Far-field spectral characterization of conical emission and filamentation in Kerr media
Daniele Faccio, Paolo Di Trapani, Stefano Minardi, Alberto Bramati, Francesca Bragheri, Carlo Liberale, Vittorio Degiorgio, Audrius Dubietis, Aidas Matijosius
By use of an imaging spectrometer we map the far-field ($θ-λ$) spectra of 200 fs optical pulses that have undergone beam collapse and filamentation in a Kerr medium. By studying the evolution of the spectra with increasing input power and using a model based on stationary linear asymptotic wave modes, we are able to trace a consistent model of optical beam collapse high-lighting the interplay between conical emission, multiple pulse splitting and other effects such as spatial chirp.
We test numerical filamentation models against experimental data about the peak intensity and filament density in laser filaments. We show that the consideration of the higher-order Kerr effect (HOKE) improves the quantitative agreement without the need of adjustable parameters.
While filaments are generally interpreted as a dynamic balance between Kerr focusing and plasma defocusing, the role of the higher-order Kerr effect (HOKE) is actively debated as a potentially dominant defocusing contribution to filament stabilization. In a pump-probe experiment supported by numerical simulations, we demonstrate the transition between two distinct filamentation regimes at 800\,nm. For long pulses (1.2 ps), the plasma substantially contributes to filamentation, while this contribution vanishes for short pulses (70 fs). These results confirm the occurrence, in adequate condition…
We show that higher-order nonlinear indices ($n_4$, $n_6$, $n_8$, $n_{10}$) provide the main defocusing contribution to self-channeling of ultrashort laser pulses in air and Argon at 800 nm, in contrast with the previously accepted mechanism of filamentation where plasma was considered as the dominant defocusing process. Their consideration allows to reproduce experimentally observed intensities and plasma densities in self-guided filaments.
Based on numerical simulations, we show that higher-order nonlinear indices (up to $n_8$ and $n_{10}$, respectively) of air and argon have a dominant contribution to both focusing and defocusing in the self-guiding of ultrashort laser pulses over most of the spectrum. Plasma generation and filamentation are therefore decoupled. As a consequence, ultraviolet wavelength may not be the optimal wavelengths for applications requiring to maximize ionization.
As a contribution to the ongoing controversy about the role of higher-order Kerr effect (HOKE) in laser filamentation, we first provide thorough details about the protocol that has been employed to infer the HOKE indices from the experiment. Next, we discuss potential sources of artifact in the experimental measurements of these terms and show that neither the value of the observed birefringence, nor its inversion, nor the intensity at which it is observed, appear to be flawed. Furthermore, we argue that, independently on our values, the principle of including HOKE is straightforward. Due to t…
In this Letter, a low-loss Kerr-driven optical filament in Krypton gas is experimentally reported in the ultraviolet. The experimental findings are supported by ab initio quantum calculations describing the atomic optical response. Higher-order Kerr effect induced by three-photon resonant transitions is identified as the underlying physical mechanism responsible for the intensity stabilization during the filamentation process, while ionization plays only a minor role. This result goes beyond the commonly-admitted paradigm of filamentation, in which ionization is a necessary condition of the fi…
The precise observation of the angle-frequency spectrum of light filaments in water reveals a scenario incompatible with current models of conical emission (CE). Its description in terms of linear X-wave modes leads us to understand filamentation dynamics requiring a phase- and group-matched, Kerr-driven four-wave-mixing process that involves two highly localized pumps and two X-waves. CE and temporal splitting arise naturally as two manifestations of this process.
According to a recent experiment, the instantaneous electronic Kerr effect in air exhibits a strong intensity dependence, the nonlinear refractive index switching sign and crossing over from a self-focusing to a de-focusing nonlinearity. A subsequent theoretical work has demonstrated that this has paradigm-changing consequences for the understanding of filamentation in air, so it is important to subject the idea of higher-order nonlinearities to stringent tests. Here we use numerical modeling to propose an experiment capable of discriminating between the standard and the new intensity-dependen…
We numerically investigate the conical emission (CE) from ultrashort laser filaments, both considering and disregarding the higher-order Kerr effect (HOKE). While the consideration of HOKE has almost no influence on the predicted CE from collimated beams, differences arise for tightly focused beams. This difference is attributed to the different relative contributions of the non-linear focus and of the modulational instability over the whole filament length.
