1. Introduction

Ytterbium doped materials are attractive for compact high-power femtosecond laser sources in the 1-µm spectral range. Femtosecond laser operation has been successfully demonstrated in a great number of Yb-doped hosts [1–5], and mode-locked output powers in the Watt range were achieved [6]. A particular attraction of Yb-doped materials is their small quantum defect, given the small Stokes shift (~600 cm^-1) between absorption and emission, which reduces the thermal load and increases the laser efficiency. Additionally, excited state absorption, up-conversion processes and cross-relaxation are practically absent in Yb-doped materials. Moreover, the broad absorption bands of these laser materials are covered by high-power InGaAs laser diodes, which permits efficient pumping.

The emission and absorption cross sections, the upper state lifetime, the splitting of the two electronic states of Yb³⁺ and the phonon energies depend strongly on the host and its anisotropy. The host also determines the thermo-mechanical properties and the allowable doping level. In this regard, the isotropic sesquioxides Sc₂O₃, Y₂O₃ and Lu₂O₃ [7] are promising for high-power applications because their thermal conductivity is higher and the ground state splitting is larger than in YAG. Furthermore, the Yb-doped sesquioxide crystals exhibit broader emission bands than Yb:YAG which makes them an excellent choice for highly efficient ultrashort-pulse laser sources. In quasi-three-level laser materials, a large ground-state splitting is important for a reduction of the thermal population of the lower laser level, resulting in less reabsorption losses. These advantages of Yb-doped sesquioxide crystals have already been exploited in cw laser experiments. Diode pumping of these materials in simple two-mirror cavities resulted in remarkable slope efficiencies [8]. Because of their very promising features, Yb-doped sesquioxides are also in the focus of current research on ceramic based laser materials [9].

Very recently, the first mode-locked laser operation based on a sesquioxide host was demonstrated in Yb:Sc₂O₃ [10]. Highly efficient mode-locked laser operation with pulses as short as 230 fs at an average power of 0.54 W was obtained at 1044 nm. Femtosecond operation was also demonstrated in a Yb:Y₂O₃ ceramic [11]. Here a pulse duration of 615 fs and an average power of 420 mW were achieved. The emission was centered at 1076 nm, which corresponds to the long wavelength band of the Yb-doped sesquioxide emission characteristics (see Fig. 1). Both lasers were passively mode-locked by a saturable absorber mirror (SAM), and diode-pumped operation was demonstrated.

Here we analyze the specific thermal characteristics and demonstrate, for the first time to our knowledge, mode-locked laser operation of Yb³⁺:Lu₂O₃. We present results obtained both, in the picosecond and the femtosecond regime.

2. Yb-doped sesquioxides

2.1 Thermal conductivity

The thermal conductivity of solids is a key parameter in electronics and optics, given the present tendency of increasing the energy density in functional materials. The thermal conductivity in insulator crystals is governed by lattice vibrations. Local heating of the crystal leads to population of phononic states which dissipate through the crystal lattice. The heat conductivity is limited by phonon scattering at the sample surfaces, surface defects, lattice defects, and impurities, as well as umklapp-processes depending on the sample temperature [12]. The thermal conductivity of a crystalline material usually decreases when doped by luminescent ions.

The thermal conductivity of yttria (Y₂O₃) was first measured by Klein and Croft [13] as 27 W/m/K. However, we could not reproduce such high values in our crystal samples. The thermal conductivity measured in our sesquioxide crystals, undoped and with Yb-doping are compiled in Table 1 and compared with corresponding values of YAG and Yb:YAG. Without Yb-doping, all investigated sesquioxide crystals generally show a higher thermal conductivity than YAG. Among the sesquioxides scandia (Sc₂O₃) has the highest thermal conductivity of 16.5 W/m/K, lutetia (Lu₂O₃) with 12.5 W/m/K the lowest at room temperature. To investigate the dependence of the thermal conductivity on Yb-doping, sesquioxide crystals with an identical doping level of 2.7–2.8% were chosen. Due to the higher cation density in sesquioxides, this doping level is comparable to 5% Yb-ion densities in YAG. Inspection of the measured values in Table 1 reveals that ytterbium-doping has the strongest effect in Sc₂O₃, with a reduction of the thermal conductivity to less than half of the value for the undoped host. A strong reduction is also observed in Y₂O₃. Despite the higher thermal conductivity of the undoped sesquioxides, neither Sc₂O₃ nor Y₂O₃ sustain this advantage when doped with Yb; both materials do not exhibit significantly improved thermal conductivities compared to the 6.8 W/m/K of Yb:YAG [14].

