584 OPTICS LETTERS / Vol. 25, No. 8 / April 15, 2000

Femtosecond Cr41:YAG laser with an L-fold cavityoperating at a 1.2-GHz repetition rate

Tatsuya Tomaru and Hrvoje Petek

Advanced Research Laboratory, Hitachi, Ltd., Hatoyama, Saitama 350-0395, Japan

Received November 12, 1999

Pulses of 55-fs width and 1.2-GHz repetition rate at 1.52 mm are generated from an L-fold cavity Cr41:YAGlaser by optimization of the lasing-beam mode inside the gain medium. The pulse width is comparable withthat obtained from a standard Z-fold cavity. The pulses are characterized by a second-harmonic-generationfrequency-resolved optical gating method. The pulse shape deviates from a sech2 function because of its broadshoulders. With further miniaturization it should be possible to extend the Cr41:YAG mode-locked operationto multigigahertz rates. 2000 Optical Society of America

OCIS codes: 140.3580, 140.4050, 320.7090, 060.4230.

High-repetition-rate femtosecond lasers are interest-ing for a variety of applications and in particularfor optical communication systems. Femtosecondlasers are promising sources for wavelength-divisionmultiplexing because they provide a broad spectralwidth that can be divided into many individualchannels.1 For instance, a spectral width of 40 nm,corresponding to a 55-fs transform-limited pulse,provides 50 channels for a channel spacing of 100 GHz(0.8 nm at 1.55 mm). A promising femtosecond lasersource at the 1.5 mm band is the Cr41:YAG laser.Repetition rates in the gigahertz range have alreadybeen demonstrated. Collings et al.2 report 200-fspulses at a 0.9-GHz cavity round-trip rate and at itsdouble and triple harmonics; they used a unique cavitythat employs a saturable Bragg ref lector. Mellishet al.3 and Risataki et al.4 produced 75-fs pulses at0.5 GHz and 125-fs pulses at 1 GHz, using a compactL-fold cavity.5,6 These pulse widths, however, arenot so narrow as the #45 fs pulses7,8 reported for astandard Z-fold cavity with a ,100-MHz repetitionrate. With an optimized L-fold cavity we expect thatsimilar operation should be possible at signif icantlyhigher rates. One of the most critical parametersfor Kerr-lens mode locking (ML) is the lasing-moderadius inside the gain medium. If focusing insidethe gain medium is too weak, Kerr-effect-inducedself-focusing is insufficient, and ML is unstable.However, if focusing is too tight, thermal lensingcounteracts self-focusing. By optimizing the focusingwe obtained 1.2-GHz operation with a 55-fs pulsewidth. In this Letter we describe cavity optimizationand characterization of the output pulses by second-harmonic-generation (SHG) frequency-resolved opticalgating (FROG).9

Figure 1 shows the L-fold cavity configuration.One end of the cavity is made from an 18-mm-long,2 mm 3 4.4 mm rectangular cross-section Cr41:YAGcrystal (IRE Polus). The crystal is cut normal tothe optic axis and coated with a dielectric stack forbroadband high ref lection (HR) and high transmis-sion, respectively, at 1550 and 1064 nm on one end;the opposite end is cut and polished slightly off theBrewster angle. The latter surface acts as an outputcoupler with an estimated coupling eff iciency of 0.5%.

0146-9592/00/080584-03$15.00/0

The crystal is in direct contact with a gold-platedcopper holder, which fits the crystal to within 5-mmaccuracy. A Peltier cooler maintains the holder at17.5 ±C. Folding mirror M2 has a radius RM2 � 30 orRM2 � 50 mm and is coated with a HR coating. TheLittrow prism is made from low-OH fused silica, andone side is coated with a HR coating. All HR coatingsare designed for .99.9% ref lectivity at 1475–1575 nmand are deposited by electron-beam evaporation.Pump light from a Nd:YVO4 laser (Spectra-Physics,Millennia IR) is focused onto the coated plane of theCr41:YAG crystal through an isolator and a lens�f � 229 mm�. The group-delay dispersion in the cav-ity is compensated for through the total cavity path byan equivalent prism pair formed by the Cr41:YAG crys-tal and the Littrow prism. ML is optimized when thetotal group-delay dispersion of the cavity is approxi-mately 2400 fs2, although optimization is not highlysensitive to group-delay dispersion. Astigmatismoriginating from folding mirror M2 is compensated forby the refraction at Brewster planes of the Cr41:YAGcrystal and the Littrow prism, which induces a focal-length change in the tangential plane.10 Accordingto our simulation with the ABCD matrix formalism,the stability region of the cavity for the sagittal planeis wider than that of the tangential plane. Whenthe folding angle is 31±–37± for RM2 � 30 mm anda 1.2-GHz cavity, the stability region of the tangen-tial plane is included in that of the sagittal plane,and the compensation for astigmatism is optimized.The experimentally optimized folding angle is �34±,

Fig. 1. Schematic of the L-fold cavity Cr41:YAGlaser: abbreviations defined in text.