Since their discovery in the mid-1990s, ultrafast laser filaments in gases have been described as products of a dynamic balance between Kerr self-focusing and defocusing by free electric charges that are generated via multi-photon ionization on the beam axis. This established paradigm has been recently challenged by a suggestion that the Kerr effect saturates and even changes sign at high intensity of light, and that this sign reversal, not free-charge defocusing, is the dominant mechanism responsible for the extended propagation of laser filaments. We report qualitative tests of the new theor…
Laser filamentation in transparent material has a wide range of applications, from three dimensional manufacturing to biological technologies. Various experimental results showed that femtosecond laser pulse filamentation in fused silica strongly depends on laser focusing conditions. However, the physical mechanism governing each regime has not been fully understood. For the first time, single and multiple re-focusing of the laser pulse in interaction of femtosecond laser pulse with fused silica, and consequent single and multiple damage zones (filaments) have been observed in our extensive th…
Powerful incoherent laser pulses can propagate in focusing Kerr media much longer distances than can coherent pulses, due to the fast phase mixing that prevents transverse filamentation. This distance is limited by 4-wave scattering, which accumulates waves at small transverse wavenumbers, where phase mixing is too slow to retain the incoherence and thus prevent the filamentation. However, we identify how this theoretical limit can be overcome by countering this accumulation through transverse heating of the pulse by random fluctuations of the refractive index. In these new regimes, the laser …
We analytically calculate the transverse energy fluxes that would be respectively induced in high-power Airy beams by the Kerr self-focusing and the Airy profile itself if they were the only active process. In experimental condition representative of laser filamentation experiments of high-power ultrashort laser pulses in air and condensed media, the Kerr lens induces transverse energy fluxes much larger than the Airy "prism" at the main peak. As a consequence, the curved plasma channels in Airy beams are not only a plasma spark on a curved focus, but indeed self-guided filaments, and their cu…
Broadband laser sources based on supercontinuum generation by femtosecond laser filamentation have enabled applications from stand-off sensing and spectroscopy to the generation and self-compression of high-energy few-cycle pulses. Filamentation relies on the dynamic balance between self-focusing and plasma defocusing, mediated by the Kerr nonlinearity and multiphoton ionization respectively. The filament properties, including the supercontinuum generation, are therefore highly sensitive to the properties of both the laser source and the propagation medium. Here, we report the anomalous spectr…
An influence of pass-through optics on femtosecond laser pulse filamentation in ambient air is analyzed for the first time both experimentally and numerically. Propagation of high-power femtosecond laser pulse through solid optical elements introduces spatiotemporal phase modulation due to the Kerr effect. This modulation may have a strong ef-fect on the pulse filamentation in air. We demonstrated that the phase modulation obtained in the thin pass-through dielectric plate reduces the distance to the filament onset and increases the plasma channel length
Nonlinear losses accompanying Kerr self-focusing substantially impacts the dynamic balance of diffraction and nonlinearity, permitting the existence of localized and stationary solutions of the 2D+1 nonlinear Schrodinger equation which are stable against radial collapse. These are featured by linear conical tails that continually refill the nonlinear, central spot. An experiment shows that the discovered solution behaves as strong attractor for the self-focusing dynamics in Kerr media.
We elaborate a new solution for the problem of stable propagation of transversely localized vortex beams in homogeneous optical media with self-focusing Kerr nonlinearity. Stationary nonlinear Bessel-vortex states are stabilized against azimuthal breakup and collapse by multiphoton absorption, while the respective power loss is offset by the radial influx of the power from an intrinsic reservoir. A linear stability analysis and direct numerical simulations reveal a region of stability of these vortices. Beams with multiple vorticities have their stability regions too. These beams can then form…
Plane waves in Kerr media spontaneously generate paraxial X-waves (i.e. non-dispersive and non-diffractive pulsed beams) that get amplified along propagation. This effect can be considered a form of conical emission (i.e. spatio-temporal modulational instability), and can be used as a key for the interpretation of the out of axis energy emission in the splitting process of focused pulses in normally dispersive materials. A new class of spatio-temporal localized wave patterns is identified. X-waves instability, and nonlinear X-waves, are also expected in periodical Bose condensed gases.
Inclusion of the instantaneous Kerr nonlinearity in the FDTD framework leads to implicit equations that have to be solved iteratively. In principle, explicit integration can be achieved with the use of anharmonic oscillator equations, but it tends to be unstable and inappropriate for studying strong-field phenomena like laser filamentation. In this paper, we show that nonlinear susceptibility can be provided instead by a harmonic oscillator driven by a nonlinear force, chosen in a way to reproduce the polarization obtained from the solution of the quantum mechanical two level equations. The re…
While propagating in transparent media, near-infrared multi-terawatt (TW) laser beams break up in a multitude of filaments of typically 100-200 um diameter with peak intensities as high as 10 to 100~TW/cm$^{2}$. We observe a phase transition at incident beam intensities of 0.4~TW/cm$^2$, where the interaction between filaments induce solid-like 2-dimensional crystals with a 2.7 mm lattice constant, independent of the initial beam diameter. Below 0.4~TW/cm$^2$, we evidence a mixed phase state in which some filaments are closely packed in localized clusters, nucleated on inhomogeneities (seeds) …
The transition from spatial to spatiotemporal dynamics in Kerr-driven beam collapse is modelled as the instability of the Townes profile. Coupled axial and conical radiation, temporal splitting and X waves appear as the effect of Y-shaped unstable modes, whose growth is experimentally detected.
Femtosecond lasers interacting with Kerr nonlinear optical materials, propagate in form of filaments due to the balance of beam diffraction by self-focusing induced by the Kerr nonlinearity. Femtosecond laser filamentation is a universal phenomenon that belongs to a general class of processes proper to ultrashort lasers processing systems, associated with the competition between nonlinearity and dispersion also known to promote optical solitons. The present work considers a model describing femtosecond laser inscriptions in a transparent medium with Kerr nonlinearity. Upon inscription, the las…
Diffraction-free Bessel beams have attracted major interest because of their stability even in regimes of nonlinear propagation and filamentation. However, Kerr nonlinear couplings are known to induce significant longitudinal intensity modulation, detrimental to the generation of uniform plasma or for applications in the processing of transparent materials. These nonlinear instabilities arise from the generation of new spatio-spectral components through an initial stage of continuous spectral broadening followed by four wave mixing. In this paper, we investigate analytically and numerically th…
Modern laser sources nowadays deliver ultrashort light pulses reaching few cycles in duration, high energies beyond the Joule level and peak powers exceeding several terawatt (TW). When such pulses propagate through optically-transparent media, they first self-focus in space and grow in intensity, until they generate a tenuous plasma by photo-ionization. For free electron densities and beam intensities below their breakdown limits, these pulses evolve as self-guided objects, resulting from successive equilibria between the Kerr focusing process, the chromatic dispersion of the medium, and the …
