We demonstrate the generation, spectral broadening and post-compression of second harmonic pulses using a thin beta barium borate (BBO) crystal on a fused-silica substrate as the nonlinear interaction medium. By combining second harmonic generation in the BBO crystal with self-phase modulation in the fused-silica substrate, we efficiently generate millijoule-level broadband violet pulses from a single optical component. The second harmonic spectrum covers a range from long wave ultraviolet (down to 310 nm) to visible (up to 550 nm) with a bandwidth of 65 nm. Subsequently, we compress the second harmonic beam to a duration of 4.8 fs with a pulse energy of 0.64 mJ (5 fs with a pulse energy of 1.05 mJ) using chirped mirrors. The all-solid free-space apparatus is compact, robust and pulse energy scalable, making it highly advantageous for generating intense second harmonic pulses from near-infrared femtosecond lasers in the sub-5 fs regime.

The post-compression technique based on self-phase modulation of high-energy pulses leads to an increase in achievable peak power and intensity. Typically, the pulses considered in experiments have been less than 100 fs in duration. Here, the method is applied to the ELFIE laser system at the LULI facility, for a pulse of 7 J energy and an initial measured duration of 350 fs. A 5-mm-thick fused silica window and a 2 mm cyclic-olefin polymer were used as optical nonlinear materials. The 9 cm diameter beam was spectrally broadened to a bandwidth corresponding to 124 fs Fourier-limited pulse duration, and then it was partly post-compressed to 200 fs. After measuring the spatial spectra of the beam fluence, a uniform gain factor of 4 increase in the fluctuations over the studied range of frequencies is observed, due to small-scale self-focusing.

We demonstrate an efficient ultrafast source with 195 fs pulse duration, 54 W average power at 200 kHz repetition rate and near diffraction-limited beam quality. The compact setup incorporates a thin-disk Yb:YAG regenerative amplifier (RA) and a subsequent nonlinear pulse compression stage with periodic-layered Kerr media (PLKM), which is one of the multiple-thin-solid-plate schemes based on nonlinear resonator theory. In virtue of the formation of quasi-stationary spatial soliton in PLKM, the near diffraction-limited beam quality of the RA remained almost undisturbed after post-compression. The nonlinear pulse compression module is simple and efficient with a transmission of 96%. To the best our knowledge, for pulse energy over 200 μJ, this is the highest output power reported for the multiple-thin-solid-plate scheme. This source manifests an economical combination to mitigate the bandwidth limitations of Yb-based high-power chirped pulse amplifiers.

We report on compact and robust supercontinuum generation and post-compression using transmission of light through multiple thin solid plates at the SwissFEL X-ray free-electron laser facility. A single stage consisting of three thin plates followed by a chirped mirror compressor achieves compression of initially 30-fs pulses with 800-nm center wavelength to sub-10-fs duration. We also demonstrate a two-stage implementation to compress the pulses further to sub-5-fs duration. With the two-stage setup, the generated supercontinuum includes wavelengths ranging from 500 to 1100 nm. The multi-plate setup is compact, robust, and stable, which makes it ideal for applications at free-electron laser facilities such as pump-probe experiments and laser-arrival timing tools.

The input pulse of the laser PEARL with energy of 18 J and pulse duration of about 60 fs was compressed to 10 fs after passage through a 4-mm-thick KDP crystal and reflection at two chirped mirrors with sum dispersion of −200 fs2. The experiments were performed for the В-integral values from 5 to 19 without visible damage to the optical elements, which indicates that small-scale self-focusing is not a significant issue. It was shown that, by virtue of the low dispersion of the group velocity, the KDP crystal has some advantages over silica: a larger pulse compression coefficient, especially at a small value of the В-integral (B = 5, …, 9), lower absolute values of chirped mirror dispersion, and also a possibility to control the magnitude of nonlinearity and dispersion by changing crystal orientation.