2000 Optical Society of America

April 15, 2000 / Vol. 25, No. 8 / OPTICS LETTERS 585

although a precise angle is not critical for mode-lockedoperation.

We characterize the output pulses by SHGFROG. First a 300-mm-radius concave mirror colli-mates the divergent output beam from the Cr41:YAGBrewster plane. After the polarization is rotated by90± with a pair of mirrors, the beam is sent through aMach–Zehnder delay line, where two 50% beam split-ters upon 1-mm-thick fused-silica substrates divideand recombine the pulse train. At the output the twobeams are set parallel and focused by a 200-mm-radiusconcave mirror onto a 130-mm-thick b-barium boratecrystal. The second-harmonic signal is detected bya CCD linear array (Hamamatsu, M6296-01) througha 150-mm-focal length spectrometer (Acton, SP-150)with a 600-groove�mm grating (500-nm blaze). Thespectrum of the fundamental beam is measured at theoutput of another 150-mm focal-length spectrometer(Acton, SP-150) with a 300-groove�mm grating (2-mmblaze) by an InGaAs linear diode array (Hamamatsu,M6297-01). In addition to calibrating for the grat-ing eff iciency and the detector response function,we correct the detected SHG signal intensity forthe 1�l3 dependence of the SHG efficiency.11 Thealgorithm for the retrieving electric field is that ofKane et al.12

Figure 2(a) shows a typical FROG trace measuredfor the 1.2-GHz cavity with 30-mm-radius folding mir-ror M2. Although the spectra are acquired in a rangeof 650–860 nm, the signal level outside the range inFig. 2(a) was at the noise level and was therefore setto zero in the retrieving calculation. The pulse en-velope and phase retrieved from the FROG trace areshown in Fig. 2(b), and their Fourier transforms areplotted with respect to wavelength in Fig. 2(c), alongwith the directly measured spectrum. There are threenotable characteristics with respect to the pulse, whichcan be attributed to uncompensated third-order disper-sion (TOD). The first is the wide-shoulder structurein Fig. 2(b), which causes a deviation from the sech2

function (dashed curve) near the base of the pulse.This is the most characteristic manifestation of TODin the pulse.13 The second is the rather complicatedphase. Although the spectral phase in Fig. 2(c) isalmost f lat, the temporal phase in Fig. 2(b) has a cur-vature near the intensity half-maximum of the op-posite sign and a point of inf lection near the peak.The even more complex phase structure outside theinterval from 2100 to 100 fs is not significant be-cause of the low intensity. The characteristic phasenear the peak can be attributed to TOD by compari-son with Eq. (8) of Ref. 13. The third characteristicis the occurrence of the extra sharp peak at 1600 nmin Fig. 2(c). Ishida et al. observed as similar peak fora mode-locked Cr41:YAG laser and attributed it toa dispersive wave caused by TOD, which is ampli-fied by Raman gain.14 We estimate the TOD of the1.2-GHz cavity to be �9000 fs3. Although high-orderdispersion could be compensated for in ultrashortTi:Al2O3 lasers,15 it is diff icult to compensate for TODin the 1.5-mm region because the appropriate prismmaterials that could compensate for the positive TODof Cr41:YAG are not known.8

The pulse width of 55 fs and spectral width of 40 nm(full width at half-maximum) in Fig. 2 give a time–bandwidth product of dtdf � 0.29. This is unphysicalfor a true sech2 pulse shape, for which the transform-limited value is 0.315. However, the pulse has a broadshoulder structure, as noted above. Fitting the pulseenvelope to a sech2 shape gives a pulse width of either55 or 75 fs if the fit is made on the peak or the broadshoulders, respectively; the latter gives dtdf � 0.39.

The optimized cavity shows self-starting ML for anarrow range of pump powers of �2.5 W and an out-put power of 84 mW. Although the ML is relativelystable, the stability is better if one operates the laserwith a pulse width of �60 fs by tuning the Littrowprism to a slightly longer wavelength. This 60-fs op-eration is continuous for several hours.

