1. Introduction

Femtosecond mode-locked lasers are widespread to various scientific and engineering fields such as ultrafast spectroscopy, metrology, superfine material processing and microscopy, and so on. High average power femtosecond lasers are required for many of those applications. Yb³⁺ is an active ion promising both high power and high efficiency due to its small quantum defect and usability of laser-diode (LD) pumping [1]. Various host materials have been progressively investigated for ultrashort pulse lasers [2–11] and Yb³⁺:Y₃Al₅O₁₂ (Yb:YAG) laser is currently scaled up to a 60-W average power with a 810-fs duration [12]. Yb-doped sesquioxides (RE₂O₃, RE=Y, Sc, and Lu) have been the potential alternatives to Yb:YAG for power scaling because of their desirable thermal properties. The reported thermal conductivities of undoped Y₂O₃ crystals are as high as 27 W/mK [13] and 14 W/mK [14]. The thermal conductivities drops by doping Yb³⁺ but are considered to be still higher than those of the YAG with the same doping level. In addition, the strong electron-phonon interaction causes characteristic spectral broadening, especially in the case of Y₂O₃, with moderate values of cross sections. The absorption and emission spectra of 4 at.% Yb³⁺:Y₂O₃ ceramics are shown in Fig. 1. From these natures Yb-doped sesquioxides are expected to be the promising laser material for high power and ultrashort pulse lasers. However, the difficulty of crystal growth of such materials due to their high melting temperatures (2430°C in the case of Y₂O₃) has limited their application as laser materials, in which high optical quality and large sizes are required. Recently laser operation have been demonstrated with sesquioxide crystals fabricated by melt-growth methods [14–16] and mode-locked Yb³⁺:Sc₂O₃ crystalline laser with a 230-fs pulse width was also reported [17]. However, the crystal growth by conventional methods is quite difficult yet.

 

Fig. 1. Absorption coefficient (blue) and effective emission cross section (red) of 4 at.% Yb³⁺:Y₂O₃ ceramics at room temperature. Arrows indicate the pump and lasing wavelengths.

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Novel fabrication method of laser ceramics based on nanocrystalline technology [18,19] recently enables growth of rare-earth-doped Y₂O₃, Sc₂O₃ and Lu₂O₃ ceramics with sufficient optical quality. Highly efficient laser oscillations of neodymium [20,21] and ytterbium [22,23] doped ceramics have been demonstrated. As high as 72% extraction efficiency was obtained in LD-pumped Yb³⁺:Y₂O₃ ceramic lasers [23]. In this paper we report a passively mode-locked Yb³⁺:Y₂O₃ ceramic laser generating 615-fs pulses with a 420-mW average power. Future prospects for power scaling and shorter pulse generation are discussed. As far as we know, cw mode locking of a laser with a ceramic gain material is the first time.

2. Experiments

The experimental setup is schematically shown in Fig. 2. A z-fold cavity configuration was used. The pump source is a broad-stripe laser diode (Axcel Photonics Inc.) with the emission area of 1×100 µm² and the maximum output power of 4.5 W. The wavelength was temperature-tuned to 950 nm for pumping an absorption peak of Yb³⁺:Y₂O₃ below the zero-line at 976.5 nm (Fig. 1). After passing through the beam shaping optics and a cavity folding mirror, the pump beam was focused in the ceramic with 1/e² diameters of 31 µm×165 µm in air. The 1.5-mm-thick Yb³⁺:Y₂O₃ (C_Yb=8 at.%) ceramic was arranged with a Brewster angle and absorbed ~80% of pump power. The copper holder was cooled with flowing water at 18°C. This ceramic was placed between two high-reflecting mirrors (M1, M2) with 100-mm radius of curvature (ROC). Their transmittance at pump wavelength is 95% and the maximum launched pump power was 4 W. The z-fold angle was 8.5° and astigmatism was not fully compensated. The diameters of the laser mode waist in two configurations for cw and mode-locked operations are calculated by ABCD matrix formalism to be 41 µm×50 µm and 44 µm×44 µm, respectively (in air).

