Ionization Waves of Arbitrary Velocity

Flying focus is a technique that uses a chirped laser beam focused by a highly chromatic lens to produce an extended focal region within which the peak laser intensity can propagate at any velocity. When that intensity is high enough to ionize a background gas, an ionization wave will track the intensity isosurface corresponding to the ionization threshold. We report on the demonstration of such ionization waves of arbitrary velocity. Subluminal and superluminal ionization fronts were produced that propagated both forward and backward relative to the ionizing laser. All backward and all superluminal cases mitigated the issue of ionization-induced refraction that typically inhibits the formation of long, contiguous plasma channels.

Figure 1

A $1.053-\mu \mathrm{m}$ laser with tunable pulse duration $\tau$ was split into two beams. The pump beam remained $1\omega$ and was focused by a diffractive optic to produce an ionization wave of arbitrary velocity (IWAV). The probe beam was converted to $2\omega$ and diagnosed the plasma channel in a side-on geometry coincident with the plasma formation. A spectrally resolved schlieren diagnostic was used to determine the ionization front velocity.

Figure 2

(a) The flying focus velocity (i.e., the speed at which constant intensity isosurfaces move near best focus) is determined by the ratio of the chirped pulse duration to the length of the extended chromatic focal region produced by the diffractive optic. Any velocity (including faster than the speed of light) is achievable in both the forward and backward directions relative to the laser propagation. (b) For the spectrally resolved schlieren diagnostic, the expected linear slope of an edge marking the onset of plasma formation is plotted as a function of pump and probe pulse duration. The overlaid points correspond to the experimental data. Both forward- and backward-propagating ionization waves of arbitrary velocity were produced, with velocities both less than and greater than the speed of light in each direction.

Figure 3

Spectrally resolved schlieren results. (a) An example of superluminal backward propagation for $\tau \approx -22\mathrm{ps}$. The probe is negatively chirped so the direction of time is from the blue end to the red end of the spectrum. The IWAV begins at $+z$ and propagates backward to $-z$ along the pump axis. (b) A more highly superluminal example producing a nearly instantaneous line focus. (c) With $-l/c<\tau <0$, the IWAV remains superluminal but switches to forward propagating, reversing the sign of the slope. (d) When the probe is positively chirped, the direction of time is effectively reversed, and subluminal forward propagation produces a disjointed plasma channel because of ionization-induced refraction.

Figure 4

Two-dimensional schlieren and shadowgraphy of various cases. (a) The $\tau \approx -17\mathrm{ps}$ example shows a long, uniform plasma channel and is representative of all tested cases of backward propagation as well as superluminal forward propagation. (b) Subluminal forward propagation leads to plasma channel breakup because of ionization-induced refraction; (c) this also occurs for best compression, which is most similar to conventional beam propagation in that laser intensity moves forward at the group velocity.