Parabolic similaritons in optical fibres

Recent developments in nonlinear optics have brought to the fore of intensive research an interesting class of pulses with a parabolic intensity profile and a linear instantaneous frequency shift or chirp. Parabolic pulses propagate in optical fibres with normal group-velocity dispersion in a self-similar manner, holding certain relations (scaling) between pulse power, duration and chirp parameter, and can tolerate strong nonlinearity without distortion or wave breaking. These solutions, which have been dubbed similaritons, were demonstrated theoretically and experimentally in fibre amplifiers in 2000. Similaritons in fibre amplifiers are, along with solitons in passive fibres, the most well-known classes of nonlinear attractors for pulse propagation in optical fibre, so they take on major fundamental importance. The unique properties of parabolic similaritons have stimulated numerous applications in nonlinear optics, ranging from ultrashort high-power pulse generation to highly coherent continuum sources and to optical nonlinear processing of telecommunication signals. In this work, we review the physics underlying the generation of parabolic similaritons as well as recent results obtained in a wide range of experimental configurations.

Power optimization of random distributed feedback fiber lasers

We present a comprehensive study of power output characteristics of random distributed feedback Raman fiber lasers. The calculated optimal slope efficiency of the backward wave generation in the one-arm configuration is shown to be as high as ∼90% for 1 W threshold. Nevertheless, in real applications a presence of a small reflection at fiber ends can appreciably deteriorate the power performance. The developed numerical model well describes the experimental data. © 2012 Optical Society of America.

Narrow-band radiation in the random distributed feedback fiber laser

Narrow-band generation is achieved in random distributed feedback (RDFB) fiber laser by using narrow-band filters in the center of a distributed cavity. The resulting line-width of ∼0.1 nm is 10 times less than line-width in classical random distributed feedback fiber laser. Spectral properties can be optimized further. © 2012 OSA.

Inverse space-dependent force problems for the wave equation

The determination of the displacement and the space-dependent force acting on a vibrating structure from measured final or time-average displacement observation is thoroughly investigated. Several aspects related to the existence and uniqueness of a solution of the linear but ill-posed inverse force problems are highlighted. After that, in order to capture the solution a variational formulation is proposed and the gradient of the least-squares functional that is minimized is rigorously and explicitly derived. Numerical results obtained using the Landweber method and the conjugate gradient method are presented and discussed illustrating the convergence of the iterative procedures for exact input data. Furthermore, for noisy data the semi-convergence phenomenon appears, as expected, and stability is restored by stopping the iterations according to the discrepancy principle criterion once the residual becomes close to the amount of noise. The present investigation will be significant to researchers concerned with wave propagation and control of vibrating structures.

One-dimensional optical wave turbulence:experiment and theory

We present a review of the latest developments in one-dimensional (1D) optical wave turbulence (OWT). Based on an original experimental setup that allows for the implementation of 1D OWT, we are able to show that an inverse cascade occurs through the spontaneous evolution of the nonlinear field up to the point when modulational instability leads to soliton formation. After solitons are formed, further interaction of the solitons among themselves and with incoherent waves leads to a final condensate state dominated by a single strong soliton. Motivated by the observations, we develop a theoretical description, showing that the inverse cascade develops through six-wave interaction, and that this is the basic mechanism of nonlinear wave coupling for 1D OWT. We describe theory, numerics and experimental observations while trying to incorporate all the different aspects into a consistent context. The experimental system is described by two coupled nonlinear equations, which we explore within two wave limits allowing for the expression of the evolution of the complex amplitude in a single dynamical equation. The long-wave limit corresponds to waves with wave numbers smaller than the electrical coherence length of the liquid crystal, and the opposite limit, when wave numbers are larger. We show that both of these systems are of a dual cascade type, analogous to two-dimensional (2D) turbulence, which can be described by wave turbulence (WT) theory, and conclude that the cascades are induced by a six-wave resonant interaction process. WT theory predicts several stationary solutions (non-equilibrium and thermodynamic) to both the long- and short-wave systems, and we investigate the necessary conditions required for their realization. Interestingly, the long-wave system is close to the integrable 1D nonlinear Schrödinger equation (NLSE) (which contains exact nonlinear soliton solutions), and as a result during the inverse cascade, nonlinearity of the system at low wave numbers becomes strong. Subsequently, due to the focusing nature of the nonlinearity, this leads to modulational instability (MI) of the condensate and the formation of solitons. Finally, with the aid of the probability density function (PDF) description of WT theory, we explain the coexistence and mutual interactions between solitons and the weakly nonlinear random wave background in the form of a wave turbulence life cycle (WTLC).