Probing Orbital Structure of Polyatomic Molecules by High-Order Harmonic Generation

Abstract

The effects of electronic structure and symmetry are observed in laser driven high-order harmonic generation for laser aligned conjugated polyatomic molecular systems. The dependence of the harmonic yield on the angle between the molecular axis and the polarization of the driving laser field is seen to contain the fingerprint of the highest occupied molecular orbitals in acetylene and allene, a good quantitative agreement with calculations employing the strong field approximation was found. These measurements support the extension of the recently proposed molecular orbital imaging techniques beyond simple diatomic molecules to larger molecular systems. DOI: 10.1103/PhysRevLett.98.203007 PACS numbers: 33.80.Rv, 42.65.Ky, 42.65.Re High-order harmonic generation (HHG) in atomic gases by high intensity laser fields has proven a fruitful method for producing coherent extreme ultraviolet beams and attosecond pulses [1][2][3]. In molecules, HHG presents a rich set of new physical phenomena, as both the ionization and electron recombination steps of HHG are dependent on the particular symmetry of the highest occupied molecular orbital (HOMO) and its orientation with respect to the laser field [4 -9]. Because of this orientation dependence, HHG in molecules can provide a unique time resolved probe of the electronic orbital structure. Recent work has shown that the HHG spectrum from aligned molecular samples can be used to determine the molecular structure for small molecules such as N 2 and CO 2 [10 -15]. So far these studies have been confined to simple diatomic and triatomic linear molecules. The present work extends this approach to significantly more complex polyatomic molecules, and we find that the angular dependence of the HHG signal can be used to map more complex electronic orbitals.In order to perform a full tomographic reconstruction of the molecular orbital, a high degree of spatial alignment of the molecules is required; furthermore, a large enough number of harmonic orders must be produced in order to provide a complete characterization of the orbital in momentum space. The structure retrieval is then possible by either the examination of distinct interference signatures in the spectrum [10 -12] or tomographic reconstruction [13,14] or the iterative optimization of the wave functions to best match the measured spectrum [15]. The mathematical steps in structural retrieval from HHG are based upon the strong field approximation (SFA). The SFA is a single active electron model and, additionally, the influence of the laser field upon the bound electronic states, and the influence of the Coulomb potential upon the continuum electron states are both neglected. HHG in the strong field limit can be seen as a three step process [16]: (i) ionization; (ii) acceleration in the laser field; (iii) recombination back into the bound electronic state. It is known that multielectron processes become significant with increasing molecular size [17] as, for example, the polarization of the ionic core by the laser field modi...

High-order harmonic generation from polyatomic molecules including nuclear motion and a nuclear modes analysis

“…At 800 nm and intensities around 10 14 W/cm 2 , typical τ values are in the 1-to 2-fs regime, and the reason for the observed increase is the faster nuclear motion in the lighter isotope H 2 , leading to a smaller overlap of the nuclear wave packets in the recombination step. In the experiment in [5] similar results were reported for HHG from methane isotopes (CD 4 and CH 4 ).…”

“…We treat electronic dynamics in the Lewenstein model [17] following the implementation of Ref. [4] but adapt a few improvements to the latter as detailed here.…”

“…(3) within the improved stationary phase method [23][24][25], where we include electron trajectories leading from one atomic center to another. Dipole velocities for different orientations of the molecule can be obtained by applying the Euler rotation operator [4,26] to the molecular fixed wave function.…”

“…These experiments include studies of orbital structure [1][2][3][4], nuclear dynamics [5,6], and, more recently, coupled electronic and nuclear dynamics [7,8]. The interplay between nuclear motion and HHG has been subject to several theoretical studies in the case of H 2 + and H 2 [9][10][11][12] and other diatomic molecules [13] where nuclear motion is simple in the sense that there exists only one mode of vibration (along the internuclear axis).…”

Direct probing of electronic density distribution of a Rydberg state by high-order harmonic generation in a few-cycle laser pulse

“…The high-order harmonic generation (HHG) process has been considered a very effective tool for imaging the structure of an atom or molecule with angstrom spatial resolution [1][2][3][4][5][6][7][8][9][10][11], based on the three-step model [12]. According to this model, an electron is released into the continuum by tunnel ionization; then the free electron is driven by the laser field and thus gains a probability of returning to the parent ion; finally, the electron recombines with its parent ion and emits high-order harmonic photons.…”