Quantum path contribution to high-order harmonic spectra

Ultrashort pulses of uv and soft x-ray radiation with durations ranging from femtoseconds to attoseconds can be produced as high-order harmonics of the fundamental frequency of a laser beam focused into gas. Applications to fields such as spectroscopy and attosecond metrology require the control and characterization of spectral and spatial properties of the emitted radiation. These are determined by both single atom and macroscopic response of the interaction medium to the laser field. Here we present evidence that microscopic effects have a larger influence than previously thought, and can induce a splitting and a frequency shift of the harmonic lines. These results not only offer a direct diagnostic for high-order harmonic generation, but also enable us to better tune the parameters of the produced radiation, while giving a deeper insight into the fundamental physics underlying this nonlinear optical process.

Figure 1

(Color) Spectra produced with a laser energy of $5\mathrm{mJ}$, corresponding to an intensity at the focus of about $1.5\times {10}^{15}\mathrm{W}∕{\mathrm{cm}}^2$. Harmonics with orders between the 21st and the 31st are shown, with the gas jet (a) about $3\mathrm{mm}$ after the laser focus jet, (b) at the laser focus, and (c) $5\mathrm{mm}$ before the laser focus. All plots show normalized spectra.

Figure 2

(Color) Cross sections taken at (a) $0\mathrm{mrad}$ and (b) $-3.3\mathrm{mrad}$ of the measured spectra shown in Fig. 1. All the curves have been normalized to 1.

Figure 3

(Color) Harmonic spectra versus laser intensity for argon interacting with a hyperbolic secant pulse with a duration of $60\mathrm{fs}$ and a wavelength of $800\mathrm{nm}$.

Figure 4

(Color) Quantum path distribution versus frequency for harmonics generated in argon by a hyperbolic secant pulse with a duration of $60\mathrm{fs}$ for $I_m=3\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$. (a) Cutoff region, (b) plateau region.

Figure 5

(Color) Fourier Hankel transform for harmonics generated in argon by a hyperbolic secant pulse with a duration of $60\mathrm{fs}$ for $I_m=3\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$.