PHYSICAL REVIEW A 101, 023411 (2020) Polarization of high-order harmonic generation in oriented molecules with intense ultrashort laser pulses Kai-Jun Yuan , 1, 2 , * Catherine Lefebvre, 3 Szczepan Chelkowski, 2 Huizhong Lu, 2 and André D. Bandrauk 2 , † 1 Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012, China 2 Laboratoire de Chimie Théorique, Faculté des Sciences, Université de Sherbrooke, Sherbrooke, Québec, Canada J1K 2R1 3 Université du Québec, INRS-Énergie, Matériaux et Télécommunications, Varennes, Québec, Canada J3X 1S2 (Received 26 September 2019; accepted 30 January 2020; published 19 February 2020) Using numerical solutions of the time-dependent Schrödinger equation we show that in oriented molecules one can control the polarization of molecular high-order harmonic generation (MHOHG) by intense linearly polarized pulses. For oriented triangular molecules, H 3 + /H 3 2+ , one obtains even-order harmonics perpendicular to the laser polarization, whereas all odd-order harmonics have the same polarization as the laser polarization. For H 2 + /H 2 we show that only odd-order harmonics are generated for any orientation and their polarization is nearly parallel to the molecular axis. We describe these phenomena based on perturbation theory. Redshifts of the MHOHG spectra occur due to laser induced electron localization in non-Born-Oppenheimer dissociating molecules, reflecting the effect of nuclear dynamics. The numerical results illustrate the sensitivity of harmonic polarization to molecular geometry and nuclear dynamics. DOI: 10.1103/PhysRevA.101.023411 I. INTRODUCTION Rapid developments in the generation and characterization of ultrashort intense laser pulses [1,2] provide the possibility for investigating electron processes in matter on their natural attosecond (1 as = 10 −18 s) time scale [3–7]. High-order harmonic generation (HHG) has been explored extensively as a route to generate attosecond x-ray sources from atoms, molecules, and solids using these new pulses. The shortest attosecond pulse of duration 43 as has been generated from linearly polarized HHG [8]. One of the fundamental con- cepts of intense laser field atom or molecule interaction is the rescattering process in the presence of intense linearly polarized light [9]. Thus following tunneling ionization, the photoelectron remains controlled by the laser field, returning and recolliding with the parent ion after a phase (sign) change of the electric field. This simple classical model of linearly polarized laser-induced recollision with the parent ion has led to the development of a consistent theory of HHG, predict- ing maximum harmonic order [9–11] N m = (I p + 3.17U p )/ω, for an ionization potential I p and ponderomotive energy U p = E 2 0 /4ω 2 (throughout this paper, atomic units, a.u., are used unless otherwise noted) at the field amplitude E 0 and frequency ω. Molecules have additional degrees of freedom due to nu- clei which offer a useful medium for producing molecular high-order harmonic generation (MHOHG) spectra beyond the standard classical model. Both odd and even harmonics can be produced for oriented asymmetric molecules, e.g., Refs. [12–15]. It has also been found that pure even MHOHG * kjyuan@jlu.edu.cn † andre.bandrauk@usherbrooke.ca can be obtained in oriented asymmetric CO molecules with proper conditions [16]. In symmetric hydrogen molecular ion, even-order harmonics can also be obtained by setting different nuclear charges [17]. Recently, elliptically polarized MHOHG spectra have been measured experimentally in ori- ented and aligned molecules [18–20] and simulated theoret- ically [21–24] with ab initio molecular orbital models. The nonspherical geometry of molecules makes molecules ideal candidates for generating circularly polarized MHOHG and attosecond pulses by bichromatic circularly polarized laser pulses [25]. In this work we present a phenomenon in MHOHG in triangular oriented molecules which are reflection symmetric in two dimensions and asymmetric in another direction (Oy axis). More specifically, we show that when the laser polariza- tion is along the symmetry axis (Ox axis) only even harmonics are generated with polarization perpendicular polarization, i.e., along the Oy axis, whereas pure odd harmonics are gener- ated along the laser polarization (Ox axis). This is very unex- pected in the framework of the standard tunneling model [9] which predicts that polarization of all generated harmonics is always the same as the laser beam polarization. These results reveal the importance of the molecular geometry with respect to the electric-field polarization of the ionizing pulse. Results are obtained from numerical solutions of the molecular time- dependent Schrödinger equation (TDSE). The one and two electron molecules H 3 + /H 3 2+ and H 2 /H 2 + , which can be fully investigated [26,27], are used as benchmark models to illustrate the MHOHG process in ultrashort laser fields. The paper is arranged as follows. In Sec. II, we briefly de- scribe the theoretical and computational methods to simulate HHG by solving molecular TDSEs. The numerical results are presented in Sec. III. Finally, we summarize our findings in Sec. IV. 2469-9926/2020/101(2)/023411(9) 023411-1 ©2020 American Physical Society