Plasma-assisted temporal shifts of bichromatic femtosecond laser pulses in air

Terahertz and third-harmonic generation by tightly focused bichromatic femtosecond pump pulses with comparable input intensities in air is studied both experimentally and theoretically. Plasma-assisted temporal shifts in the field of intense laser pulses are shown to lead to the time delay between the pump pulses in the vicinity of the focus. This delay can be compensated by the initial time delay that is evidenced by the measured as well as calculated correlation functions of the fundamental and second harmonics. The possibility to characterize the plasma channel length from the correlation function is discussed.

Figure 1

Experimental setup. M1–M8, dielectric mirrors; L1 and L2, focusing lenses; $\lambda /4$, quarter-wave plates; BS1 and BS2, beam splitters; SH and FH beams are shown by blue and red-pink color, respectively.

Figure 2

Experimental results. Plasma filaments created by the SH (a), (b), (c) and FH pulses (d), (e), (f). Pulse energy was 0.11, 0.38, 1.53, 0.1, 0.3, and 0.5 mJ, respectively. (Here, the propagation takes place from the right to the left and dashed lines indicate positions of geometrical focus.)

Figure 3

Typical experimental amplitude spectrum of generated THz pulses. Modulation of the spectrum resulted from the absorption in used THz filters such as Si wafers.

Figure 4

Experimental results. Normalized typical THG (a) and THz (b) cross-correlations. In (a) the solid, dashed, and dotted lines correspond to FH/SH pulse energies of 0.5/0.92, 0.1/0.014, and 0.5/0.014, respectively, while in (b) these lines correspond to 0.1/0.99, 0.5/0.1, and 0.1/0.1. All energy values are given in mJ.

Figure 5

Experimental results. Dependence of the temporal peak THG (a) and THz (b) signal position on the energy of FH pulses. In (a) the SH pulse energies were 1.5 mJ (red circles) and 14 $\mu \mathrm{J}$ (blue squares). In (b) the SH pulse energy was 25 $\mu \mathrm{J}$. In (b), in order to enhance the THz yield FH and SH polarizations were set to be circular [11].

Figure 6

Dependencies of the overall THz power on SH (a) and FH (b) pulse energies for the fixed delays between the FH and SH pulses. In (a) and (b) time delay increments are 15 and 5 fs, respectively.

Figure 7

Numerical results. Dependence of (a) plasma density, (b) FH intensity, and (c) the on-axis time position of the maximum intensity on the propagation distance in the vicinity of the lens focus. Input FH energy: ${\eta }_0=3.3$ $\mu \mathrm{J}$ (black solid line), $4{\eta }_0$ (blue dashed line), and $16{\eta }_0$ (red solid line). $\mathrm{\Delta }=0$ fs. (Here, the propagation takes place from the left to the right.)

Figure 8

Numerical results. Dependence of the output THz energy on the time delay. Input FH energy: ${\eta }_0=3.3$ $\mu \mathrm{J}$ (black squares) and $16{\eta }_0=0.053$ mJ (red squares).

Figure 9

Numerical results. Dependence of the FH (black lines) and SH (red lines) (a) intensity and (b) its maximum on-axis time position on the propagation distance. $\mathrm{\Delta }=0$ fs (solid lines) and $-\mathrm{\Delta }=20$ fs (dashed lines). FH input energy: $4{\eta }_0=13.2$ $\mu \mathrm{J}$.

Figure 10

Numerically calculated FH and SH intensity profiles at the focus. FH input energy: $4{\eta }_0=13.2$ $\mu \mathrm{J}$. Pulses propagate towards the negative time.

Figure 11

Numerically calculated output spectra of THz and TH radiation. FH input energy: $4{\eta }_0=13.2$ $\mu \mathrm{J}$. Here, $\theta =\sqrt{{\beta }_x^2+{\beta }_y^2\phantom{{}^l}}/k_{30}$ is the angle while ${\theta }^{\prime }=\sqrt{{\beta }_x^2+{\beta }_y^2\phantom{{}^l}}/k_{10}$ is a parameter not representing the real angle. The THz angle ${\theta }_{\text{THz}}=\frac{{\nu }_0}{\nu }{\theta }^{\prime }$, where ${\nu }_0=375$ THz is the FH frequency and $\nu$ is the frequency of the THz radiation.

Figure 12

Numerical results. Comparison of the impacts of ${\chi }^{\left(3\right)}$ nonlinearity [solid line, Eqs. (1, 2, 3, 4)] and plasma current [dashed line, Eq. (A1)] to the THz yield.