High-order-harmonic generation from dense water microdroplets

We report on high-order-harmonic generation from micrometer-sized liquid water droplets. In pump-probe experiments, the influence of the time delay onto the emission of harmonic radiation is systematically studied. Phase-matching aspects are observed by controlling the focal position and the intensity of the probe pulse. The spatiotemporal dynamics of the droplet during interaction with intense laser pulses are studied by controlling the intensity of the pump pulse. We find transient phase-matching conditions and the expansion dynamics of the droplet to be of major influence on the harmonic yield.

Figure 1

(a) Optical setup for the generation of pump and probe pulse by a Mach-Zehnder interferometer. The pump-probe time delay $\tau$ is adjusted by a linear positioning stage. (b) Setup of the liquid droplet source. See text for description.

Figure 2

(a) Harmonic intensity versus wavelength and harmonic order. The spectrum was taken at a pump-probe time delay of $\tau =3.5\mathrm{ns}$ at an intensity of the pump pulse of $7.0\times {10}^{14}{\mathrm{W}/\mathrm{cm}}^2$, an intensity of the probe pulse of $3.7\times {10}^{14}{\mathrm{W}/\mathrm{cm}}^2$ and a focal parameter of $z<0\mathrm{mm}$. (b) Calculated density of the target as function of time for three intensities of the pump pulse. The colored areas roughly mark different thermodynamical densities. Blue: liquid and clustered media, green: clustered media and high-density gas, yellow: gas.

Figure 3

(a) Harmonic intensity versus order and pump-probe time delay. The spectra were taken at an intensity of the pump pulse and of the probe pulse of $4.5\times {10}^{14}{\mathrm{W}/\mathrm{cm}}^2$. The focal position was $z=-2\mathrm{mm}$. (b) Harmonic intensity versus order at four different pump-probe time delays. The spectra show normalized data from Fig. 3a. Note that the broadening of the harmonic lines with increasing order originates from its presentation as a function of harmonic order and is chosen for better visibility.

Figure 4

Harmonic intensity versus order at three different pump-probe time delays. All parameters were set comparable to Fig. 3. For better visibility, the data is plotted versus harmonic order.

Figure 5

(a) Harmonic intensity versus order and focal position at fixed delay $\tau =1.0\mathrm{ns}$. The intensity of the pump pulse and of the probe pulse were set to $4.5\times {10}^{14}{\mathrm{W}/\mathrm{cm}}^2$. The schematics at the top mark the different positions of the focus relative to the droplet, with respect to the propagation direction shown as red arrow. (b) Outline of the nineteenth harmonic order and (c) the eleventh harmonic order along the focal position $z$.

Figure 6

(a) Harmonic yield versus order and intensity of the pump pulse. The intensity of the probe pulse is kept at a constant level of $3.66\times {10}^{14}{\mathrm{W}/\mathrm{cm}}^2$ at a delay of $\tau =1.0\mathrm{ns}$. (b) Harmonic yield versus order and intensity of the probe pulse. The intensity of the pump pulse is kept at a constant level of $2.0\times {10}^{14}{\mathrm{W}/\mathrm{cm}}^2$ at a delay of $\tau =3.5\mathrm{ns}$. In both measurements, the focal position was $z=-2\mathrm{mm}$. Due to visibility, the data is plotted versus harmonic order.

Figure 7

Outline from Fig. 6a. Harmonic yield of the twenty-fifth harmonic order versus the intensity of the pump pulse.

Figure 8

Outline from Fig. 6b. Harmonic yield versus intensity of the probe pulse for the thirteenth (a), nineteenth (b), twenty-first (c), and twenty-third harmonic order (d).

Figure 9

Blueshift and spectral broadening of the thirteenth harmonic order (a) and the fifteenth harmonic order (b) with respect to the pump-probe time delay. The dashed line indicates the nonshifted spectral line. The spectra were taken at an intensity of the probe pulse of $3.6\times {10}^{14}{\mathrm{W}/\mathrm{cm}}^2$ at a focal position of $z<0\mathrm{mm}$. (c) and (d) Evolution of spectral splitting of the eleventh harmonic order (c) and of the fifteenth harmonic order (d) with respect to different pump-probe time delays. The spectra were taken at an intensity of the probe pulse of $7.0\times {10}^{14}{\mathrm{W}/\mathrm{cm}}^2$ at a focal position of $z>0\mathrm{mm}$.