Optical Pulse Dynamics in Active Metamaterials with Positive and Negative Refractive Index

We study numerically the propagation of two-color light pulses through a metamaterial doped with active atoms such that the carrier frequencies of the pulses are in resonance with two atomic transitions in the $\Lambda$ configuration and that one color propagates in the regime of positive refraction and the other in the regime of negative refraction. In such a metamaterial, one resonant color of light propagates with positive and the other with negative group velocity. We investigate nonlinear interaction of these forward- and backward-propagating waves, and find self-trapped waves, counter-propagating radiation waves, and hot spots of medium excitation.Comment: 9 pages, 6 figure

Averaging For Solitons With Nonlinearity Management

We develop an averaging method for solitons of the nonlinear Schr{\"o}dinger equation with periodically varying nonlinearity coefficient. This method is used to effectively describe solitons in Bose-Einstein condensates, in the context of the recently proposed and experimentally realizable technique of Feshbach resonance management. Using the derived local averaged equation, we study matter-wave bright and dark solitons and demonstrate a very good agreement between solutions of the averaged and full equations.Comment: 6 pages, 5 figures, in pres

Controlling pulse propagation in optical fibers through nonlinearity and dispersion management

In case of the nonlinear Schr\"odinger equation with designed group velocity dispersion, variable nonlinearity and gain/loss; we analytically demonstrate the phenomenon of chirp reversal crucial for pulse reproduction. Two different scenarios are exhibited, where the pulses experience identical dispersion profiles, but show entirely different propagation behavior. Exact expressions for dynamical quasi-solitons and soliton bound-states relevant for fiber communication are also exhibited.Comment: 4 pages, 5 eps figure

Stochastic Pulse Switching in a Degenerate Resonant Optical Medium

Using the idealized integrable Maxwell-Bloch model, we describe random optical-pulse polarization switching along an active optical medium in the Lambda-configuration with disordered occupation numbers of its lower energy sub-level pair. The description combines complete integrability and stochastic dynamics. For the single-soliton pulse, we derive the statistics of the electric-field polarization ellipse at a given point along the medium in closed form. If the average initial population difference of the two lower sub-levels vanishes, we show that the pulse polarization will switch intermittently between the two circular polarizations as it travels along the medium. If this difference does not vanish, the pulse will eventually forever remain in the circular polarization determined by which sub-level is more occupied on average. We also derive the exact expressions for the statistics of the polarization-switching dynamics, such as the probability distribution of the distance between two consecutive switches and the percentage of the distance along the medium the pulse spends in the elliptical polarization of a given orientation in the case of vanishing average initial population difference. We find that the latter distribution is given in terms of the well-known arcsine law

Nonlinearity Management in Higher Dimensions

In the present short communication, we revisit nonlinearity management of the time-periodic nonlinear Schrodinger equation and the related averaging procedure. We prove that the averaged nonlinear Schrodinger equation does not support the blow-up of solutions in higher dimensions, independently of the strength in the nonlinearity coefficient variance. This conclusion agrees with earlier works in the case of strong nonlinearity management but contradicts those in the case of weak nonlinearity management. The apparent discrepancy is explained by the divergence of the averaging procedure in the limit of weak nonlinearity management.Comment: 9 pages, 1 figure

Instabilities of dispersion-managed solitons in the normal dispersion regime

Dispersion-managed solitons are reviewed within a Gaussian variational approximation and an integral evolution model. In the normal regime of the dispersion map (when the averaged path dispersion is negative), there are two solitons of different pulse duration and energy at a fixed propagation constant. We show that the short soliton with a larger energy is linearly (exponentially) unstable. The other (long) soliton with a smaller energy is linearly stable but hits a resonance with excitations of the dispersion map. The results are compared with the results from the recent publicationsComment: 20 figures, 20 pages. submitted to Phys. Rev.

Investigation of Benthic Foraminiferal Non-Traditional Stable Isotopes to Reconstruct Methane Fluxes in Sedimentary Environments

Methane (CH4) is an important greenhouse gas, with a global warming potential much higher than carbon dioxide (CO2) on a short time scale. Even if the residence time of CH4 in the atmosphere is relatively short (tens of years), one of the products of CH4 oxidation is CO2, a greenhouse gas with a much longer residence time in the atmosphere (tens to hundreds of years). CH4 has been proposed as one of the trigger mechanisms for rapid global climate change today and in the geological past. With regards to the geological past, numerous studies proposed the benthic foraminiferal carbon isotope ratio (Delta13C) as a tool to reconstruct the impact of marine CH4 on rapid climate changes; however, the investigation of modern benthic foraminiferal Delta13C have produced inconclusive results. CH4 has a distinctive hydrogen isotope (Delta(D)) and Delta13C signature compared to seawater, and sulfate reduction, often coupled to CH4 anaerobic oxidation in sediments, changes the sulfur isotope signature (Delta34S) of the remaining sulfate in porewater. Therefore, we hypothesize that the Delta(D) and Delta34S signature of infaunal benthic foraminiferal species can provide a complementary approach to Delta13C to study CH4 dynamics in sedimentary environments. Here, we present the preliminary results obtained analyzing Uvigerina peregrina Delta(D) and Delta34S from three different locations at Hydrate Ridge, offshore Oregon. Unfortunately, the lack of chemical data related to the moment of foraminiferal calcification makes difficult to build a robust relationship among the U. peregrina stable isotopes and the CH4 fluxes at the sampling sites. However, our results look very promising, as each site is characterized by a different Delta(D) and Delta34S signature. We emphasize that this study represents the first step in the development of new proxies (Delta(D)) and Delta34S), which may complement the more traditional benthic foraminiferal Delta13C values, to reconstruct marine CH4 fluxes in the geological past