OPTICS LETTERS / Vol. 24, No. 18 / September 15, 1999
High-energy conversion efficiency of transient stimulated Raman scattering in methane pumped by the fundamental of a femtosecond Ti:sapphire laser I. G. Koprinkov,* Akira Suda, Pengqian Wang, and Katsumi Midorikawa The Institute of Physical and Chemical Research (RIKEN), Hirosawa 2-1, Wako-shi, Saitama 351-0198, Japan Received April 14, 1999 We studied stimulated Raman scattering in pressurized methane in the highly transient regime pumped by 140-fs 0.7-mJ pulses from a Ti:sapphire (Ti:S) laser tuned at 750 nm. Energy-conversion eff iciency of the f irst Stokes of more than 15% was achieved, with no strong sign of saturation with as much as 40 atm 共1 atm 苷 760 Torr兲 of Raman gas pressure. To our knowledge, this is the highest conversion efficiency of transient stimulated Raman scattering generated directly from the fundamental of a Ti:S laser. 1999 Optical Society of America OCIS codes: 190.7110, 190.2640, 320.2250, 290.5910.
Generation of new femtosecond optical emissions is an important task for ultrafast science and technology, as at present the mature technology in this field is limited to only a few primary laser sources. Stimulated Raman scattering (SRS) is one of the well-established and efficient ways of shifting the emissions of existing lasers. At femtosecond-pulse excitation, SRS develops as a highly transient process,1 as the pump pulse is much shorter than the dephasing time T2 of practically all molecular gases. Generally, the short pump pulse limits the efficiency of the Raman conversion with respect to the steady-state case. Transient stimulated Raman scattering (TSRS) has been studied experimentally by use of femtosecond2,3 or subpicosecond dye lasers,4 femtosecond Ti:sapphire lasers,5 – 9 and femtosecond10 or picosecond11 – 13 excimer-laser-amplif ied emissions. In the last case the SRS showed very high conversion eff iciency, exceeding 50%.12,13 The advantage in this case comes from both the relatively longer but still transient picosecond pump pulses and the short-wavelength radiation, for which the enhancing effect of the excited electronic molecular states is much stronger. In the case of subpicosecond or femtosecond dye laser excitation, high Raman-conversion efficiency 共⬃20%兲 is also achievable.2 – 4 Nearly the same range of conversion eff iciency was obtained with secondharmonic pumping of femtosecond Ti:sapphire (Ti:S) lasers.5 – 7 However, the Raman-conversion efficiency pumped by the fundamental of a femtosecond Ti:S laser was still low, ⬃1% in H2 .5 This efficiency is not high enough (7%) even for Ti:S laser pulses with a duration of a few picoseconds,14 whereas second-harmonic pumping gave a 23% conversion eff iciency for the first Stokes wave in these experiments. As is clear from these results, the problem with eff icient Raman conversion of femtosecond pulses directly from the fundamental of a Ti:S laser has not yet been satisfactorily solved. The importance of this problem is even greater if one keeps in mind that the Ti:S laser is the most basic and widespread ultrafast laser technology. In this Letter we report on SRS in methane 共CH4 兲 pumped by 140-fs pulses from a Ti:S laser with a Stokes 0146-9592/99/181308-03$15.00/0
conversion eff iciency exceeding 15%. Improvement of the efficiency of the SRS at the specif ied time– wavelength operating range is brief ly considered based on a transient Raman-gain analysis.1 Although at TSRS the Stokes intensity does not obey the familiar exponential law, Is 苷 Is 共o兲 exp共gIp l兲, in the high-gain-limit exponential gain exp共GT 兲 is given by1 ∑µ ∏1/2 ∂ Z GT 艐 8gl Ip dt 兾T2 . (1) According to relation (1), the suitable TSRS medium should have a high steady-state Raman gain g and a short dephasing time T2 at the same time so that it is able to respond faster to the forcing laser field. Consequently, not all media that are known as highly Raman active at steady-state excitation, e.g., H2 and CH4 , are by all means suitable for TSRS. Depending on pressure, the dephasing time in CH4 is approximately 13 (Ref. 15) to 30 (Ref. 11) times shorter than that in H2 . Although at the same time the steadystate Raman-gain coeff icient in CH4 is a few times smaller than that in H2 ,7 it is expected that pressurized CH4 will be a more eff icient TSRS medium, and its advantage should become more pronounced