Session N7: Focus Session: High Harmonic Generation

Probing time-resolved large-amplitude molecular vibrations with high-order harmonics generated by ultrashort laser pulses

We present a theory that incorporates the vibrational degrees of freedom in high-order harmonic generation (HHG) of molecules with intense infrared lasers [1]. This theory extends the previously developed quantitative rescattering theory (QRS) for HHG from fixed-nuclei molecules, by accounting for the effect of lasers on the vibrational wavefunctions. The induced time-dependent transition dipoles for each fixed nuclear geometry are added up coherently, weighted by the laser-driven time-dependent nuclear wave packet distribution. We show that the nuclear wave packet can be strongly modified by the driving laser. The validity of this model is first checked against results from the solution of the time-dependent Schr\"{o}dinger equation for a model system. The theory is then applied to explain time-resolved HHG spectra for molecules measured in pump-probe experiments.\\[4pt] Work done in collaboration with Anh-Thu Le, Kansas State University; Robert Lucchese, Texas A\&M University; and Toru Morishita, University of Electro-communications, Japan.\\[4pt] [1] Anh-Thu Le, Toru Morishita, R. R. Lucchese and C. D. Lin, Phys. Rev. Lett. \textbf{109}, 203004 (2012).   

XUV Laser Assisted Control of High Harmonic Generation

We have conducted a theoretical study to investigate control of the high-order harmonic generation (HHG) emitted by a one-electron atomic system by using an XUV laser pulse. In this scheme, a linearly polarized 800 nm three-cycle driving laser field is incident upon a He$^{+}$ ion. While initially prepared in the ground state, the electron is promoted to an excited state using a second, linearly polarized XUV laser pulse tuned to resonance with the energy level transition. By selecting the driving laser intensity so that ionization from the ground state is strongly disfavored, we are afforded control over the time of ionization and the initiation of the HHG process. The span of the plateau of the resulting harmonic spectrum is equivalent to that of HHG from an ion prepared in the ground state, but the harmonic emission is stronger in magnitude. Excitation through the tail end of the driving pulse additionally allows control of the location of the cutoff within the spectrum.   

Electron correlations in harmonic generation spectra of beryllium

By solving the full dimensional two-active-electron time-dependent Schr\"{o}dinger equation in an intense ultrashort laser field, we show that even electron correlations occurring over a narrow energy interval have a significant effect on such strong field processes as high harmonic generation (HHG). As the laser pulse frequency varies from 1.2 eV to 1.8 eV, several harmonics become resonant sequentially with particular autoionizing states, which greatly enhances their intensities. Such resonance features in Be HHG spectra are found to be three times more pronounced than for He [1]. Unlike for He, whose doubly-excited states are at very high energies above the ground state, those for Be lie at lower energies, making \emph{ab initio} calculations for frequencies near those of the Ti: sapphire laser feasible in the multiphoton regime. These results demonstrate the crucial role of electron correlation effects on HHG processes in this regime.\\[4pt] [1] J.M. Ngoko Djiokap and A.F. Starace, Phys. Rev. A \textbf{84}, 013404 (2011).   

High-order harmonic generation from a coherent superposition of atomic and molecular states

In our previous work [1] we studied numerically pump-probe schemes for monitoring electron motion in molecules and in atoms using a mid-infrared intense few femtosecond probe laser pulse which generate high-order harmonics (HHG) from a coherent superposition of electronic states prepared by a weak femtosecond UV pump pulse from an initial bound state. We showed that contour graphs of HHG signal as function of time delay and harmonic order show striking regularities. In this work, by studying HHG in simpler systems we identify even more clear interference patterns in HHG as function of the pump-probe delay and explain these regularities using an extended three-step model based on quantum trajectories. In particular, by varying the time delay between two pulses one can shift (up or down) the harmonic frequency in a continuous way. We explain this continuous frequency red-shift as a result of interference between a long trajectory originating from the lower state (and returning to the same state) and a short trajectory originating from the upper state (and returning to the lower state). \\[4pt] [1] T. Bredtmann, S. Chelkowski, A.D. Bandrauk, J. Phys. Chem. \textbf{116}, 11398 (2012).   

