Drying front in a sloping aquifer: Nonlinear effects

[1] The profiles for the water table height h(x, t) in a shallow sloping aquifer are reexamined with a solution of the nonlinear Boussinesq equation. We demonstrate that the previous anomaly first reported by Brutsaert [1994] that the point at which the water table h first becomes zero at x = L at time t = t(c) remains fixed at this point for all times t > t(c) is actually a result of the linearization of the Boussinesq equation and not, as previously suggested [Brutsaert, 1994; Verhoest and Troch, 2000], a result of the Dupuit assumption. Rather, by examination of the nonlinear Boussinesq equation the drying front, i.e., the point x(f) at which h is zero for times t greater than or equal to t(c), actually recedes downslope as physically expected. This points out that the linear Boussinesq equation should be used carefully when a zero depth is obtained as the concept of an average'' depth loses meaning at that time.

Frequency and temporal effects in linear optical quantum computing

Typically linear optical quantum computing (LOQC) models assume that all input photons are completely indistinguishable. In practice there will inevitably be nonidealities associated with the photons and the experimental setup which will introduce a degree of distinguishability between photons. We consider a nondeterministic optical controlled-NOT gate, a fundamental LOQC gate, and examine the effect of temporal and spectral distinguishability on its operation. We also consider the effect of utilizing nonideal photon counters, which have finite bandwidth and time response.

Compensating for dispersion and nonlinear Kerr effect without phase conjugation

We propose the use of a dispersive medium with a negative nonlinear refractive-index coefficient as a way to compensate for the dispersion and the nonlinear effects resulting from pulse propagation in an optical fiber. The undoing of pulse interaction might allow for increased bit rates.

All-optical nonlinear signal processing at a RZ receiver

We propose a novel all-optical signal processor for use at a return-to-zero receiver utilising loop mirror intensity filtering and nonlinear pulse broadening in normal dispersion fibre. The device offers reamplification and cleaning up of the optical signals, and phase margin improvement. The efficiency of the technique is demonstrated by application to 40 Gbit/s data transmission.

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.

Nonlinear spectral shaping and optical rogue events in fiber-based systems

We provide an overview of our recent work on the shaping and stability of optical continua in the long pulse regime. Fibers with normal group-velocity dispersion at all-wavelengths are shown to allow for highly coherent continua that can be nonlinearly shaped using appropriate initial conditions. In contrast, supercontinua generated in the anomalous dispersion regime are shown to exhibit large fluctuations in the temporal and spectral domains that can be controlled using a carefully chosen seed. A particular example of this is the first experimental observation of the Peregrine soliton which constitutes a prototype of optical rogue-waves.

Nonlinear pulse shaping in fibres for pulse generation and optical processing

The development of new all-optical technologies for data processing and signal manipulation is a field of growing importance with a strong potential for numerous applications in diverse areas of modern science. Nonlinear phenomena occurring in optical fibres have many attractive features and great, but not yet fully explored, potential in signal processing. Here, we review recent progress on the use of fibre nonlinearities for the generation and shaping of optical pulses and on the applications of advanced pulse shapes in all-optical signal processing. Amongst other topics, we will discuss ultrahigh repetition rate pulse sources, the generation of parabolic shaped pulses in active and passive fibres, the generation of pulses with triangular temporal profiles, and coherent supercontinuum sources. The signal processing applications will span optical regeneration, linear distortion compensation, optical decision at the receiver in optical communication systems, spectral and temporal signal doubling, and frequency conversion. © Copyright 2012 Sonia Boscolo and Christophe Finot.

Dissipative nonlinear structures in optical fiber systems I : dissipative dispersion managed solitons in mode-locked lasers

In this first talk on dissipative structures in fiber applications, we extend theory of dispersion-managed solitons to dissipative systems with a focus on mode-locked fibre lasers. Dissipative structures exist at high map strengths leading to the generation of stable, short pulses with high energy. Two types of intra-map pulse evolutions are observed depending on the net cavity dispersion. These are characterized by a reduced model and semi-analytical solutions are obtained.

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.

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.

Nonlinear penalties in long-haul optical networks employing dynamic transponders

We report for the first time, the impact of cross phase modulation in WDM optical transport networks employing dynamic 28 Gbaud PM-mQAM transponders (m = 4, 16, 64, 256). We demonstrate that if the order of QAM is adjusted to maximize the capacity of a given route, there may be a significant degradation in the transmission performance of existing traffic for a given dynamic network architecture. We further report that such degradations are correlated to the accumulated peak-to-average power ratio of the added traffic along a given path, and that managing this ratio through pre-distortion reduces the impact of adjusting the constellation size of neighboring channels. (C) 2011 Optical Society of America

Nonlinear penalties in dynamic optical networks employing autonomous transponders

We report for the first time on the limitations in the operational power range of network traffic in the presence of heterogeneous 28-Gbaud polarization-multiplexed quadrature amplitude modulation (PM-mQAM) channels in a nine-channel dynamic optical mesh network. In particular, we demonstrate that transponders which autonomously select a modulation order and launch power to optimize their own performance will have a severe impact on copropagating network traffic. Our results also suggest that altruistic transponder operation may offer even lower penalties than fixed launch power operation.