Oriented Rotational Wave-Packet Dynamics Studies via High Harmonic Generation

We produce oriented rotational wave packets in CO and measure their characteristics via high harmonic generation. The wave packet is created using an intense, femtosecond laser pulse and its second harmonic. A delayed 800 nm pulse probes the wave packet, generating even-order high harmonics that arise from the broken symmetry induced by the orientation dynamics. The even-order harmonic radiation that we measure appears on a zero background, enabling us to accurately follow the temporal evolution of the wave packet. Our measurements reveal that, for the conditions optimum for harmonic generation, the orientation is produced by preferential ionization which depletes the sample of molecules of one orientation.

Figure 1

(a) Plot of two-color laser fields: Red line $E_{\omega }\cos (\omega t)$.-.fundamental field. Blue line $E_{2\omega }\cos (2\omega t+{\phi }_{2\omega })$ - second harmonic. Black line $E_{\mathrm{total}}(t)=E_{\omega }\cos (\omega t)+E_{2\omega }\cos (2\omega t+{\phi }_{2\omega })$, ${\phi }_{2\omega }=0$, $E_{2\omega }=0.43E_{\omega }$ - the total field in the pump beam. The relative field ratio shown in the plot is the same as used in our experiment. (b) Half cycle total ionization rate of the CO molecule as a function of the angle between the molecular axis and the electric force calculated for intensity $1.5\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ at 800 nm. “C”side points toward 0°.

Figure 2

Schematic of experimental setup. A $\lambda /2$ wave plate (WP1,WP2) and a thin film polarizer (TFP1, TFP2) were used in the pump and the probe arms to continuously control the pulse energies. The pump beam was demagnified [$1.5:1$ telescope (TL)] to ensure full overlap with the probe beam when focused on the jet. The probe beam was delayed using a computer-controlled delay line (DL). The parallel, but spatially separated, pump and probe beams impinge on a spherical $\mathrm{f}=500\mathrm{mm}$ focusing mirror (FL, shown as a lens for clarity). The pump and probe beams overlap on the gas jet with a small angle (1°) between their propagation directions.

Figure 3

Logarithmic image of the measured high harmonic signal (along the line marked as “Probe”) and harmonics produced by the pump beam (along the line marked as “Pump”). (A) No orientation $t_{\mathrm{delay}}=7200\mathrm{f}\sec $. (B) Maximum orientation $t_{\mathrm{delay}}=8850\mathrm{f}\sec $.

Figure 4

(a) Measured even and odd harmonic signal as a function of the phase delay ${\phi }_{2\omega }$ between fundamental and second harmonic fields. The odd harmonic intensity (H11) is normalized to its maximum value. (b) Plot of the measured angle dependence of a selection of harmonics taken at the time of maximum orientation by changing the angle $\theta$ of the probe polarization relative to the orientation angle.

Figure 5

Upper plot: A rotational alignment wave packet measured in CO excited by impulsive alignment with a superposition of 800 nm and 400 nm laser pulses. Using this rotational wave packet the time dependence of the 11th harmonic (dashed green curve) and the 19th harmonic (solid blue curve) in CO is shown near the time of their first full revival $t_{\mathrm{rev}}$ (set at $t_{\mathrm{rev}}=0$). The harmonic signal normalized to the base line. Lower plot: An orientational wave packet in CO excited by the same superposition of 800 nm and 400 nm laser pulses. The red dash-dotted curve shows the time dependent signal for the 14th harmonic.