Probing the origin of elliptical high-order harmonic generation from aligned molecules in linearly polarized laser fields

A recent experiment [Phys. Rev. Lett. 102, 073902 (2009)] has demonstrated that elliptically polarized high-order harmonic generation can be produced from linearly polarized driving fields for aligned molecular systems. In order to reveal the underlying physical mechanisms of elliptical harmonics, we present fully ab initio and high-precision calculations and analyses of the amplitude, phase, and polarization state of the harmonic radiation from molecular hydrogen ions with arbitrary orientation. We find that high ellipticity arises from molecular orbital symmetry and two-center interference effects. Our ab initio exploration and findings lead to a general rule that the ellipticity becomes high for molecular orbitals represented by a symmetric combination of atomic orbitals, whereas it becomes low for molecular orbitals represented by an antisymmetric combination. This finding also applies to the general case of aligned linear molecules.

Figure 1

(a) A linear molecule is aligned to the $z$ axis, and the driving laser field is linearly polarized with the orientation angle $\Theta$. The induced dipole moment producing the harmonic radiation has two components $d_z$ and $d_x$ with respect to the molecular axis. The same vector is represented by $d_{\parallel }$ and $d_{\perp }$, which are parallel and perpendicular to the laser polarization direction, respectively. Panels (b) and (c) show pictures of the symmetric $1{\sigma }_g$ orbital and the antisymmetric $1{\sigma }_u$ orbital of ${\mathrm{H}}_2{}^{+}$, respectively.

Figure 2

Amplitude, phase, and ellipticity of harmonic signals as a function of orientation angle: Panels (a)–(c) show the 57th harmonic ($H=57$) from the $1{\sigma }_g$ state of ${\mathrm{H}}_2{}^{+}$ at the intensity $3\times {10}^{14}$ W/cm${}^2$, and panels (d)–(f) show the 31st harmonic ($H=31$) from the $1{\sigma }_u$ state of ${\mathrm{H}}_2{}^{+}$ at the intensity $2\times {10}^{14}$ W/cm${}^2$. Panels (a) and (d) show the normalized amplitudes of the parallel ($\parallel$) and perpendicular ($\perp$) components, panels (b) and (e) show their phase difference, and panels (c) and (f) show the computed ellipticity.

Figure 3

Ellipticity of the harmonic signals from ${\mathrm{H}}_2{}^{+}$ with various orientation angles: (a) the $1{\sigma }_g$ state at the intensity $3\times {10}^{14}$ W/cm${}^2$ and (b) the $1{\sigma }_u$ state at the intensity $2\times {10}^{14}$ W/cm${}^2$. The legend in (b) applies to both (a) and (b).