The pulse shaping dynamics of a diode-pumped laser oscillator with active multipass cell was studied experimentally and numerically. We demonstrate the generation of high energy subpicosecond pulses with a pulse energy of up to 25.9µJ at a pulse duration of 928fs directly from a thin-disk laser oscillator. These results are achieved by employing a selfimaging active multipass geometry operated in ambient atmosphere. Stable single pulse operation has been obtained with an average output power in excess of 76W and at a repetition rate of 2.93MHz. Self starting passive mode locking was accomplished using a semiconductor saturable absorber mirror. The experimental results are compared with numerical simulations, showing good agreement including the appearance of Kelly sidebands. Furthermore, a modified soliton-area theorem for approximating the pulse duration is presented.
©2008 Optical Society of America
Ultrashort laser pulses in the microjoule regime are of prime importance for many applications, including high-speed micromachining , pumping of optical parametric oscillators and amplifiers, as well as basic research, e.g. in high-field physics or for the generation of attosecond electron pulses [2, 3, 4, 5]. As compared to external amplifiers [3, 6], ultrafast oscillators are very attractive due to their simplicity and compactness. To some extend the pulse energies from an oscillator can be increased by using extended resonator cavities [5, 7, 8] or by cavity dumping [9, 10]. Previous maximum pulse energies obtained directly from an oscillator in ambient atmosphere were below 2µJ. These pulse energies were limited by the strong self-phase modulation (SPM) of air . Higher pulse energies were obtained in a He-flooded cavity with pulse energies of 5.1µJ  and 11µJ  at subpicosecond pulse lengths. One way to decrease the SPM is to use larger output-coupling (OC) rates in combination with a high-gain medium. In order to reach high average powers together with high pulse energies a thin-disk (TD) laser crystal is the medium of choice , allowing for power scalability by increasing the beam size and exploiting the excellent cooling properties of the TD. However, the low gain of a TD laser has to be overcome. Therefore, we have increased the round trip gain by passing the gain medium successively under different angles within one round trip by use of a novel active multipass cell (AMC). This approach has previously been used in laser amplifiers with conventional solid-state rod geometries , as well as in thin-disk amplifiers . Recently we have obtained pulse energies of 13.4µJ with an active multipass cell operated in air . Here, we report on the generation of pulse energies of up to 25.9µJ in ambient atmosphere by increasing the pump-spot size on the TD and by the use of different semiconductor saturable absorber mirrors (SESAMs) .
2. Experimental results with an active multipass geometry
Experiments have been performed with 11 and 13 passes through an AMC. Whereas the experiments with 13 passes were done for a further increase of the pulse energy, a more detailed analysis at various pump powers and by use of different SESAMs was accomplished for the laser operating with 11 passes through the AMC.
At a repetition rate of 3.4MHz, corresponding to 11 passes through the AMC—or 44 passes through the gain medium —, a pulse energy of up to 20µJ at a maximum average output power of 68Wwas obtained. The laser was operated at a total pump power of 219Wand an OC rate of ≈ 64%. A pulse duration of 811fs, deduced from the autocorrelation assuming an ideal sech 2 shape, and a spectral bandwidth of 1.48nm (FWHM) at a center wavelength of 1030nm was measured. The resulting time bandwidth product of 0.34 is within 10% of the transform limit of 0.315 for soliton pulses.
The experimental setup of the laser is shown in Fig. 1. The telescopic mirrors (M2 and M7) had a focal length of 1.25m. Six dispersive mirrors were included in the AMC design with a total GDD of -0.18ps2 per cavity round trip. The dispersive mirrors had a reflectivity of about 99.85% and >132 bounces within each round trip. The Yb:YAG disk had a thickness of 60µm and a wedge angle of 0.1°. The pumping chamber provided 20 passes through the gain medium, leading to an estimated absorption of less than 73% for the fiber-coupled 940nm pump power. The estimation was done by a numerical simulation that simulated rate equations between gain, laser power, and pump power. The optical to optical efficiency was 31%, whereas when taking into account the anticipated amount of pump absorption an effective optical to optical efficiency can be calculated to be 42%.
While in the experiments described here the same pump chamber and TD as in Ref.  was used, in contrast to Ref.  the laser was operated at a larger spot size on the TD (1mm in radius), in order to minimize thermal lensing and to increase the maximum possible pump power without risking damage of the disk. The CW background as observed in Ref.  at wavelengths far off the peak wavelength of the pulses was found to be enlarged for small mode radii or imprecise overlap of the various modes on the TD. A precise adjustment of the mode radii with respect to the pump mode size is especially difficult for a large dioptric power of the TD, which was observed for a small pump spot size and large pump powers as described in Ref. . By using a larger pump spot width (1mm) the dioptric power of the TD was mostly eliminated. Hence, better control of the mode radii was possible and the CW background was completely suppressed for all pump powers.
