Perturbative High Harmonic Wave Front Control

We pattern the wave front of a high harmonic beam by intersecting the intense driving laser pulse that generates the high harmonic with a weak control pulse. To illustrate the potential of wave-front control, we imprint a Fresnel zone plate pattern on a harmonic beam, causing the harmonics to focus and defocus. The quality of the focus that we achieve is measured using the spectral wave-front optical reconstruction by diffraction method. We will show that it is possible to enhance the peak intensity by orders of magnitude without a physical optical element in the path of the extreme ultraviolet (XUV) beam. Through perturbative wave-front control, XUV beams can be created with a flexibility approaching what technology allows for visible and infrared light.

Figure 1

Schematic diagram of experimental setup. The inset shows details in the nonlinear gas medium. In the case illustrated in the figure (converging perturbing field with $R<0$), high harmonics are generated in the red circle area, covering the bottom part of the multiring zone plate pattern which is constructed by interference between the loosely focused 800 nm driving and tightly focused 400 nm perturbing beams. The $m=1$ components of harmonics converge to the zone plate real foci, and the $m=-1$ components diverge from virtual foci. The SWORD (spectral wave-front optical reconstruction by diffraction) slit is used for measuring the one-dimensional ($y$) lineout of the XUV wave front [16].

Figure 2

Far field divergence measurement of high harmonic spectra including the $m=\pm 1$ components and the undeflected ($m=0$) harmonic beam when (a) $R=-2.3\mathrm{mm}$, and (b) $R=2.2\mathrm{mm}$. The nonlinear gas medium is placed 5 mm before the driving laser focus.

Figure 3

SWORD measurement of the $m=\pm 1$ components of H22 radiation. (a) Measured intensity (solid line) and phase (dashed line) distribution along $y$ or vertical direction of the $m=1$ (right) and $m=-1$ (left) components of H22 radiation at the SWORD slit ($z=0$). The perturbing wave-front radius of curvature is $R=-2.8\mathrm{mm}$. (b) Intensity $y$ distribution of XUV field at $z$ positions before the SWORD slit, reconstructed from XUV field at the slit in (a) through backpropagation. The nonlinear gas medium is placed 10 mm before the driving laser focus. The arrow shows the propagation direction of laser and harmonic beams.

Figure 4

Simulation of H22 zone plate foci and comparison with experiments. (a) Experimental (circle) and simulation (solid lines) results of real focal length. (b) Experimental (circle) and simulation (solid lines) results of real focal spot size. Both (a) and (b) are plotted as a function of the radius of curvature of the control beam wave front, $R$. (c) The intensity spatial profiles of focused H22 beams generated by narrow driving beam (blue line, $1/e^2$ size $w=80\mu \mathrm{m}$) and wide driving beam (red line, $1/e^2$ size $w=250\mu \mathrm{m}$) with the medium placed 10 mm before the driving beam focus. The driving beam intensities and other parameters for these two cases are the same (except the beam size), and the perturbing wave-front curvature is $R=-2\mathrm{mm}$. The narrow driving beam ($w=80\mu \mathrm{m}$) induced H22 intensity is artificially multiplied by 100 times for comparison with the wide driving beam case ($w=250\mu \mathrm{m}$).