New developments in the study of optical parabolic pulses in normally dispersive fibers

We report two recent studies dealing with the evolution of parabolic pulses in normally dispersive fibres. On the one hand, the nonlinear reshaping from a Gaussian intensity profile towards the asymptotic parabolic shape is experimentally investigated in a Raman amplifier. On the other hand, the significant impact of the fourth order dispersion on a passive propagation is theoretically discussed: we numerically demonstrate flat-top, coherent supercontinuum generation in an all-normal dispersion-flattened photonic crystal fiber. This shape is associated to a strong reshaping of the temporal profile what becomes triangular.

Dissipative nonlinear structures in optical fiber systems II : self-similar parabolic pulses in active fibers

In this second talk on dissipative structures in fiber applications, we overview theoretical aspects of the generation, evolution and characterization of self-similar parabolic-shaped pulses in fiber amplifier media. In particular, we present a perturbation analysis that describes the structural changes induced by third-order fiber dispersion on the parabolic pulse solution of the nonlinear Schrödinger equation with gain. Promising applications of parabolic pulses in optical signal post-processing and regeneration in communication systems are also discussed.

Experimental investigation of inter-modal cross-gain modulation and transient effects in a two mode group erbium doped fiber amplifier

We report what we believe to be the first experimental study of inter-modal cross-gain modulation and associated transient effects as different spatial modes and wavelength channels are added and dropped within a two-mode amplifier for SDM transmission.

Performance comparison of 2R and 3R optical regeneration schemes at 40 Gb/s for application to all-optical networks

This work numerically analyzes the performances of a 2R (reamplification and reshaping) regenerator based on a nonlinear optical loop mirror and a 3R (reamplification, reshaping, and retiming) regenerator using a nonlinearly enhanced amplitude modulator in 40-Gb/s standard single-mode fiber (SMF)-based optical networks with large amplifier spacing. The characteristics of one(600 km of SMF) and two-step regeneration are examined and the feasibility of wavelength-division multiplexing (WDM) operation is demonstrated.

Auto-solitons guided by in-line nonlinear optical loop mirrors in dispersion-managed communication systems

Summary form only given. Both dispersion management and the use of a nonlinear optical loop mirror (NOLM) as a saturable absorber can improve the performance of a soliton-based communication system. Dispersion management gives the benefits of low average dispersion while allowing pulses with higher powers to propagate, which helps to suppress Gordon-Haus timing jitter without sacrificing the signal-to-noise ratio. The NOLM suppresses the buildup of amplifier spontaneous emission noise and background dispersive radiation which, if allowed to interact with the soliton, can lead to its breakup. We examine optical pulse propagation in dispersion-managed (DM) transmission system with periodically inserted in-line NOLMs. To describe basic features of the signal transmission in such lines, we develop a simple theory based on a variational approach involving Gaussian trial functions. It, has already been proved that the variational method is an extremely effective tool for description of DM solitons. In the work we manage to include in the variational description the point action of the NOLM on pulse parameters, assuming that the Gaussian pulse shape is inherently preserved by propagation through the NOLM. The obtained results are verified by direct numerical simulations

Statistics of three interacting optical solitons

We examine the statistics of three interacting optical solitons under the effects of amplifier noise and filtering. We derive rigorously the Fokker-Planck equation that governs the probability distribution of soliton parameters.

On the theory of self-similar parabolic optical pulses

Self-similar optical pulses (or “similaritons”) of parabolic intensity profile can be found as asymptotic solutions of the nonlinear Schr¨odinger equation in a gain medium such as a fiber amplifier or laser resonator. These solutions represent a wide-ranging significance example of dissipative nonlinear structures in optics. Here, we address some issues related to the formation and evolution of parabolic pulses in a fiber gain medium by means of semi-analytic approaches. In particular, the effect of the third-order dispersion on the structure of the asymptotic solution is examined. Our analysis is based on the resolution of ordinary differential equations, which enable us to describe the main properties of the pulse propagation and structural characteristics observable through direct numerical simulations of the basic partial differential equation model with sufficient accuracy.

