Phase Matching of High-Order Harmonics in Hollow Waveguides

Abstract: We investigate the case of phase-matched high-harmonic generation in a gas-filled capillary waveguide, comparing in detail theory with experiment. We observe three different regimes of phase matching: one where atomic dispersion balances waveguide dispersion, another corresponding to non-collinear Cerenkov phase-matching, and a third where atomic dispersion and plasma dispersion balance. The role of atomic dispersion is demonstrated by studying the dependence of the harmonic signal for several gases. We also predict and provide preliminary evidence of a regime where phase-matching occurs only at specific fractional ionization levels, leading to an output signal that is sensitive to the absolute phase of the carrier wave.

• The paper investigates and optimizes phase matching for high-harmonic generation in gas-filled capillary waveguides using theoretical models and experiments.
• The research identifies and characterizes three distinct phase matching regimes within hollow waveguides based on balancing atomic, waveguide, and plasma dispersion.
• Experimental results confirm that precise gas parameter control is crucial for optimal phase matching, with implications for developing ultrafast light sources.

Phase Matching of High-Order Harmonics in Hollow Waveguides

This paper elaborates upon the study of phase-matched high-harmonic generation (HHG) within gas-filled capillary waveguides. The investigation explores several distinct regimes of phase matching, backed by both theoretical models and experimental results. The key objective is to understand and optimize the phase matching for enhancing the conversion efficiency from fundamental laser light to high-order harmonics.

Overview of High-Harmonic Generation

High-harmonic generation arises when intense laser interactions with atoms lead to the emission of coherent harmonics extending into the soft-x-ray region. This paper positions HHG at the intersection of classical and quantum physics, noting its potential for creating sub-femtosecond-duration pulses. Essential to maximization of conversion efficiency in HHG is the careful design of atomic interactions and macroscopic propagation dynamics, particularly the control of phase matching over extended interaction lengths.

Phase Matching Regimes in Capillary Waveguides

The authors identify three primary regimes for phase matching within capillary waveguides:

1. Atomic and Waveguide Dispersion Balance: This regime emerges when atomic dispersion counteracts waveguide dispersion. Primarily observed at lower ionization levels, the authors demonstrate that achieving phase matching in this context is feasible by modulating the gas pressure within the waveguide.
2. Atomic and Plasma Dispersion Balance: At higher intensities, plasma dispersion becomes significant, leading to a regime where phase matching occurs only at specified ionization levels. This balance is sensitive to carrier wave phase, presenting new dynamics in optimization that were previously unexplored.
3. Non-collinear Cerenkov Phase Matching: In this regime, the phase mismatch is compensated by non-collinear emission angles, reminiscent of Cerenkov radiation. This results in angular divergence in the harmonic emission, observed when phase matching occurs without a direct pathway via the capillary axis.

Experimental Results and Models

The research highlights experimental results by using Ti:sapphire amplifier laser pulses focused within hollow capillaries filled with various gaseous media. A significant finding is the correlation between gas species' atomic dispersion and the optimum pressure required for effective phase matching. This is intricately modeled to understand the underlying dynamics driven by ionization levels and beam intensity.

Simulation results depict the necessity for precise control over parameters such as gas density and pressure to achieve desired phase matching, reinforced by experimental observations of phase matching pressure peaks. The work reveals that the strong absorption in the high-energy harmonic regime can be mitigated by selecting specific media and pressure regimes.

Implications and Speculations

The findings present implications for the development of novel ultrafast light sources and HHG-based applications. By finely tuning the interaction parameters, researchers can optimize harmonic orders and energy ranges, enhancing the applicability of HHG in spectroscopy, imaging, and quantum dynamics. The paper suggests that carrier-phase sensitivity in phase matching could be exploited to generate highly controlled, attosecond pulses, offering new prospects for temporal precision.

Conclusion

In summary, this paper comprehensively explores the sophisticated dynamics of phase matching in HHG within hollow waveguides. It expands on the theoretical and experimental understanding of how dispersion interactions contribute to harmonic generation and conversion efficiency. By tailoring the conditions within capillary waveguides, new frontiers in the control and application of HHG are opened, making it a significant contribution to both fundamental research and practical advancements in ultrafast optics.