Atomic characteristics and high-order harmonic spectra: extension of ab-initio numerical calculations to larger systems


High-order harmonic generation (HHG) is a highly nonlinear process where an electron driven by an intense, typically infrared, laser pulse ionizes, accelerates in the laser field and recombines with the parent ion, emitting a photon with frequency many times that of the driving field. The coherent radiation emitted from many atoms in the focus of the driving laser leads to the generation of an ultrashort ultraviolet or x-ray laser pulse. Numeric solution of the time-dependent Schr¨odinger equation (TDSE) accurately describes the single-electron process, including the low-energy region of the emission spectrum for which the atomic potential and excited states play a significant role. The coherent macroscopic response (e.g., from a gas jet) involves the emission of a very large number of atomic radiators (e.g., 1015) that each interacts with the driving laser at different peak intensities and carrier-envelope phases. Full ab-initio simulation of the macroscopic response using exact numeric single-electron calculations are not feasible.

In this thesis, we present results of three projects related to high-order harmonic genera-tion with a focus on the below- and near-threshold regime, in which excited states of the atom and the specific form of the atomic potential play an important role. First, we present a re-producible ab-initio method to produce benchmark tests between calculations based on the time-dependent Schr¨odinger equation (TDSE) in the single-active-electron approximation (SAE) and time-dependent density functional theory (TDDFT) in the highly nonlinear multiphoton and tun-neling regime of strong-field physics. As key to the benchmark comparison we obtain an analytic form of SAE potentials based on density functional theory, which we have applied for different atoms, ions, and molecules. Using these potentials, we find remarkable agreement between the results of the two independent numerical approaches (TDDFT and SAE-TDSE) for the high-order harmonic yields in helium, demonstrating the accuracy of the SAE potentials as well as the predic-tive power of SAE-TDSE and TDDFT calculations for the nonperturbative and highly nonlinear strong-field process of high harmonic generation in the ultraviolet and visible wavelength regime.

Next, we investigate resonance enhancement of near-threshold HHG, identifying similar res-onance effects in broad parameter regimes, including hydrogen driven by near- and mid-infrared pulses as well as helium with 400 nm lasers. We differentiate behavior that may be explicable through semi-classical trajectory models (generally at higher intensity) from features which are not consistent with these models.

In the last part of the thesis, we develop a macroscopic description of high-order harmonic radiation resulting from the interaction of atomic systems with an intense laser pulse using ab-initio solutions of the time-dependent Schr¨odinger equation (TDSE). We show that for this highly nonlinear process, interpolation can be performed across laser intensity for a given wavelength, limiting the number of full time-dependent Schr¨odinger equation calculations to about one hundred. The significantly reduced computational time as compared to more sophisticated methods opens a path toward the extension of macroscopic high harmonic calculations based on ab-initio microscopic results to more complex targets and interactions. We investigate the near-threshold regime of the spectra, showing that the degree of coherence of the off-harmonic radiation generated during the pulse is much lower than that of the harmonics, but this radiation extends to larger divergence angles than the harmonic signals – providing the option for separation of the different signals in this part of the spectrum. Finally, we analyze high harmonic generation from the spatial phase distribution for broadband Gaussian pulses with a negative Porras factor, showing an interference pattern in the angular distribution of below- and near-threshold harmonics, which is not present for the monochromatic Gouy phase distribution.

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Department of Physics
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University of Colorado Boulder
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