Spatially resolved filament wavefront dynamics

Abstract

Spatially resolved wavefront measurements are presented during nonlinear self-collapse and provide the first detailed characterization of wavefront evolution during filament formation. The wavefront dynamics of key nonlinear processes including Kerr self-focusing, ionization and plasma defocusing, and dynamic spatial replenishment are identified and resolved in both the filament core and reservoir regions. These results are analyzed and interpreted with respect to numerical simulations and provide insight into fundamental aspects of filamentation. They also inform applications based on phase manipulation, such as external beam guiding, and present a new method for measuring the nonlinear index of refraction, n 2. Filament formation is based on the nonlinear self-collapse of optical beams 1. Kerr self-focusing (KSF) enables this process by overcoming diffractive spreading when the peak-power of a beam exceeds the critical value for the propagation medium 2,3. This leads to increasing local intensities that surpass the ionization threshold of the medium 4. The presence of electrons decreases the local index of refraction, balancing KSF and resulting in an extended, highly confined plasma channel known as a filament 5. The unique nature of filaments has inspired both practical and academic interest in their capabilities. The properties of filaments have been well-characterized in several studies through measurements of the plasma channel density, lifetime, length, and diameter 6-10. The shape 11 , intensity 12 , spectral and temporal modifications 13-15 , and polarization 16 of the beam formed within the filament have also been studied in detail. The exploration of these properties has produced several novel filament-based applications including white-light seeded parametric amplification 17-19 , pulse compression 20,21 , white-light LIDAR 22,23 , sensing and spectroscopy 24-26 , cloud clearing 27,28 , material modification 29-31 , and guided discharges 32,33. The input (pre-collapse) wavefront of filament-forming beams has also been exploited to control filament properties after collapse, potentially aiding these applications. Altering the initial wavefront conditions allows the plasma density 34 , filament length 35 , spectral broadening 36 , and number of filaments 37-40 to be controlled. It also allows filaments to be organized as arrays, which is useful for nonlinear beam combination and external beam guiding 41-44. The filament-filament interactions within these arrays are of critical importance and are influenced by the transverse spatial structure of each filament's plasma, intensity, and wavefront profiles. However, the wavefront progression during collapse and within the filament itself has been largely ignored. Previous studies of the transverse filament wavefront profile have not measured the full collapse process or have lacked spatial resolution 45-47. The spatio-temporal nonlinear phase contributions within a filament have been previously been measured interferometrically, but these works do not inclu...