Pressure optimization of high harmonic generation in a differentially pumped Ar orH2 gas jetM. Sayrac, A. A. Kolomenskii, S. Anumula, Y. Boran, N. A. Hart, N. Kaya, J. Strohaber, and H. A. Schuessler Citation: Review of Scientific Instruments 86, 043108 (2015); doi: 10.1063/1.4917302 View online: http://dx.doi.org/10.1063/1.4917302 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/86/4?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Diagnostics of composition and size of clusters formed in supersonic jets of Ar–Kr gas mixtures Low Temp. Phys. 41, 637 (2015); 10.1063/1.4928921 Influence of Nitrogen Gas Flow Rate on the Electrical Behavior of an Atmospheric Pressure Dielectric BarrierJet Discharge AIP Conf. Proc. 1328, 324 (2011); 10.1063/1.3573766 Characterization of neutral density profile in a wide range of pressure of cylindrical pulsed gas jets Rev. Sci. Instrum. 71, 2329 (2000); 10.1063/1.1150619 Enhancement of soft x-ray emission from a cryogenically cooled Ar gas jet irradiated by 25 fs laser pulse Appl. Phys. Lett. 76, 1819 (2000); 10.1063/1.126176 Rotationally inelastic scattering of jet cooled H 2 O with Ar: State-to-state cross sections and rotationalalignment effects J. Chem. Phys. 110, 8543 (1999); 10.1063/1.478762

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REVIEW OF SCIENTIFIC INSTRUMENTS 86, 043108 (2015)

Pressure optimization of high harmonic generation in a differentiallypumped Ar or H2 gas jet

M. Sayrac,1,a) A. A. Kolomenskii,1 S. Anumula,1 Y. Boran,1 N. A. Hart,1 N. Kaya,1J. Strohaber,2 and H. A. Schuessler11Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843-4242, USA2Department of Physics, Florida A&M University, Tallahassee, Florida 32307, USA

(Received 19 February 2015; accepted 30 March 2015; published online 13 April 2015)

We experimentally studied the dependence of high harmonic generation in argon and molecularhydrogen on pressure changes in a gas jet that cause variations of the phase matching conditionsand absorption. The study was performed at a peak laser intensity of ∼1.5 × 1014 W/cm2. To enablemeasurements over a wide range of pressures, we employed differential pumping with an additionalcell (∼20 cm3 volume) enclosing the gas jet. By increasing the pressure in the gas jet up to a maximumof 1.5 bars with argon or 0.5 bars with hydrogen, we observed an increase in the high harmonic(HH) yield until an optimum pressure of 0.2 bars was reached for Ar, beyond which the output begandecreasing. For H2, we observed an increase of the HH output up to the maximum pressure of 0.5 bars.This pressure-dependence study allowed us to achieve a tenfold enhancement in the high harmonicyield at the optimum pressure. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4917302]

I. INTRODUCTION

The approach to generate extreme ultraviolet (XUV)radiation and attosecond pulses based on high harmonicgeneration (HHG) in gases with short laser pulses has createdmuch interest in the scientific community.1 With this approach,it is possible to produce attosecond bursts of intense coherentradiation in the extreme ultraviolet and the soft x-ray rangeswith a table top laser system2 as opposed to an x-ray free-electron laser that requires much larger installations andexpenditures. HHG leads to high spatial coherence XUVsources3,4 that open up several new avenues, such as studies insolid state physics,5,6 atomic7 and molecular8,9 spectroscopy,and biological and nano-imaging.10–12

The HHG process can be described by a semi-classicalthree-step model,13,14 which was verified by a strong fieldquantum mechanical treatment.15 Efficient harmonic genera-tion requires a linearly polarized laser field with sufficientlyhigh intensity to ionize the target at which point the freedelectrons can accelerate in the laser field. The recombinationof these field-accelerated electrons with the parent ioniccore can produce photons with much higher energies thanthat of the fundamental radiation. The collective behaviorof these microscopic photonic responses of the atomic ormolecular species in the interaction region, taking into accounttheir interference and propagation, results in a macroscopicsource of coherent XUV radiation.13 The XUV bursts takeplace each half optical cycle and result in a series ofhigh harmonics (HHs) of odd orders when the medium isstatistically symmetric in the polarization plane of the laserfield. The maximum photon energy (cutoff energy) of theHHs spectrum is determined by the ionization potential of

a)muhammedsayrac@physics.tamu.edu.

the target and the ponderomotive energy, which is the kineticenergy gained by the free electrons in the laser electric field,and is given as Emax = Ip + 3.17Up; here, Ip is the ionizationpotential of the target and Up is the ponderomotive energy,Up (eV) = 9.33 × 10−20 × I × λ2, where I(W/cm2) is the laserintensity and λ (nm) is the fundamental wavelength.14

