June 1, 2009 / Vol. 34, No. 11 / OPTICS LETTERS 1651

Measurement of molecular rotational temperaturein a supersonic gas jet with high-order

harmonic generation

Kazumichi Yoshii, Godai Miyaji, and Kenzo Miyazaki*Advanced Laser Science Research Section, Institute of Advanced Energy, Kyoto University, Kyoto 611-0011, Japan

*Corresponding author: miyazaki@iae.kyoto-u.ac.jp

Received February 25, 2009; revised April 17, 2009; accepted April 24, 2009;posted April 28, 2009 (Doc. ID 107974); published May 22, 2009

We apply high-order harmonic generation to sensitive measurements of the molecular rotational tempera-ture in a thin supersonic gas beam. The method uses nonresonant pump and probe femtosecond laser pulsesto generate harmonic radiation from coherently rotating molecules. The rotational temperature of moleculescan be derived accurately with high spatial and temporal resolutions from the Fourier spectrum of time-dependent signals. The validity of this method was tested for an expanding flow of an N2 beam with a rapidtemperature decrease. The results show the versatile applicability of this method. © 2009 Optical Society ofAmerica

OCIS codes: 190.1900, 300.6400, 320.7100.

Pulsed supersonic molecular beams have been usedextensively in a variety of fields of molecular sciencesuch as spectroscopy, nonlinear optics, and chemicaldynamics. Major advantages of a supersonic beamare associated with its ability to generate an isolatedensemble of collision-free molecules with extremelylow temperature and to make microscopic experi-ments possible [1]. In the experiment using a molecu-lar beam, the rotational temperature Trot is one of themost important parameters to characterize the mo-lecular system concerned. The most powerful tool tomeasure Trot in a thin supersonic beam has been co-herent anti-Stokes Raman scattering (CARS), wheretunable pulsed lasers are usually used to observe thespectrum in resonance to the rotational levels [2,3].The development of spectroscopic methods usingCARS has greatly improved the accuracy of Trot mea-surement to study detailed rotational dynamics in apulsed molecular beam. In addition to the frequencydomain measurement, time-domain CARS spectros-copy has also been developed using femtosecond (fs)laser pulses [4,5], which has the advantage of hightemporal resolution. However, CARS spectroscopy, aswell as related nonlinear optical methods such as de-generate four-wave mixing (DFWM), often meetssome difficulties arising from the complexity of mo-lecular rotational transitions, e.g., nonresonant back-ground and signal frequencies close to those of pumplaser pulses [5,6].

In this Letter we report a sensitive and versatilemethod to measure Trot in a supersonic molecularbeam, which has high spatial and temporal resolu-tions in a broad experimental range of molecularbeams. The method employs a pump and probe tech-nique with fs laser pulses, where the pump pulse cre-ates a rotational wave packet that leads to temporalalignment of molecules, and the probe pulse gener-ates high-order harmonic radiation from aligningmolecules [7,8]. In contrast to CARS spectroscopyand DFWM, the present method detects harmonic ra-diation in a vacuum UV spectral region far from the

fundamental wavelength concerned. The harmonic

0146-9592/09/111651-3/$15.00 ©

signal measured as a function of time delay �t be-tween the pump and probe pulses provides us withdefinite information of Trot in the supersonic molecu-lar beam.

The experimental setup was the same as in ourprevious experiments [7–9]. Briefly, the linearly po-larized, 40 fs, 800 nm pump and probe pulses witha time delay �t are produced from the output of aTi:sapphire laser system. These pulses were col-linearly focused with a 500 mm focal-length lens intoa pulsed N2 beam, where the spot size was measuredto be 70 �m. The pump pulse induces a transientalignment of molecules through the formation of a ro-tational wave packet, which is recurrent under field-free conditions, and the delayed probe pulse gener-ates high harmonic radiation from coherentlyrotating molecules as a function of �t. The pump andprobe intensities were optimized for the measure-ment of Trot in the N2 beam and fixed at 0.75 and2.2�1014 W/cm2, respectively. The harmonic radia-tion produced was detected by an electron multipliermounted on a vacuum ultraviolet monochromator.

