1. Introduction

Ytterbium-based solid-state lasers have attracted increasing interest over the past few years as high-power diode-pumped femtosecond oscillators operating near 1 µm. The Yb ion, employed as dopant in laser active materials, has a very simple energy level structure, consisting of only two electronic manifolds. The low quantum defect specific of this ion reduces the thermal load on the host material and increases the laser global efficiency. The absence of additional parasitic levels eliminates undesired effects such as excited-state absorption, upconversion, cross-relaxation, and concentration quenching, providing the possibility of high doping levels. Moreover, the broad and intense absorption spectra of Yb-doped active media around 960 nm is well matched with the emission wavelength of commercially available high-power InGaAs laser diode, allowing direct diode pumping and the implementation of compact laser sources.

Various Yb-doped crystals and glasses have been tested in the femtosecond regime. Generally, crystals have the advantages of high emission cross-sections and good thermal behavior, but due to their ordered structure they also have narrow emission bandwidths. On the other hand, glasses show very broad and smooth emission spectra, which is the fundamental property for generation of ultrashort pulses, but their poor thermal conductivities and mechanical resistance, and the weak emission cross-sections are strong limitations on the development of laser systems with high average power. Pulse durations of less than 100 fs were demonstrated with Yb-doped crystals such as borates Sr₃Y(BO₃)₃ [1] and Ca₄GdO(BO₃)₃ [2], tungstates NaY(WO₄)₂ [3], KLu(WO₄)₂ [4], vanadates Gd_0.64Y_0.36VO₄ [5], as well as Yb-doped silicate and phosphate glasses [6]. Among crystals, fluorides are promising hosts due to their low phonon energy, which makes them suitable for operation in the IR spectral region, together with broad emission cross section and favorable thermo-optical properties. In particular, YLF (LiYF₄) has better thermo-optical coefficients than those found in isotropic hosts like YAG [7, 8] and its large thermal conductivity allows efficient heat extraction; moreover, Yb³⁺:YLF has a wide emission cross-section, with peak value at the lasing wavelength comparable to that found in Yb³⁺:Sr₃Y(BO₃)₃ and Yb³⁺:Ca₄GdO(BO₃)₃.

Yb³⁺:YLF crystal has been successfully tested in continuous-wave regime by various authors [9, 10]. Mode-locked laser operation was already demonstrated in other fluoride hosts such as Yb:CaF₂ crystal [11], with pulses as short as 150 fs and average output power of 880 mW, and in Yb:fluoride phosphate glass [12], which generated slightly longer pulses with 160-fs duration and maximum output power of 250 mW.

In this paper, we report on the first demonstration of passive mode-locked laser operation of an Yb-doped YLF crystal. Crystal growth process, spectroscopic measurements, resonator configuration, and mode-locked laser results are presented. Pulses with minimum duration of 196 fs at 54 mW average output power were obtained exploiting the E‖c polarization.

2. Growth process and spectroscopic measurements of Yb:YLF crystal

The crystal growth apparatus consists of a home-made Czochralski furnace with conventional resistive heating (see ref. [10] for more details). The samples were grown using LiF and YF ₃ powders as raw material for the host and adding 5% mol of YbF₃ powder to the melt (5N-purified powders, from AC Materials, Tarpon Springs, FL, USA). Since the segregation coefficient of Yb³⁺ ions in YLF is close to 1 (see Ref. [13]), we assume that the dopant concentration in the crystal is equal to that in the melt.

 

Fig. 1. Room-temperature absorption and emission cross sections of Yb³⁺ ions in YLF crystal with electric field polarizations (a) E‖c, and (b) E⊥c. Emission cross sections were evaluated with the reciprocity method for wavelengths shorter than 1020 nm and with the β-τ method for wavelengths longer than 1020 nm.

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Room-temperature absorption coefficient measurements were performed in the wavelength region from 850 to 1100 nm (² F _7/2→² F _5/2 transition), by means of a CARY 500 spectrophotometer with resolution of 0.6 nm. The absorption cross section was calculated dividing the absorption coefficient by the density of dopant ions in the crystal (6.98×10 ²⁰ ions/cm³).

The polarized emission cross section was evaluated both by the β-τ method [14] and the reciprocity method [10], because it is well known that, even with low doping level, Yb ³⁺ undergoes reabsorption effects.