at femtosecond excitation. Let us recall that low-efficiency femtosecond SRS from the fundamental of a Ti:S laser 5 has been reported R in a H2 medium. Of course, highenergy f luence 共 Ip dt兲 of the pump pulses and a long interaction length l are also important for efficient TSRS. However, many factors, e.g., group-velocity mismatch7 (GVM) and interplay with competitive processes [self-phase modulation and self-focusing 3,4 (SF)] can inf luence the efficiency of TSRS in a real experiment. These factors need extensive treatment in particular experimental conditions, which is beyond the scope of this Letter. We consider only the TSRS capabilities of the CH4 molecule. Closer examination of relation (1) shows that the crucial parameter for the transient Raman gain is the differential Raman-scattering cross section, ds兾dV,16 which is represented in relation (1) by the steadystate Raman gain. As no experimental data were 1999 Optical Society of America
September 15, 1999 / Vol. 24, No. 18 / OPTICS LETTERS
found at the Ti:S laser wavelength, we converted (and averaged) all available cross-section data for the CH4 molecule, measured at different wavelengths15,17 than the Ti:S laser wavelength, using the following explicit expression for the Raman cross section18: vs 4 ds 苷 共4pe0 hc dV ¯ 2 兲2 √ É X 3 mfi mig i
1 1 1 2 vp vig 1 vs
! É2 .
To make our results comparable with other similar calculations15 we assumed a single electronic level at ˜ 1 F2 兲 Rydberg state of the CH4 ⬃70 000 cm21 [the A共 molecule] as the intermediate resonance. The cross section at 800 nm (near the Ti:S laser gain maximum) was determined to be 3.55 3 10231 cm2 兾sr mol. Using this cross section, we obtained a number of transient Raman-gain characteristics, as shown in Fig. 1. A 100-mm beam-waist diameter and an interaction length equal to the confocal parameter of an equivalent Gaussian beam were assumed. The 0.1– 10-mJ energy range, which covers the majority of the present Ti:S chirped-pulse-amplification systems, was considered. As follows from Fig. 1, low threshold pressure [e.g., 5 atm 共1 atm 苷 760 Torr兲 at 1-mJ pump energy allowed us to achieve GT 苷 25]15 and high transient Raman gain are typical for the CH4 medium. Such a conclusion can be also deduced from comparative TSRS experiments at different wavelengths.7,11,13 The scheme of our experimental setup is shown in Fig. 2. The pump laser is a femtosecond Ti:S oscillator (Spectra-Physics Tsunami) –regenerative amplifier (BMI a 2 10) chirped-pulse-amplification system tuned to 750 nm and operating at a 10-Hz repetition rate. The output pulses are compressed by a grating compressor to 140 fs and typically have a 0.7-mJ pulse energy. The Raman cell was 80 cm long and sealed with 10-mm uncoated quartz windows. A suitable dielectric total-ref lectance mirror was used to suppress the Ti:S laser emission after the Raman cell. To separate the first Stokes wave we used a color filter (Sigma Koki ITF-83RT) that totally cut the anti-Stokes region and the second Stokes wave 共1.33 mm兲 and transmitted less than 8% of the third Stokes wave 共2.18 mm兲. The output from the Raman cell was analyzed by use of a fiber-optic spectrometer with 0.8-nm resolution. Energy was measured with a Laser Probe, Inc., Rm3700 energy meter and an RJP-735 pyroelectric probe. We specify the following experiment as highly TSRS, since the pump-pulse duration tp obeys the relations tp , 1022 T2 and tp , 1023 tss , where tss is the characteristic time to reach the steady state. When we focused 0.4-mJ Ti:S laser pulses with a 0.4-m spherical lens to produce ⬃6.3 3 1013 W兾cm2 pump intensity inside the Raman cell, a highly complicated spectrum consisting of discrete lines and a supercontinuum was observed as a result of combined action among SF, self-phase modulation, four-wave mixing, and SRS. The threshold of the purely electronic processes was lower than that of SRS, and these processes were dominant in intensity at pressures up to
