Bright Coherent Ultrahigh Harmonics in the keV X-Ray Regime from Mid-Infrared Femtosecond Lasers

Abstract: High harmonic generation traditionally combines ~100 near-infrared laser photons, to generate bright, phase matched, extreme ultraviolet beams when the emission from many atoms adds constructively. Here we show that by guiding a mid-infrared femtosecond laser in a high pressure gas, ultrahigh harmonics can be generated up to orders > 5000, that emerge as a bright supercontinuum that spans the entire electromagnetic spectrum from the ultraviolet to > 1.6 keV, allowing in-principle the generation of pulses as short as 2.5 attoseconds. The multi-atmosphere gas pressures required for bright, phase matched emission also supports laser beam self-confinement, further enhancing the x-ray yield. Finally, the x-ray beam exhibits high spatial coherence, even though at high gas density, the recolliding electrons responsible for high harmonic generation encounter other atoms during the emission process.

• The paper demonstrates ultrahigh harmonic generation using 3.9 µm mid-IR lasers to produce coherent x-rays up to 1.6 keV.
• The methodology employs high-pressure gas environments (35–80 atm) to optimize phase matching and enhance spatial coherence.
• The study outlines potential for generating sub-attosecond x-ray pulses, advancing ultrafast spectroscopy and imaging techniques.

Overview of "Bright Coherent Ultrahigh Harmonics in the keV X-ray Regime from Mid-Infrared Femtosecond Lasers"

This paper, authored by Popmintchev et al. and published in Science in 2012, addresses advancements in high harmonic generation (HHG) facilitated by mid-infrared femtosecond lasers. The research details significant progress toward generating ultrahigh harmonics capable of producing coherent x-rays with energies extending up to 1.6 keV. These advances highlight the potential of HHG in observing ultrafast processes at the nanoscale, given its promising applications in spectroscopy and structural dynamics.

Key Contributions

• Ultrahigh Harmonics Generation: By using 3.9 µm wavelength mid-infrared lasers, the study demonstrates the capacity to progress into the keV x-ray regime through HHG, achieving photon energies extending far beyond previous EUV limits of ~150 eV typically attained with 0.8 µm Ti:Sapphire lasers.
• Phase Matching: A pivotal focus is on achieving efficient macroscopic phase matching, which is improved by operating under multi-atmosphere pressures. This condition not only stabilizes phase matching but also facilitates self-confinement of the laser beam, leading to an enhancement in x-ray yields.
• Coherent X-ray Beams: Despite the increased complexity at higher gas densities, which involve the interactions of recolliding electrons with multiple atoms, the resulting x-ray emissions maintain high spatial coherence. This coherence is essential for applications in coherent diffractive imaging.
• Chirp Compensation: Calculations anticipate that compensating for the supercontinuum's chirp could potentially enable the creation of single-cycle x-ray pulses with durations as brief as 2.5 attoseconds, thus emphasizing the precision required for temporal phase control in HHG.

Numerical Insights and Experimental Realizations

• The experimental setup employs an OPCPA laser system generating 10 mJ pulses at the desired wavelength, with the HHG process occurring in a helium-filled waveguide at pressures reaching 80 atm.
• The study showcases the HHG spectrum's remarkable breadth, spanning multiple inner-shell absorption edges and implying broad application potential in element-specific x-ray spectroscopy.
• A critical result is the documentation of x-ray flux scaling with gas pressure, achieving optimal emission at approximately 35 atm and emphasizing the balance of phase matching and reabsorption.

Practical and Theoretical Implications

This work foregrounds practical applications in time-resolved x-ray spectroscopy and coherent diffractive imaging. By advancing HHG sources into the keV range with consistent phase matching, the research paves the way for observing electron dynamics and material transformations at unprecedented resolutions and time scales. Theoretically, the study unifies the understanding of HHG from the UV through the x-ray regimes, refining the model of phase matching by considering complex microscopic and macroscopic interactions.

Future Directions

Enhancing the HHG process for longer interaction lengths and tackling challenges related to dispersion and plasma effects presents a logical trajectory for future investigations. Moreover, extending this technology towards even shorter-wavelength emissions and broader spectral supercontinua could unlock zeptosecond time scales and open new frontiers in ultrafast science.

The potential to exploit low-Z gases such as helium for soft and hard x-ray generation through innovative waveguide and pressure management strategies underscores the horizon for HHG to play a pivotal role in evolving spectroscopic techniques, thereby contributing significantly to fields like materials science, chemistry, and fundamental physics.