1. Introduction

In the past decade, femtosecond lasers have spread their application in numerous scientific and engineering fields such as ultrafast spectroscopy, metrology, nonlinear microscopy, and superfine material processing. For those applications, high power, high efficiency, and compact femtosecond lasers are required. Yb³⁺ is the most interesting ion satisfying those needs. Its broad absorption and emission spectra allow directly laser-diode (LD)-pumped femtosecond laser. Moreover, its small quantum defect, absence of excited state absorption, upconversion, and cross-relaxation cause less thermal load and enable highly efficient operation. The emission and absorption spectra and thermal conductivity depend strongly on a host material. The femtosecond lasers based on various kinds of Yb-doped materials have been progressively demonstrated [1–8]. The average power has been scaled up to 60 W by a mode-locked thin-disk Yb³⁺:Y₃Al₅O₁₂ (Yb:YAG) laser [3] and as short as 47 fs pulses were obtained by a mode-locked Yb³⁺:CaGdAlO₄ laser [8].

Yb-doped crystalline sesquioxides Yb³⁺:Y₂O₃, Yb³⁺:Sc₂O₃, and Yb³⁺:Lu₂O₃ are very attractive gain media for high power femtosecond lasers since they have desirable thermal properties [9]. In the case of Lu₂O₃ single crystal, the thermal conductivity was reported to be 12.5 W/mK [10]. Although the thermal conductivities depend on the concentration of Yb³⁺ ions, they are considered to be still higher than that of Yb:YAG with the same concentration. Among them, Yb³⁺:Lu₂O₃ single crystal has the highest thermal conductivity of 11 W/mK with Yb-doping (Yb concentration of 2.7 at.%), while that of Yb:YAG at the same doping level is about 6.8 W/mK [10]. In addition they show broader emission bands than Yb:YAG due to their strong electron phonon interaction. They also have high nonlinear refractive indices. In the case of Lu₂O₃ ceramic, it is (3.96±1.77)×10^-13 esu while that of YAG is (2.51±0.71)×10^-13 esu [11], which can enhance self-phase modulation effect so that spectral broadening and Kerr-lens effect are easy to occur.

While crystalline sesquioxides are thus promising host materials for high power lasers, they have high melting points of more than 2400 °C. The growth of sesquioxide single crystals with a sufficient optical quality and large sizes are thus so difficult that their application has been limited as laser materials. Recent years Yb-doped sesquioxide single crystals [10,12] made by a special melt-growth method and their cw and first mode-locked sesquioxide laser operations with as short as 220 fs pulses [13,14] have been reported. However, the method still has limitation of sizes and quality. Recently we have succeeded in fabrication of rare-earth-doped sesquioxide laser ceramics with sufficient optical quality by a novel fabrication method of laser ceramics based on nanocrystalline and vacuum sintering technologies [15,16]. The ceramics have micro-scale grains and nano-scale grain boundaries. In the case of Nd³⁺:Lu₂O₃ ceramics, the average grain size is about 1 µm and the average grain boundary thickness is about 9.3 Å [17], which realizes the high transparency of our ceramics. Our ceramics have stronger fracture toughness than that of single crystals [18] so that ceramics are the best candidates for high power laser system because the thermal fracture limit is proportional to the thermal conductivity and fracture toughness. We have reported cw laser operations of Yb³⁺:Y₂O₃, Yb³⁺:Sc₂O₃, and Yb³⁺:Lu₂O₃ ceramics [19–21] and mode-locked laser operations [22–24] of Yb³⁺:Y₂O₃ ceramics. In the case of Yb³⁺:Y₂O₃ ceramics as high as 72% extraction efficiency in a cw operation and as short as 188 fs pulses in mode-locking were obtained. By other group as short as 280 fs mode-locked Yb³⁺:Y₃(ScAl)₂Al₃O₁₂ ceramic laser [25] has been reported. In this way the ceramic technologies enable investigation of new materials that have serious difficulties to grow as single crystals.

In this paper we report a diode-pumped passively mode-locked Yb³⁺:Lu₂O₃ ceramic laser generating 357 fs pulses with an average power of 352 mW. The efficiency against the absorbed pump power is as high as 32% with laser-diode pumping. To our knowledge this is the first demonstration of a diode-pumped mode-locked Yb³⁺:Lu₂O₃ ceramic laser.