The cw laser for a reference operated along the dashed lines in Fig. 2. The two arms were slightly imbalanced with 70 and 60-cm lengths. A 5% output coupler was used. For passive mode locking, a semiconductor saturable absorber mirror (SESAM) [24] was placed in one of the arms. Our SESAM is commercially available one (BATOP GmbH), which has a 2% saturable absorption at 1064 nm, 70-µJ/cm² saturation fluence, and 20-ps carrier lifetime. The laser beam was focused onto the SESAM by a concave mirror (M3, ROC=300 mm) with the fold angle of 3°. The calculated beam diameters on the SESAM are 131 µm×133 µm. A SF10 Brewster prism pair with a 63-cm separation was inserted in another arm for dispersion compensation. A 2% output coupler was placed at this end. The pulse shape was measured with background-free autocorrelation with a 0.5-mm-thick type-I β-BaB₂O₄.

 

Fig. 2. Schematic of the diode-pumped mode-locked Yb³⁺:Y₂O₃ ceramic laser. L’s, lenses for pump beam shaping: L1, f=8 mm aspherical; L2, f=-6.4 mm cylindrical; L3, f=70 mm cylindrical; L4, f=75 mm doublet. M’s, high-reflecting mirrors; OC’s, output couplers; P’s, SF10 Brewster prisms. Dashed lines indicate the beam lines in a cw operation. Oscillograms of the mode-locked pulse trains are shown in the lower right.

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3. Results

In the case of cw laser operation, output powers of 1.5 W in multimode and 1.05 W in ~TEM₀₀ mode were obtained at the maximum pump power of 4 W (3.3 W absorbed). The extraction efficiency (32% in the case of TEM₀₀) seems relatively low, which is mainly due to mismatching between the pump and laser modes. The lasing wavelength was 1076 nm.

When the SESAM and prism pair were incorporated, a self-Q switching behavior was observed in a low pump power regime and then switched to cw mode locking at a 2.8-W pump power. At this transition the output power jumped from ~250 to ~300 mW because the absorption of the SESAM was fully saturated. The maximum average output power was 420 mW at a pump power of 3.3 W (2.6 W absorbed). When the pump power was further increased, the SESAM was damaged soon and then mode locking stopped, because the fluence on the SESAM exceeded its damage threshold (~1 mJ/cm²). The output power in cw operation was 750 mW at the same pump power.

Figure 3 shows the intensity autocorrelation trace and spectrum of the mode-locked pulses at the maximum power of 420 mW. The sech²-fit pulse width is 615 fs and the spectral width is 2.0 nm centered at 1076.5 nm. The time-bandwidth product is 0.318, indicating almost transform-limited pulses were generated. Small intensity modulation around the peak of the spectrum was reproduced; the reason is unclear. The repetition rate was 98 MHz and then the pulse energy and peak power were 4.3 nJ and 7 kW, respectively.

The output beam profile near the output coupler is shown in Fig. 4. The elliptical beam shape was caused by the astigmatism in the cavity. The ratio of 3:4 is smaller than the predicted value (3:5), which may be due to a thermal lens effect in the ceramic. The ${M_{\mathrm{x}}}^2$ and ${M_{\mathrm{y}}}^2$ values were evaluated to be less than 1.1, which indicates the spatial quality was also nearly diffraction-limited.

 

Fig. 3. (a) Intensity autocorrelation trace of the mode-locked pulses. Solid curve : fit with sech² pulse shape. (b) Spectrum of them. FWHMs are shown by arrows.

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Fig. 4. Contour plot of the output beam profile.