The high round trip gain allowed for output-coupling (OC) rates of up to 78% (with 13 passes through the AMC), which is - to our knowledge - the highest OC rate of any TD laser reported so far. Thereby the ratio of intracavity pulse energy to external energy was greatly reduced, such that helium flooding could be avoided. Strong SPM balanced by large negative group delay dispersion (GDD) resulted in soliton mode locking as the predominant pulse shaping mechanism . The B-integral per round trip was calculated to be B=0.9rad (for 32µJ pulses before OC) at maximum, mainly originating from the nonlinear refractive index of air. For a Gaussian beam, the SPM-coefficient can be calculated according to
with n 2 being the nonlinear refractive index of the material and w the spot size at the respective position. It was found that for the resonator cavity used in this work the SPM coefficient caused by air can be calculated for a Gaussian beam by using the formula
Here, N img is the number of passes through the AMC plus the number of telescopic arrangements, e.g. 4 f imaging arrangements, outside of the AMC and a respective fraction for the remaining part of the cavity, alltogether taken twice for one complete round trip. This formula is independent of the mode size on the TD and the actual focal length of the mirrors in the AMC; consequently, it can be used for easily calculating the SPM coefficient for different number of passes through the AMC. With a nonlinear refractive index of air of 4.0·10-23m2/W , a total SPM coefficient of ≈37.5·10-3MW-1 was calculated (N img,ext=1.4 for the part outside the AMC); the contribution caused by the TD is smaller than 2%. Dispersive mirrors introduced a total GDD of -0.1787ps2 per round trip including the positive dispersion introduced by the gain medium.
The beam profile measured at maximum output power with a commercial camera-based system was close to diffraction limited (an M2<1.3 was measured for the largest external pulse energies at a micromachining setup behind an acousto-optic modulator).
Passive mode locking of the laser was started and stabilized with the help of a SESAM . In contrast to the experiments in Ref.  a larger mode radius of 450µm was chosen on the SESAM. Operation at even larger spot sizes was unstable, due to a nonspherical curvature of the SESAM surface; the chosen spot size still leads to a strong saturation (F/F sat ≈65, with F and F sat being the fluence and saturation fluence, respectively) at the maximum internal pulse energy of approximately 32µJ (20µJ external pulse energy). The mode size was controlled with a camera-based system. Due to a remaining slight thermal lens dioptric power, partly caused by the highly dispersive chirped mirrors (HDCMs), the mode size on the SESAM decreased to a minimum of 400µm for smaller internal pulse energies with less pump power. As a result, Q-switched mode locking (QML) was further suppressed as compared to the case without any change in mode size on the SESAM. No degradation of the SESAM (or any other optical component) was observed during several hours of operation.
Experiments with 11 passes through the AMC have been performed with four different SESAMs; the SESAMs were characterized by using a pump-probe setup with 80fs pulses at 1030nm and pulse fluences, similar to those in the laser cavity. The reflectivity curve of the SESAM was fitted with a macroscopic model function as given by :
resulting in the parameters as listed in Tab. 1. R lin is the linear reflectivity of the unsaturated SESAM, R ns the nonsaturable loss in absence of two-photon absorption (TPA), and F 2 is the rollover coefficient, attributed to TPA for the pulses used in the pump-probe setup. The modulation depth of the SESAM is then given by ΔR=R lin-R ns. The SESAMs had a fast relaxation time of some hundred femtoseconds and a slow relaxation component with a relaxation time of some tens of picoseconds. The results of the experiments with 11 passes through the AMC at various pump powers are listed in Tab. 2, whereas only the parameters for the experiments with the highest energy available for single pulse operation are shown for each specific SESAM, with exception of additional experiments at lower pump powers for operation with SAM-B1. The amplitude noise was measured by using the statistics function of the oscillscope that was used. The respective root mean square (RMS) noise as listed in Tab. 2 is given by the standard deviation of the area below the oscilloscope trace within a time window encompassing one complete pulse trace; measured over a respectable number of pulses, it includes high and also very low frequency noise components. Operation with SAM-R1 and SAM-R2 showed a much larger RMS noise, partly caused by operation closer to the critical energy for QML as a result of the larger modulation depth, and due to a different mounting procedure (SAM-R1 and SAM-R2 were mounted on a copper plate by use of silver conductive paste) that is presumably more sensitive to thermal effects.
The relationship between GDD, SPM, external pulse energy, and pulse length was independent of the actual SESAM that was used. When assuming an exponential increase of the pulse energy inside the resonator an average intracavity pulse energy can be calculated. In combination with the soliton area theorem [21, 18] a modified soliton area theorem for a laser comprising an AMC can then be found:
Here, β 2 is the total GDD per round trip, γSPM the SPM coefficient, OC the output coupling rate, and E P, ext the external pulse energy of the resonator. The pulse length over energy according to this modified version of the soliton area theorem is plotted in Fig. 2 together with the measured pulse durations over external pulse energy for all experiments with 11 passes through the AMC and an OC rate of 64%. Hence, soliton mode locking was confirmed by the applicability of this modified version of the soliton area theorem.
