Tomography of high harmonic generation in a cluster jet.
ABSTRACT Tomographic measurement of high harmonic generation in a cluster jet was demonstrated by programming the cluster density distribution with a laser machining technique. The growth of harmonic energy with the propagation of the pump pulse was resolved by scanning the end of the argon cluster distribution in the path of the pump pulse. A downstream shift of the position of rapid growth and a decrease of the slope with increasing backing pressure as results of changes in the phase-matching condition were observed, which explains the presence of an optimal backing pressure.
Tomography of High Harmonic Generation in a Cluster Jet
Department of Physics, National Taiwan University, Taipei, Taiwan
Cheng-Cheng Kuo, Ming-Wei Lin, Jyhpyng Wang, and Szu-yuan Chen
Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei, Taiwan
Department of Physics, National Chung Cheng University, Chia-Yi, Taiwan
Abstract: Tomography of high harmonic generation in a cluster jet was achieved by using laser
machining. The growth curves help explain the optimal backing pressure, which is ascribed to the
change in phase matching condition.
©2006 Optical Society of America
OCIS codes: (190.2620) Frequency conversion; (220.4610) Optical fabrication; (110.6960) Tomography
To extend the practical application of high harmonic generation it is imperative to produce high harmonics with
shorter wavelength and higher energy conversion efficiency. Many methods for achieving this goal has been
reported or proposed. Among them the use of atomic cluster jet is considered to be a promising scheme. High
harmonic generation in a cluster jet has been reported by Donnelly et al. [1-2], in which an extension of the
harmonic cutoff energy and associated increase in conversion efficiency with respect to that for monomers were
observed. Furthermore, it was proposed that the unique index of refraction of bulk nanoplasma gas can be used to
attain phase matching of high harmonic generation in the condition of high ionization level, which may lead to
dramatic increase of harmonic order and intensity [3,4]. To date, all the reported experimental investigations on high
harmonic generation from clusters focused on the dependence of harmonic intensity on the microscopic properties of
clusters. The growth of harmonics with laser beam propagation in a bulk cluster jet has not been studied
experimentally. Such experiments may help us characterize the macroscopic effects, which is important for the
understanding of the harmonic generation process and its optimization.
Fig. 1. Experimental setup. (OAP: off-axis parabolic mirror.)
A 10-TW, 45-fs, 810-nm, and 10-Hz Ti:sapphire laser system based on chirped-pulse amplification (upgraded
from the system shown in Ref. 5) was used in this experiment. The linearly-polarized laser beam was split into two.
One served as the pump pulse for driving high-order harmonic generation, and the other, set to be 6 ns earlier than
the pump pulse, was used as the machining pulse. The pulse duration of the pump pulse was set at 180 fs with
positive chirp for maximum harmonic intensity, while that of the machining pulse was set at 45 fs for highest
intensity. The 8-mJ pump pulse was focused by an f/38 off-axis parabolic mirror to a focal spot of 30 μm in FWHM
(full width at half maximum) onto the center of a cluster jet. Propagating perpendicularly to the pump pulse, the 4-
cm-diameter machining pulse was imaged from the location of the knife edge onto the interaction region by a
spherical lens of 20-cm focal length with a demagnification factor of 3. In the meantime it was focused in the
vertical direction to a width of 20 μm in FWHM by this spherical lens in combination with a cylindrical concave
lens of 75-cm focal length. This line focus overlapped with the propagation path of the pump pulse inside the cluster
jet and its intensity within this region exceeded the threshold of optical-field ionization. The setup is shown in Fig. 1.
The argon cluster slit-jet has a density profile of a 3.5-mm flattop region with 750-μm slopes at both edges. The
average atom density increased linearly with increasing backing pressure and reached 2.5×1019 cm-3 at 3×106 Pa
(400 psi) backing pressure, corresponding to a cluster size of 2.7×106 atoms and a cluster radius of 28 nm. Based on
the laser machining technique as that in Ref. 6, by scanning the knife-edge position the end of the region in which
the pump pulse interacts with argon clusters was varied and the growth of harmonic intensity with pump-pulse
propagation in the cluster jet was resolved. A flat-field spectrometer was used to measure the x-ray emission
spectrum in the direction of pump-pulse propagation. The conversion efficiency of the harmonics was 1.5×10-7 for
the 27th harmonic at 40-psi backing pressure.
Figure 2 shows the total energy in harmonics as a function of cluster-jet backing pressure. It was found that there
is an optimal cluster-jet backing pressure for maximizing the energy of harmonics and it increases with increasing
harmonic order. To reveal the main cause for the decrease of harmonic energy at high backing pressures, we used
the tomography technique to measure the energy of harmonics as a function of position in the cluster jet for 40-psi,
200-psi, and 400-psi backing pressures. The results for the 25th harmonic are shown in the inset of Fig. 2. In the
figure, the cluster distribution extends between 0−5 mm. As shown, for higher backing pressure significant growth
of the 25th harmonic starts at a later position and the slope is smaller. It is such a dependence of growth position and
slope on backing pressure that leads to the decrease of harmonic energy at the exit of the cluster jet for higher
backing pressure and thus the presence of an optimal backing pressure. In addition, it was also observed that from
the 23rd to the 33rd harmonics the regions of fast growth overlap to within 0.4 mm at both backing pressures of 200
psi and 400 psi. This indicates that the variation of the positions of fast growth and saturation with respect to
backing pressure is not due to larger x-ray reabsorption at higher backing pressure, because the strong dependence
of reabsorption coefficient on harmonic order in this region would make the result sensitive to harmonic order.
Therefore, the dominant effect for the observed growth curves and the optimal backing pressure should be the
phase-matching condition which may change significantly for different backing pressures as a result of varying
Fig. 2. Energy of harmonics as a function of cluster-jet backing pressure for various harmonic orders. Inset shows
the energy of the 25th harmonic as a function of position for cluster-jet backing pressures of 40 psi, 200 psi, and
At 40-psi backing pressure the growth curve of harmonics starts at a nonzero energy at zero position. This is
because that at low backing pressure (40 psi) the hydrodynamic expansion of the plasma produced by the machining
beam did not produce an evacuated channel vertically wide enough to cover the entire region of high harmonic
generation driven by the pump pulse. A wider line focus with sufficient intensity should be able to extend the
reliability of this tomography technique to low density cases.
 T. D. Donnelly et al., Phys. Rev. Lett. 76, 2472 (1996).
 J. W. G. Tisch et al., J. Phys. B 30, L709 (1997).
 T. Tajima et al., Phys. Plasma 6, 3759 (1999).
 J. W. G. Tisch et al., Phys. Rev. A 62, 041802(R) (2000).
 H.-H. Chu et al., Appl. Phys. B 79, 193 (2004).
 C.-H. Pai et al., Phys. Plasma 12, 070707 (2005).