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We develop a new model of laser-matter interaction based on Optical Bloch Equations, which includes photo-ionization, impact ionization, and various relaxation processes typical of dielectric materials. This approach is able to describe the temporal evolution of the electron dynamics in the conduction band driven by few-cycle laser pulses of any wavelength. Moreover, the nonlinear polarization response of both centrosymmetric and non-centrosymmetric materials can be described while ensuring the proper selection rules for the harmonics emission.

We analytically and numerically investigate the propagation of ultrashort tightly focused laser pulses in vacuum, with particular emphasis on Hermite-Gaussian and Laguerre-Gaussian modes. We revisit the Lax series approach for forward-propagating linearly-polarized laser pulses, in order to obtain Maxwell-consistent and symmetry-preserving analytical solutions for the propagation of all field components beyond the paraxial approximation in four-dimensional geometry (space and time). We demonstrate that our solution conserves the energy, which is set by the paraxial-level term of the series. The full solution of the wave equation towards which our series converges is calculated in the Fourier space. Three-dimensional numerical simulations of ultrashort tightly-focused pulses validate our analytical development.

We disclose an unanticipated link between plasmonics and nonlinear frequency down-conversion in laser-induced gas-plasmas. For two-color femtosecond pump pulses, a plasmonic resonance is shown to broaden the terahertz emission spectra significantly. We identify the resonance as a leaky mode, which contributes to the emission spectra whenever electrons are excited along a direction where the plasma size is smaller than the plasma wavelength. As a direct consequence, such resonances can be controlled by changing the polarization properties of elliptically-shaped driving laser pulses. Both, experimental results and 3D Maxwell consistent simulations confirm that a significant terahertz pulse shortening and spectral broadening can be achieved by exploiting the transverse driving laser beam shape as an additional degree of freedom.

We investigate terahertz emission from two-color fs-laser-induced microplasmas. Under strongest focusing conditions, microplasmas are shown to act as point-sources for broadband terahertz-to-far-infrared radiation, where the emission bandwidth is determined by the plasma density. Semi-analytical modeling allows us to identify scaling laws with respect to important laser parameters. In particular, we find that the optical-to-THz conversion efficiency crucially depends on the focusing conditions. We use this insight to demonstrate by means of Maxwell-consistent 3D simulations, that for only 10-$\mu$J laser energy a conversion efficiency well above $10^{-4}$ can be achieved.

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.

Broadband ultrashort terahertz (THz) pulses can be produced using plasma generation in a noble gas ionized by femtosecond two-color pulses. Here we demonstrate that, by using multiple-frequency laser pulses, one can obtain a waveform which optimizes the free electron trajectories in such a way that they reach the highest velocity at the electric field extrema. This allows to increase the THz conversion efficiency to the percent level, an unprecedented performance for THz generation in gases. Besides the analytical study of THz generation using a local current model, we perform comprehensive 3D simulations accounting for propagation effects which confirm this prediction. Our results show that THz conversion via tunnel ionization can be greatly improved with well-designed multicolor pulses.