Generation of circularly polarized XUV and soft X-ray high-order harmonics by 1 homonuclear and heteronuclear diatomic molecules subject to bichromatic 2 counter-rotating circularly polarized intense laser fields Recently, studies of bright circularly polarized high-harmonic beams from atoms in the soft X-ray region as a source for X-ray magnetic circular dichroism measurement in a tabletop-scale setup have received considerable attention. In this paper, we address the problem with molecular

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... gets and perform a detailed quantum study of H + 2 , CO, and N2 molecules in bichromatic counter-rotating circularly polarized laser fields where we adopt wavelengths (1300 nm and 790 nm) and intensities (2 × 10 14 W/cm 2 ) reported in a recent experiment [Proc. Natl. Acad. Sci. U.S.A. 595 112, 14206 (2015)]. Our treatment of multiphoton processes in homonuclear and heteronuclear diatomic molecules is nonperturbative and based on the time-dependent density functional theory for multielectron systems. The calculated radiation spectrum contains doublets of left and right circularly polarized harmonics with high-energy photons in the XUV and soft X-ray range. Our results reveal intriguing and substantially different nonlinear optical responses for homonuclear and heteronuclear diatomic molecules subject to circularly polarized intense laser fields. We study in detail the below-and above-threshold harmonic regions and analyze the ellipticity and phase of the generated harmonic peaks. I. INTRODUCTION 10 High-order-harmonic generation (HHG) is an attrac-11 tive table-top source of coherent, bright, and tunable 12 extreme ultraviolet (XUV) and soft X-ray radiation 13 with applications in coherent diffractive imaging, ultra-14 fast holography, and time resolved measurements [1-6]. 15 Moreover, circularly polarized HHG may find additional 16 applications in nanolithography, ultrafast spin dynamics, 17 and magnetic circular dichroism [1, 7-13]. 18 However, until recently bright HHG was limited to lin-19 ear polarization due to the difficulty of controlling ellip-20 tically and circularly polarized harmonics and their effi-21 ciency. When an atom or molecule is driven by a laser 22 field with slightly elliptical polarization, the electron has 23 some probability of re-colliding with its parent ion it was 24 initially released from, and this results in the generation 25 of harmonics with slight elliptical polarization. However, 26 the HHG efficiency drops drastically with increasing el-27 lipticity of the driving field compared to the case of lin-28 early polarized harmonics generated from linearly polar-29 ized laser radiation [14, 15]. In contrast, for circularly po-30 larized driving lasers, the probability of re-collision and 31 the emission of high harmonics is completely suppressed. 32 A direct approach for generating circularly polarized 33 HHG was suggested 22 years ago [16, 17], and recently 34 measured by Fleischer et al. [7]. In this scheme, circu-35 larly polarized HHG are driven by co-propagating circu-36 larly polarized bichromatic fields that rotate in opposite 37 * d.telnov@spbu.ru † sichu@ku.edu directions (counter-rotating) and interact with argon gas. 38 This experiment [7] opened up the possibility and motiva-39 tion of generating bright circularly polarized HHG com-40 parable to the flux efficiency of linearly polarized HHG. 41 Recently, Fan et al. [1] did just that, they generated 42 bright circularly polarized soft X-ray HHG beams with 43 photon energies greater than 160 eV and flux compara-44 ble to the HHG flux obtained using linearly polarized 45 800 nm driving lasers. These bright circularly polarized 46 high-order-harmonic beams in the soft X-ray region were 47 generated from He, Ne, and Ar atoms, and used to imple-48 ment X-ray magnetic circular dichroism measurements in 49 a tabletop-scale setup [1]. Previously, such radiation has 50 only been available at large-scale X-ray facilities such as 51 synchrotrons. 52 Bright circularly polarized soft X-ray high-order-53 harmonic beams generated by atomic gases have been 54 used in recent experimental studies to probe magnetic 55 materials, such as the M-shell absorption edges of Co 56 [12], and N 4,5 absorption edges of Gd [1]. The experi-57 ments validated the high degree of circularity, brightness, 58 and stability of this light source [1, 12]. 59 While an impressive progress has been achieved in gen-60 eration of bright circularly polarized XUV and soft X-ray 61 radiation by atomic targets, this area remains largely un-62 explored for molecular systems. In this work, we show 63 that generation of bright XUV and soft X-ray radia-64 tion with circular polarization is also possible in diatomic 65 molecules. We perform an all-electron nonperturbative 66 investigation of multiphoton processes of homonuclear 67 (H + 2 and N 2 ) and heteronuclear (CO) diatomic molecules 68 in bichromatic counter-rotating circularly polarized in-69 tense laser fields. The H + 2 molecule is the simplest two- 70