Tomography of high harmonic generation in a
cluster jet
Chih-Hao Pai
Department of Physics, National Taiwan University, Taipei 106, Taiwan Cheng-Cheng Kuo, Ming-Wei Lin, Jyhpyng Wang, and Szu-yuan Chen Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan
Jiunn-Yuan Lin
Department of Physics, National Chung Cheng University, Chia-Yi 621, Taiwan
Received December 9, 2005; accepted December 21, 2005; posted January 4, 2006 (Doc. ID 66558) 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 in-creasing backing pressure as results of changes in the phase-matching condition were observed, which ex-plains the presence of an optimal backing pressure. © 2006 Optical Society of America
OCIS codes: 190.2620, 220.4610, 110.6960.
High-order harmonic generation based on optical-field ionization of atoms is an active optical-field of research since it is a promising approach for the production of coherent short x-ray pulses that has widespread po-tential applications.1The highest-order harmonic re-ported reached a 1 nm wavelength,2and the shortest pulse duration reached the subfemtosecond time scale.3
To extend the practical application of high har-monic generation it is imperative to produce high harmonics with a shorter wavelength and higher en-ergy conversion efficiency. Many methods for achiev-ing this goal have been reported or proposed. Among them the use of an atomic cluster jet is considered to be a promising scheme. High harmonic generation in a cluster jet has been reported by Donnelly et al.4and others.5,6 The observed harmonic cutoff energy for clusters shows an extension with respect to that for monomers. This extension and an associated increase in conversion efficiency were ascribed to the recombi-nation of dissociated electrons with ions that are dif-ferent from the parent ones in a cluster.7–9 Further-more, it was proposed that the characteristic index of refraction of bulk nanoplasma gas can be used to at-tain phase matching of high harmonic generation un-der the condition of a high ionization level,10,11which may lead to a dramatic increase of harmonic order and intensity. To date, all the reported experimental investigations on high harmonic generation from clusters have focused on the dependence of harmonic intensity on the microscopic properties of clusters. The growth of harmonics with laser beam propaga-tion in a bulk cluster jet has not been studied experi-mentally. Such experiments may help us characterize the macroscopic effects, which is important for an un-derstanding of the harmonic generation process and its optimization.
Measurement of the growth curves (Maker’s fringe) of harmonic generation in an atomic gas cell
has been achieved by translating the exit window of the gas cell. The data provided direct characteriza-tion of the effects of absorpcharacteriza-tion and phase matching on the efficiency of high harmonic generation.12 How-ever, the gas-cell technique cannot be used in a clus-ter jet. In this Letclus-ter, we present a tomographic tech-nique for studying high harmonic generation in cluster jets. The technique is based on the pro-gramming of plasma density distribution by laser machining.13 The growth of harmonic energy as a function of the interaction length was resolved by scanning the end of the cluster density distribution in the path of the pump pulse. A downstream shift of the starting position of rapid growth and a decrease of the slope with increasing backing pressure were observed. These effects yield an optimal backing pressure for high harmonic generation in argon clus-ter jets.
A 10 TW, 45 fs, 810 nm, and 10 Hz Ti:sapphire la-ser system based on chirped-pulse amplification (up-graded from the system reported in Ref. 14) was used in this experiment. The linearly polarized laser beam was split in two. One beam 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 duration of the 8 mJ pump pulse was set at 180 fs with positive chirp for maximum harmonic production, while the dura-tion of the 30 mJ machining beam was set at 45 fs for maximum intensity. The setup is shown in Fig. 1. The 8 mm diameter pump pulse was focused by an f / 38 off-axis parabolic mirror onto the center of a cluster jet. The focal spot size of the pump beam was 30m full width at half-maximum (FWHM) with 90% energy enclosed in a Gaussian-fit profile, corre-sponding to a peak intensity of 2.4⫻1015W / cm2.
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 984 OPTICS LETTERS / Vol. 31, No. 7 / April 1, 2006
by a spherical lens of 20 cm focal length with a de-magnification factor of 3. In the meantime it was fo-cused in the vertical direction to a width of 20m in FWHM by this spherical lens in combination with a cylindrical concave lens of 75 cm focal length. This line focus overlapped the propagation path of the pump pulse inside the cluster jet, and the intensity of the machining beam within the overlapped region ex-ceeded the threshold of optical-field ionization. The knife edge, which had a variable transverse position, was used to adjust the region irradiated by the ma-chining beam. The argon cluster jet was produced by using a slit nozzle on a pulsed valve,15and its density profile is a 3.5 mm flat-top region with 750m slopes at both edges. The average atom density increased linearly with increasing backing pressure and reached 2.5⫻1019cm−3 at 3⫻106Pa (400 psi),
corre-sponding to a cluster size of 2.7⫻106atoms and a
cluster radius of 28 nm. In the region that was not blocked by the knife, the machining beam ionized and heated the clusters. After 6 ns the region that was ionized by the machining beam was evacuated as a result of hydrodynamic expansion. By scanning the knife-edge position the end of the interaction region was varied. In this way the growth of harmonic in-tensity with pump-pulse propagation in the cluster jet was resolved tomographically. Note that such a measurement cannot be accomplished by using a set of gas jet nozzles of various lengths, because the atom density, the cluster size, and the jet profile all change with different nozzles. In that case it will be difficult to vary the interaction length while keeping other pa-rameters fixed.
