Molecular High-order Harmonic Generation Spectra Research Articles

Polarization of high-order harmonic generation in oriented molecules with intense ultrashort laser pulses

Using numerical solutions of the time-dependent Schr\odinger 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, ${\mathrm{H}}_{3}{}^{+}/{\mathrm{H}}_{3}{}^{2+}$, one obtains even-order harmonics perpendicular to the laser polarization, whereas all odd-order harmonics have the same polarization as the laser polarization. For ${\mathrm{H}}_{2}{}^{+}/{\mathrm{H}}_{2}$ 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.

Nonperturbative time-dependent density-functional theory of ionization and harmonic generation in OCS and CS2molecules with ultrashort intense laser pulses: Intensity and orientational effects

Molecular high-order harmonic generation (MHOHG) and molecular orbital ionization rates are calculated for the nonsymmetric OCS and symmetric CS${}_{2}$ molecules using numerical solutions of Kohn-Sham (KS) equations of time-dependent density functional theory in the nonlinear nonperturbative regime of laser-molecule interactions for different laser-molecule orientations and intensities. It is found that the ionization of inner-shell KS molecular orbitals contributes significantly to the ionization and MHOHG processes for intensities I \ensuremath{\ge} 3.5 \ifmmode\times\else\texttimes\fi{} 10${}^{14}$ W/cm${}^{2}$. Ionization rate maxima correspond to the alignment of maximum KS orbital densities with the laser pulse polarization instead of orbital ionization potentials. Furthermore, degeneracies of orbitals are removed as a function of laser-molecule angle, thus affecting ionization rates, the MHOHG spectra, and their polarizations, the latter allowing for identifying inner-orbital ionization.

Generation of circularly polarized attosecond pulses by intense ultrashort laser pulses from extended asymmetric molecular ions

We present a method for generation of single circularly polarized attosecond pulses in extended asymmetric HHe${}^{2+}$ molecular ions. By employing an intense ultrashort circularly polarized laser pulse with intensity $4.0\ifmmode\times\else\texttimes\fi{}{10}^{14}$ W/cm${}^{2}$, wavelength 400 nm, and duration 10 optical cycles, molecular high-order-harmonic generation (MHOHG) spectra with multiple plateaus exhibit characters of circular polarization. Using a classical laser-induced collision model, double collisions of continuum electrons first with neighboring ions and then second with parent ions are presented at a particular internuclear distance and confirmed from numerical solutions of a time-dependent Schr\"odinger equation. We analyze the MHOHG spectra with a Gabor time window and find that, due to the asymmetry of HHe${}^{2+}$, a single collision trajectory of continuum electrons with ions can produce circularly polarized harmonics, leading to single circularly polarized attosecond pulses for specific internuclear distances.

Monitoring attosecond dynamics of coherent electron-nuclear wave packets by molecular high-order-harmonic generation

A pump-probe scheme for preparing and monitoring electron-nuclear motion in a dissociative coherent electron-nuclear wave packet is explored from numerical solutions of a non-Born-Oppenheimer time-dependent Schr\odinger equation. A mid-ir intense few-cycle probe pulse is used to generate molecular high-order-harmonic generation (MHOHG) from a coherent superposition of two or more dissociative coherent electronic-nuclear wave packets, prepared by a femtosecond uv pump pulse. Varying the time delay between the intense ir probe pulse and the uv pump pulse by a few hundreds of attoseconds, the MHOHG signal intensity is shown to vary by orders of magnitude, thus showing the high sensitivity to electron-nuclear dynamics in coherent electron-nuclear wave packets. We relate this high sensitivity of MHOHG spectra to opposing electron velocities (fluxes) in the electron wave packets of the recombining (recolliding) ionized electron and of the bound electron in the initial coherent superposition of two electronic states.

