Effect of molecular alignment and orientation on elliptically polarized high-order harmonic generation

We present a theoretical investigation of the influence of molecular alignment and orientation on elliptically polarized high-order harmonic generation (HHG) from CO molecules exposed to a linearly polarized pulse. The results show that the ellipticity of HHG observed in a partially aligned or oriented CO molecular ensemble significantly deviates from that of the individual response. Additionally, we find that the ellipticity of HHG in the CO molecular ensemble exhibits strong dependence on the degree of molecular alignment/orientation as well as the time delay between the alignment/orientation and probe pulses. More importantly, under the proper alignment/orientation angle, a large HHG ellipticity can be achieved from the partially aligned/oriented molecular ensemble at a moderate degree of alignment/orientation. These findings relax the experimental requirement of a high degree of molecular alignment/orientation for harmonic generation with large ellipticity.

Figure 1

(a) The parallel and perpendicular harmonic spectra for an oriented CO molecule. (b) Same as panel (a), but for an aligned CO molecule. (c) The relative phase of the parallel and perpendicular harmonic components. The green and pink lines are for the oriented and aligned CO molecules, respectively. Here, the angle $\beta$ between the CO molecular axis and the polarization direction of the probe pulse is ${45}^{\circ }$. (d) A sketch of our simulation for a CO molecule.

Figure 2

(a) Evolution of the alignment factor $\langle {\cos }^2\theta \rangle$ with the time delay $\tau$ between the alignment and probe pulses. The intensity, wavelength, and duration of the alignment pulse are $4.5\times {10}^{13} \mathrm{W}/{\mathrm{cm}}^2$, 800 nm, and 50 fs, respectively. The molecular rotational temperature is 12.5 K. The insets are the angular distribution $\rho \left(\theta \right)$ for the aligned CO molecular ensemble at $\tau =4.07$ and 4.63 ps. (b) The alignment factor $\langle {\cos }^2\theta \rangle$ at $\tau =4.07$ ps as a function of the intensity of the alignment pulse and the rotational temperature of CO molecules.

Figure 3

(a) and (b) The ellipticity distributions of the 15th and 25th harmonics as functions of the alignment factor $\langle {\cos }^2\theta \rangle$ and alignment angle $\alpha$ for the CO molecular ensemble. (c) The ellipticities of the 15th and 25th harmonics with respect to the angle $\beta$ for an individual CO molecule. (d) The angular distribution of the CO molecular ensemble for $\langle {\cos }^2\theta \rangle =0.35$ and aligned at $\alpha ={70}^{\circ }$ (blue dashed line) and ${35}^{\circ }$ (red solid line). (e) and (f) Same as panel (d), but for $\langle {\cos }^2\theta \rangle =0.6$ and 0.9, respectively.

Figure 4

(a) and (b) The ellipticity distributions of the 31st and 37th harmonics as functions of the alignment factor $\langle {\cos }^2\theta \rangle$ and the alignment angle $\alpha$ for the CO molecular ensemble. (c) The ellipticities of the 31st and 37th harmonics with respect to the angle $\beta$ for an individual CO molecule. (d) The angular distribution of the CO molecular ensemble for $\langle {\cos }^2\theta \rangle =0.35$ and aligned at $\alpha ={50}^{\circ }$. (e) and (f) Same as panel (d), but for $\langle {\cos }^2\theta \rangle =0.75$ and 0.9, respectively.

Figure 5

(a) and (b) The ellipticity distributions of the 15th and 31st harmonics as functions of the time delay $\tau$ between the alignment and probe pulses and the alignment angle $\alpha$ for the CO molecular ensemble. Here, the parameters of the alignment pulse are same as those in Fig. 2.

Figure 6

(a) Evolution of the orientation factor $\langle \cos \theta \rangle$ (blue solid line) and the alignment factor $\langle {\cos }^2\theta \rangle$ (red dashed line) with the time delay $\tau$ between the orientation and probe pulses. The orientation pulse contains two parallel pulses. The wavelengths and intensities of these two pulses are 800 and 400 nm, $9\times {10}^{13}$ and $3\times {10}^{13} \mathrm{W}/{\mathrm{cm}}^2$, respectively. The durations of these two pulses are both 70 fs. The relative phase between these two pulses is 0 and the molecular rotational temperature is 20 K. The inset is the angular distribution $\rho \left(\theta \right)$ for the oriented CO molecular ensemble at $\tau =7.94$ ps. (b) The orientation factor $\langle \cos \theta \rangle$ at $\tau =7.94$ ps as a function of the intensity of $2\omega$ laser filed and the rotational temperature of CO molecules.

Figure 7

(a)–(d) The ellipticity distributions of the 15th, 31st, 16th, and 26th harmonics as functions of the orientation factor $\langle \cos \theta \rangle$ and the orientation angle $\alpha$ for the CO molecular ensemble.

Figure 8

(a) and (b) The ellipticity distributions of the 15th and 31st harmonics as functions of the time delay $\tau$ between orientation and probe pulses and the orientation angle $\alpha$ for the CO molecular ensemble. Here, the parameters of the orientation pulse are same as those in Fig. 6.