion Tm-doped mode-locked fiber laser. The influences of the modulation depth and saturation power of saturable absorber on the pulse dynamics are presented. The simulation results show that these parameters are crucial to achieve high pulse energy and high pulse peak power pulsed laser near 2-\mu m wavelength.

Enhanced stability of dispersion-managed mode-locked fiber lasers with near-zero net cavity dispersion by high-contrast saturable absorbers

We experimentally investigate the stability of dispersion-managed mode-locked fiber lasers using carbon-nanotube-based saturable absorbers (SAs) with different modulation depths. An unstable operation region of the mode-locked fiber laser with near-zero net cavity dispersion is observed, where the laser produces random pulse burst rather than stable pulse train. Through the implementation of high-contrast SAs in the laser, the unstable region is found to be shrunk by ~31.3% when the modulation depth of the SAs increases from 6.4% to 12.5%. The numerical simulation is consistent with the experimental observation.

Higher-order equilibria of temporal soliton molecules in dispersion-managed fibers

Bound states of two or three solitons in dispersion-managed fibers (soliton molecules) were experimentally demonstrated recently. We investigate with a modified perturbation analysis whether the binding mechanism creates a unique stable equilibrium of the relative positions of the solitons in the molecule. Indeed, we find a multitude of equilibrium states, alternatingly stable and unstable. This holds for either case: nearest neighbor solitons having the same or the opposite phase. The number of equilibria are limited by the level of the radiation background. The state with the smallest separation and the highest binding energy (``ground state'') always occurs for opposite-phase pulses; the lowest-order state for in-phase pulses is always unstable. Stable long-chain molecules can be built with a mixture of different nearest-neighbor equilibrium separations. Our results agree with our numerical simulations and experimental results, and connect well with certain results in the literature.

Intrachannel cross-phase modulation-induced phase shift in high-speed dispersion-managed optical fiber transmission system

We investigate the intrachannel cross-phase modulation (IXPM)-induced phase shift in optical return-to-zero pulse propagating in a periodically dispersion-managed long-haul optical fiber transmission line. Necessary dynamical equations for various pulse parameters have been derived using variational analysis to estimate the phase shift. These equations are solved by the Runge–Kutta method. The analytical result is verified by numerical simulation based on split-step Fourier method. We therefore explore the effects of various parameters, such as transmission distance, input power, duty cycle, dispersion map strength, and residual dispersion, on phase shift for a 40 Gb/s single-channel transmission system. We also check the impact of variation of bit rate on phase shift. We find that IXPM-induced phase shift can be mitigated by proper adjustment of dispersion management and different pulse parameters like duty cycle, dispersion map strength, and peak power.

Sub-100 fs and Passive Harmonic Mode-Locking of Dispersion-Managed Dissipative Fiber Laser With Carbon Nanotubes

We reported numerically and experimentally the dissipative soliton operation from a dispersion-managed passively mode-locked erbium fiber laser based on carbon nanotubes (CNTs). Outside compressing the dissipative soliton pulses with spectral width of 35 nm, pulses with 95 fs duration have been obtained. Harmonic mode-locking of the dissipative solitons has also been observed. It suggests that the formation of harmonic mode-locking in mode-locked fiber lasers is independent of the concrete features of the solitons. Additionally, we numerically and experimentally showed that the net dispersion value play a crucial role on the operation regimes of the dispersion-managed fiber laser and the characteristics of the output pulses.

Stability ofN-soliton molecules in dispersion-managed optical fibers

We investigate the stability of $N$-soliton molecules in dispersion-managed optical fibers with focus on the recently realized 2- and 3-soliton molecules. We calculate their binding energy using an averaged nonlinear Schr$\rm{\ddot o}$dinger equation. A combination of variational and numerical solutions to this equation shows that it describes well the intensity profiles and relative separations of the experimental molecules. Extending the calculation to larger values of $N$, the binding energy per soliton is found to saturate at N $N\ge7$.

