Polarisation states of high harmonic generation from aligned molecules

This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. We present detailed theoretical calculations based on the recently developed quantitative rescattering theory (QRS) for polarisation and ellipticity of high-order harmonics from aligned N 2 and O 2 generated with mid-infrared linearly polarised laser pulses. Within the QRS, the two polarisation states of high-order harmonics are due to the high-energy photons emitted with polarisation parallel or perpendicular to the direction of the same returning electron wave packet in the photo-recombination process. The complex transition dipoles responsible for these two components have, in general, difference phases, which results in the ellipticity of emitted harmonics. Our results show clear target-species dependent polarisation states. In particular, we found strong harmonic ellipticity in aligned N 2 , but weak ellipticity in aligned O 2 for harmonics below 100 eV. We further show the factorisation of the macroscopic high harmonic generation under typical experimental conditions. This implies that results of polarisation measurements are quite robust to the macroscopic phase matching conditions. 1. Introduction High-order harmonic generation (HHG), one of the most important nonlinear processes, occurs when an atomic or molecular gas is placed in an intense laser field [1]. Due to the symmetry, the emitted HHG is polarised parallel to the driving laser polar-isation if the gas is isotropic, as in case of atomic or unaligned molecular targets. However, for aligned molecules, a harmonic component perpendicular to the driving laser polarisation is expected to be present [2]. Clearly, one needs a good level of molecular alignment in order to produce a sufficient amount of HHG perpendicular component as it goes to zero for the isotropic case. It is therefore not surprising that polarisation measurements for emitted harmonics were reported only quite recently [3–6]. These experimental data on harmonic polarisation from …