High harmonic generation with intense infrared few-cycle laser pulses

Further shortening of attosecond pulse duration via high harmonic generation (HHG) can be achieved utilizing few-cycle pulses at wavelengths longer than 800 nm, because the HHG cut-off shifts towards higher photon energies proportional to the square of the laser wavelength [1]. The IR spectral range at 1800 nm is accessed by choosing the narrow band Idler of a white light seeded optical parametric amplifier which enables passive carrier envelope phase (CEP) stabilization. Pulse compression is achieved via the combined action of nonlinear propagation in a hollow-core fiber (HCF) followed by subsequent linear propagation through fused silica (FS) in the anomalous dispersion regime, enabling sub-millijoule sub-two-cycle pulses [2,3]. HHG spectra from Xenon [4] and cyclohexadiene isomers will be presented demonstrating the benefit of using those ultrashort IR pulses for HHG spectroscopy. To amplify those pulses in the millijoule range, we introduce the concept of Fourier-plane Optical Parametric Amplification (FOPA). The key idea for amplification of octave-spanning spectra without loss of spectral width is to amplify the broad spectrum ``slice by slice.'' Opposed to traditional schemes where amplification takes place in time domain, we propose to amplify different spectral parts independently of each other in the spectral domain. The spectral dispersion is carried out according to a 4-f setup which performs an optical Fourier transformation of time domain input pulses into the spectral domain and vice versa. After amplification which takes place in the Fourier plane, the pulses are transformed back into the time domain. As a first demonstration, the FOPA was used to amplify 0.1 mJ sub-two-cycle pulses to 1.4 mJ denoting 14 fold amplification. Driving the process of HHG from Neon and Helium with those pulses have enabled to generate soft X-ray spectra extending beyond the Oxygen K-edge ($\sim$540 eV) denoting a first step towards the generation of isolated attosecond pulses in the water window spectral range.\\[4pt] [1] P. B. Corkum, Phys. Rev. Lett. Vol. 71, 1994 (1993).\\[0pt] [2] B. E. Schmidt et al. Appl. Phys. Lett. Vol. 96, 121109 (2010).\\[0pt] [3] B. E. Schmidt et al. Opt. Express Vol. 19, 6858 (2011).\\[0pt] [4] A. D. Shiner et al. Nat. Phys. Vol. 7, 464 (2011).   

Macroscopic phase matching condition of higher order harmonics generation

We perform a quantitative study to understand the role of phase matching on higher order harmonics generation. Higher order harmonics are mainly generated via the interaction of high intensity ultrashort laser pulses with gas medium. With the advance in high harmonics generation studies, harmonics are now being used as a probe in atomic, molecular studies. Higher order harmonics generation is a macroscopic phenomenon and experiences phase matching conditions. By changing lens position, we change Gouy phase of driving laser and by clipping the driving beam with an iris of adjustable diameter, we change transverse spatial phase. We observed two preferred regions of phase matching as we move the lens position in propagation direction. The harmonic spectrum and yield changes drastically as we move the lens in propagation direction. We have noticed individual harmonics follow different phase matching conditions. Spatial modification of the driving laser changes the phase matching conditions dramatically and preferred regions of phase matching are redistributed. Also the total harmonic yield can be increased by optimizing the spatial clipping of the driving laser.   

Optimizing High Harmonic Generation for Studying Excited State Dynamics

We demonstrate the generation of ultraviolet~(UV) radiation in the range of 10--70~eV via high harmonic generation~(HHG) using high energy~(30~mJ/pulse), high average power~(30~W) drive lasers. The HHG process driven by a high energy, many cycle laser pulse~(27~fs at 780~nm) produces a UV spectrum with $\sim$80~nJ of energy in a single harmonic. Such high photon fluence leads to saturation of single photon transitions and allows us to access non-linear dynamics in atomic and molecular systems, for instance driving two photon transitions using two different harmonic photons. Additionally we have developed experimental apparatus to isolate two different harmonic frequencies and vary the relative time delay between them to perform time-resolved pump/probe spectroscopy of excited state dynamics. Following UV excitation most molecules will undergo radiationless decay through a non-Born-Oppenheimer processes and our pump/probe technique will allow us to follow these complicated dynamics. The femtosecond duration pulses intrinsically produced by HHG allow for the necessary temporal resolution of these dynamics. I will discuss our current progress in optimizing high pulse energy HHG and show our experimental results for studying molecular dynamics using UV pulse pairs.