Integrability and conservation laws for the nonlinear evolution equations of partially coherent waves in noninstantaneous Kerr media.

It is shown that the evolution equations describing partially coherent wave propagation in noninstantaneous Kerr media are integrable and have an infinite number of invariants. A recursion relation for generating these invariants is presented, and it is demonstrated how to express them in the coherent density, self-consistent multimode, mutual coherence, and Wigner formalisms.

Influence of higher-order dispersion on modulational instability and pulse broadening of partially incoherent light.

The Wigner-Moyal equation for the Wigner distribution of a partially incoherent optical wave field propagating in dispersive and nonlinear media has been generalized to include the effects of both arbitrary order of dispersion and arbitrary nonlinearity. The theory predicts partial incoherence to enhance the pulse broadening during linear wave pulse propagation. Furthermore, an application of the theory to the modulational instability of constant amplitude waves shows how higher-order dispersion affects the instability growth rate.

Propagation properties of chirped soliton pulses in optical nonlinear Kerr media.

An investigation is made of the formation of a single soliton, or a pair of solitons, from initially nontransform limited pulses in a nonlinear Kerr medium having anomalous dispersion. A qualitative physical explanation is given for the formation of soliton pairs. Approximate solutions for the amplitudes and the velocities of the generated solitons are established and corroborated by numerical solutions of the Zakharov-Shabat eigenvalue problem.

Multifilament structures in relativistic self-focusing.

A simple model is derived to prove the multifilament structure of relativistic self-focusing with ultraintense lasers. Exact analytical solutions describing the transverse structure of waveguide channels with electron cavitation, for which both the relativistic and ponderomotive nonlinearities are taken into account, are presented.

Features of modulational instability of partially coherent light: importance of the incoherence spectrum.

It is shown that the properties of the modulational instability of partially coherent waves propagating in a nonlinear Kerr medium depend crucially on the profile of the incoherent field spectrum. Under certain conditions, the incoherence may even enhance, rather than suppress, the instability. In particular, it is found that the range of modulationally unstable wave numbers does not necessarily decrease monotonically with increasing degree of incoherence and that the modulational instability may still exist even when long wavelength perturbations are stable.

Transverse modulational instability of partially incoherent soliton stripes.

Based on the Wigner distribution approach, an analysis of the effect of partial incoherence on the transverse instability of soliton structures in nonlinear Kerr media is presented. It is explicitly shown that for a Lorentzian incoherence spectrum the partial incoherence gives rise to a damping which counteracts, and tends to suppress, the transverse instability growth. However, the general picture is more complicated and it is shown that the effect of the partial incoherence depends crucially on the form of the incoherence spectrum. In fact, for spectra with finite rms-width, the partial incoherence may even increase both the growth rate and the range of unstable, transverse wave numbers.

Statistical theory for incoherent light propagation in nonlinear media.

A statistical approach based on the Wigner transform is proposed for the description of partially incoherent optical wave dynamics in nonlinear media. An evolution equation for the Wigner transform is derived from a nonlinear Schrödinger equation with arbitrary nonlinearity. It is shown that random phase fluctuations of an incoherent plane wave lead to a Landau-like damping effect, which can stabilize the modulational instability. In the limit of the geometrical optics approximation, incoherent, localized, and stationary wave fields are shown to exist for a wide class of nonlinear media.

Axisymmetric relativistic self-channeling of laser light in plasmas.

By using an improved cavitation model, relativistic self-channeling structures are derived, which make it possible to propagate laser powers exceeding the critical one for self-focusing. A propagation mode for high laser power is also presented which is qualitatively different from those in the weakly relativistic case. Structural stability analysis shows that stable self-wave-guide propagation can take place.

Approximate solutions of two-way diffusion equations.

In this paper, a general and systematic scheme is formulated for finding approximate solutions of two-way diffusion equations. This expansion scheme is valid for arbitrary mean-free path and can be carried out to any desired accuracy. Its potential is demonstrated by constructing approximate solutions for two problems concerning the kinetics of an electron beam, and the accuracy is found to be very good even when only a few terms are included in the expansion. The approximate solutions found are compared with numerical calculations and previous analytical work in the literature.

Cognitive decline and cerebral vasoreactivity in asymptomatic patients with severe internal carotid artery stenosis.