Optimization strategy to find shapes of soliton molecules

Frequently, a certain solution of a nonlinear wave equation is of interest, but no analytic form is known, and one must work with approximations. We introduce a search strategy to find solutions of the propagation of soliton molecules in a dispersion-managed optical fiber and to determine their shape with some precision. The strategy compares shapes before and after propagation and invokes an optimization routine to minimize the difference. The scheme is designed to be implemented in an experiment so that all fiber parameters are taken into account. Here, we present a full numerical study and a verification of convergence; we validate the method with cases of known solutions. We also compare the performance of two optimization procedures, the Nelder–Mead simplex method and a genetic algorithm.

Fiber looped phase conjugation of polarization multiplexed signals for pre-compensation of fiber nonlinearity effect

Compensation of nonlinear distortion of polarization-multiplexed (PolMux) signals in optical fiber is evaluated experimentally using all-optical signal pre-distortion and fiber loop phase-conjugation at the transmitter. An improved bit error rate is shown for high baud rate, 80 Gb/s RZ-DPSK PolMux signals before transmission in a 728 km long dispersion-managed fiber link employing a direct detection receiver. The partial compensation of nonlinear distortion for both single channel and 3 × 80 Gb/s WDM PolMux signals is observed, despite the impact from the inter-polarization nonlinearity and the associated polarization scattering. Evidence of the limited compensation of inter-polarization nonlinearity is shown.

Flexible Transponder Design Aided by Agile Binary Bit Encoder

In order to accommodate variable bit rates and achieve flexible transmission distances, a binary bit encoding scheme is incorporated in the dual-polarization (DP) quadrature phase-shift keying (QPSK) transmitter to manipulate the signal polarization multiplexing schemes into polarization-multiplexed (PolMux), polarization-switched (PolSw), and polarization-alternated (PolAl) schemes, such that the transmission bit rate could vary among 4B, 3B, and 2B, where B stands for the baud rate of the DP-QPSK signal. With the versatile polarization schemes, the trade-off between the transmission performance and system bit rate could be flexibly adjusted depending on the system requirements and conditions. The performance of these modulation formats has been evaluated experimentally at 32 Gbaud in a dispersion-managed fiber (DMF) link. At a 0.5 dB system margin, the transmission reach of PolSw and PolAl QPSK increased to ∼6400 and ∼8500  km, respectively, compared to the ∼4500  km transmission distance using the PolMux QPSK signal. This improvement is attributed to the lower bit rate of PolSw QPSK (96  Gbits/s) and PolAl QPSK (64  Gbits/s) and to the superior characteristics of the PolSw and PolAl schemes. For example, PolAl QPSK performs as good as the PolMux BPSK format to show similar receiver sensitivity. At the end, a flexible transponder platform with full software-defined optics features is discussed using the proposed flexible transmitter configuration and other techniques, such as optical multi-tone generation and adaptive forward error correction, to enable the transponder to carry standard 10G/40G/100G data.

Double Wronskian solutions of a nonlinear Schrödinger equation in an averaged dispersion-managed fiber system

A nonlinear Schrödinger equation in the presence of chirp and loss terms, which describes the optical solitons in an averaged dispersion-managed (DM) fiber system with fiber losses, is studied via symbolic computation. N-soliton solutions are constructed and verified with the Wronskian technique. Analytic one-, two- and three-soliton solutions are discussed. The soliton has a linear frequency chirp. Soliton width increases exponentially while soliton amplitude, energy and speed decrease exponentially along the DM fiber. As the chirp-loss coefficient increases, soliton width gets wider, while soliton amplitude, energy and speed become smaller. Interactions between the two solitons and among the three solitons are discussed and illustrated. For the larger initial soliton separations, interactions result in some smaller envelopes, which soon disappear due to the chirp-loss effect. When the soliton separations almost reaches zero, solitons interact quasi-periodically along the DM fiber, while each soliton undergoes broadening and decaying.

Numerical simulation of a dispersion-managed active harmonically mode-locked fiber laser using a spectral double-grid technique

A comprehensive lumped model approach has been presented in this paper for the simulation of a dispersion-managed active mode-locked fiber laser. A key aspect of our model is that it operates simultaneously at two different spectral scales, corresponding to the gain bandwidth of the erbium-doped fiber and the frequency content of the mode-locked laser (MLL) pulse. The lumped model consists of a detailed amplifier model that is evolved using a predictor–corrector-based adaptive approach. Convergence analysis of this algorithm is also presented in this paper, highlighting the step size reduction achieved when the amplifier migrates from linear to saturation regime. A simple adaptive frequency domain approach is followed to control the fine grid spectral points and the coarse grid wavelengths. Such an approach has been used to simulate a harmonic MLL cavity in two widely different dispersion regimes facilitated by a pair of chirped fiber Bragg gratings. We validate our model by comparing such simulated results with carefully planned experiments.