Various experiments have been carried out using differentlaser intensities, pulse durations, wavelengths, and gas media,and their results were shown to be in qualitative agreementwith the above cutoff law.16–18 On the other hand, experi-mentally obtained cutoff energies can deviate from calculatedvalues due to such factors as the geometrical phase (Gouyphase), and the divergence of the laser beam together withoptical imperfections, which cause a lower laser intensity anda lower HH yield than is expected in the medium.18–20

The importance of focusing conditions for the output ofHHs has been investigated previously by other groups.16,21

Since the XUV output inherently has a quadratic dependenceon the atomic density,3,17,22 as is expected for a coherentprocess, an increase in the atomic density of the gas mediumseems to be a straightforward way to increase the HH output.23

However, enabling this seemingly simple approach dependson several factors such as gas dispersion and absorption, whichmodify the phase matching conditions and limit the quadraticdependence24 of the harmonic signal.

In this paper, we aim at increasing the HH output byoptimizing the pressure of Ar or H2 in a gas jet. Severalexperiments have been performed to improve conversionefficiency by optimizing gas pressure in the interactionregion for different experimental configurations, and theresults clearly depend on the generation geometry of themedium.25–28 We confined our study to one particular geom-etry, where the gas jet is enclosed in a differentially pumpedcell to enable measurements over a wide range of pressurevalues.

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II. EXPERIMENTAL SETUP

We used a Ti:Sapphire laser system that produces pulsesof up to 1 mJ in energy, 50 fs in duration, and at a repetition rateof 1 kHz, which were spectrally centered around a wavelengthof 800 nm. Harmonics were generated in a gas jet producedby burning holes with the laser beam in a squeezed nickel(Ni) tube (0.8 mm outer and 0.6 mm inner size), whichcarried the gas. The laser beam was focused by a 40 cmfocal length lens yielding an estimated peak intensity at thefocus of 1.5 × 1014 W/cm2. The gas jet (GJ) was enclosed,as is shown in Fig. 1, in a cell having a volume of about20 cm3 with the main portion of the ejected gas removed by aseparate roughing pump (Oerlikon, Scroll 15), which enabledworking at relatively high pressures in the interaction region(R2). The input hole (IH) and the output hole (OH) of the

FIG. 1. Schematic of the experimental arrangement of the gas jet assemblyand differential pumping: (a) front view of the inside of the main chambercontaining the gas jet cell and the turbo molecular pump behind it. Thedifferential pumping is created between the region of high pressure R2and the main chamber, region R1; region R3 is connected to an additionalroughing pump, removing the main portion of the gas directly from the gasjet cell before it reaches region R1; IR: infrared radiation and XUV: extremeultraviolet radiation. (b) Enlarged oblique view of the central part of the gasjet cell. IH: input hole, OH: output hole, TH: tube hole, BH: bottom hole, andGJ: gas jet.

cell for passing the radiation are of 1.5 mm diameter (seeFig. 1(b)). The cell had also a 1.5 mm tube hole (TH) on thetop for the Ni tube, sealed at the end. A bottom hole (BH) witha similar diameter was used for centering the Ni tube. The laserbeam was focused on the gas jet to produce high harmonics,which were detected using an XUV spectrometer (McPherson,248/310G). In this spectrometer, XUV radiation was diffractedby a grating (133.6 groves/mm) to a micro-channel plate(MCP), which detected the different HHs. The image fromthe phosphorous screen mounted at the back side of the MCPwas projected onto a charge-coupled device (CCD) camera;this latter image of spectrally resolved HHs was acquired witha LabVIEW program for subsequent processing.

Pumping of the main chamber, containing the gas jetcell, and a two-stage differential pumping on the path of theXUV radiation to the spectrometer were needed to reducethe absorption due to the gas and to maintain low pressure(≤5 × 10−6 millibars) at the MCP of the XUV spectrometer.The pressure requirements of the MCP and pressure loadson the turbo molecular pump (Pfeiffer, TMU-521-YP), usedfor evacuating the main chamber, set the upper limit of theachievable pressure in the gas jet. Maximum pressure limit(∼7 × 10−3 millibars) in the main chamber is directly relatedto the load on the turbo molecular pump that was determinedmainly by the flow to the main chamber through the holes IHand OH. The large front and back openings in the gas jet cell,directly connected through the tubing to the roughing pump,as is shown in Fig. 1(b), assure that only a small portion ofthe total gas flow leaks to the main chamber.