High-peak-power transform-limited narrow-linewidth nanosecond all-fiber lasers are desired in a range of applications. However, their linewidths will be broadened by self-phase modulation (SPM). We propose a novel concept that generates transform-limited laser pulses by temporally shaping the pulse seed. The impact of the pulse shape on SPM-induced spectral broadening was studied numerically and experimentally. It was found theoretically that the square-shape pulsed laser is immune to SPM-induced spectral broadening. Based on this principle, we built a high-peak-power, linearly polarized, square-shape nanosecond all-fiber laser in a master oscillator power amplifier (MOPA) configuration. Stimulated Brillouin scattering (SBS) limited peak powers of 4.02 kW, 5.06 kW, 6.52 kW and 9.30 kW were obtained at pulse widths of 8 ns, 7 ns, 6 ns and 5 ns. Thanks to the square-shape pulsed seed, the linewidths at maximum peak power remained at 129.5 MHz, 137.6 MHz, 156.2 MHz and 200.1 MHz, respectively, close to the transform-limited values of 110.8 MHz, 126.6 MHz, 147.7 MHz and 177.3 MHz.

This paper presents an investigation on the self-focusing of a cosh-Gaussian laser beam in the thermal quantum plasma (TQP) by taking into account the effects of relativistic nonlinearity. An appropriate nonlinear Schrödinger equation has been solved analytically by applying the variational approach. The self-focusing and the self-phase modulation are examined under a variety of parameters. The self-trapping of a cosh-Gaussian laser beam is further studied at various values of the decentered parameter, b with different absorption levels, ${k}^{\prime}_i$. Numerical analysis shows that these parameters play a vital role in propagation characteristics. The significant contribution of the quantum effects to enhance the self-focusing and minimize the longitudinal phase has been observed. Further, a comparison has been made with the classical relativistic (CR), the relativistic cold quantum (RCQ), and the thermal quantum (TQ) regimes. The self-focusing is found to occur earlier and is strongest for the case of TQP in the present analysis.

In this paper, we have investigated the propagation characteristics of cosh-Gaussian laser beam in magnetoplasma using relativistic nonlinearity. The field distribution in the medium is expressed in terms of beam width parameter an and decentred parameter b. An appropriate nonlinear Schräodinger equation has been solved analytically using variational approach. The behaviour of beam width parameter with dimensionless distance of propagation ξ for various b values is examined. Self-phase modulation and self-trapping is also studied under variety of parameters. Further, the effect of magnetic field on self-focusing of the beam have been explored.

Nonlinear parabolic partial differential equation governing the evolution of complex envelope in slowly varying envelope approximation is solved using variational approach. The basic nonlinear phenomena of relativistic and ponderomotive self-focusing in a plasma are taken into account. Self-focusing, self-phase modulation as well as self-trapping of dark hollow Gaussian beam is studied for higher orders of hollow Gaussian beam (n).

The nonlinear parabolic partial differential equation governing the evolution of the complex envelope in the slowly varying envelope approximation is solved using the variational approach. The basic nonlinear phenomena of relativistic and ponderomotive self-focusing in a plasma channel are taken into account. Self-focusing, self-phase modulation as well as self-trapping of laser beam is studied in a variety of situations. Further, in the absence of dissipation mechanisms, the stability of the beam is also studied.

An analytical formalism of self focusing and self-phase modulation of an intense short pulse laser in a plasma due to relativistic and ponderomotive nonlinearities is developed. In the paraxial ray approximation, the pulse retains its Gaussian radial profile, however, its spot size varies with the distance of propagation in a periodic manner. It is influenced by self focusing. The frequency of the laser undergoes red shift. For a tanhyperbolic temporal profile of pulse, the red-shift is maximum at the foot of the pulse and decreases slowly as one goes to higher and higher intensity portions. The effect of ponderomotive nonlinearity is very significant in this respect. The maximum downshift occurs at a distance at which the laser acquires a minimum spot size. With retarded time normalized axial intensity increases more at z ~ Rd and the radial intensity is also more narrowly peaked at z ~ Rd, where Rd = 2π r02/λ is the Rayleigh length, r0 and λ are the spot size and wavelength of the laser pulse respectively.

The problem of nonlinear self-focusing of elliptic Gaussian laser beam in collisionless magnetized plasma is studied using variation approach. The dynamics of the combined effects of nonlinearity and spatial diffraction is presented. With a and b as the beam width parameters of the beam along x and y directions, respectively, the phenomenon of cross-focusing is observed where focusing of a results in defocusing of b and vice versa. Although no stationary self-trapping is observed, oscillatory self-trapping occurs far below the threshold. The regularized phase is always negative.

Recent advances of the photon kinetic theory are illustrated here, with examples taken from plasma physics (forward Raman scattering), and from nonlinear optics (self-phase modulation). This theory can provide a unified view of nonlinear optical phenomena involving photon beams with an arbitrary spectrum.