⬃10 atm. Using a 1-m focal-length optic reduced the pump intensity in the focus to ⬃1 3 1013 W 兾cm2 . This intensity made the development of SF and the accompanying supercontinuum more gradual with CH4 pressure, but the threshold of the accompanying processes was still lower than that of the SRS. Interplay among these processes was discussed in Ref. 3. In that study, by proper reduction of the pump energy (to less than 100 mJ) and the focusing length, other nonlinear processes were suppressed at the threshold of SRS. This method was not followed here, as the energy threshold of the TSRS is higher at the longer Ti:S laser wavelength (see Fig. 1) and requires inconvenient high pressure. This is why the actual experiments were performed with a 1-m focusing optic and the full-range pump energy (0.7 mJ) that was found to be nearly optimal for high Raman conversion. The threshold of the SRS at the specif ied pumping conditions was reached at ⬃7 atm. This result corresponds surprisingly well to the predicted value (see Fig. 1), since the analytical expression for the transient Raman gain was derived by consideration of the pump and the first Stokes emissions only and of a number of simplifications.1 Our explanation is that at the first Stokes threshold the anti-Stokes lines and the higher-order Stokes lines have not yet been generated, whereas the generated emissions do not significantly deplete the pump beam. SF develops gradually with pressure, as was verif ied by observation of the spot of the supercontinuum. That spot was trapped by the self-focused pump beam and appeared as a well-rounded white spot in the beam center, whose diameter gradually decreased with gas pressure. No catastrophic SF was observed. As a result, no dramatic changes of the pump-beam parameters that affect the TSRS threshold could occur. Of course, some mutual compensation of different effects cannot be excluded. At nearly twice the threshold pressure, the Raman emission strongly dominates the other emissions. The full Raman spectrum observed within the
Fig. 1. Transient Raman gain versus pump-laser energy.
Fig. 2. Experimental setup: M1 , M2 , mirrors; TRM, total-ref lectance mirror; L1 , L2 , lenses; F’s, filters; GP, glass plate.
OPTICS LETTERS / Vol. 24, No. 18 / September 15, 1999
Fig. 3. Raman spectrum at 40 atm and 0.7-mJ pumppulse energy. The Stokes and the anti-Stokes lines are not on the same scale.
of the pump pulse1), which is traveling faster, will reach the undepleted part of the pump pulse. This enhanced scattering, however, leads to less transient Raman pulse shortening in a medium with high GVM.7 In conclusion, based on TSRS theory, pressurized CH4 has been found to be one of the most suitable media for efficient Raman conversion of femtosecond laser pulses, especially the fundamental of a Ti:S laser. Good correspondence between the predicted and the measured SRS thresholds was found. To our knowledge, the highest conversion efficiency (exceeding 15%) from TSRS pumped directly by the fundamental of the Ti:S laser was achieved. *Permanent address, Institute of Applied Physics, Technical University of Sof ia, 1756 Sof ia, Bulgaria; e-mail, [email protected]
Fig. 4. First Stokes energy versus pump-pulse energy.
detection range (380–1100 nm) of our system is shown in Fig. 3. The anti-Stokes lines had a ring-shaped spatial distribution, which means that they arise from the Raman-resonance four-wave mixing. The lowest-order anti-Stokes lines can be also detected with lower intensity outside the rings, showing that pure anti-Stokes Raman scattering also takes place. The dependence of the first Stokes energy and its energyconversion efficiency on the pump energy taken at 20 and 35 atm is shown in Fig. 4. The data near the Raman threshold are not included because of unstable triggering of the energy meter. No signs of saturation were observed under the experimental conditions. Energy-conversion efficiency exceeding 15% was achieved for the first Stokes S1 . To the best of our knowledge, this is the highest conversion eff iciency from TSRS pumped by the fundamental of a Ti:S laser. The bandwidth of the first Stokes wave is 5.6 THz, corresponding to 57 fs of a transform-limited sech pulse. In looking for an effective medium for TSRS of ultrashort laser pulses near 10 fs, one should also take into account GVM between the pump and the Stokes pulses, which at the 390-nm pump wavelength is four times larger in CH4 共8.7 fs兾cm兲 than in H2 共2 fs兾cm兲.7 This problem is alleviated slightly at the longer fundamental wavelength of the Ti:S laser. In the case of normal dispersion GVM may even result in enhanced Raman scattering, as the Stokes pulse (which in the TSRS is generated at the trailing edge
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