The maximum pressure reached in the interaction region(R2) was estimated to be ∼1.5 bars for Ar and ∼0.5 bars forH2. The main reason for the dependence of the upper pressurelimit on the gas type is due to the fact that the compressionratio for the turbo molecular pump defined as the ratio ofthe outlet pressure to the inlet pressure is determined by theformula: K ∼ exp ( f vB/vm),29 where vB is the blade speed ofthe pump, vm =

√8RT/πM is the mean molecular speed, R is

the molar gas constant, T is the temperature, M is the molarmass of the gas, and the factor f depends on the numberand configuration of blades of the pump. Thus, the K-valueis exponentially increasing with the square root of the molarmass of the gas via the dependence on the mean molecularspeed of the gas, and as a result, the compression ratio for Argas is a factor ∼130 higher than for H2, meaning that H2 isharder to pump than Ar owing to 20 times smaller molar massof H2 compared to Ar.

The gas leakage due to the openings in the gas cell (IHand OH) to the main chamber (R1) (see Fig. 1) determined themaximal pressure ratio in the gas jet, when the valve to theadditional roughing pump was opened or closed. This ratiowas experimentally determined by comparing the outputs ofHHs in two different cases with opened or closed valve byadjusting the flow through the gas jet and measuring thepressure in the main chamber. This pressure ratio, or moreprecisely the pressure gain, was found to be ∼15 for Ar and∼5 for H2. The gas jet pressure (region R2) was estimated bymeasuring the consumption of gas from a small size lecturebottle (in this case, additional pumping from region R3 wasdisabled), taking into account the diameters of the IH and OH

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holes in the Ni tube (∼100 µm). This gas jet pressure wasdetermined to be ∼50 millibars, which corresponded to thepressure in the main chamber (R1) ∼2.5 × 10−3 millibars.

III. RESULTS

Harmonic generation was measured and compared fortwo cases, corresponding to different gas jet pressures (inR2): (1) the additional pumping with the roughing pump wasdisabled (the valve to the roughing pump was closed) and (2)the additional pumping was enabled (the valve was opened).The HHs spectra for Ar gas are shown in Fig. 2.

In the Ar gas jet without additional pumping, we reachedpressures of up to ∼0.12 bars, while with additional pumping,we reached up to ∼1.5 bars. The pressure dependence ofthe HH output for Ar is shown in Fig. 3; we observedodd harmonics from 17th to 29th order. The maximumoutput was achieved at an optimum pressure of ∼0.2 bars(∼5 × 1018 atoms/cm3) for all harmonics (Fig. 3).

For H2 gas jet without additional pumping, we reachedpressures up to ∼0.09 bars, while with additional pumping,pressures up to ∼0.5 bars could be reached. The HHs spectrafor H2 are presented in Fig. 4. The pressure dependences of theHHs output for H2 gas are shown in Fig. 5. We observed oddHHs from 17th to 25th with their output exhibiting saturationat a pressure approaching∼0.5 bars (∼1.25 × 1019 atoms/cm3)(Fig. 5).

Since both gases have similar ionization potentials (Ip∼ 15.6 eV for Ar30 and Ip ∼ 15.4 eV for H2

31), the above-mentioned formula for the cutoff energy gives, for both gases,about 42 eV. The experimentally observed cutoffs are 29thHH (∼45 eV) for Ar and 25th (∼39 eV) for H2. The highestharmonics were also more difficult to observe for H2, since inthis case, the signal was about 20 times lower than for Ar.

FIG. 2. HHG spectra at different gas jet pressures of Ar. Red lines arefor disabled additional pumping, and blue lines are for enabled additionalpumping.

FIG. 3. Ar pressure dependence of HHs output normalized to the maximumoutput, reached at optimum pressure ∼0.2 bars. Blue solid lines are exper-imental results, and red dashed lines are calculations with the 1D model.Further explanations are given in the text.

IV. THEORETICAL 1D MODEL

To calculate the pressure dependence of the HHs, we usedthe one dimensional model of Ref. 22,

SHHG ∝4Labs

2P2Aq2

1 + 4π2

(Labs

2

Lcoh2

)×

(1 + e

−LmedLabs − 2 cos

(π

Lmed

Lcoh(t))

e−Lmed2Labs

). (1)

FIG. 4. HHG spectra at different gas jet pressures of H2. Red lines arefor disabled additional pumping, and blue lines are for enabled additionalpumping.

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FIG. 5. H2 pressure dependence of HHs output normalized to the maximumoutput, reached at ∼0.5 bars. Blue solid lines are experimental results, andred dashed lines are calculations with the 1D model. Further explanations aregiven in the text.

