Phase-Matching of High-Order Harmonics Driven by Mid- Infrared Light

Abstract: We demonstrate that phase-matched frequency upconversion of ultrafast laser light can be extended to shorter wavelengths by using longer driving laser wavelengths. Experimentally, we show that the phase-matching cutoff for harmonic generation in argon increases from 45 to 100 eV when the driving laser wavelength is increased from 0.8 to 1.3 micrometers. Phase matching is also obtained at higher pressures using a longer-wavelength driving laser, mitigating the unfavorable scaling of the single-atom response. Theoretical calculations suggest that phase-matched high harmonic frequency upconversion driven by mid-infrared pulses could be extended to extremely high photon energies.

Phase-Matching of High-Order Harmonics Driven by Mid-Infrared Light

This paper investigates the extension of high-order harmonic generation (HHG) to shorter wavelengths through the utilization of mid-infrared laser driving pulses. The authors demonstrate both experimentally and theoretically that phase-matched frequency upconversion can be achieved at significantly higher photon energies by employing longer driving wavelengths, specifically transitioning from the conventional 0.8 µm to 1.3 µm. This research presents noteworthy findings for the enhancement of coherent light sources, particularly in the extreme ultraviolet (XUV) and soft x-ray spectral regions.

Key Findings and Numerical Results

The authors perform experiments using argon as the nonlinear medium and effectively extend the phase-matching cutoff from 45 eV, achievable with a 0.8 µm laser, to 100 eV utilizing a 1.3 µm laser. The results demonstrate higher HHG efficiency at elevated pressures. This effectively mitigates the adverse scaling of single-atom yield reduction associated with longer wavelengths, which is characterized by a scaling factor of approximately $\lambda^{-5.5}$. They also report HHG emission up to 200 eV, marking the highest photon energy produced using a 1.3 µm driving laser.

Theoretical and Practical Implications

The paper elucidates the phase matching mechanism within a hollow waveguide structure, highlighting optimal conditions where neutral atom dispersion counterbalances free electron plasma dispersion. The authors establish that optimal phase-matching conditions, achieved by fine-tuning gas pressure, lead to efficient harmonic generation up to the critical ionization level.

The practical implications of this work are profound, offering a path toward producing bright coherent x-rays suitable for biological imaging and materials science at photon energies approaching 1 keV. Importantly, this research suggests that using longer wavelengths for HHG could be a viable method for generating highly efficient x-rays without resorting to quasi-phase-matching strategies that are inherently less efficient than true phase-matching.

Future Directions

The advancements detailed in this study open avenues for further research in optimizing phase-matching conditions using various gases and exploring other mid-IR wavelengths to reach the predicted photon energy of ~1 keV. These efforts are critical as the scientific community continues to push the boundaries of coherent x-ray applications and attosecond pulse generation. The insights gained from such exploration could lead to significant enhancements in spectroscopic techniques, high-resolution imaging, and investigation of ultrafast dynamics in matter.

In conclusion, the paper makes a significant contribution to understanding and improving HHG with mid-infrared pulses, offering insights that will aid in the advancement of extreme ultraviolet science and technology. These findings provide a solid foundation for further experimental and theoretical inquiries into efficient upconversion mechanisms for high photon energies.