Higher-order Kerr improve quantitative modeling of laser filamentation

Exceeding the Boundaries of the Paraxial Spatiotemporal Nonlinear Optics and Filamentation for Ultrashort Laser Pulses

An impressive phenomenon of observed plasma instability and conical emission under the propagation of ultrashort laser pulses in the air is reported. The discussed novel findings demonstrating nonlinear effects are incapable to be explained in the standard spatiotemporal paraxial optics. Three main mechanisms are investigated. The first one is related to the nonlinear nonparaxial mechanisms for waveguiding of femtosecond pulses, and the second one considers the mechanism of single filament formation at weak ionization. The third mechanism demonstrates a new physical effect leading to collision ionization with intensities in the range of 10¹⁰-10¹¹ W/cm². Furthermore, a new ionization regime of instability is suggested at intensities below the critical thresholds for multiphoton and tunnel ionization. The experimental results and findings are supported by theoretical analyses and numerical simulations.

Non-instantaneous third-order optical response of gases in low-frequency fields

It is commonly assumed that for low-intensity short optical pulses far from resonance, the third-order optical nonlinear response is instantaneous. We solve the three-dimensional time-dependent Schrödinger equation for the hydrogen atom and show that this is not the case: the polarization is not simply proportional to the cube of the electric field even at low intensities. We analyze the fundamental-frequency and third-harmonic nonlinear susceptibilities of hydrogen, investigate their dependence on intensity, and find that the delays in the Kerr response rapidly approach the femtosecond time-scale at higher intensities, while the delays in the third harmonic generation remain much lower. We also propose an experimental scheme to detect and characterize the above effects.

Measuring the Kerr nonlinearity via seeded Kerr instability amplification: conceptual analysis

Whereas the Kerr nonlinearity is well understood in the perturbative limit of nonlinear optics, there is considerable discussion about its functional form and magnitude at extreme intensities, at which point matter starts to ionize. Here, we introduce a concept to answer this question and theoretically analyze its feasibility. We demonstrate that seeded Kerr instability amplification provides clear signatures from which functional form and magnitude of the Kerr nonlinearity can be extracted in the non-perturbative limit of nonlinear optics.

Quasi-steady-state air plasma channel produced by a femtosecond laser pulse sequence

A long air plasma channel can be formed by filamentation of intense femtosecond laser pulses. However, the lifetime of the plasma channel produced by a single femtosecond laser pulse is too short (only a few nanoseconds) for many potential applications based on the conductivity of the plasma channel. Therefore, prolonging the lifetime of the plasma channel is one of the key challenges in the research of femtosecond laser filamentation. In this study, a unique femtosecond laser source was developed to produce a high-quality femtosecond laser pulse sequence with an interval of 2.9 ns and a uniformly distributed single-pulse energy. The metre scale quasi-steady-state plasma channel with a 60–80 ns lifetime was formed by such pulse sequences in air. The simulation study for filamentation of dual femtosecond pulses indicated that the plasma channel left by the previous pulse was weakly affected the filamentation of the next pulse in sequence under our experimental conditions.

Optical Spectroscopy Using Gas-Phase Femtosecond Laser Filamentation

Femtosecond laser filamentation occurs as a dynamic balance between the self-focusing and plasma defocusing of a laser pulse to produce ultrashort radiation as brief as a few optical cycles. This unique source has many properties that make it attractive as a nonlinear optical tool for spectroscopy, such as propagation at high intensities over extended distances, self-shortening, white-light generation, and the formation of an underdense plasma. The plasma channel that constitutes a single filament and whose position in space can be controlled by its input parameters can span meters-long distances, whereas multifilamentation of a laser beam can be sustained up to hundreds of meters in the atmosphere. In this review, we briefly summarize the current understanding and use of laser filaments for spectroscopic investigations of molecules. A theoretical framework of filamentation is presented, along with recent experimental evidence supporting the established understanding of filamentation. Investigations carried out on vibrational and rotational spectroscopy, filament-induced breakdown, fluorescence spectroscopy, and backward lasing are discussed.

Pattern dynamics and filamentation of femtosecond terawatt laser pulses in air including the higher-order Kerr effects

Plasma defocusing and higher-order Kerr effects on multiple filamentation and pattern formation of ultrashort laser pulse propagation in air are investigated. Linear analyses and numerical results show that these two saturable nonlinear effects can destroy the coherent evolution of the laser field, and small-scale spatial turbulent structures rapidly appear. For the two-dimensional case, numerical simulations show that blow-up-like solutions, spatial chaos, and pseudorecurrence can appear at higher laser intensities if only plasma defocusing is included. These complex patterns result from the stochastic evolution of the higher- or shorter-wavelength modes of the laser light spectrum. From the viewpoint of nonlinear dynamics, filamentation can be attributed to the modulational instability of these spatial incoherent localized structures. Furthermore, filament patterns associated with multiphoton ionization of the air molecules with and without higher-order Kerr effects are compared.

Femtosecond laser filament array generated with step phase plate in air

Femtosecond laser filament arrays are generated in air by using three kinds of step phase plates with π phase lag, namely, the semicircular phase plate (SCPP), the quarter-circle phase plate (QCPP) and eight-octant phase plate (EOPP). Experimental results and simulations show that filament arrays consisting of two, four and eight filaments, respectively, are produced by three phase plates. The transverse patterns of the filament arrays are determined by the geometrical shapes of the phase plates. At the same time, the separation distances are found to vary with the focal lengths of the used lenses. We further propose that by using an axicon, filament array in the form of ring shape could be realized while the lengths of the filaments could be significantly elongated at the same time. Our study has suggested a realistic method to generate filament array by the step phase plate with π phase lag.

Higher-order Kerr effect and harmonic cascading in gases

The higher-order Kerr effect (HOKE) has recently been advocated to explain measurements of the saturation of the nonlinear refractive index in gases. Here we show that cascaded third-harmonic generation results in an effective fifth-order nonlinearity that is negative and significant. Higher-order harmonic cascading will also occur from the HOKE, and the cascading contributions may significantly modify the observed nonlinear index change. At lower wavelengths, cascading increases the HOKE saturation intensity, while for longer wavelengths cascading will decrease the HOKE saturation intensity.