Modeling of Light Filamentation for Nonlinear Imaging and Waveguiding

Ultrashort pulses are capable of extremely high powers; in addition to enabling various applications in defense, sensing, and imaging, they provide a useful arena in which to study nonlinear optical phenomena that are observable only at high intensities. Due to these effects, which can include ionization and thermal blooming, simulation of ultrashort pulse propagation is a complicated multiphysics problem. We provide an overview of techniques used to simulate the propagation of ultrashort pulses in the nonlinear regime, including the formation of light filaments due to the competition of Kerr self-focusing and defocusing (e.g. via plasma generation). We discuss both carrier-resolved and envelope propagation models, and present a derivation of one of the former. Next, we describe several recent applications in the field of nonlinear microscopy, with particular attention to the role of simulations to provide predictions which inform and explain the theory present in real-world laboratory experiments. In particular, we study the ability of the supercontinuum generation that occurs in the filamentation regime in Yttrium Aluminum Garnet (YAG) ceramics to enable Coherent Anti-Stokes Raman Scattering Spectroscopy as well as ultrafast 3D imaging via nonlinear fluorescence. Lastly, we discuss the modeling of thermal waveguiding and shockwaves as a result of the formation of intense filaments in air.