Coherent control of high-harmonic generation using waveform-synthesized chirped laser fields

We show that waveform-synthesized chirped laser fields are efficient tools for coherent harmonic control. A single harmonic order, or two harmonic orders, can be selectively enhanced by using a two-color field allowing a moderate linear chirp for each color. Different harmonic orders within a wide spectral range can be selectively enhanced by adjusting the laser parameters. Our theory bridges two current harmonic control techniques, namely, single-color phase shaping and multicolor amplitude synthesis, and opens the door to new harmonic control possibilities.

Figure 1

Harmonic spectra selectively enhancing H20 (left), H26 (center), and H47 (right). The inset of each panel zooms in the target harmonic with its nearest neighbors. A two-color field ($800\text{nm}+267$ nm) has been used. The three spectra are obtained using the same intensity but different relative phases and chirp rates.

Figure 2

Harmonic spectra selectively enhancing H20 (left), H40 (center), and H47 (right) using 400 nm as the second color. The inset of each panel zooms in the target harmonic with its nearest neighbors. The three spectra are obtained using the same intensities but different relative phases and chirp rates.

Figure 3

Left: The solid blue curve shows the center part of the laser electric field that generates the harmonic spectrum shown in the right panel of Fig. 1 and the dashed red curve shows the corresponding field without chirp for the purpose of comparison. Right: The harmonic spectra generated from these two laser fields. The inset zooms in the target harmonic order selected to be enhanced. An enhancement of 30 times has been obtained for H47.

Figure 4

(a),(b) Wavelet analysis for H47: time profile (blue) and the corresponding dipole phases at the peaks (red circles) for the chirp-optimized laser field (a) and for the chirp-free laser field (b). (c),(d) Contributions from different half cycles to H47: for the chirp-optimized laser field (c) and for the chirp-free laser field (d). Each circle corresponds to a half-cycle contribution. A total number of 50 half cycles are included, although most of them have small amplitudes and cannot be visually distinguished from the center of the polar plots. (e),(g) Wavelet analysis and half-cycle analysis for H49. (f),(h) Wavelet analysis and half-cycle analysis for H51. All polar plots use the same radial scale.

Figure 5

Selective enhancement of two harmonic orders of interest. Left: Selective enhancement of H19 and H21. Right: Selective enhancement of H22 and H26. Inset of each panel zooms in a small spectral region around the target harmonic orders.

Figure 6

Intensity-averaged harmonic spectra that selectively enhance (left) H14 with a fundamental intensity of $1.2\times {10}^{14}$ ${\mathrm{W}/\mathrm{cm}}^2$, and (right) H18 with a fundamental intensity of $2.5\times {10}^{14}$ ${\mathrm{W}/\mathrm{cm}}^2$. Insets zoom in the target harmonics.