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4. Discussion

As is shown in Fig. 1, Yb³⁺:Y₂O₃ ceramics have broad spectra due to strong electron-phonon interaction. There is some uncertainty in determination of the cross sections because rare-earth ions can be situated in two possible site symmetries [25]. We evaluated here the emission cross section as effective values by use of the measured emission lifetime of 0.82 ms and refractive index of 1.89 [26]. The effective cross section at the laser wavelength of 1076 nm is 0.4×10^-20 cm². The critical intracavity pulse energy, which gives the transition point from self-Q switching to cw mode locking [27], is then calculated to be 360 nJ in the case without dispersion compensation. In order to operate the laser below the damage threshold of the SESAM, soliton mode locking [27] is required for mode locking our 1076-nm Yb³⁺:Y₂O₃ ceramic laser, by managing self-phase modulation and negative group-velocity dispersion. The observed transition intracavity pulse energy of 128 nJ is well below the value mentioned above. Even in that case the fluence on the SESAM amounts to 0.94 mJ/cm², already comparable to the damage threshold. The maximum output power is then limited to be 420 mW at present. The operation near above the transition is the origin of the fluctuation in the intensities of the pulse train (Fig. 2). For further output power and stability, optimization of the ROC of M3 and the transmittance of OC2 is required to decrease the critical intracavity pulse energy with a moderate coupling efficiency. We also have a plan to replace the SESAM with higher damage-threshold ones in near future. We believe the output power can then be raised to a 1-W level.

The optical-to-optical efficiencies with respect to the launched and absorbed pump powers are 13% and 16%, respectively. These values are comparable with or even higher than the typical efficiencies of diode-pumped mode-locked Yb-doped solid-state lasers reported so far. If care is taken for mode matching of the pump and laser by, for example, use of cylindrical cavity mirrors [3], the efficiency will increase by a factor of 2, which would be comparable to the 30% efficiency in a Ti:sapphire-laser pumped femtosecond Yb³⁺:Sc₂O₃ crystalline laser [17]. The ceramic nature imposes no additional difficulties on mode-locking and such highly efficient operation is enabled due to its excellent transparency and quality.

Sub-100-fs pulse generation by use of the broad emission band is also to be pursued. The linewidth of the 1076-nm band is 18 nm in FWHM, which corresponds to the minimum pulse width of 68 fs. The relatively long prism separation in the current setup may elongate the pulse width of the fundamental soliton. However, when the separation was shortened to less than 50 cm, the spectrum exhibited heavily modulated shapes, which is possibly due to multipulsing instability [28]. The characteristic high nonlinear refractive indices of sesquioxides (n ₂~12×10^-16 cm²/W for Y₂O₃) [29,30] impose careful adjustment of the net dispersion for the shortest pulse operation. On the contrary, it will be advantageous for Kerrlens mode locking, which may be more suitable for much shorter pulse formation [8].

Even though the 1031-nm band has a larger emission cross section (1.0×10^-20 cm²), lasing at the 1076-nm band selectively occurs because of its lower threshold. The strong ground-state absorption around 1030 nm, which is characteristic in a quasi-three level system, makes it difficult to lase at the 1031-nm transition. When output couplers with T≥30% were used in the cw laser cavity, the lasing wavelength switched to 1031 nm (~600-mW output power), which well indicates the 1031-nm band potentially has a higher net gain than the 1076-nm band. Shortening the gain length or cooling the ceramic decreases the absorption loss and also enables lasing at the 1031-nm band [23]. The larger cross section is preferable for suppression of Q-switching instability [27], and then will enable higher output power operation with an intracavity pulse energy well below the damage threshold of the SESAM. Threshold control and intense pumping for enough absorption saturation are the key points for high-efficiency operation at the 1031-nm band. These are the subjects to be targeted in the next stage.

5. Summary

Mode locking of an Yb³⁺:Y₂O₃ ceramic laser has been successfully demonstrated. Transform-limited 615-fs, 4.3-nJ pulses are generated with an average power of 420 mW, which will be scaled to shorter pulses with higher power. Highly transparent Yb³⁺:Y₂O₃ ceramics with high thermal conductivity and broad emission spectrum will be one of the most promising material for high-average power ultrashort pulse laser.