Table 1. Thermal conductivity in W/m/K of different sesquioxide crystals in comparison to YAG with and without Yb-doping. Values in [] are estimated.

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In contrast to the other sesquioxides, however, Lu₂O₃ stands out with only a soft decrease of the thermal conductivity to 11.0 W/m/K due to ytterbium doping. This can be explained by the fact that ytterbium and lutetium exhibit very similar masses and bonding forces. Therefore, ytterbium-doping causes only a small disturbance to the crystal lattice and affects phonon scattering only slightly. Consequently, the thermal conductivity of Yb-doped lutetia is nearly twice higher than that of Yb-doped YAG. This renders lutetia a very promising host for ytterbium based high power laser systems. Our experimental result confirms theoretical predictions of Gaumé et al. [15], who already proposed Lu₂O₃ as the material with the lowest drop in thermal conductivity when doped with ytterbium ions.

2.2. Spectroscopic properties

Comparative studies of 13 available Yb-doped hosts evaluating the output yield (P_out/P_pump) and the slope efficiency on the basis of the spectroscopic characteristics predicted that KGd(WO₄)₂, KY(WO₄)₂, Sc₂O₃, and Lu₂O₃, are the most efficient representatives of this class of materials for longitudinal pumping [16]. The monoclinic double tungstates KGd(WO₄)₂ and KY(WO₄)₂ stand out because of their large absorption and emission cross sections [3]. In contrast, the isotropic sesquioxides Sc₂O₃ and Lu₂O₃ [8] are more promising for high-power applications as the strong anisotropy of the thermo-mechanical properties of KGd(WO₄)₂ and KY(WO₄)₂ is a serious limitation.

The absorption and emission cross sections of Yb:Lu₂O₃ are shown in Fig. 1. The laser wavelength near 1033 nm corresponds to the transition from the lowest level of the ²F_5/2 upper state to the third level of the ²F_7/2 lower state. This transition exhibits the highest gain resulting in a reduced reabsorption loss (inset Fig. 1).

 

Fig. 1. Absorption σ_abs and emission cross section σ_em of Yb:Lu₂O₃ and energy-level diagram with the relevant transitions (inset). The points indicate the pump- and laser transitions.

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3. Experimental laser setup

The laser experiments are performed with a Ti:sapphire laser as a pump source, which emits up to 2 W at 976 nm. The cavity setup is illustrated in Fig. 2. For the experiments a 1.33-mm-thick 2.7% Yb/Lu-site (7×10²⁰ Yb³⁺ atoms/cm³) Lu₂O₃ crystal was employed with an aperture of 3×5 mm² and used under Brewster angle. No special provision was made for cooling the sample. The Ti:sapphire beam was focused by an f=6.28 cm lens through the folding mirror M₂, and 70% of the incident pump radiation were absorbed by the crystal.

 

Fig. 2. Setup of the mode-locked Yb: Lu₂O₃ laser: SAM - saturable absorber mirror; M₁ - focusing mirror (ROC=10 to 15 cm); M₂, M₃ - folding mirrors (ROC=10 cm), P₁, P₂ - SF6 prisms; M₄, M₅ - output couplers (T=1 to 5%).

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We studied a Z-shaped astigmatically compensated resonator with two curved folding mirrors (radius-of-curvature: ROC=10 cm) with a 30-µm cavity waist at the position of the Yb:Lu₂O₃ crystal. One arm contained an additional focusing mirror M₁ (ROC=10 or 15 cm) to increase the intensity on the saturable absorber mirror, which acts as an end mirror. The other arm contained a plane output coupling mirror. In this arm two dispersion compensating prisms could be included. The SAM (BATOP GmbH, Germany) high-reflection band extends from 995 to 1095 nm with 2% of saturable absorption, 70 µJ/cm² saturation fluence, and a 20 ps relaxation time constant. The non-saturable loss was specified by the supplier as less than 0.3%.