2. Spectroscopic properties

The absorption and emission spectra of Yb³⁺:Lu₂O₃ ceramic at room temperature are shown in Fig. 1. There are many uncertainties in determination of the cross sections of rare-earth-doped sesquioxides because rare-earth ions can be situated in two possible site symmetries (C₂ and C_3i) [26]. In this work the effective absorption cross section is calculated under the assumption that the Yb³⁺ ions substitute in the C₂ and C_3i sites by the inherent ratio of 3 : 1 and the Yb³⁺ ions in the C_3i sites have no absorption. The effective emission cross section is estimated based on ref. [27] where a measured emission lifetime of 0.82 ms and a refractive index of 1.91 are used. In Fig. 1 there is a difference between the absorption and emission cross section at the 976 nm peak, which can be caused by the aforementioned uncertainties and reabsorption of fluorescence. Yb³⁺:Lu₂O₃ has the emission cross section peaks at 1032 nm (σ _e=0.93×10^-20 cm²) and at 1078 nm (σ _e=0.30×10^-20 cm²). Although the peak at 1032 nm is larger than the peak at 1078 nm, reabsorption loss at 1032 nm is stronger than at 1078 nm. In the case of a low output-coupling resonator or an optically thick ceramic, the lasing threshold at 1078 nm is lower than that at 1032 nm so that lasing at 1078 nm selectively occurs [23]. In order to suppress Q-switching instability a larger emission cross section is desirable [28], so that we have to use optically thin ceramics that have low reabsorption loss or some spectral selective elements in order to get oscillation at the 1032 nm emission band.

 

Fig. 1. Absorption and emission spectra (²F_7/2↔²F_5/2) of Yb³⁺:Lu₂O₃ ceramic. The absorption and emission spectra were measured with 1 at.%, 1 mm and 0.3 at.%, 1mm ceramics respectively. Arrows indicate the pump and lasing wavelengths in this experiment.

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In this work we used pumping at the 976 nm sharp peak. The absorption peak at 976 nm (σ _a=3.2×10^-20 cm²) is about three times larger than the 949 nm peak (σ _a=1.1×10^-20 cm²). Pumping at 976 nm allows us to use an optically thin ceramic that has a small reabsorption loss at the 1032 nm emission band. However, the absorption band at 976 nm (FWHM~3 nm) is narrower than the FWHM of a typical high-power LD (4~5 nm for ~5 W diodes) so that the maximum absorption efficiency was limited to about 60~70%.

3. Experiments

The experimental setup of mode-locked Yb³⁺:Lu₂O₃ ceramic laser is shown in Fig. 2. We employed a Z-shaped cavity configuration. The pump source was a broad-stripe LD that emits up to a 5 W power around 976 nm with the emission area of 1×100 µm and was cooled by water (~18 °C) in order to match the center wavelength to the absorption peak at 3.5~4 W pump power. The pump beam was focused in a 3 at.% 1 mm-thick Yb³⁺:Lu₂O₃ ceramic with 1/e² diameters of 27×180 µm by passing through four beam-shaping lenses and a cavity-folding mirror. The maximum launched pump power was about 4.2 W. The ceramic was arranged at the Brewster angle and mounted in a water-cooled copper holder that was placed at the center of two folding mirrors (M1, M2) with 100 mm radii of curvature (ROC). The folding mirrors were antireflection coated below 980 nm and have high reflectivity (R>99.9%) above 1020 nm. The z-fold angle was about 9° and astigmatism was partially compensated. The diameters of the laser mode waists in the ceramic were estimated by ABCD matrix formalism to be 45×84 µm in both configurations of cw (dashed line in Fig. 2) and mode-locked (solid line in Fig. 2) operations.

 

Fig. 2. Experimental setup of the diode-pumped mode-locked Yb³⁺:Lu₂O₃ ceramic laser.

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At first we performed the cw operation with a 5% output coupler (OC1) and a high-reflectance end mirror (HR). The lengths of the two arms were about 60 and 70 cm. For a passively mode-locked oscillation, another 5% output coupler (OC2) and a semiconductor saturable absorber mirror (SESAM, BATOP GmbH) were used in the respective arms. The total cavity length was about 150 cm. OC2 was wedged by about 30 minutes to avoid reflection at its back surface. If we use a parallel output coupler, it can generate a sub-pulse separated by the time interval corresponding to its thickness, even though there is an anti-reflection coating on the back surface. In the other end the SESAM was placed which has a 2% saturable absorption around 1045 nm, 30 µJ/cm² saturation fluence, and 10 ps carrier lifetime. The laser beam was focused onto the SESAM by a concave mirror (M3, ROC=400 mm) with the folding angle of 2°. The diameters of the focused spot on the SESAM were about 183×180 µm. For dispersion compensation we used an SF10 Brewster prism pair (P) with the tip-to-tip separation of 48 cm and a chirped mirror (M4) with the group-velocity dispersion (GDD) of -250 fs² around 1030 nm. The total negative GDD of this cavity was about -2800 fs² per a round trip. This GDD was necessary in order to achieve soliton mode locking.