The aim of the study was to correlate cognitive decline and cerebral vasoreactivity in 150 asymptomatic right-handed patients with severe ≥70% unilateral internal carotid artery (ICA) stenosis and to evaluate the role of intracranial collateral circulation during cognitive testing. Cognitive assessment was performed by means of Montreal Cognitive Assessment (MoCA) and Mini Mental State Exam (MMSE) scales. Cerebrovascular reactivity (CVR) and intracranial collateral circulation were evaluated by means of breath holding index (BHI) and transcranial color Doppler (TCD) sonography. The results were compared with 150 right-handed controls matched for demographic variables and vascular risk factors. Patients with severe unilateral ICA stenosis had MMSE scores within a normal range, but MoCA scores were lower than normal. By examining the side of the observed stenosis, it has been noted that patients with left-sided ICA stenosis had lower MoCA scores in categories of language and episodic memory performance, while patients with right-sided ICA stenosis had lower MoCA scores in a category of visual-spatial skills. All patients had BHI values lower than normal. Subjects with a single intracranial collateral artery recruited had slightly better cognitive results than the patients with two or more collateral arteries activated. Results of the study showed that altered cerebrovascular reactivity and cerebral hypoperfusion might be responsible for the reduction of specific cognitive functions ipsilateral to the ICA stenosis, therefore BHI and MoCA might be useful tools when screening for cognitive decline in asymptomatic patients with severe ICA stenosis.

Generalized dressing method for nonlinear evolution equations describing partially coherent wave propagation in noninstantaneous Kerr media.

A generalized dressing method is presented for integration of the nonlinear evolution equation of the coherent density function describing partially coherent wave propagation in a noninstantaneous Kerr media. As an example an exact, partially coherent multisource N-soliton solution is derived. It is also demonstrated how this method is applicable for construction of solutions to the equivalent coupled system of nonlinear Schrödinger equations of the self-consistent multimode theory.

Modulational instability of coherent optical-fiber transmission signals.

We point out the importance of the modulational instability as a possible limiting factor for coherent optical-fiber transmission.

Asymptotic linear dispersion of optical pulses in the presence of fiber nonlinearity and loss.

The asymptotic dispersive broadening of soliton pulses in optical fibers in the presence of weak losses has recently, following extensive numerical calculations, been shown to be less than the linear dispersion. We derive an explicit analytical approximation for the asymptotic dispersion that is in good agreement with numerical results. We also consider the case of strongly damped frequency-chirped pulses, where again the action of the nonlinearity is found to affect the long-term asymptotic properties of the pulses.

Propagation characteristics of frequency-chirped super-Gaussian optical pulses.

It is demonstrated that the rms width of optical pulses propagating along an optical fiber varies parabolically with distance, irrespective of initial pulse form or frequency chirp. This result is used to analyze the propagation characteristics of super-Gaussian optical pulses with respect to pulse broadening, pulse compression, and information- carrying capability. Comparison with the corresponding properties for Gaussian pulses clearly shows the optimum character of the latter.

Nonlinear asymmetric pulse distortion in long optical fibers.

Short pulses propagating in long optical fibers are shown to be asymmetrically distorted as a result of a nonlinear effect that is not included in the conventional nonlinear Schrödinger equation describing nonlinear pulse propagation. This effect may be responsible for pulse asymmetries observed in recent experiments.

Analysis of propagation of Raman-pump-supported solitons in a nonlinear-optical fiber.

Propagation of a soliton in a lossy fiber with Raman energy transfer from a continuous pump wave is analyzed under the assumptions that the soliton amplitude is much larger than the pump wave and that the soliton is sufficiently narrow. It is demonstrated that the Raman amplification mechanism gives rise to a continuous downshift of the central frequency of the soliton in agreement with recent numerical simulations.

Nonlinearly enhanced chirp pulse compression in single-mode fibers.

The possibility of combining linear-frequency chirp and fiber nonlinearity to obtain high compression ratios of optical pulses is assessed.

Importance of self-phase modulation for amplitude- and phase-modulated coherent optical transmission systems: a comparison.

We demonstrate that the amount of self-phase modulation in a coherent optical transmission system grows more slowly for a phase-modulated than for an amplitude-modulated signal. Signal degradation is discussed in terms of variations in the spectral contents of the amplitude and phase modulations, and explicit analytical expressions are given for the linear modulation indices of phase and amplitude of phase-shift keying coherent transmission systems.