Linear and Nonlinear Optics of Broad-Band Laser Pulses: Diffraction.

The typical spectrally limited laser pulse in the near-infrared region is narrow-band up to 40-50 fs. Its spectral width Δk is much smaller than the carrying wavenumber k0 (Δk ≪ k0) . For such kinds of pulses, on distances of a few diffraction lengths, the diffraction is of a Fresnel's type and their evolution can be described correctly in the frame of the well-known paraxial evolution equation. The technology established in 1985 of amplification through chirping of laser pulses triggered remarkable progress in laser optics along with the construction of femtosecond (fs) laser facilities producing high intensity fields of the order of 1015-1021 W/cm2. However, the duration of the pulse was quickly shortened from picoseconds down to 5-6 fs, which have a broad-band nature (Δk ∼ k0). The linear and nonlinear propagation dynamics of broad-band pulses is quite different form their narrow-band counterparts. Here, we review the appropriate theoretical approach to study the evolution of the pulse. Moreover, we shed light on the different diffraction regimes inherent to both narrow-band and broad-band laser pulses and compare them to unveil the main differences. Using this very method, in subsequent papers, we will investigate the influence of the dispersion and nonlinearity on the laser pulse propagation in isotropic media.

Avalanche parametric conversion and white spectrum generation from infrared femtosecond pulses in glasses.

The observation of discrete lines in the white spectrum at the initial stage of filamentation of powerful femtosecond laser pulses, propagating in silica glasses, as well as the filamentation without plasma channels observed in the experiments in air, pushed us to look for other nonlinear mechanisms for describing these effects. In this paper, we present a new parametric conversion mechanism for asymmetric spectrum broadening of femtosecond laser pulses towards higher frequencies in isotropic media. This mechanism includes cascade generation with THz spectral shift for solids and GHz shift for gases. The process works simultaneously with the four-photon parametric wave mixing. The theoretical model proposed agrees well with the experimental data.

Electromagnetic shock wave in nonlinear vacuum: exact solution.

An analytical approach to the theory of electromagnetic waves in nonlinear vacuum is developed. The evolution of the pulse is governed by a system of nonlinear wave vector equations. An exact solution with its own angular momentum in the form of a shock wave is obtained.

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.

Collapse arrest and self-guiding of femtosecond pulses.

Nonlinear evolution of femtosecond pulses in media with weak dispersion and power slightly above the critical for self-focusing in the framework of generalized non-paraxial amplitude equation is analyzed. It is found that this nonlinear non-paraxial regime strongly depends from the initial form of the pulses. In case of long pulse (small transverse and large longitudinal size), the dynamics is closer to nonlinear paraxial dynamics of a laser beam, and the difference consists in large spectral and longitudinal spatial modulation of the long pulse. The non-paraxial terms play an important role on the evolution of light bullets and light disks. In regime of light bullets (relatively equal transverse and longitudinal size) weak self-focusing without pedestal and collapse arrest is obtained. Non-collapsed regime of light disks (pulses with small longitudinal and large transverse size) is also observed. Our results are in good agreement with the recent experiments on nonlinear propagation of femtosecond pulses. For first time is demonstrated that such non-paraxial model can explain effects as spectral broadening, collapse arrest and nonlinear wave guide behavior.