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

Dark and antidark solitons in the modified nonlinear Schrödinger equation accounting for the self-steepening effect

In this paper, the modified nonlinear Schrödinger equation is investigated, which describes the femtosecond optical pulse propagation in a monomodal optical fiber. Based on the Wadati-Konno-Ichikawa system, another type of Lax pair and infinitely many conservation laws are derived. Dark and antidark soliton solutions in the normal dispersion regime are obtained by means of the Hirota method. Parametric regions for the existence of the dark and antidark soliton solutions are given. Asymptotic analysis of the two-soliton solution shows that collisions between two solitons (two antidark solitons, two dark solitons, and dark and antidark solitons) are elastic. In addition, collision between dark and antidark solitons reveals that dark and antidark solitons can co-exist on the same background in the normal dispersion regime.

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.

Spatial ring emission and filament formation in an optical fiber with a saturable nonlinear cladding

We present numerical simulations of Gaussian beam propagation in an optical fiber with a linear core and a saturable self-focusing cladding. Cylindrical nonlinear waves are emitted from the core into the cladding and are initially localized only in the radial direction, forming rings. These rings can break their cylindrical symmetry through a transverse instability, which yields filaments localized both azimuthally and radially, most of which stay close to the core for long propagation distances.

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.