A.B. Moubissi

A collective variable approach for dispersion-managed solitons

We present a method to express the generalized nonlinear Schr¨ odinger equation, for pulse propagation in dispersion managed fibre-optic links, in terms of pulse parameters, called collective variables (CVs), such as pulse width, amplitude, chirp and frequency. The CV equations of motion are derived by imposing a set of constraints on the CVs, to minimize the soliton dressing during propagation.

Analytical design of densely dispersion-managed optical fiber transmission systems with Gaussian and raised cosine return-to-zero Ansatze

We propose an easy and efficient way to analytically design densely dispersion-managed fiber systems for ultrafast optical communications. This analytical design is based on the exact solution of the variational equations derived from the nonlinear Schrodinger equation by use of either a Gaussian or a raised-cosine (RC) Ansatz. For the input pulses of dispersion-managed optical fiber transmission systems we consider a RC profile and show that RC return-to-zero pulses are as effective as Gaussian pulses in high-speed (160-Gbits/s) long-distance transmissions.

Average dispersion decreasing densely dispersion-managed fiber transmission systems

The authors propose an average dispersion decreasing densely dispersion-managed (A4DM) fiber line, which can substantially improve the performance of high-speed optical transmission systems. They show that the A4DM fiber lines have many advantages over densely dispersion-managed fiber lines.

Analytical design of dispersion-managed fiber system with map strength 1.65

Abstract We present an easy analytical method for designing dispersion-managed fiber systems with map strength of 1.65, where the transmission lines have minimal pulse–pulse interactions.

On the designing of densely dispersion-managed optical fiber systems for ultrafast optical communication

We present some theoretical and experimental results which suggest the possibility of constructing a non-empirical methodology of designing optical transmission systems with ultra high bit-rate per channel. Theoretically, we present an average dispersion decreasing densely dispersion-managed (A4dm) fiber system, which exhibits many advantages over the densely dispersion-managed fiber system, such as the possibility of transmitting chirp-free Gaussian pulses at 160 Gbit/s per channel over transoceanic distances, with a reduced energy and minimal intra-channel interaction. Experimentally we present generation of a 160-GHz picosecond pulse train at 1550 nm using multiple four-wave mixing temporal compression of an initial dual frequency beat signal in the anomalous-dispersion regime of a non-zero dispersion shifted fiber. A complete intensity and phase characterization of the pulse train by means of a frequency-resolved optical gating technique is achieved, showing generation of transform-limited pedestal-free Gaussian pulses.RésuméNous présentons des résultats théoriques et expérimentaux qui suggèrent la possibilité de construire une méthodologie non empirique de conception de lignes à très haut débit par canal (≥ 160 Gbit/s). Théoriquement nous présentons la ligne de transmissiona4dm, où la gestion de la non-linéarité s’effectue en faisant décroître par palier la dispersion moyenne le long du pas d’amplification. Cette ligne démontre la possibilité de transmettre des impulsions gaussiennes initialement non chirpées à un débit de 160 Gbit/s sur des distances transocéaniques, avec un niveau d’énergie nettement plus petit que dans le cas de lignes à haute densité de gestion de la dispersion et sans gestion de la non-linéarité. Expérimentalement, nous présentons des résultats mettant en évidence la génération d’un train d’impulsions picosecondes à une fréquence de répétition de 160 GHz et à la longueur d’onde de 1550 nm. La technique mise en oeuvre repose sur la compression temporelle non linéaire d’un battement de deux fréquences injectées dans une fibre optique à dispersion décalée en régime de dispersion anormale. Le processus physique non linéaire à l’origine de la compression temporelle est un mélange à quatre ondes en cascades. Une caractérisation complète en intensité et en phase du train d’impulsions ainsi généré est réalisée à l’aide d’une technique d’autocorrélation résolue en fréquence. Cette caractérisation met clairement en évidence la génération d’un train d’impulsions gaussiennes en limite de Fourier et sans piédestal.

Optimized Hermite-gaussian ansatz functions for dispersion-managed solitons

Abstract By theoretical analysis, we show that the usual procedure of simply projecting the dispersion-managed (DM) soliton profile onto the basis of an arbitrary number of Hermite-gaussian (HG) polynomials leads to relatively accurate ansatz functions, but does not correspond to the best representation of DM solitons. Based on the minimization of the soliton dressing, we present a simple procedure, which provides highly accurate representation of DM solitons on the basis of a few HG polynomials only.

Note on collective variable theory of nonlinear Schrödinger solitons

Inconsistencies arise in a recently developed collective variable theory of nonlinear Schrodinger solitons, as a result of a particular formulation of the energy-conservation principle in terms of the time derivative of the phase of the original field. We show that the inconsistencies are resolved either by correctly reformulating the energy-conservation principle or by directly averaging the nonlinear Schrodinger equation.

Design of dispersion-managed fiber systems for transmitting chirp-free Gaussian pulses

We present a general method to analytically design a dispersion-managed (DM) fiber system for any desired fiber (dispersion, nonlinearity and losses) and pulse (width and energy) parameters. This analytical design allows one to transmit chirp-free Gaussian pulses (for very long distances) in almost all kinds of DM fiber systems that have appeared so far in the literature, including systems with dispersion map length greater, equal or shorter with respect to the amplification period.

Wavelength conversion from 1.3 µm to 1.5 µm in single-mode optical fibres using Raman-assisted three-wave mixing

We theoretically analyse the achievement of wide-range all-optical wavelength conversion of a 1.31 µm signal to an idler wave in the 1.5 µm spectral region by Raman-assisted three-wave mixing in single-mode optical fibres. Raman-assisted three-wave mixing allows efficient conversion on a large frequency detuning bandwidth while alleviating the need for stringent phase-matching conditions.

Collective variable analysis of the nonlinear Schrödinger equation for soliton molecules in fibers

We present a description of soliton molecules in terms of its collective variables namely temporal separation between two consecutive pulses, peak-power of each pulse, center-of-mass, chirp, frequency and phase of the whole molecule. Assuming the Hermite–Gaussian ansatz to represent the temporal profile of the molecule, we derive a set of six differential equations for the evolution of the collective variables in the limit of the bare or variational approximation. Then we perform numerical experiments to confirm the ability of the proposed approach for two-soliton molecule propagating along a Dispersion-managed fiber for anomalous, zero or normal averaged dispersion.