The stability of the ML also depends on the curva-ture of folding mirror M2 and on the cavity length.The experimentally optimized pulse widths and out-put powers for several cavity configurations are sum-marized in Table 1, along with the calculated beamradii inside the Cr41:YAG crystal. The calculationwith the ABCD matrix formalism is for Cr41:YAG

Fig. 2. (a) Typical FROG trace of the Cr41:YAG laseroutput pulses. (b) Retrieved pulse envelope and phasefrom (a). The sign of dispersion is defined such that apositive second derivative implies positive dispersion. Asech2 pulse shape corresponding to a 55-fs width is shownfor comparison (dashed curve). (c) Fourier transform ofthe data in (b). Open circles show the directly measuredspectrum for comparison.

586 OPTICS LETTERS / Vol. 25, No. 8 / April 15, 2000

Table 1. Beam Radii and Output Characteristics

w1 w2

Repetition Sagittal Tangential Sagittal Tangential Pulse Width Output PowerRM2 �u� �mm� Rate (GHz) �mm� �mm� �mm� �mm� (fs) (mW)

30 (34±) 1.2 ,37 ,46 .134 .115 55 841.0 ,31 ,38 .158 .131 71 740.75 ,25 ,30 .198 .162 Unstable ML

50 (28±) 1.0 ,57 ,80 .102 .98 82 1060.75 ,42 ,59 .122 .101 68 770.5 ,30 ,42 .162 .121 Impossible ML

Pump beam 24 24 141 141

crystal length Lcry � 18 mm and Littrow prism lengthLprism � 10 mm. Because the beam radius depends onthe position of M2, we describe the maximum valueof beam radius w1 at the coated end and the mini-mum value of w2 at the Brewster end of the Cr41:YAGcrystal with the help of the symbols , and ., re-spectively. The laser operation is optimized in themiddle of the stability region where w1 is maximizedand w2 is minimized; i.e., the beam radius does notvary rapidly inside the crystal as would happen nearthe stability limits of the cavity. The pump beam’s ra-dius is also calculated by the ABCD matrix formalismfrom the specified beam parameters of the Nd:YVO4laser. The cavity configuration that gives a narrowerpulse width also generally shows more-stable ML andis self-starting. By contrast, a cavity in which MLis unstable needs to be started by translation of M2or by tilting of the Littrow prism. The best perfor-mance is obtained for the cavity with RM2 � 30 mmand fr � 1.2 GHz. Because the smallest beam radiusregion inside the crystal dominates the nonlinear in-teractions, we believe that the most-stable operationcorresponds to the optimal value of w1. The best per-formance is obtained for w1 of ,37 and ,46 mm in thesagittal and tangential planes, respectively. Softer ortighter focusing gives worse results. The former caseis easily understood: When the beam is weakly fo-cused, Kerr-effect-induced self-focusing is insufficient,and ML is unstable. For the latter case, there are twopossible explanations for the worse performance: oneis too small a mode diameter compared with the gainvolume, and the other is thermal lensing. To testthese two possibilities we investigate the effect of thepump laser waist on the operation of the RM2 � 30 mmand fr � 0.75 GHz cavity, which has sagittal and tan-gential radii that are most comparable with those of thepump beam. When the pump beam radii are changedto w1 � 16 and w2 � 209 mm with a pair of lenses�f � 229 and f � 287 mm�, ML is impossible and, inaddition, mode-locked operation is degraded for othercavity configurations in Table 1. This result is consis-tent with the interpretation of a thermal lensing limiton the minimum mode radius. Therefore the optimumcavity configuration is determined by a trade-off be-tween the strength of the nonlinear interaction andthermal lensing.

In summary, we have optimized an L-fold cav-ity Cr41:YAG laser for a repetition rate of 1.2 GHz.

Achievement of the demonstrated 55-fs pulse width isto our knowledge the best performance reported for.100-MHz operation. The pulse shape was character-ized by SHG FROG measurement. The pulse shapedeviates from a sech2 function, and it has wide shoul-ders. Although the spectral phase is almost f lat, thetemporal phase has a complicated structure. Thesecharacteristics can be explained by TOD. Becauseoptimum operation is obtained at the highest repeti-tion rate, further miniaturization should make higher-repetition-rate operation possible.

We thank S. Saito, S. Matsunami, and N. Moriya forfabrication of the mechanical parts of the laser and N.Sarukura and V. Kubecek for valuable advice regard-ing Cr41:YAG lasers. T. Tomaru’s e-mail address istomaru@harl.hitachi.co.jp.

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