## Dynamics of collapsing ultrashort laser pulses

Wave collapse occurs in a few branches of physics. An example in nonlinear optics is Kerr-induced self-focusing of light, which manifests itself as a catastrophic increase of intensity when the power exceeds a threshold known as critical power *P*_{cr}. The collapse can be arrested by several mechanisms, of which the plasma defocusing is typically responsible when ionization happens for sufficiently intense pulse. The dynamic competition between self-focusing and plasma defocusing leads to the propagation of intense pulses over a long distance. This phenomenon is known as filamentation and has stimulated a number of applications such as supercontinuum generation for spectroscopy, atmospheric remote sensing, pulse compression, and THz generation.

The nonlinear dynamics in self-focusing and filamentation is remarkably complex and rich in its behavior. Our group have investigated a number of universal features associated with wave collapse such as self-similar evolution [Phys. Rev. Lett. 90, 203902 (2003); Opt. Express 14, 5468 (2006)], pulse splitting [Phys. Rev. Lett. 77, 3783 (1996); Opt. Express 19, 9309(2011)], shock formation [Phys. Rev. Lett. 84, 3582 (2000)], and loss of phase [Phys. Rev. Lett. 108, 043902 (2012)]. We have studied the control of collapse and filamentation by altering initial conditions including spatial profile [Opt. Express 13 4594 (2005)] and phase profile [Phys. Rev. Lett. 96, 133901 (2006), Phys. Rev. Lett. 99, 133902 (2007)], or by using another beam [Phys. Rev. A 75, 023813 (2007); Phys. Rev. A 81, 061803(2010)]. We also explore the filamentation dynamics in wider parameter space, for example, at high pressures [Phys. Rev. A 95, 013412 (2017)], or at longer wavelength [Opt. Express 19, 9118 (2011)]. We are equipped with a terawatt class Ti:sapphire laser system, a high energy optical parametric amplifier, and a non-collinear difference frequency generator. These laser sources allow us to carry out experiments over a wide range of wavelength, and we are in particular interested in the mid-infrared regime, much of which is still unexplored.

Here we show some of our recent projects:

## Loss of polarization in collapsing beams of elliptical polarization

The phenomenon of self-focusing leading to beam collapse has attracted a lot of interest for applications involving filamentation and high harmonic generation (HHG), such as in atmospheric sensing, pulse compression and terahertz generation. Many of these applications are polarization sensitive, hence studying the polarization state of collapsing beams is of great importance. When an elliptically polarized beam travels through a nonlinear medium, the polarization angle of the beam rotates. For linearly and circularly polarized beams, polarization angle remains the same. This is known as the nonlinear ellipse rotation phenomenon. Based on this, we theoretically predict complete loss of polarization angle for collapsing beams of elliptical polarization and experimentally investigate polarization instabilities in post-collapse beams with respect to the input power, *P*_{in}. This is analogous to the “loss of phase” effect predicted by Fibich and Klein [Nonlinearity 24, 2003 (2011)] and recently demonstrated by Shim *et al.* [Phys. Rev. Lett. 108 (2012)]. Using simulations we predict that in collapsing beams, nonlinear ellipse rotations of polarization lead to complete loss of polarization for elliptically polarized input. In other words, the output polarization angle becomes strongly dependent on *P*_{in}, and small fluctuations in *P*_{in} lead to > 2π rotations of the polarization angle, making it impossible to predict the output polarization angle for a given input polarization angle – thus effectively resulting in the “loss of polarization”. Experimentally, we find evidence of this effect by observing that fluctuations in the angle of polarization increase dramatically when *P*_{in }> *P*_{cr} compared to when the power was low [CLEO 2017 paper FM3F.7].

## Intense pulse propagation in gas-filled waveguides

Propagation of ultrashort pulses in gas-filled waveguides allows for relatively long interaction lengths with high peak intensity, thus dramatically enhancing the nonlinear effects. Understanding the propagation dynamics is important to optimize applications such as high-order harmonic generation [Science 336, 1287(2012); Science 350, 1225(2015)]. The pulses are confined in a bounded domain by glancing incidence reflection in capillary tubings, or by anti-resonant reflection in photonic crystal fibers, and their spatial profiles are restricted to a combination of discrete modes. The spatial confinement also alters the dispersion, which has a great impact on the temporal dynamics. A proper dispersion can enable stable nonlinear propagation of ultrashort pulses over several centimeters in high-pressure, gas-filled waveguides with intensities approaching 1014 W/cm2, as we demonstrate through simulation [CLEO 2016 paper FM4A.5]. The critical power *P*_{cr} of a hollow waveguide retains to that of Townes profile in a bulk medium [Opt. Lett. 25 335 (2000)].

For moderate intensity, monomode guiding is feasible, and we have demonstrated nonfrequency-shifted temporal solitons with peak powers greater than 5.5 megawatts in Xe-filled hollow-core photonic band-gap fiber by exploiting its anomalous dispersion [Science 301, 1702 (2003)]. When ionization-induced refraction and/or self-focusing excites higher-order modes, the spatial and temporal dynamics are strongly coupled. We show in simulation that spatio-temporal localization of ultrashort pulses in gas-filled hollow waveguide can be achieved through the combined effect of plasma defocusing and reflection from the capillary walls, and shorter wavelength pulses and smaller capillary diameters are beneficial for reaching higher peak intensity [CLEO 2016 paper FTu4N.7].