Quantum path interference in the wavelength-dependent below-threshold harmonic generation

Abstract

We have theoretically investigated the wavelength-dependent below-threshold harmonic (BTH) generation in different laser intensity regimes. Based on the simulations of the time-dependent Schr\"odinger equation, we find a periodic fluctuation in the wavelength-dependent BTH yields with laser intensities in the magnitude of ${10}^{13}\phantom{\rule{0.28em}{0ex}}\mathrm{W}/{\mathrm{cm}}^{2}$. This result shows significant differences from the resonance peak structures in the recent study with intensities about ${10}^{12}\phantom{\rule{0.28em}{0ex}}\mathrm{W}/{\mathrm{cm}}^{2}$ [Xiong et al., Phys. Rev. Lett. 112, 233001 (2014)]. By performing both the quantum path analysis and time-frequency transform of the harmonic spectra, we demonstrate that the difference in the wavelength-dependent BTH yields is due to the complicated quantum path distributions of BTHs with the intensities in the magnitude of ${10}^{13}\phantom{\rule{0.28em}{0ex}}\mathrm{W}/{\mathrm{cm}}^{2}$. And the periodic fluctuation is further demonstrated to originate from the interference between the two quantum paths that dominate the harmonic generation.