The pulsed supersonic N2 beam of 160 �s durationis jetted into vacuum from the 1 mm diameternozzle of a piezoelectric valve. The pulsed valve wassynchronously operated with the fs laser at a repeti-tion rate of 10 Hz. The source pressure P0 in thevalve was changed in a range from 1 to 9 atm atroom temperature. The pulsed valve attached on avacuum chamber was mounted on a positioningstage, and the distance x between the nozzle exit andthe optic axis was changed by translating the stage(see the inset in Fig. 3).

In the present study we assume that the rotationaldistribution in the gas jet was in thermal equilibriumwith a Boltzmann distribution. Then the recently de-veloped theory provides the nth harmonic signal permolecule as a function of �t [10,11]. The validity oftheoretical expressions for N2 and O2 has been veri-fied with our recent experimental study [9]. For theN used in this work, the harmonic signal is given as

2

2009 Optical Society of America

1652 OPTICS LETTERS / Vol. 34, No. 11 / June 1, 2009

S�n���t� � c1 + c2��cos2 �����t� + c3��cos2 ��2���t�

+ c4��cos4 �����t� + ¯ , �1�

where ci is the coefficient depending on the intensityand duration of the probe pulse [10,11]. The innerbrackets of ��cos2��� and subsequent terms stand forthe expectation value for the rotational wave packetconsisting of coherently populated rotational statesat �t=0, and the outer brackets correspond to thethermal average over the Boltzmann distribution atTrot. It is noted that the time-dependent harmonicsignal S�n� is dominated by the initial rotational tem-perature Trot included in such thermally averagedterms as ��cos2 ��� once the rotational wave packet isformed at �t�0 with the pump pulse. The evaluationof Trot in the experiment can be made accurately bycomparing the frequency spectrum of the observedtime-dependent harmonic signal with the theoretical,because the spectrum is very sensitive to the distri-bution of rotational states at the unique fitting pa-rameter Trot, as shown below.

Figure 1 shows (a) typical examples of the time-dependent harmonic signal observed at the relativeposition x /D=0.1 for P0=1 atm (upper trace) and thesignal ���t� calculated for the same pump and probeintensities (lower trace) and (b) their correspondingfrequency spectra [12]. In the calculation for N2, weused only the single dominant term ���t��c2��cos2 �����t� to reproduce the signal and its fre-quency spectrum, since the other terms provide theidentical rotational distribution to derive Trot [9]. InFig. 1, the best agreement between theory and ex-periment is obtained for Trot=110 K. As discussed in

Fig. 1. (Color online) (a) Time-dependent 19th harmonicsignals observed at x /D=0.1 for P0=1 atm (upper) and cal-culated (lower) for Trot=110 K and (b) their frequency spec-tra. The inset in (b) indicates the rotational distribution atTrot=110 K. The pump and probe intensities used in theexperiment and calculation are 0.75 and 2.2�1014 W/cm2,

respectively.

detail in previous studies [8,10], the time-dependentbehavior of a harmonic signal is dominated by thebeat frequency ���EJ+2−EJ� /2�= �4J+6�Bc be-tween any pair of rotational states populated throughthe Raman transition �J= ±2, where EJ is theeigenenergy of a state with the angular momentumJ, B is the rotational constant, and c is the speed oflight. The frequency spectrum represents a distribu-tion of coherently rotating molecules, and their co-herent superposition produces the characteristictime-dependent signal, including the revival struc-ture of molecular alignment. The inset in the lowerspectrum of Fig. 1(b) represents the initial rotationaldistribution at Trot=110 K. Since N2 is a homo-nuclear molecule with a nuclear spin of 1, the popu-lation F�J0� of even- and odd-J0 states has a ratio of2:1. This population alternation is clearly seen in thedistribution of �. As shown in the inset in Fig. 1(b),the initial population is peaked at J=4. This popula-tion peak is shifted to the J=6 state for �=30Bc withthe pump pulse. The experimental result shown inFig. 1(b) includes the additional small-frequencycomponents that originate from the higher terms inS�n�, as discussed in our previous studies [8,10].

