(3+1)-dimensional numerical simulations of femtosecond laser filaments in air: toward a quantitative agreement with experiments

Dissipative solitons in the discrete Ginzburg-Landau equation with saturable nonlinearity

The modulational instability of nonlinear plane waves and the existence of periodic and localized dissipative solitons and waves of the discrete Ginzburg-Landau equation with saturable nonlinearity are investigated. Explicit analytic expressions for periodic solutions with a zero and a finite background are derived and their stability properties investigated by means of direct numerical simulations. We find that while discrete periodic waves and solitons on a zero background are stable under time evolution, they may become modulationally unstable on finite backgrounds. The effects of a linear ramp potential on stable localized dissipative solitons are also briefly discussed.

Spectral dynamics of THz pulses generated by two-color laser filaments in air: the role of Kerr nonlinearities and pump wavelength

We theoretically and numerically study the influence of both instantaneous and Raman-delayed Kerr nonlinearities as well as a long-wavelength pump in the terahertz (THz) emissions produced by two-color femtosecond filaments in air. Although the Raman-delayed nonlinearity induced by air molecules weakens THz generation, four-wave mixing is found to impact the THz spectra accumulated upon propagation via self-, cross-phase modulations and self-steepening. Besides, using the local current theory, we show that the scaling of laser-to-THz conversion efficiency with the fundamental laser wavelength strongly depends on the relative phase between the two colors, the pulse duration and shape, rendering a universal scaling law impossible. Scaling laws in powers of the pump wavelength may only provide a rough estimate of the increase in the THz yield. We confront these results with comprehensive numerical simulations of strongly focused pulses and of filaments propagating over meter-range distances.

Measurements of fluence profiles in femtosecond laser filaments in air

We introduce a technique to measure fluence distributions in femtosecond laser beams with peak intensity of up to several hundred terawatts per square centimeter. Our approach is based on the dependence of single-shot laser ablation threshold for gold on the angle of incidence of the laser beam on the gold sample. We apply this technique to the profiling of fluence distributions in femtosecond laser filaments at a wavelength of 800 nm in air. The peak intensity is found to be clamped at a level that depends on the external beam focusing. The limiting value of the peak intensity attainable in long-range 800 nm air filaments, under very loose focusing conditions (f-number above ∼500), is about 55  TW/cm².

Higher-order Kerr improve quantitative modeling of laser filamentation

We test numerical filamentation models against experimental data about the peak intensity and electron density in laser filaments. We show that the consideration of the higher-order Kerr effect improves the quantitative agreement without the need of adjustable parameters.

Analytical solitary-wave solutions of the generalized nonautonomous cubic-quintic nonlinear Schrödinger equation with different external potentials

A large family of analytical solitary wave solutions to the generalized nonautonomous cubic-quintic nonlinear Schrödinger equation with time- and space-dependent distributed coefficients and external potentials are obtained by using a similarity transformation technique. We use the cubic nonlinearity as an independent parameter function, where a simple procedure is established to obtain different classes of potentials and solutions. The solutions exist under certain conditions and impose constraints on the coefficients depicting dispersion, cubic and quintic nonlinearities, and gain (or loss). We investigate the space-quadratic potential, optical lattice potential, flying bird potential, and potential barrier (well). Some interesting periodic solitary wave solutions corresponding to these potentials are then studied. Also, properties of a few solutions and physical applications of interest to the field are discussed. Finally, the stability of the solitary wave solutions under slight disturbance of the constraint conditions and initial perturbation of white noise is discussed numerically; the results reveal that the solitary waves can propagate in a stable way under slight disturbance of the constraint conditions and the initial perturbation of white noise.

Saturation of the all-optical Kerr effect

Saturation of the intensity dependence of the refractive index is directly computed from ionization rates via a Kramers-Kronig transform. The linear intensity dependence and its dispersion are found to be in excellent agreement with complete quantum mechanical orbital computations. Higher-order terms concur with solutions of the time-dependent Schrödinger equation. Expanding the formalism to all orders up to the ionization potential of the atom, we derive a model for saturation of the Kerr effect. This model widely confirms recently published and controversially discussed experimental data and corroborates the importance of higher-order Kerr terms for filamentation.

Boosted X waves in nonlinear optical systems

X waves are spatiotemporal optical waves with intriguing superluminal and subluminal characteristics. Here we theoretically show that for a given initial carrier frequency of the system localized waves with genuine superluminal or subluminal group velocity can emerge from initial X waves in nonlinear optical systems with normal group velocity dispersion. Moreover, we show that this temporal behavior depends on the wave detuning from the carrier frequency of the system and not on the particular X-wave biconical form. A spatial counterpart of this behavior is also found when initial X waves are boosted in the plane transverse to the direction of propagation, so a fully spatiotemporal motion of localized waves can be observed.

Self-compression of 2 microm laser filaments

We numerically study the filamentation of ultrashort laser pulses at 2 microm carrier wavelength in noble gases (argon, xenon) and in air. Compared with filamentation in the near-visible domain (800 nm), mid-infrared optical sources with durations close to a single cycle can be generically produced at various pressures and powers near the self-focusing threshold. The mechanism by which self-compression takes place mainly involves optical self-focusing, pulse steepening and plasma defocusing. On-axis spectra and spectral phases are discussed. Delivering single-cycled pulses at long wavelengths has important applications in the generation of high-order harmonics and isolated attosecond pulses.

Temporal self-restoration of compressed optical filaments

We numerically investigate the propagation of a self-compressed optical filament through a gas-glass-gas interface. Few-cycle light pulses survive a sudden and short order-of-magnitude increase of nonlinearity and dispersion, even when all conservative estimates predict temporal spreading or spatial breakup. Spatiotemporal distortions are shown to self-heal upon further propagation when the pulse refocuses in the second gas. This self-healing mechanism has important implications for pulse compression techniques handled by filamentation and explains the robustness of such sources.