Quantum Path Interference in the Wavelength Dependence of High-Harmonic Generation

We investigate the dependence of the intensity of radiation due to high-harmonic generation as a function of the wavelength $\lambda$ of the fundamental driver field. Superimposed on a smooth power-law dependence observed previously, we find surprisingly strong and rapid fluctuations on a fine $\lambda$ scale. We identify the origin of these fluctuations in terms of quantum path interferences with up to five returning orbits significantly contributing.

Figure 1

Integrated harmonic yield $\Delta I$ between 20 and 50 eV as a function of $\lambda$ calculated on a coarse mesh with $\Delta \lambda =50\mathrm{nm}$. (●) Peaceman-Rachford (PR) method, (□) pseudospectral (PS) method. (Solid line) fit $\Delta I\propto {\lambda }^{-x}$: (a) hydrogen, (b) argon.

Figure 2

Fluctuations of the harmonic yield $\Delta I$ as a function of the fundamental wavelength $\lambda$ and the photon energy $E$ for hydrogen. An oscillatory behavior of the yield as a function of $\lambda$ emerges after integrating over vertical strips [upper panel and Fig. 3a].

Figure 3

Variations in the integrated harmonic yield (20–50 eV) in a narrow range of $\lambda$. (a) Comparison between the TDSE solution with the SFA including 5 quantum paths for hydrogen. (b) Build up of the interference pattern with increasing number of quantum trajectories within the SFA. Thin dashed line: 1 (short) trajectory, thin dotted line: 2 (short and long) trajectories, bold dashed line (dotted line): inclusion of the shortest 5 (10) trajectories. (c) as (a) but for argon.

Figure 4

Variation of the modulation period $\delta \lambda$ with the fundamental wavelength $\lambda$ for hydrogen. (▪) TDSE, (▴) SFA. (Solid line) ${\lambda }^{-2}$ scaling [see Eq. (6)].