The frequency spectrum depends on only Trot whenthe pump and probe intensities are fixed for a mo-lecular species. To see the sensitivity of the frequencydistribution to Trot, the time-dependent 19th har-monic signal was observed at a different positionx /D=1.5 for a higher pressure of P0=9 atm, wherethe jetted molecules were expected to have a muchlower rotational temperature. Figure 2 shows the re-sults of the (a) observed (upper) and calculated(lower) time-dependent harmonic signals and (b)

Fig. 2. (Color online) (a) Time-dependent 19th harmonicsignals observed at x /D=1.5 for P0=9 atm (upper) and cal-culated (lower) for Trot=20 K and (b) their frequency spec-tra. The inset indicates the rotational state distribution atTrot=20 K. The pump and probe intensities are the same as

in Fig. 1.

June 1, 2009 / Vol. 34, No. 11 / OPTICS LETTERS 1653

their frequency spectra, where the best agreementbetween theory and experiment is obtained for a ro-tational temperature of Trot=20 K. The frequencyspectrum represents the peak amplitude at J=4 with�=22Bc in this distribution. It is clear that the shiftfrom �=30Bc in Fig. 1(b) to 22 Bc for the peak am-plitude is due to a decrease from Trot=110 K to 20 Kand the resulting relative increase in the initialpopulations of lower rotational states, as shown inthe inset of Fig. 2(b).

The above result is consistent with the well-knownfact that Trot in the free expansion of a supersonicmolecular beam decreases with an increase in x /Dand/or P0 [13,14]. In particular, the decrease in Trot isso rapid in a region of non-isentropic gas expansion,which is usually observed for a small value of x /D[14]. To see this and to confirm the applicability of thepresent method, we measured Trot as a function ofx /D ��2� for different P0 using the 19th harmonicsignals. The result is shown in Fig. 3. As expected, arapid decrease in Trot is observed in the region ofx /D=0.1−1.0, e.g., Trot=110 K decreases to 50 K atP0=1 atm. For comparison, we calculated the trans-lational temperature T in the same region of x /D, as-suming the isentropic expansion of molecular gas[14], which is usually less than Trot. The calculationprovided T=245 K at x /D=0.1 and its monotonousdecrease to T=94 K at x /D=1.5. As shown in Fig. 3,the measured value of Trot is much lower than thecalculated value of T. This characteristic property ofTrot in a region of small x /D reconciles with those re-ported so far for the pulsed supersonic free jets of N2[15] and other molecules [16,17].

The present technique provides a versatile way tomeasure Trot, since the nonresonant fs laser can com-monly be applied to different kinds of molecules. Wehave confirmed that Trot in pulsed O2 and CO2 beamscan be estimated accurately with this method. The

Fig. 3. Rotational temperature in the supersonic N2 gasjet measured as a function of the distance x /D from the

nozzle for different source pressures.

temporal resolution in this measurement is on a psscale with a spatial resolution in the focused beamsize. In addition, the time-domain measurement hasallowed us to evaluate Trot of an ensemble of low-density molecules by observing multiphoton ioniza-tion of aligned molecules with a time-of-flight massspectrometer [18]. The results obtained will be pre-sented and discussed elsewhere.

In summary, we have demonstrated a sensitive andversatile method to measure rotational temperaturein a pulsed supersonic molecular beam, which isbased on the observation of the time-dependenthigh-order harmonic signal from coherently rotatingmolecules. The results obtained are consistent withthose reported so far.

The authors thank A. Abdurrouf for helpful discus-sion. This work is partially supported by the Grant-in-Aid for Scientific Research (A) 18206010.References and Notes

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