Nonlinear pulse propagation in optical fibers

Diffraction of femtosecond pulses; nonparaxial regime

We present a systematic study of linear propagation of ultrashort laser pulses in media with dispersion, dispersionless media, and vacuum. The applied method of amplitude envelopes makes it possible to estimate the limits of the slowly varying amplitude approximation and to describe an amplitude integrodifferential equation governing propagation of optical pulses in the single-cycle regime in solids. The well-known slowly varying amplitude equation and the amplitude equation for the vacuum case are written in dimensionless form. Three parameters are obtained defining different linear regimes of optical pulse evolution. In contrast to previous studies we demonstrate that in the femtosecond region the nonparaxial terms are not small and can dominate over the transverse Laplacian. The normalized amplitude nonparaxial equations are solved using the method of Fourier transforms. Fundamental solutions with spectral kernels different from those according to Fresnel are found. Exact unidirectional analytical solution of the nonparaxial amplitude equations and the 3D wave equations with initial conditions compatible with Gaussian light bullets are obtained also. One unexpected new result is the relative stability of light bullets (pulses with spherical and spheroidal spatial form) when we compare their transverse enlargement with paraxial diffraction of light beams in air. It is important to emphasize here the case of light disks, i.e., pulses whose longitudinal size is small with respect to the transverse one, which in some partial cases are practically diffractionless over distances of a thousand kilometers. A new formula that calculates the diffraction length of optical pulses is suggested. Finally, propagation of single-cycle pulses in air and vacuum was investigated, and a coronal (semispherical) form of diffraction at short distances was observed.

Dark solitary waves in optical fibers

It is argued that the form of dark solitary wave solution [~tanh p(z - u(g)t)] previously predicted is highly questionable because the radial dependence of the field was not properly treated. In this Letter a previously developed method for exactly treating the radial dependence of the field is extended to dark-pulse wave solutions, and a new class of solutions is presented that exists in the anomalous dispersion region of the fiber. The average intensity for these solutions exhibits a double hump, in contrast to the single hump associated with the bright-pulse wave.

Exact radial dependence of the field in a nonlinear dispersive dielectric fiber: bright pulse solutions

The propagation of nonlinear optical pulses in fibers is discussed, taking into account physical effects arising from nonlinearity, dispersion, and transverse confinement. The wave equation is solved by treating the radial dependence of the field in an exact way. The conditions supporting bright solitary waves are presented and compared with previous results.

Role of intensity fluctuations in nonlinear pulse propagation

The effect of intensity fluctuations and the finite coherence time of the field on the propagation of nonlinear optical pulses is discussed. In particular, the statistical properties of the carrier are shown to affect the power level for soliton propagation.

Theory of nonlinear pulse propagation in inhomogeneous waveguides

An approximate treatment of solitons (nonlinear pulses) in inhomogeneous waveguides is presented. We find that, for slowly varying inhomogeneity, both bright and dark solitons are supported by waveguides. These solitons acquire a time-dependent velocity and acceleration but otherwise propagate through the waveguide without changing shape.