Circularly polarized molecular high-order harmonic generation inH2+with intense laser pulses and static fields

Molecular high-order harmonic generation (MHOHG) by a combined intense circularly polarized laser pulse and static electric field has been studied from the appropriate time-dependent Schr\"odinger equation (TDSE) for the ${{\mathrm{H}}_{2}}^{+}$ molecular ion. It is found that for a particular static field strength derived from a classical model, efficient MHOHG spectra are obtained with maximum energy ${I}_{p}$ $+$ 9.05${U}_{p}$, where ${I}_{p}$ is the ionization potential and ${U}_{p}={E}_{0}^{2}/4{m}_{e}{\ensuremath{\omega}}_{0}^{2}$ is the ponderomotive energy at amplitude ${E}_{0}$ and frequency ${\ensuremath{\omega}}_{0}$ of the circularly polarized laser pulse. The static field controls recollision of the electron with parent ions and is confirmed by numerical solutions of the ${{\mathrm{H}}_{2}}^{+}$ TDSE at equilibrium. To produce circularly polarized MHOHG spectra, a combination of an elliptically polarized pulse and a static electric field is found to be most efficient. A time-frequency analysis obtained via Gabor transforms is employed to identify electron recollision times responsible for the generation of these high-order harmonics. It is found that only single recollision trajectories contribute to the circularly polarized harmonics, thus generating new sources for high-frequency circularly polarized attosecond pulses.

Molecular high-order harmonic generation in a nonlinear two-electron molecule: the equilateral H+3

Molecular high-order harmonic generation (MHOHG) is studied from appropriate time-dependent Schrödinger equation (TDSE) solutions of a 2D equilateral two-electron H+3 molecular ion in interaction with an intense (5 × 1014 W cm−2) few-cycle 800 nm linearly polarized laser pulse. The nonperturbative time-dependent Born–Oppenheimer (static nuclei) two-electron wavefunction is used to calculate the MHOHG spectrum as a function of the laser–molecule orientation and internuclear distance R. Three-centre interferences in the MHOHG spectrum are shown to be sensitive functions of the laser–molecule orientation and R. A comparison is made of the MHOHG spectrum at the ground state equilibrium distance, Re, at an intermediate R where a three-photon transition (1A′1 → 1E′) occurs, and finally at internuclear distance Rc where enhanced ionization can occur due to the nonlinear electron–laser interaction. Analytic expressions for MHOHG spectra interferences are derived based on a recollision model and are compared to the exact 2D TDSE simulations.

Reading molecular messages from high-order harmonic spectra at different orientation angles

We investigate the orientation dependence of high-order harmonic generation (HHG) from H(2) (+) with different internuclear distances irradiated by intense laser fields both numerically and analytically. The calculated molecular HHG spectra are found to be sensitive to the molecular axis orientation relative to incident laser field polarization and internuclear separation. In particular, our simulations demonstrate that at certain harmonic orders the envelopes of the HHG spectra taken at different orientation angles intersect. Moreover, the position of intersection is largely independent of the laser intensity while strongly dependent on the internuclear separation. This striking "intersection" phenomenon is identified as arising due to intramolecular two-center interference in the HHG and can be used to probe the molecular instantaneous structure.

Impact of electron ionization on the generation of high-order harmonics from molecules

When the laser frequency is tuned to be equal to the molecular electronic excitation, high-order harmonics are generated due to the electronic dipole transitions between the corresponding two potential-energy surfaces (PES). A natural, often taken, choice is the PES of the field-free molecular system. In this special choice the ionization phenomenon is not considered. Only the effect of the dissociation is considered. The method we developed enables one to remain within the framework of the 2-PES approximation and yet to include also the ionization effect in the calculations of molecular high-order harmonic generation spectra. In this approach the coupling between the electronic and nuclear motions is taken into consideration by using coupled complex adiabatic PES. As an illustrative numerical example, we calculated the high harmonic generation (HHG) spectra of ${\mathrm{H}}_{2}^{+}$ in a 730-nm laser with the intensity of $8.77\ifmmode\times\else\texttimes\fi{}{10}^{13}{\mathrm{W}/\mathrm{c}\mathrm{m}}^{2}.$ The inclusion of the ionization in our approach not only enables the electrons to tunnel through the effective static potential barrier, but also apply an asymmetric force which accelerates the electron before ionization takes place. Therefore, indirectly the inclusion of the ionization by the laser field may lead eventually to an enhanced HHG spectra in comparison with the calculated one when the ``natural'' choice of the field-free 2PES is taken.