Experimental investigation of inter-modal cross-gain modulation and transient effects in a two mode group erbium doped fiber amplifier

We report what we believe to be the first experimental study of inter-modal cross-gain modulation and associated transient effects as different spatial modes and wavelength channels are added and dropped within a two-mode amplifier for SDM transmission.

New developments in the study of optical parabolic pulses in normally dispersive fibers

We report two recent studies dealing with the evolution of parabolic pulses in normally dispersive fibres. On the one hand, the nonlinear reshaping from a Gaussian intensity profile towards the asymptotic parabolic shape is experimentally investigated in a Raman amplifier. On the other hand, the significant impact of the fourth order dispersion on a passive propagation is theoretically discussed: we numerically demonstrate flat-top, coherent supercontinuum generation in an all-normal dispersion-flattened photonic crystal fiber. This shape is associated to a strong reshaping of the temporal profile what becomes triangular.

Dissipative nonlinear structures in optical fiber systems II:self-similar parabolic pulses in active fibers

In this second talk on dissipative structures in fiber applications, we overview theoretical aspects of the generation, evolution and characterization of self-similar parabolic-shaped pulses in fiber amplifier media. In particular, we present a perturbation analysis that describes the structural changes induced by third-order fiber dispersion on the parabolic pulse solution of the nonlinear Schrödinger equation with gain. Promising applications of parabolic pulses in optical signal post-processing and regeneration in communication systems are also discussed.

On the theory of self-similar parabolic optical pulses

Self-similar optical pulses (or “similaritons”) of parabolic intensity profile can be found as asymptotic solutions of the nonlinear Schr¨odinger equation in a gain medium such as a fiber amplifier or laser resonator. These solutions represent a wide-ranging significance example of dissipative nonlinear structures in optics. Here, we address some issues related to the formation and evolution of parabolic pulses in a fiber gain medium by means of semi-analytic approaches. In particular, the effect of the third-order dispersion on the structure of the asymptotic solution is examined. Our analysis is based on the resolution of ordinary differential equations, which enable us to describe the main properties of the pulse propagation and structural characteristics observable through direct numerical simulations of the basic partial differential equation model with sufficient accuracy.

Picosecond soliton transmission using concatenated nonlinear optical loop-mirror intensity filters

The issues involved in employing nonlinear optical loop mirrors (NOLMs) as intensity filters in picosecond soliton transmission were examined in detail. It was shown that inserting NOLMs into a periodically amplified transmission line allowed picosecond solitons to be transmitted under conditions considered infeasible until now. The loop mirrors gave dual function, removing low-power background dispersive waves through saturable absorption and applying a negative feedback mechanism to control the amplitude of the solitons. The stochastic characteristics of the pulses that were due to amplifier spontaneous-emission noise were investigated, and a number of new properties were determined. In addition, the mutual interaction between pulses was also significantly different from that observed for longer-duration solitons. The impact of Raman scattering in the computations was included and it was shown that soliton self-frequency shifts may be eliminated by appropriate bandwidth restrictions.

Performance comparison of 2R and 3R optical regeneration schemes at 40 Gb/s for application to all-optical networks

This paper numerically analyzes the performances of a 2R (reamplification and reshaping) regenerator based on a nonlinear optical loop mirror and a 3R (reamplification, reshaping, and retiming) regenerator using a nonlinearly enhanced amplitude modulator in 40-Gb/s standard single-mode fiber (SMF)-based optical networks with large amplifier spacing. The characteristics of one- (600 km of SMF) and two-step regeneration are examined and the feasibility of wavelength-division multiplexing operation is demonstrated. © 2005 IEEE.

16,000 km, 10 Gbits-1 soliton transmission over standard fibre by reduction of interactions through optimum amplifier positioning

We show that by optimizing the amplifier position in a two-stage dispersion map, the (dispersion-managed) soliton-soliton interaction can be reduced, enabling transmission of 10-Gbits-1 solitons over standard fiber over 16,000 km

Statistics of three interacting optical solitons

We examine the statistics of three interacting optical solitons under the effects of amplifier noise and filtering. We derive rigorously the Fokker-Planck equation that governs the probability distribution of soliton parameters.