Comprehensive analysis of phase matching in high-order harmonic generation of mixed gases

High-order harmonic generation (HHG) in gas mixtures has been explored as a strategy to enhance spectral output by combining the favorable properties of different noble gases. However, experimental results often show reduced efficiency compared to optimized pure gases. In this work, we present a comprehensive analysis of HHG in various noble gas mixtures using both experimental data and a one-dimensional theoretical model based on phase matching. We demonstrate that reduced harmonic yields in mixed gases are primarily due to suboptimal phase matching conditions and atomic dipole phase differences, which suppress coherent buildup through destructive interference. Even in the absence of significant dipole phase differences, phase mismatching and absorption effect further limit efficiency. Our study provides a unified framework incorporating single-atom response, phase mismatch, and absorption effects to explain and predict HHG behavior in mixed gases. These insights clarify the limitations of gas mixing and offer guidance for optimizing HHG sources in complex gaseous environments.