4. Yb:Lu₂O₃ mode-locked laser: results

Using the setup of Fig. 2 with a 5% output coupler, yet without intracavity prisms, the laser operated in the picosecond regime at a pulse repetition rate of 109 MHz. In the mode-locked regime the maximum pump efficiency reached 32%. Pulses as short as 1.16 ps at 1033.5 nm could be achieved at a maximum average output power of 470 mW. The measured slope efficiency amounted to 44%. Although the Yb:Lu₂O₃ crystal was not actively cooled, thermal problems did not occur. The measured autocorrelation traces are well fitted assuming a sech²-pulse shape. In Fig. 3 the autocorrelation functions are shown together with the emission spectra at maximum output power. Both, experimental data (squares) and the fit (line) are plotted. The 5.5 nm broad spectrum (FWHM) could support pulses of about 200 fs duration, which means that the experimentally obtained pulse duration in the picosecond regime exceeds the Fourier limit by a factor of 6 (Fig. 3(a)). At lower output powers the pulse duration remained unchanged but the pulse spectral width decreased by 70%.

 

Fig. 3. Autocorrelation trace and spectrum (inset) in the picosecond (a) and in the femtosecond regime (b).

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For femtosecond operation, the ROC=15 cm focusing mirror M1 was used to increase the pulse fluence on the SAM. Additionally, two 60°-SF6 prisms with a tip-to-tip separation of 41 cm were inserted in the output coupling arm (Fig. 2). These prisms compensate for the positive group-velocity dispersion inside the cavity and balance the self-phase modulation introduced by the Kerr nonlinearity of the laser crystal. For femtosecond operation, a 3% output coupler was used. The resulting pulse repetition rate is 97 MHz. The deconvolved FWHM of the pulse is 220 fs, and the central wavelength is 1033.5 nm (Fig. 3(b)). The time-bandwidth-product amounts to 0.334, which is close to the Fourier limit (0.315). The obtained pulse duration is substantially shorter than the 340 fs limit reported for Yb:YAG [2], which can be attributed to the larger gain bandwidth of Yb:Lu₂O₃. In contrast to the ceramic-based results of Ref. [11], stable short-pulse operation was achieved in the band with the largest emission cross section (apart from the zero-line band at 976 nm), which also coincides with the most pronounced Yb:YAG transition at 1032 nm.

The output power versus the absorbed pump power in the femtosecond configuration is shown in Fig. 4, both below and above the mode-locking threshold. The measured cw lasing threshold amounted to 380 mW of absorbed pump power. The slight increase of output power in the transition from the cw to the mode-locked regime is due to the saturated loss of the SAM. Mode-locked operation was obtained at a maximum output power of 266 mW, corresponding to a pulse energy of 3 nJ or 14-kW peak power. From these experimental data we deduce a slope efficiency of 23% and a maximum pump efficiency of 15.5%. The lower efficiency compared to the picosecond results is mainly due to insertion losses of the SF6 prisms. The observed transversal mode structure of the Yb:Lu₂O₃ laser remained basically TEM₀₀. For all arrangements investigated, the mode-locked operation was stable for hours, without evidence of dropping out or tendencies toward passive Q-switching [17].

 

Fig. 4. Output power versus absorbed pump power of the femtosecond Yb:Lu₂O₃ laser and below the mode-locking threshold (cw – continuous wave).

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Compared to Yb:Sc₂O₃ [10], Yb:Lu₂O₃ exhibits a somewhat lower efficiency. This can be attributed to the imperfect crystal quality of the available Yb:Lu₂O₃ sample. The stronger visible fluorescence in lutetia is an indication for existing impurities in the crystal lattice.

5. Summary

In conclusion, we have generated the shortest pulses out of a sesquioxide laser and experimentally demonstrated that Yb:Lu₂O₃ is a very promising isotropic crystal for high-power mode-locked lasers in the 1 µm range. Compared to Yb:YAG, lutetia exhibits a larger gain bandwidth and higher thermal conductivity. In contrast to other Yb-doped hosts, Yb doping does not significantly corrupt the thermal conductivity in Lu₂O₃.

Self-starting passive mode-locking with pulses as short as 220 fs was achieved at 1033.5 nm. The demonstrated maximum output powers of 470 mW and 266 mW in the picosecond and femtosecond regime, respectively, are not yet a limit. Output powers in the Watt range can be expected when crystals with a higher optical quality – less impurities – and higher pump powers are applied.