Uncovering multiple orbitals influence in high harmonic generation from aligned

Recent measurements on high-order harmonic generation (HHG) from N2 aligned perpendicular to the driving laser polarization [B. K. McFarland el al, Science 322, 1232 (2008)] have shown a maximum at the rotational half-revival. This has been interpreted as the signature of the HHG contribution from the molecular orbital just below the highest occupied molecular orbital (HOMO). By using the recently developed quantitative rescattering theory combined with accurate photoionization transition dipoles, we show that the maximum at the rotational half-revival is indeed associated with the HOMO-1 contribution. Our results also show that the HOMO-1 contribution becomes increasingly more important near the HHG cutoff and therefore depends on the laser intensity. PACS numbers: 42.65.Ky, 33.80.Eh Submitted to: J. Phys. B Uncovering multiple orbitals influence in high harmonic generation from aligned N2 2 High-order harmonic generation (HHG) has been extensively investigated both experimentally and theoretically over the last two decades [1]. Until very recently, the HHG has been understood as being due to tunneling ionization of an electron from the highest occupied molecular orbital (HOMO) and recombining back to the HOMO. The contribution from lower molecular orbitals are routinely neglected. That is not surprising since tunneling is a highly nonlinear process, and therefore highly selective to the HOMO due to energy considerations. In general, the neglect of the contribution from lower molecular orbitals are not justified for systems with nearly degenerate HOMO and HOMO-1, in other words, when the energy gap between the HOMO and lower molecular orbitals are much smaller than the ionization potential from the HOMO. Furthermore, for some molecular alignment, tunneling ionization from the HOMO is suppressed due to symmetry of the wavefunction [2]. Clearly, in that case the neglect of lower molecular orbitals is questionable. These two favorable conditions for observing HOMO-1 contribution are present in N2, where the 1πu HOMO-1 has a binding energy of 16.93 eV, quite close to the binding energy of the 3σg HOMO (15.58 eV). Early theoretical calculations based on the strong-field approximation (SFA) model [3, 4] have shown that harmonic yields from aligned N2 are maximum if the molecules are aligned along the laser polarization direction. These results are in good agreements with the pump-probe delay time experimental data [5, 6] as well as the recent more direct measurements [7]. On the other hand, the contribution from the HOMO-1 is expected to peak near 90◦. Although the two molecular orbitals contribute to different alignment regions in the total harmonic yields, it is still a very challenging task to disentangle the HOMO-1 since its contribution is expected to be relatively weak. This is in strong contrast to the traditional single-photon photoionization where electrons are generally ionized from many MOs with comparable strengths (see, for example, [8]). In the recent experiment McFarland et al [9] reported that they have successfully observed the contribution from HOMO-1 in aligned N2. That has been achieved within the pump-probe scheme with perpendicular pump-probe polarizations. For low harmonic orders below H23, the harmonic signals behave similarly to inverted < cos θ >, i.e., inverse of the degree of molecular alignment. For higher harmonics, McFarland et al observed a maximum at the rotational half-revival, where inverted < cos θ > is minimum. Furthermore, the maximum at the half-revival is found to be quite pronounced in the HHG cutoff region, which depends on the intensity of the driving laser. The goal of this paper is to show theoretically that the main features observed by McFarland et al [9] are indeed the signature of the HOMO-1 contribution. To support our claim, we have carried out calculations by using the recently developed quantitative rescattering theory (QRS) [10]. The photoionization transition dipole and its phase are obtained from state-of-the-art molecular photoionization calculations [11]. The QRS theory is based on the rescattering picture and it has been shown to give accurate results comparable with that from the time-dependent Schrödinger equation (TDSE) for rare-gas atoms [14, 13] and molecular ion H+2 [15]. The QRS has also been shown Uncovering multiple orbitals influence in high harmonic generation from aligned N2 3 0.0 1.0x10 2.0x10 3.0x10 4.0x10 0 10 20 30 40 50 60 70 80 90 0.0 1.0x10 2.0x10 3.0x10 Io ni za tio n ra te (a .u .) HOMO HOMO-1 (x5) HOMO-2 (x20) (a)