4. Results and discussion

The output powers as functions of the launched pump power are shown in Fig. 3. In the multi-mode cw operation (dashed line in Fig. 2), oscillation at 1078 nm selectively occurred. During the oscillation, the residual pump power was measured at the right side of M2 (in Fig. 2) to estimate the absorbed pump power. A maximum output power of 2 W in multimode was obtained with a maximum launched pump power of 4.2 W (3 W absorbed). By incorporating a slit as a mode selective element, a maximum output power of 1.2 W in ~TEM₀₀ mode was obtained. The beam pattern was slightly elliptical because of imperfect compensation of astigmatism. Due to the insertion loss of the slit the threshold increased and then the lasing wavelength changed to 1034.5 nm from 1078 nm in ~TEM₀₀ mode. At the lower pump power region the pump spectral peak was shorter than the 976 nm absorption peak so that the absorption efficiency was very small and it caused nonlinearity in the evolutions in Fig. 3. In the case of ~TEM₀₀ mode operation the optical-to-optical efficiency is about 28%. The maximum absorption efficiency is about 60~70% and the mode-matching factor between the pump mode area and the lasing mode area in this experiment was about 50%. It can be expected that by improving the spectral width of the pump source and mode-matching factor, more than twice higher efficiency will be possible.

 

Fig. 3. Output power versus launched pump power. The cw operation at 1078 nm in multimode (circles), TEM₀₀ mode at 1034.5 nm (squares) and mode-locked operation at 1033.5 nm (triangles) are shown. The curves are for eye guides.

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For mode-locked operation, the SF10 prism pair, SESAM, and chirped mirror were incorporated. Due to their insertion loss the lasing wavelength changed to 1033.5 nm from 1078 nm. Cw mode-locked oscillation at a repetition rate of 97 MHz started when the launched pump power rose to 2.35 W, and then the output power jumped to ~130 mW from ~120 mW due to the absorption saturation of the SESAM. The threshold fluence on the SESAM was estimated to be about 120 µJ/cm². The shortest pulses were obtained with an output power of 352 mW and a launched pump power of 3.05 W (~1.1 W absorbed). An efficiency of 32% with respect to the absorbed pump power was obtained. The intensity autocorrelation and spectrum of the shortest pulses are shown in Fig. 4(a). By assuming a sech² pulse, the autocorrelation trace corresponds to a 357 fs pulse. The spectral bandwidth of 3.2 nm gives an almost transform-limited time-bandwidth product of Δτ×Δν=0.32.

In this experiment the shortest pulse width was limited by multi-pulse instability [29]. By increasing the launched pump power above 3.05 W, at first a cw ingredient added to the spectrum. After that, pulse splitting occurred and then the pulse width became broader (~460 fs) with the cw ingredient disappearing. After the pulse splitting, the output power jumped to ~370 mW from ~360 mW. The maximum average power of 660 mW with the maximum launched pump power of 4.2 W (~2.4 W absorbed) was obtained. The time intervals between the pulses were 5-7 ps (Fig. 4(b)) depending on the absorbed pump power, which is shorter than the 10 ps carrier lifetime of the SESAM. After pulse splitting the emission spectra of mode-locked pulses become narrower so that it can oscillate within the high gain region. The total gain thus increases and multi-pulse generation occurs with higher output power. Although the spectrum became narrower than that in a single-pulse operation, it showed no serious modulations. In order to suppress multi-pulse instability, increasing negative dispersion and decreasing the fluence on the SESAM are useful. Due to the high nonlinear refractive indices of sesquioxides, it needs larger negative dispersion. Yb³⁺:Lu₂O₃ laser at 1032 nm operates as a three-level laser, so that higher pump intensity will be required to obtain broader gain bandwidth and shorter pulse width.

 

Fig. 4. (a) Autocorrelation trace and spectrum (inset) of the shortest pulses at a 3.05 W launched pump power. The experimental data (points) and a sech2-fitting curve (solid curve) are shown. (b) Autocorrelation trace in a multi-pulse operation at a launched pump power of 4.2 W.

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5. Conclusion

We successfully demonstrated a directly diode-pumped SESAM mode-locked Yb³⁺:Lu₂O₃ ceramic laser. Almost transform-limited 357 fs pulses with the average power of 352 mW were obtained. To our knowledge this is the first time operation of mode- locked Yb³⁺:Lu₂O₃ ceramic laser. We believe that a desirable thermal property and strong fracture toughness of the ceramic will enable high-power femtosecond laser and optimizing the resonator design will enable generation of sub 200 fs pulses with the SESAM and much shorter pulse generation by Kerr-lens mode locking.