Quantitative rescattering theory of high-order harmonic generation for polyatomic molecules

We report applications of the quantitative rescattering theory (QRS) for calculation of high-order-harmonic generation (HHG) from polyatomic molecules in ultrashort linearly polarized intense laser pulses, using the example of the CCl${}_4$ molecule. In particular, we present a detailed analysis and a treatment for the phase of the electron returning wave packet, which recollides with the parent molecular ion to emit high-energy photons. Our results show that Cooper-type minimum structures in the molecular photoionization cross section lead to quite distinguishable minima in the HHG spectra, even for unaligned polyatomic molecules.

Figure 1

(a) Asymptotic wave function of a HOMO (denoted as HOMO1) of CCl${}_4$. (b) Phase of the returning electron wave packet for H55 at $\varphi ={60}^{\circ }$. The asymptotic wave function at $\varphi ={60}^{\circ }$ is also shown (red line). (c) Same as (b), but for H71 and the asymptotic wave function at $\varphi ={90}^{\circ }$. (d) Wave-packet phase difference between ${\theta }_A={100}^{\circ }$ and ${\theta }_B={120}^{\circ }$ (points A and B in the inset) and between ${\theta }_B={120}^{\circ }$ and ${\theta }_C={140}^{\circ }$ (points B and C in the inset). Here $\varphi$ is fixed at ${240}^{\circ }$. The inset shows the asymptotic wave function.

Figure 2

(a) Real and (b) imaginary parts of the photoionization transition dipole from HOMO1 of CCl${}_4$ at a photon energy of 54.4 eV vs the laser polarization direction (or the electron emission direction) $\Omega =\{\theta ,\varphi \}$.

Figure 3

(a) Ionization rate from HOMO1 of CCl${}_4$ vs the laser polarization direction, calculated by the MO-ADK theory [33] for a laser intensity of $0.55\times {10}^{14}$ W/cm${}^2$. (b) Asymptotic electron density for HOMO1 of CCl${}_4$. See text for more details.

Figure 4

(a) Amplitude (scaled by ${\omega }^2$) of the returning electron wave packet vs emitted photon energy $\omega$ for a typical case of an 1800-nm wavelength laser pulse with an intensity of $0.55\times {10}^{14}$ W/cm${}^2$ and a 40-fs pulse duration. (b) HHG spectra from HOMO1 for different laser polarization directions (as shown in the legend). (c) HHG spectra for a fixed laser polarization direction (or fixed molecular alignment) at $\theta ={80}^{\circ },\varphi ={140}^{\circ }$ from the three degenerate HOMOs. Only envelopes (odd harmonics) are shown.

Figure 5

Induced dipole amplitude (vertical axis) and phase (color code) for H79 (photon energy of 54.4 eV) from HOMO1 of CCl${}_4$ vs the laser polarization direction $\Omega =\{\theta ,\varphi \}$. The phase is given in units of $\pi$ rad. Laser parameters are the same as in Fig. 4.

Figure 6

HHG spectra from CCl${}_4$ for different laser pulses for the case of isotropic molecular distribution. Laser parameters are given in the text. The yield from an 1800-nm laser pulse (black line) has been multiplied by a factor of 50. Only envelopes are shown.

Figure 7

Transition dipole amplitude for CCl${}_4$ at a photon energy of (a) 41 eV, (b) 48 eV, and (c) 60 eV vs the laser polarization direction.

Figure 8

Theoretical HHG spectra from CCl${}_4$, trans-C${}_2$H${}_2$Cl${}_2$, and CH${}_4$. Results have been shifted vertically for clarity. Only envelopes are shown.

Figure 9

Extracted total photoionization “cross section” from HHG spectra for (a) CCl${}_4$ and (b) CH${}_4$. The theoretical total PICS calculated by the epolyscat code [32] are also shown.