Generation of below-threshold even harmonics by a stretchedH2+molecular ion in intense linearly and circularly polarized laser fields

Abstract

We explore the mechanism of below-threshold even-harmonic generation of the H + 2 molecular ion subject to intense near-infrared linearly and circularly polarized laser fields. The task is accomplished by accurate treatment of the time-dependent Schrödinger equation in prolate spheroidal coordinates within the generalized pseudospectral formalism. Even harmonics are detected in the harmonic spectra of stretched molecules, mostly with the internuclear separations of 5 to 9 a.u. Consecutive dynamic localization of the electron density near each of the nuclei is responsible for the broken inversion symmetry, which in turn leads to emission of low-order even harmonics. An intuitive picture of the process is provided by the analysis of the time evolution of the electron density and time-frequency spectra of the dipole acceleration. A clear theoretical explanation of the phenomenon is given within the Floquet formalism.

Photoelectron momentum distributions of the hydrogen molecular ion driven by multicycle near-infrared laser pulses

“…In Table I, we list the kinetic energies of a photoelectron from H + 2 and He + given by Eq. (19). When the internuclear distance of H + 2 stretches beyond the equilibrium distance R = 2, however, our TDSE results also deviate from Eq.…”

“…TABLE I. Ionization energy (I p ) and the kinetic energy (KE) of an photoelectron given by Eq. (19) in eV. Also shown is the integer n 0 defined in Eq.…”

“…(19), which are listed in Table I, except for the case R = 5 in (b). Given that the lowest-order p s in Figure 3(b) has a node at θ p = ±π/2, we must assume it is the s = 0 spectra corresponding to the absorption of 13 (= n 0 + s) odd photons, but its spectral energy in Figure 4(b) seems upshifted by ∼ 0.8 eV, about 1/2 the fundamental frequency ω o , compared to the photoelectron energies in Table I.…”

“…This shift of energy in the ATI spectra of H + 2 driven in parallel with the molecular axis may be related to the field-induced coupling of the lowest-two states (a.k.a. charge resonance) [15,18,19], but its exact causes are yet unknown.…”

“…The calculation is based on the generalized pseudospectral (GPS) method for the solution of the 3D-TDSE [15,16] and the Volkov-wave propagation in the momentum space [17]. The GPS method has been used previously to study the high harmonic spectra of H + 2 in linear [16] and circular [18,19] driving laser fields. This paper complements their results for the PMD and ATI spectra.…”