Dissipative nonlinear structures in optical fiber systems III:dissipative solitons via nonlinear mapping

In the third and final talk on dissipative structures in fiber applications, we discuss mathematical techniques that can be used to characterize modern laser systems that consist of several discrete elements. In particular, we use a nonlinear mapping technique to evaluate high power laser systems where significant changes in the pulse evolution per cavity round trip is observed. We demonstrate that dissipative soliton solutions might be effectively described using this Poincaré mapping approach.

Mode-locked semiconductor lasers with optical injection

We perform characterization of the pulse shape and noise properties of quantum dot passively mode-locked lasers (PMLLs). We propose a novel method to determine the RF linewidth and timing jitter, applicable to high repetition rate PMLLs, through the dependence of modal linewidth on the mode number. Complex electric field measurements show asymmetric pulses with parabolic phase close to threshold, with the appearance of waveform instabilities at higher currents. We demonstrate that the waveform instabilities can be overcome through optical injection-locking to the continues wave (CW) master laser, leading to time-bandwidth product (TBP) improvement, spectral narrowing, and spectral tunability. We discuss the benefits of single- and dual-tone master sources and demonstrate that dual-tone optical injection can additionally improve the noise properties of the slave laser with RF linewidth reduction below instrument limits (1 kHz) and integrated timing jitter values below 300 fs. Dual-tone injection allowed slave laser repetition rate control over a 25 MHz range with reduction of all modal optical linewidths to the master source linewidth, demonstrating phase-locking of all slave modes and coherence improvement.

Concatenated all-optical loop mirror switches

Synthesis of a sharp switching characteristic is experimentally demonstrated by concatenation of nonlinear optical loop mirrors. A novel configuration has been used which results in three terminal operation of the device. This device can be used as a logic gate and for pulse shaping to produce square pulses. © 1993 Taylor and Francis Ltd.

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.

The effects of optical activity and absorption on two wave mixing in Bi12SiO20

We consider non-degenerate two-wave mixing in photorefractive Bi12SiO20. It is shown theoretically that the presence of absorption and optical activity in the photorefractive media may result in a number of maxima for the gain as the frequency detuning between the two beams is varied. Further, when the beam interaction is used for optical amplification, there may also exist an optimum crystal length beyond which there is a reduction in the useful gain obtainable. Experimental results are presented in confirmation of the theory.

Low jitter, long distance pulse transmission near net fibre dispersion zero wavelength

The authors study experimentally ~10 ps return-to-zero pulse propagation near the net dispersion zero of an optical fibre transmission line. Stable near-jitter-free propagation was observed over 70 Mm. Pulse stabilisation and ASE suppression were achieved through the saturable aborber mechanism of nonlinear polarisation rotation.

Autosoliton transmission in dispersion-managed systems guided by in-line nonlinear optical loop mirrors

We examine the feasibility of optical pulse transmission in dispersion-managed fiber systems with in-line nonlinear optical loop mirrors. Applying numerical analysis, we find regimes of stable propagation over long distances in such lines, with a significant increase in the signal-to-noise ratio. © 2000 Optical Society of America.

Self-similar parabolic optical solitary waves

We study solutions of the nonlinear Schrödinger equation (NLSE) with gain, describing optical pulse propagation in an amplifying medium. We construct a semiclassical self-similar solution with a parabolic temporal variation that corresponds to the energy-containing core of the asymptotically propagating pulse in the amplifying medium. We match the self-similar core through Painlevé functions to the solution of the linearized equation that corresponds to the low-amplitude tails of the pulse. The analytic solution accurately reproduces the numerically calculated solution of the NLSE.

All-optical signal regeneration by temporal slicing of nonlinearly flattened optical waveform

A novel all-optical time domain regeneration technique using nonlinear pulse broadening and flattening in normal dispersion fiber and subsequent temporal slicing by an amplitude modulator (or a device performing a similar function) is proposed. Substantial suppression of the timing jitter of jitter-degraded optical signals is demonstrated using the proposed approach. © 2005 IEEE.

Evolution of optical pulses in fiber lines with lumped nonlinear devices as a mapping problem

We analyze the steady-state propagation of optical pulses in fiber transmission systems with lumped nonlinear optical devices (NODs) placed periodically in the line. For the first time to our knowledge, a theoretical model is developed to describe the transmission regime with a quasilinear pulse evolution along the transmission line and the point action of NODs. We formulate the mapping problem for pulse propagation in a unit cell of the line and show that in the particular application to nonlinear optical loop mirrors, the steady-state pulse characteristics predicted by the theory accurately reproduce the results of direct numerical simulations. © 2005 Springer Science+Business Media, Inc.

Quantum-dot mode-locked lasers with dual-mode optical injection

Quantum-dot mode-locked lasers are injection-locked by coherent two-tone master sources. Spectral tuning, significantly improved time-bandwidth product, and low jitter are demonstrated without deterioration of the pulse properties.

Adaptive pulse shaping through BER Feedback

We propose a simplified approach to optical signal pre-distortion based on adaptive pulse shaping through unconventional use of a MZ modulator. The scheme allows natural tailoring of transmitted pulses by optimising the received pulse.

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

Passive nonlinear pulse shaping in normally dispersive fiber

We propose a simple method for passive nonlinear optical pulse shaping that utilizes pulse prechirping and nonlinear propagation in a normally dispersive nonlinear fiber to generate various temporal waveforms of practical interest from conventional laser pulses.

All-optical nonlinear fibre signal processing

All-optical technologies for data processing and signal manipulation are expected to play a major role in future optical communications. Nonlinear phenomena occurring in optical fibre have many attractive features and great, but not yet fully exploited potential in optical signal processing. Here, we overview our recent results and advances in developing novel photonic techniques and approaches to all-optical processing based on fibre nonlinearities. Amongst other topics, we will discuss phase-preserving optical 2R regeneration, the possibility of using parabolic/flat-top pulses for optical signal processing and regeneration, and nonlinear optical pulse shaping. A method for passive nonlinear pulse shaping based on pulse pre-chirping and propagation in a normally dispersive fibre will be presented. The approach provides a simple way of generating various temporal waveforms of fundamental and practical interest. Particular emphasis will be given to the formation and characterization of pulses with a triangular intensity profile. A new technique of doubling/copying optical pulses in both the frequency and time domains using triangular-shaped pulses will be also introduced.