Here, P is the gas pressure in the jet, Aq is the dipole amplitudeof the qth-order harmonic, Labs and Lmed are the absorptionlength and the medium length, and Lcoh is the coherencelength, Lcoh = π/∆k, where the wave vector mismatch ∆kbetween infrared and XUV light is given as

∆k = ∆kat + ∆kelec + ∆kGouy + ∆k fat. (2)

The first term in Eq. (2) is the atomic dispersiongiven by ∆kat ∼ 2πqP

�1 − n f

� �nIR − nq

�/λ,4,32 where q is

the harmonic order, nIR and nq are the refractive indexes ofthe gas per 1 bar for IR and HHs wavelengths, respectively,and n f ∼ 0.2 is the ionization fraction of Ar+ at intensity∼1.5 × 1014 W/cm2.33

The second term in Eq. (2) is the electronic dispersiongiven by∆kelec ∼ PqNereλ,4,32 which besides P and q dependsalso on the free electron density per 1 bar (Ne) in theinteraction region, classical electron radius (re), and thewavelength (λ).

The third term is the geometrical phase shift (Gouy phase)contribution that depends on the laser focusing conditions andis given by ∆kGouy ∼ (q − 1) ∂ tan−1 (z/zR) /∂z, where zR isthe Rayleigh range and z is the displacement from the focalpoint along the laser beam.20,34,35

The last term in Eq. (2), referred to as atomic phase,depends on the quantum path and is different for shortand long trajectories.36 This is given by ∆kφat = −α∇I,37

where ∇I is the variation of the intensity along the beamin the gas cell. For electrons following the short trajectory,α ∼ 2 × 10−14 cm2/W and for those travelling along the longtrajectory, α ∼ 22 × 10−14 cm2/W.36–38

Evaluating all the contributions to the wave vectormismatch in Eq. (2) allowed us to determine the coherencelength (Lcoh) and, by using the absorption length calculatedfrom available data39 (Fig. 6), to find the pressure dependenceof the HHs output from Eq. (1). It is assumed that the longand short trajectories equally contribute to the total harmonicsignals.38,40

FIG. 6. Absorption length (Labs) as a function of gas jet pressure for 21st,23rd, and 25th HHs: (a) for Ar gas and (b) for H2 gas (blue dashed line for21st harmonic, black dashed line for 23rd, and red dashed line for 25th).

Figures 3 and 5 show the comparison of calculationswith the 1D model and the experimental results for HHs from21st to 25th order for Ar and H2, respectively. The results ofcalculations (red dashed lines) are in reasonable agreementwith the experimental data.

The calculations were performed with the 1D model ofEq. (1), assuming that for each harmonic Aq is constant. Forthe observed maximum harmonic output, the pressure at thegas jet was such that the concentration of the gas atoms wasrelatively high, providing a stronger output. On the other hand,the absorption and phase-mismatch were not yet affecting theHHG output too strongly.

One of the main difficulties of the harmonic generation isdue to re-absorption of XUV radiation in the gas medium.Without the additional pumped cell enclosing the gas jet,the gas jet extends to a larger distance, thus increasing there-absorption effect of the generated XUV radiation. Thisdecreases the efficiency of the HHs. With the differentialpumping, the gas density is more localized within theenclosing cell, and thus, the HHs’ propagation length withinthe region with elevated pressure is reduced, thereby reducingreabsorption.

An important point is that the maximum of the HHs’output peak was observed for about the same pressure valuefor all harmonic orders as shown in Figs. 3 and 5 for Ar and H2,respectively. This indicates that reabsorption is not playing anessential role in the HHG signal, since otherwise the maximal

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outputs for different harmonics would correspond to differentpressures.

V. CONCLUSIONS

In this study, we experimentally investigated pressure-dependence effect on the output of HHG for two gases,Ar and H2, and compared the experimental results witha 1D theoretical model. Argon is often used for HHGsince it produces relatively high HHs outputs. Although Arand H2 have similar ionization potentials, they exhibiteddifferent HHs outputs and pressure dependences at the sameexperimental conditions. We have shown that at intensities∼1.5 × 1014 W/cm2 and for our experimental conditions, theoptimum pressures yielding a tenfold increase in the HHoutput were found to be ∼0.2 bars for Ar and ∼0.5 barsfor H2, as compared to direct employment of the gas jetwithout a differentially pumped cell. The HH signal in thecase of H2 was about 20 times lower than for Ar for thesame experimental conditions. Maximal outputs for differentharmonics were reached at about the same pressure values,which provides evidence that the XUV radiation reabsorptionwas relatively weak. The optimum pressure that maximizesthe HHs signals reflects the trend of quadratic increase withthe gas density on the one hand and the effect of the phasemismatch and absorption that tend to increase with pressureon the other hand.41,42 The observed experimental pressuredependences are in agreement with simulations based on the1D model.

The described optimized XUV radiation source can findapplications in bio- and nano-imaging investigations, forstudies of fast dynamical processes in a pump-probe schemeas well as for spectroscopy experiments in the XUV region.

ACKNOWLEDGMENTS

This work was supported by the Robert A. WelchFoundation Grant No. A1546 and the Qatar Foundation underGrant No. NPRP 5-994-1–172. M. Sayrac acknowledgessupport from the Ministry of National Education of theRepublic of Turkey.

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