QML and double pulsing was observed for operation with all SESAMs at very large and small pump powers; thereby setting a lower and upper limit, respectively, for stable mode locking. The range of operation for each SESAM is highlighted in Fig. 2. Whereas QML is mostly influenced by the modulation depth and the saturation fluence  the onset of double pulsing is affected only by the modulation depth of the SESAM . A large modulation depth should prevent double pulsing. However, for pulses in the picosecond regime (>1ps) small modulation depths of the SESAM were sufficient, whereas for subpicosecond pulses double pulses could only be suppressed by use of SESAMs with larger modulation depths, as can be seen from the results of the experiments shown in Fig. 2.
Operation with SAM-B1, having a small modulation depth and therefore only a small tendency for QML, showed a large stable continuous-wave mode locking (CWML) operation range, which can be seen in Fig. 3. In the figure, the output power is plotted over the pump power, whereas the pump powers leading to the occurence of double pulses and QML are highlighted. The results for this specific SESAM at various pump powers are shown here in more detail. SAM-B1 was already used in the experiments described in Ref.  to initiate and stabilize mode locking.
With SAM-B1 a maximum pulse energy of 16.2µJ at a pulse length of 1086fs and an average output power of 55W was obtained before double pulses were observed. As can be seen in Fig. 4, the spectral bandwidth was 1.08nm at a center wavelength of 1030.1nm, resulting in a TBP of 0.33, which is within 10% of the transform limit of 0.315 for soliton pulses. A total B-integral per round trip of 0.56rad was estimated. The beam profile for stable CWML at the largest pump power is shown in the inset of Fig. 3.
Despite the large number of passes through the TD the resonator was not only stable over the full range of pump powers but even allowed for nearly diffraction-limited operation and stable ML for most of this range, due to the negligible change of thermal lens dioptric power of the disk, caused by the larger diameter of the pump spot as compared to the experiments in Ref. . The larger pump spot, requiring a larger laser mode, is the reason for an increase in the critical energy according to the QML criterion. Hence, in contrast to the experiments described in Ref. , for pump powers below 55W, QML rather than CW operation was observed.
Increasing the number of passes through the AMC towards 13, i.e. 52 passes through the gain medium, a maximum average output power of 76W was obtained at a total pump power of 236W and an OC rate of 78%. At a repetition rate of 2.93MHz this corresponds to a pulse energy of 25.9µJ. The spectrum measured at this pulse energy is shown in Fig. 5 and the auto-correlation trace is shown in Fig. 6. A pulse duration of 928fs, deduced from the autocorrelation assuming an ideal sech2 shape, and a spectral bandwidth of 1.22nm (FWHM) at a center wavelength of 1030nm was measured. The resulting time bandwidth product of 0.32 is within 10% of the transform limit of 0.315 for soliton pulses. For mode locking the laser SAM-R1 was used. Different to the experiments with 11 passes through the AMC, Kelly sidebands  were visible at the outer sides of the spectrum. They are caused by an increased total GDD due to the additional passes through the AMC. Within the figure also the spectrum as given by numerical simulations is shown, showing Kelly sidebands at the respective positions. In order to adjust the position of the Kelly sidebands, the GDD and third order dispersion (TOD) were used as fit parameters, resulting in a total GDD of -0.193ps2 and a TOD of -0.00226ps3. The width of the spectrum was further adjusted by using the pulse energy as fit parameter, resulting in a pulse energy of 24.52µJ. With an SPM coefficient of 44.45·10-9MW-1, the resulting pulse length according to Eq. (4) would be 943fs, whereas the simulations resulted in a pulse length of 938fs. Both are in good agreement with the experimentally obtained pulse duration.
3. Result and conclusion
In conclusion, we have demonstrated a subpicosecond laser oscillator producing pulse energies beyond the 20µJ level without external amplification. The laser was operated in ambient atmosphere. Pulse energies of up to 25.9µJ have been obtained with an unamplified solid-state laser oscillator comprising an AMC within the laser cavity. We presented detailed experimental results on this laser architecture, which appears to be the least complex for generating high energy pulses directly from an oscillator. The concept allowed for (i) an easy alignment of the components, (ii) enough GDD by only few dispersive mirrors to compensate for the SPM due to air, (iii) enough gain to overcome cavity losses, (iv) a high OC and thus low intracavity pulse energies, and (v) a large gain bandwidth for the generation of subpicosecond pulses. A modified version of the soliton area theorem was presented for approximating the relationship between external pulse energy, GDD, SPM, and pulse length of a laser oscillator with AMC and large output-coupling rate.
Even higher pulse energies can be obtained by increasing the resonator length further, e.g. by introducing an additional passive multipass cell into the laser resonator. However, the experiments were not limited by the pump-power density at the moment, which can be increased by using more passes of the pump light over the TD, increasing the pump absorption from ≈ 74% to 100%, or by using a pump diode with larger output power. Instead, the obtained pulse energies were limited by the onset of double pulsing. The occurrence of multiple pulsing can be most likely attributed to the decreased modulation depth of the SESAMs caused by TPA.
This work was partly funded by the German Federal Ministry of Education and Research, contract 13N8580 and by a grant from the Ministry of Science, Research and the Arts of Baden-Württemberg. We thank J. Demsar, M. Beyer, and H. Schäfer for access to the pump-probe setup.
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