Model for ultrashort laser pulse-induced ionization dynamics in transparent solids

A comprehensive model of ultrafast laser-induced plasma generation intended for coupling with pulse propagation simulations in transparent solids is introduced. It simultaneously accounts for the changing spectrum of a propagating ultrashort laser pulse while coupling to the evolution of the energy-resolved nonequilibrium free-carrier distribution. The presented results indicate that strong pulse chirps lead to ionization dynamics that are not captured by the standard monochromatic treatment of laser-induced plasma formation. These results have strong implications for ultrafast laser-solid applications that depend on ionization in a strong nonlinear focus.

Figure 1

Keldysh's photoionization rate as a function of intensity and laser wavelength in fused silica with a band gap of 9 eV and reduced electron-hole mass of 0.86 rest electron masses.

Figure 2

Electron-phonon energy and momentum relaxation times extracted from the rates calculated in Ref. [28].

Figure 3

Photoionization rates as a function of time for the unchirped, negatively chirped, and positively chirped pulses according to Eq. (1) using the instantaneous intensity and instantaneous frequency.

Figure 4

Electron energy distributions after exposure to (a) the unchirped pulse, (b) the negatively chirped pulse, and (c) the positively chirped pulse described in Sec. 3.

Figure 5

(a) Total ionization yield $N$ and (b) the average electron energy of the distributions from Fig. 4 as functions of time.

Figure 6

(a) The average momentum relaxation time ${\tau }^{\mathrm{c}}$ and (b) the electron-electron collision time ${\tau }^{\mathrm{ee}}$ of the distributions from Fig. 4 as functions of time.

Figure 7

(a) The peak ionization yield $N_{\max }$ and (b) energy transmission (pulse energy in units of the incident pulse energy) as functions of the propagation distance $z$.

Figure 8

The instantaneous frequency (a) and (b), intensity (c) and (d), and normalized transmitted spectra (e) and (f), at propagation distances of $z=0$ and $20\mu \text{m}$, respectively. The negatively chirped pulse is shown as the blue dashed line, the unchirped pulse is shown as the black solid line, and the positively pulse is shown as the red dotted line.