Experiments on the generation of parabolic pulses in fibers with length-varying normal chromatic dispersion

The experimental results for the propagation of high-power pulses in fibers with length-varying chromatic dispersion are presented.     

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. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 2, pp. 277–289, August, 2005.     

Fractal Iso-Contours of Passive Scalar in Two-Dimensional Smooth Random Flows

A passive scalar field was studied under the action of pumping, diffusion and advection by a 2D smooth flow with Lagrangian chaos. We present theoretical arguments showing that the scalar statistics are not conformally invariant and formulate a new effective semi-analytic algorithm to model scalar turbulence. We then carry out massive numerics of scalar turbulence, focusing on nodal lines. The distribution of contours over sizes and perimeters is shown to depend neither on the flow realization nor on the resolution (diffusion) scale r _d for scales exceeding r _d . The scalar isolines are found to be fractal/smooth at scales larger/smaller than the pumping scale. We characterize the statistics of isoline bending by the driving function of the Löwner map. That function is found to behave like diffusion with diffusivity independent of the resolution yet, most surprisingly, dependent on the velocity realization and time (beyond the time on which the statistics of the scalar is stabilized).     

Wrinkling of vesicles during transient dynamics in elongational flow

Recent experiments by Kantsler et al. [Phys. Rev. Lett. 99, 178102 (2007)10.1103/PhysRevLett.99.178102] have shown that the relaxational dynamics of a vesicle in external elongation flow is accompanied by the formation of wrinkles on a membrane. Motivated by these experiments we present a theory describing the dynamics of a wrinkled membrane. The formation of wrinkles is related to the dynamical instability induced by negative surface tension of the membrane. For quasispherical vesicles we perform analytical study of the wrinkle structure dynamics. We derive the expression for the instability threshold and identify three stages of the dynamics. The scaling laws for the temporal evolution of wrinkling wavelength and surface tension are established, confirmed numerically, and compared to experimental results.     

Simultaneous spatial and spectral transparency in ultralong fiber lasers

We demonstrate that ultralong Raman lasers can be used to generate a transmission medium with simultaneous transparency over the spatial and the spectral domains. Numerical calculations show this cross-domain transparency to be preserved when the medium is used for transmitting high-intensity signals, which makes ultralong lasers an ideal experimental test bed for the study of multifrequency nonlinear interactions in optical fiber waveguides. Full spatiospectral transparency is experimentally obtained over a 20 nm x 20 km window.     

Breathing solitons in optical fiber links

We introduce the concept of “breathing” solitons to describe the dynamics of optical pulses in transmission lines with passive compensation of fiber chromatic dispersion. The “breathing” pulse can be used as the information carrier. The theory presented is complimentary to the concept of the guiding-center soliton. It is shown that an average bright soliton can propagate in a system with large variations of the dispersion, including segments with high normal dispersion. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 10, 814–819 (25 May 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Reduced-power optical solitons in fiber lines with short-scale dispersion management

We examine the properties of dispersion-managed (DM) solitons in fiber lines with dispersion-compensation period L much shorter than amplification distance Z(a) . DM solitons in systems with short-scale dispersion compensation have reduced power compared with DM solitons in previously studied regimes with L>/=Z(a) power (for the same local and average dispersion and the same pulse width). As a result, chirped DM soliton transmission with reasonably low power can be realized with shorter pulses when DM solitons in systems with large L/Z(a) ratios have energies that are too high to be used in practice.     

Theory of guiding-center breathing soliton propagation in optical communication systems with strong dispersion management

We present a theory of chirped breathing pulse propagation in optical transmission systems with strong dispersion management. Fast changes of pulse width and chirp over one period are given by a simple model that is verified by direct numerical simulations. An average pulse evolution in the leading order is described by the nonlinear Schr?dinger equation, with additional parabolic potential that can be a trapping (when a grating is used) or a nontrapping (without a grating) type.     

Dispersion-dominated nonlinear fiber-optic channel

We propose to apply a large predispersion (having the same sign as the transmission fiber) to an optical signal before the uncompensated fiber transmission in coherent communication systems. This technique is aimed at simplification of the following digital signal processing of nonlinear impairments. We derive a model describing pulse propagation in the dispersion-dominated nonlinear fiber channel. In the limit of very strong initial predispersion, the nonlinear propagation equations for each Fourier mode become local and decoupled. This paves the way for new techniques to manage fiber nonlinearity.     

Theory of average pulse propagation in high-bit-rate optical transmission systems with strong dispersion management

A theory of signal transmission in high-bit-rate optical communication systems with large variations of dispersion (strong dispersion management) is presented. It is found that the averaged propagation of a chirped breathing optical pulse along the line is described by the nonlinear Schrödinger equation with an additional parabolic potential. The shape of the averaged pulse is intermediate between the sech-type soliton and a Gaussian pulse. The rapidly decaying Gaussian wings of such pulses allow denser information packing in comparison with the use of sech-type fundamental solitons.