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

Abstract

A recent experiment [Phys. Rev. Lett. 102, 073902 (2009)] has demonstrated that elliptically polarized highorder 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. High-order harmonic generation (HHG) is one of the most rapidly developing topics in strong-field atomic, molecular, and optical physics today, leading to the recent advancement of the attosecond science [1][2][3] and the feasibility of frequency-comb generation in the extreme ultraviolet to vacuum ultraviolet regimes [4][5][6][7], etc. Traditionally, the power (or radiation energy) spectra have been the main topic of HHG studies both experimentally and theoretically. However, recent developments in molecular alignment technology [8] open a possibility of investigating other HHG properties including the phase [9-11] and polarization [12][13][14] of the harmonic radiation.For ensembles of atoms or unaligned molecules, the polarization of the harmonics is expected to be the same as the polarization of the driving laser field. For aligned molecules, however, the harmonic radiation has two components: one parallel and another perpendicular to the laser polarization direction. Experiments [12,13] showed that the linear polarization state of HHG driven by linearly polarized laser fields is tilted due to the nonvanishing perpendicular component of HHG. Recently, the elliptical polarization state of HHG driven by linearly polarized laser fields has been measured [14]; speculations on its possible origins include, for example, multielectron effects and the influence of the Coulomb potential. An experiment [14] showed high ellipticity for N 2 HHG but no ellipticity for CO 2 HHG. Controversially, a theory including multiple electronic continuum dynamics predicts elliptical HHG from aligned CO 2 [15]. In general, according to the selection rules [16], elliptical harmonic radiation is expected unless the molecular alignment is parallel or perpendicular to the driving laser polarization. The widely used strong-field approximation (SFA), however, cannot predict this ellipticity of HHG at all because only the parallel component Since the mechanism of the elliptical HHG is still under debate and largely unknown, it is most desirable and timely to perform a fully ab initio study to explore and cla...

Ellipticity of odd-even harmonics from oriented asymmetric molecules in strong linearly polarized laser fields

“…HHG can be well described by a three-step model [3,4] and has been shown to have promising applications in attosecond physics [5,6] and ultrafast imaging of molecular orbitals [7][8][9], Previous studies on HHG mainly focus on the power spectra of the harmonics emitted along the laser polarization (i.e., the parallel harmonics). Recently, great attention has been paid to the polarization of harmonics from aligned symmetric molecules, such as H2 + [10] and N2 [11][12][13][14]. Experimental and theoretical studies show that the elliptical polarization state of harmonics can be generated from aligned molecules irradiated by a linearly polarized laser field.…”

“…Experimental and theoretical studies show that the elliptical polarization state of harmonics can be generated from aligned molecules irradiated by a linearly polarized laser field. The possible origin of the ellipticity of HHG has been attributed to the multielectron effect [11], the Coulomb effect [13,14], twocenter interference [10], and quantum-mechanical uncertainty of the electron motion [15], As this polarization of HHG is closely related to not only the parallel harmonics and the harmonics emitted perpendicular to the laser polarization (i.e., the perpendicular harmonics) but also the phase of the harmonics, it provides other deep insights into the mechanism of the molecular HHG [16].…”

Generating isolated elliptically polarized attosecond pulses from oriented CO gas medium using linearly polarized driving pulses

“…The intensity (I ) and phase (ϕ) of the harmonic components can be given by I j (q) = |a j (q,β)| 2 and ϕ j (q) = arg[a j (q,β)] (j = x,z), respectively. The ellipticity ε is determined by the amplitude ratio and the phase difference of the two components [37]:…”

Ellipticity of near-threshold harmonics from stretched molecules

“…This ellipticity mechanism of lower-order harmonics is different from that of HOH. The latter has been shown to be associated with the multielectron effect [27,28], quantum orbits considering the multicenter characteristic of the molecule [29], the Coulomb effect [30,31], two-center interference [32], quantum-mechanical uncertainty of the electron motion [33], the interplay of different HHG routes [34], etc.. This ellipticity of lower-order harmonics provides a potential manner for generating elliptically-polarized VUV pulses.…”