Femtosecond laser systems based on Ti:sapphire andoperated at 1 kHz have become one of the most pop-ular ultrafast laser systems for a wide range of ex-periments from ultrafast spectroscopy and x-ray gener-ation to material processing. Many applications willeither benef it from or be possible only with high aver-age power or multikilohertz repetition rates. After afirst successful attempt to operate a Ti:sapphire lasersystem at a 10-kHz repetition rate,1 development oflaser systems with multikilohertz repetition rates wasreported in several papers.2 – 5 A new generation ofdiode-pumped solid-state lasers, such as the CoherentCorona and the Positive Light Evolution, has presentednew possibilities for multikilohertz femtosecond sys-tems design with average and peak powers suitablefor generation of high harmonics.4 The experimentswith a combination of laser and synchrotron radiationfor short-pulse hard-x-ray generation6 as well as ap-plications for material processing will benef it greatlyfrom use of such laser systems.
In longitudinally pumped laser crystals the originof thermal effects is the Stokes shift between thepump and the emission wavelengths. For Ti:sapphirepumped at 532 nm, even when the quantum efficiencyis close to unity, approximately 30% of pump powerwill be dissipated as heat. The heat source is assumedto be of the same spatial shape as the pump radia-tion, so the temperature profile created by the pumppower inside a laser rod produces refractive-indexand optical distortion distributions that are specificfor each pump beam. These distributions have beenactively investigated with different approaches to theproblem.7 – 10 In the most comprehensive approaches,authors have addressed finite-element analysis tocharacterize the energy deposition within the rod andthe resultant temperature and stress f ields as well asthe induced optical aberrations.8,11 Gaussian profilesof second and infinite orders are typical ones for pumplaser beams that are usually used in modeling.7 Theradial temperature profile exhibits quadratic behaviornear the axis of the rod for Gaussian pump shape,
0146-9592/04/020198-03$15.00/0
and only radial uniform thermal loading will resultin quadratic phase behavior within the entire pumpregion. It was found8,10,11 that the induced phase shiftdeviates 10% from a parabolic shift at 0.75 wp for aGaussian pump beam and at 1.3 wp for a uniform,or top-hat, pump beam. For lasers usually used aspump sources for Ti:sapphire amplifiers the top-hatshape is a good approximation of their highly multi-mode beams, so thermally induced phase distortioncan be described over the extent of the pump beamwith good accuracy if one considers only the parabolicaberration-free term and treats the induced phasedistortion as aberration-free focusing.9,12
For our experiments we used a Nd:YAG CoherentCorona laser, which is able to produce as much as80 W of output radiation at 532 nm, to pump theTi:sapphire laser rod. Pumping the Ti:sapphire rodat full pump power will induce strong thermal lensing,which will drastically change the cavity and pumpmode parameters. To compensate for the inducedthermal lensing, the use of some static optical elementsin an amplif ied beam path was proposed.3,10 Anothermethod for decreasing thermal lensing drasticallyis to cool the Ti:sapphire crystal to liquid-nitrogentemperature.4,13,14 Such a radical procedure elimi-nates thermal lensing but needs additional cryogenicequipment and entails continuous consumption ofliquid nitrogen.
We investigated the propagation of the intracavityand the pump laser beams by using an ABCD matrixformalism. A restriction on the application of thismethod is that only those optical elements that retainspherical wave fronts are permitted. This meansthat a thermally induced change in the refractiveindex should have a quadratic dependence on axialcoordinates, a condition that is pretty well satisfiedfor a top-hat beam shape. The gain rod was dividedinto numerous slices, and each of them was considereda combination of a dielectric plate and a thin lens.First we determined the size and power of the pumpbeam, as well as the temperature distribution along
the rod axes, taking into account the self-depositedheat. Then for each slice of the gain rod the opticalstrength of the thermal lens was calculated underDirichlet conditions.11 Bulging of the gain rod faceswas introduced into the matrix for the last slices,11
but the lensing effects caused by thermal stresswere neglected because they were weak.7,8,11 Duringthe calculation, steady-state beam parameter q wasdetermined from the self-consistency requirement thatit repeat itself after a round-trip through the cavitywith a given accuracy.
