Nonlinear atom optics and bright gap soliton generation in finite optical lattices

We theoretically investigate the transmission dynamics of coherent matter wave pulses across finite optical lattices in both the linear and the nonlinear regimes. The shape and the intensity of the transmitted pulse are found to strongly depend on the parameters of the incident pulse, in particular its velocity and density: a clear physical picture for the main features observed in the numerical simulations is given in terms of the atomic band dispersion in the periodic potential of the optical lattice. Signatures of nonlinear effects due the atom-atom interaction are discussed in detail, such as atom optical limiting and atom optical bistability. For positive scattering lengths, matter waves propagating close to the top of the valence band are shown to be subject to modulational instability. A new scheme for the experimental generation of narrow bright gap solitons from a wide Bose-Einstein condensate is proposed: the modulational instability is seeded in a controlled way starting from the strongly modulated density profile of a standing matter wave and the solitonic nature of the generated pulses is checked from their shape and their collisional properties

Interaction of N solitons in the massive Thirring model and optical gap system: the Complex Toda Chain Model

Using the Karpman-Solov''ev quasiparticle approach for soliton-soliton interaction I show that the train propagation of N well separated solitons of the massive Thirring model is described by the complex Toda chain with N nodes. For the optical gap system a generalised (non-integrable) complex Toda chain is derived for description of the train propagation of well separated gap solitons. These results are in favor of the recently proposed conjecture of universality of the complex Toda chain.Comment: RevTex, 23 pages, no figures. Submitted to Physical Review

Coupled-mode equations and gap solitons in a two-dimensional nonlinear elliptic problem with a separable periodic potential

We address a two-dimensional nonlinear elliptic problem with a finite-amplitude periodic potential. For a class of separable symmetric potentials, we study the bifurcation of the first band gap in the spectrum of the linear Schr\"{o}dinger operator and the relevant coupled-mode equations to describe this bifurcation. The coupled-mode equations are derived by the rigorous analysis based on the Fourier--Bloch decomposition and the Implicit Function Theorem in the space of bounded continuous functions vanishing at infinity. Persistence of reversible localized solutions, called gap solitons, beyond the coupled-mode equations is proved under a non-degeneracy assumption on the kernel of the linearization operator. Various branches of reversible localized solutions are classified numerically in the framework of the coupled-mode equations and convergence of the approximation error is verified. Error estimates on the time-dependent solutions of the Gross--Pitaevskii equation and the coupled-mode equations are obtained for a finite-time interval.Comment: 32 pages, 16 figure

Vector treatment of second-harmonic generation produced by tightly focused vignetted Gaussian beams

10.1364/JOSAB.21.002206Journal of the Optical Society of America B: Optical Physics21122206-2212JOBP

Characteristics of second-harmonic generation in HeXLN

We study second harmonic generation in hexagonally poled LiNbO3. We model this process theoretically assuming an undepleted pump, and use the Fraunhofer approximation to determine the required optical path lengths. The results of this procedure are in good agreement with experiments

Nonlinear frequency conversion in two dimensional poled nonlinear crystals

We review our work on two dimensionally poled nonlinear materials. We have characterised the crystals at both high and low power and have started to model their behaviour. The results are compared with work using high power picosecond sources and future work is discussed

Slow light gap solitons

Book Summary:The exotic effects of slow light have been widely observed in the laboratory. However, current literature fails to explore the wider field of slow light in photonic structures and optical fibers.Reflecting recent research, Slow Light: Science and Applications presents a comprehensive introduction to slow light and its potential applications, including storage, switching, DOD applications, and nonlinear optics. The book covers fundamentals of slow light in various media, including atomic media, semiconductors, fibers, and photonic structures. Leading authorities in such diverse fields as atomic vapor spectroscopy, fiber amplifiers, and integrated optics provide an interdisciplinary perspective. They uncover potential applications in both linear and nonlinear optics.While it is impossible to account for all the captivating developments that have occurred in the last few years, this book provides an exceptional survey of the current state of the slow light field