Two-soliton and three-soliton molecules in optical fibers

An experimental study of bound states of two solitons and of three solitons in dispersion-managed fibers is presented. The existence regime and stability of such soliton molecules is investigated. With a programmable pulse shaper we can flexibly shape launch signals; received signals are detected in amplitude and phase, and in relative position and velocity. An equilibrium separation is demonstrated for both two-soliton and three-soliton soliton molecules. It is also shown that stable molecules are possible only with antiphase pulses. Both types of soliton molecule are viable for transmission in the same fiber, at the same wavelength. Together with single solitons this opens the possibility of quaternary data transmission in a soliton-based format.

Demonstration of digital phase-sensitive boosting to extend signal reach for long-haul WDM systems using optical phase-conjugated copy

We demonstrate a hybrid optical/digital phase-sensitive boosting (PSB) technique for long-haul wavelength division multiplexing (WDM) transmission systems. The approach uses four-wave mixing (FWM) to generate a phase-conjugated idler alongside the original signal. At the receiver, the signal and idler are jointly detected, and the phases of the idler symbols are conjugated and summed with the signal symbols to suppress noise and nonlinear phase distortion. The proposed hybrid PSB scheme is independent of modulation format and does not require an optical phase-locked loop to achieve phase matching required by conventional phase-sensitive amplifiers. Our simulation and experimental results of 112-Gb/s dual-polarization quadrature phase-shift-keying (DP-QPSK) transmission confirmed the principle of the PSB scheme, attaining a Q-factor improvement of 2.4 dB over conventional single-channel transmission after 4,800 km of dispersion-managed fiber (DMF) link at the expense of 50% reduction in spectral efficiency and extending the system reach by 60% to 7,680 km.

Performance comparison between digital back propagation (DBP) and pilot-aided method for fiber nonlinearity compensation in different fiber links

We numerically investigate and compare the performance of fiber nonlinearity compensation using digital back propagation (DBP) method and pilot-aided method in coherent optical transmission systems using different fiber links. Simulations for wavelength division multiplexed (WDM) 112Gb/s polarization division multiplexed quadrature phase shift keying (PDM-QPSK) systems with dispersion unmanaged (no DM) and dispersion managed (DM) fiber links are implemented. System Q-factor and maximum transmission distance at bit error rate (BER) of 3.8ÿ10⿿3 are calculated for performance comparison. The results show that, for system with no DM fiber link, DBP method outperforms pilot-aided method, because DBP method has better performance for intra-channel fiber nonlinearity compensation. However, for system with DM fiber link where inter-channel fiber nonlinearity plays an important role, pilot-aided method performs better than DBP method, because of its ability for inter-channel fiber nonlinearity compensation.

WDM Signal All-Optical Precompensation of Kerr Nonlinearity in Dispersion-Managed Fibers

Compensation of the Kerr nonlinearity in dispersion-managed optical fiber links is demonstrated for 100-GHz-spaced wavelength division multiplexing (WDM) 40-Gb/s return-to-zero-differential phase-shift keying signals using all-optical nonlinear predistortion and phase-conjugation at the transmitter. Measurements of the bit-error rate (BER) reveal a Q2-factor improvement from 1.3 to 2.9 dB for transmission of one to four WDM channels in a standard single-mode fiber link. Although signal distortion is primarily from intrachannel nonlinearity, the BER is also degraded by linear and nonlinear interchannel crosstalk.

Pulse generation and propagation in dispersion-managed ultralong erbium-doped fiber lasers mode-locked by carbon nanotubes

We present a study of pulse generation and propagation in erbium-doped fiber lasers with cavity length varying from 8m to 3.5km. We demonstrate that soliton effect determines the pulse stabilization in ultralong cavities, measuring pulses with an average 7.0ps pulsewidth for cavity lengths between 2.25 and 3.5km. We also demonstrate that, by filling fundamental soliton requirements, pulsewidth can be determined by length and total dispersion cavity parameters.