We have modeled the mode distribution insidea three-mirror astigmatically compensated cavity.Figure 1 shows the stability ranges for the cavityconsisting of R1 � 200 mm and R2 � 1000 mm concavemirrors, a plane output coupler, and a 30-mm-longTi:sapphire crystal. The stability ranges are shownfor a tangential beam that is more sensitive to ther-mal lensing. The cavity has two stability ranges,which behave quite differently with increasing pumppower. The position of the second stability rangeis heavily dependent on the pump power and on thecrystal’s temperature, and therefore stable opera-tion within this range is possible only for a narrowrange of pump power and is not useful for practicalapplications. Within the first stability range at acrystal temperature of 120 K, thermal lensing has anegligible effect, which is opposite that at 300 K whenthe mode parameters are changed so drastically thatit is not possible to find a stable cavity configurationfor the entire pump power range 20–80 W. At 200 Kthe inf luence of thermal lensing is more pronouncedthan at 120 K; nevertheless the mode diameters arealmost the same for the different pump powers withinmost of the stability ranges. Furthermore, at 200 Kthe mode size in the gain medium changes by 10%if the pump power increases to 80 W, which meansthat we can expect stable laser operation with alinear dependence of the output power on the pumppower.
To test the chosen cavity in the experiment, we de-signed a Ti:sapphire laser running in a gain-switchedmode. The Ti:sapphire rod (; 5 3 30 mm3; CrystalSystems; 90% absorption at 532 nm) was cooled to210 K by thermoelectric elements and placed into asmall evacuated chamber to prevent water conden-sation. The pump beam from the Corona laser wasfocused through one of the curved mirrors into thecrystal to a spot size of approximately 0.5 mm. Themaximum output power of 27.2 W at 10 kHz wasobtained with a slope eff iciency of 35% and a pulseduration of 27 ns. The output beam had a Gaussianspatial beam shape, and M2 was measured to be 2and 1.4 in s and p planes, respectively, for outputpowers of 15 W. A further increase of the outputpower led to the appearance of higher modes in theoutput beam. The TEM00 cavity mode size at theposition of the laser rod was calculated to be 310 mm,that is, smaller than the pump mode size, because ofthat the unsaturated gain in the outer region of thepump profile permits higher-order modes oscillation.Aberrant thermal lensing, which manifests itself as ahigh-order transfer ring structure, was insignificant
in our laser because the ratio of the cavity mode spotto the pump mode spot was well below unity.8
For regenerative amplif ication the output couplerwas replaced by a high ref lector, and a Pockelscell–broadband thin-film polarizer combination wasinserted into the cavity. A modif ied Medox Pockelscell was driven in a prebias mode, was cooled bywater, and could be operated at repetition rates upto 25 kHz. Without seeding, the amplif ier operatedin a cavity-dumped mode, and it produced as muchas 16 W of output power with a TEM00 spatial beamprofile; 30-fs, 0.5-nJ pulses from a self-mode-lockedTi:sapphire oscillator stretched to 250 ps were used asa seed. At the maximum pump power the injected
Fig. 1. Beam waist on the plane output coupler as a func-tion of the distance between the rod surface and cavity’sback concave mirror �R1 � 20 cm� for three rod tempera-tures T .
Fig. 2. Output power, number of round trips, andround-trip amplification of the regenerative amplif ier at10 kHz as a function of pump power.
Fig. 3. Spectrum of x-ray radiation emitted by thehigh-repetition-rate plasma source from a liquid-galliumtarget.
pulses were boosted to 1.6 mJ, which corresponds toa maximum amplif ication factor of 3.2 3 106. Thenumber of passes through the amplifying crystal, ad-justed for the maximum output power, was calculatedfrom the time delay between seeding and dumping.We estimated the experimentally achieved averageround-trip gain from the total gain for each pumppower value and corresponding round-trip number.Figure 2 summarizes the data for 10-kHz operation.The demonstrated gain correlates well with the gaincalculated for a Ti:sapphire multipass amplif ier4 undersimilar pumping conditions. The output beam wasexpanded with a mirror telescope to 30-mm diameterto prevent thermal distortion of the 1500 groove�mmgrating surface used in the pulse compressor. Aftercompression, pulses with energy of as much as 0.8 mJand a pulse duration of 60 fs FWHM were generated.The amount of amplif ied spontaneous emission wasmeasured, as the seed was blocked, to be less than1%. Second-harmonic radiation was generated in0.5-mm-thick beta-barium-borate crystal, and as muchas 2.1 W of power with a pulse duration close to 60 fswas obtained. The performance of the amplif ierwas tested at repetition rates of as much as 20 kHzwhile the pump pulse’s energy was maintained near3 mJ. The average output power was graduallyincreased from 5.5 W at 10 kHz to 11.8 W (6.5 Wcompressed) at 20 kHz.
