High-order harmonic generation in the presence of a resonance

We investigate high-order harmonic generation from laser-irradiated systems that support a shape resonance. From the numerical solution of the time-dependent Schrodinger equation, we calculate the harmonic spectra and the time-frequency analysis of the harmonic intensity and phase. The analysis reveals the separate contributions of the short and long trajectories as well as the resonance. A range of harmonics is strongly enhanced by the presence of the resonance irrespective of the pulse length. The signature of the resonance remains significant after coherent summation over intensities as a simple method to simulate macroscopic effects. The time-frequency analysis supports the recently proposed four-step mechanism of the enhanced harmonic generation process.