A flat-field spectrometer consisting of an aperiodic grazing-incident cylindrical grating and a 16-bit x-ray CCD camera was used to measure the x-ray emission spectrum and the divergence angle in the direction of pump-pulse propagation. The spectral range was 17–37 nm. Aluminum filters were used to block transmitted laser pulses and attenuate x-ray emission. By calibrating the grating reflectivity, the filter transmittance, and the CCD response, we ob-tained the absolute emission yield. The conversion ef-ficiency of the harmonics was 1.5⫻10−7 for the 27th
harmonic at 3⫻105Pa (40 psi) backing pressure.
Figure 2 shows the total energy in each harmonic 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 that increases with increasing harmonic order, simi-lar to what was observed in an experiment using
monomer gas in a hollow fiber.16The optimal backing pressure may be a result of the phase-matching con-dition or the trade-off between increased gain and in-creased reabsorption with increasing average atom density.
To determine the main cause for the decrease of harmonic energy at high backing pressures, we used the tomographic technique described above to mea-sure the energy of the 25th harmonic as a function of position in the cluster jet at 1.5⫻106Pa (200 psi) and
3⫻106Pa (400 psi) backing pressures. The results
are shown in Fig. 3. By Rayleigh scattering and in-terferometry, the cluster radii for these backing pres-sures were measured to be 19 and 28 nm, respectively.17 In the figure, the cluster distribution extends from 0 to 5 mm. Along the beam propagation direction the spatial resolution of the tomographic measurement was better than 20m, as shown by the sharpness of side-scattering images in Ref. 13. As shown in the figure, for higher backing pressure sig-nificant growth starts at a later position and the slope is smaller. Such a dependence of growth rate on backing pressure leads to a drop-off of overall har-monic production for high backing pressures and thus to the appearance of an optimal backing pres-Fig. 1. Setup of the machining beam and the pump beam.
OAP, off-axis parabolic mirror.
Fig. 2. Energy of the harmonics as a function of cluster-jet backing pressure for various harmonic orders. The peaks are normalized to the same height for viewing convenience.
Fig. 3. Energy of the 25th harmonic as a function of posi-tion for cluster-jet backing pressures of 200 and 400 psi. The curve for 400 psi is multiplied by 2 for viewing convenience.
sure. 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 1.5⫻106 and 3⫻106Pa. The latter case is shown
in Fig. 4. This indicates that the variations of the po-sitions of fast growth and saturation with respect to backing pressure are not due to larger x-ray reab-sorption at higher backing pressure, because the strong dependence of the 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 con-dition, which may change significantly for different backing pressures as a result of varying cluster size. At a backing pressure of 3⫻105Pa (40 psi), which
is optimal for the production of the 27th and the 29th harmonics, the growth of harmonic energy as a func-tion of the interacfunc-tion length shows various oscilla-tory growth behaviors for different harmonic orders. However, at such a low pressure the hydrodynamic expansion of the plasma produced by the machining beam did not evacuate a gas region that was verti-cally wide enough to cover completely the region of high harmonic generation. As a result, even with the knife edge at zero position the harmonic energy was not zero. This was different from the cases of 1.5 ⫻106 and 3⫻106Pa. Therefore a vertically wider
line focus with sufficient intensity is required for re-liable extension of this tomographic technique to the low-density cases. Currently the maximum energy used for the machining pulse is limited by self-focusing and filamentation in the BK7 line-self-focusing optics and the vacuum window. These limitations can be greatly relieved if low-n2 optics made from CaF2
are used.
In summary, by using a tomographic technique based on laser machining we have shown that the
growth of high harmonics in a cluster jet as a func-tion of the interacfunc-tion length can be experimentally resolved. The measurements help to identify the dominant factor that limits the growth of high har-monics. The technique demonstrated in this Letter can thus provide the information required for design-ing various schemes for phase-matchdesign-ing and quasi-phase-matching of high-order harmonic generation in a cluster jet.
This work was partly supported by National Sci-ence Council of Taiwan grant NSC 94-2112-M-001-010. S.-Y. Chen’s e-mail address is sychen @ltl.iams.sinica.edu.tw.
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Fig. 4. Energy of the harmonics as a function of position at a cluster-jet backing pressure of 400 psi for various har-monic orders.