One of the intended applications of the laser sys-tem described here is the generation of noncoherentshort-pulse x-ray continuum. We directed �3 W(10 kHz) of the laser radiation toward a vacuumchamber where a liquid-gallium jet15 was locatedand focused it with a 7-cm focal-length sphericallens to an intensity of 3 3 1014 W�cm2. The spec-trum of the plasma-generated x-ray photons detectedwith a silicon-photodiode-based energy-dispersivex-ray detector (XR-100CR; Amptek, Inc.) is shownin Fig. 3. The spectrum exhibits a continuum witha maximum near 3.2 keV, which is predominantlyfree–free collisions (bremsstrahlung) emission from
the plasma. The x-ray photon yield is estimated tobe 5.1 3 107 photons�s. Ultrafast x-ray absorptionspectroscopy may be one of the interesting future appli-cations of this x-ray continuum source.5 Replacementof a currently used spherical optic by an off-axishigh-numerical-aperture parabola will allow us toincrease the intensity on the target to more than1016 W�cm2. With such laser field intensity it ispossible to efficiently produce K-shell radiation, whichoriginates from collisions of high-energy electrons withcold target material, and to carry out time-resolveddiffraction experiments at multikilohertz repetitionrates.
In conclusion, we have demonstrated a compact,all-solid-state laser system operated up to a 20-kHzrepetition rate. Average powers of 27 and 16 Wwere obtained at 10 kHz for gain-switched and re-generatively amplified pulses, respectively. Aftercompression, 0.8-mJ pulses at 10 kHz and 0.32-mJpulses at 20 kHz were generated. Successful applica-tion for noncoherent x-ray continuum generation wasdemonstrated.
The authors gratefully acknowledge support fromthe Bundesministerium für Bildung und Forschungand thank A. Toss for help with the x-ray spec-trum detection. N. Zhavoronkov’s e-mail address [email protected].
References
1. J. Squier, G. Korn, G. Mourou, G. Vaillancourt, and M.Bouvier, Opt. Lett. 18, 625 (1993).
2. Q. Fu, F. Seier, S. K. Gayen, and R. R. Alfano, Opt.Lett. 22, 712 (1997).
3. Y. Nabekava, T. Togashi, T. Sekikawa, S. Watanabe,S. Konno, T. Kojima, S. Fujikawa, and K. Yasui, Appl.Phys. B 70, S171 (2000).
4. S. Bacckus, R. Bartels, S. Thompson, R. Dollinger, H.Kapteyn, and M. Murnane, Opt. Lett. 26, 465 (2001).
5. Y. Jiang, T. Lee, W. Li, G. Ketwaroo, and C. G.Rose-Petruck, Opt. Lett. 27, 963 (2002).
6. R. V. Shoenlein, S. Chattopadhyay, H. H. W. Chong,T. E. Glover, P. A. Heinmann, C. V. Shank, A. A. Zho-lents, and M. S. Zolotorev, Science 287, 2237 (2000).
7. S. B. Satton and G. F. Albrecht, Appl. Opt. 32, 5256(1993).
8. J. Frauchiger, P. Alberts, and H. P. Weber, IEEE J.Quantum Electron. 28, 1046 (1992).
9. M. E. Innocenti, H. T. Yura, C. N. Fincher, and R. A.Fields, Appl. Phys. Lett. 56, 1831 (1990).
10. F. Salin, C. Le Blanc, J. Squier, and C. Barty, Opt.Lett. 23, 718 (1998).
11. C. Pf istner, R. Weber, H. P. Weber, S. Merazzi, andR. Gruber, IEEE J. Quantum Electron. 30, 1605 (1994).
12. N. Zhavoronkov, A. Avtukh, and V. Mikhailov, Appl.Opt. 36, 8601 (1997).
13. M. G. Holland, J. Appl. Phys. 33, 2910 (1962).14. P. A. Schulz, IEEE J. Quantum Electron. 27, 1039
(1991).15. G. Korn, A. Thoss, H. Stiel, U. Vogt, M. Richardson,
T. Elsaesser, and M. Faubel, Opt. Lett. 27, 866 (2002).