For the β-τ calculations, we used the room-temperature fluorescence spectra of the ² F _5/2→² F _7/2 transition and the lifetime of the ² F _5/2 manifold. The pump source was a laser diode tuned at 927 nm. The fluorescence signal was chopped and focused on the input slit of a monochromator with resolution of 0.6 nm. The signal at the output of the monochromator was detected by a cooled InSb detector and processed by lock-in standard technique. The spectra was normalized to account for the optical response of the system using a black-body source at 3000 K. The lifetime measurements of the ² F _5/2 manifold were carried out with an experimental apparatus similar to that adopted for the fluorescence measurements. The excitation source was a pulsed tunable Ti:sapphire laser with 30 ns pulse duration at 10 Hz repetition rate. The decay time curve exhibits a single exponential behaviour that has been fitted with a value of τ=2.1±0.3 ms, in agreement with the literature [15].

 

Fig. 2. Gain cross-sections of Yb³⁺ ions in YLF crystal for inversion parameter β of 0.1, 0.15, 0.2, and 0.25, with electric field polarizations (a) E‖c, and (b) E⊥c.

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For the reciprocity method the absorption coefficient data have been used together with the energy level data [13] and with the partition function [14]. The comparison between the data confirms that the cross sections calculated with the β-τ method reproduce the correct trend for wavelengths longer than 1020 nm, but are underestimated for wavelengths shorter than 1020 nm because of the strong reabsorption, leading to incorrect evaluation of the peak values.

Figure 1 shows the absorption and emission cross-sections for both polarizations E‖c and E⊥c. The most intense absorption peak lies in the E‖c polarization at 959 nm with a FWHM of 10 nm, particularly suitable for diode pumping. On the other hand, the emission cross-sections have maximum values of 11×10^-21 cm² at 993 nm with the polarization E‖c, and 4.1×10^-21 cm² at 1017 nm with the polarization E⊥c. The results closely match those reported in a previous publication [15].

Mode-locking performance of the Yb:YLF laser can be estimated calculating the gain cross-sections σ_g with the formula σ_g=βσ_e-(1-β)σ_a, where β is the ratio of the number of excited ions to the total number of ions, σ_e and σ_a are the emission and absorption cross-sections, respectively. The gain cross-sections corresponding to four different values of β are plotted in Fig. 2 for E‖c and E⊥c polarizations. From these curves, the E‖c polarization is expected to give best performance in terms of average output power and pulse duration. Moreover, the oscillation wavelength is predicted to be around 1022 nm for both polarizations.

3. Experimental setup

The scheme of the resonator and the pump system adopted during laser experiments is shown in Fig. 3. We used two different pump sources: LD1 is a laser diode with a maximum power of 2.8 W at 968 nm, coupled to a fiber with core diameter of 50 µm; the laser diode LD2 has a maximum power of 5Wat 957 nm and is coupled to a fiber with core diameter of 100 µm. The pump beams coming from LD1 and LD2 are first collimated and then focused onto the active crystal by two different pairs of antireflection-coated plano-convex lenses, specifically F1, F2 (38 and 50 mm focal lengths, respectively) for LD1, and F3, F4 (25 and 50 mm focal lengths, respectively) for LD2. The calculated spot sizes inside the active crystal, taking into account the defocalization due to the curved cavity mirrors M1 and M2, are ~75µm and ~230µm for the beams from LD1 and LD2, respectively. The 3.1-mm-thick Yb(5%):YLF crystal, inserted in a copper holder cooled by a Peltier thermo-electric cooler, is placed inside the resonator between the two curved high-reflectivity (HR, reflectivity>99.9%) folding mirrors M1 and M2 with 75-mm radius of curvature (ROC). The crystal is oriented at Brewster angle to minimize Fresnel losses of the laser beam, exploiting the E‖c or E⊥c polarization directions. The mode radius inside the gain medium, calculated by ABCD matrix formalism, is 21µm×29µm. The folding angles provided by mirrors M1 and M2 are set to 11° to give optimum compensation of laser beam astigmatism introduced by Brewster interfaces. To start passive mode-locking we used a semiconductor saturable absorber mirror (SESAM; Batop, Germany) designed for operation at 1045 nm, with 10 ps relaxation time constant, 2% saturable absorption and saturation fluence of 90 µJ/cm². The cavity mode is focused onto the SESAM to a waist of ~42µm by a HR curved mirror with ROC of 100 mm. Two HR chirped mirrors M4 and M5 were used for dispersion compensation in the resonator arm containing the output coupler.

 

Fig. 3. Scheme of the mode-locked Yb:YLF laser cavity and pump system. LD1, LD2: laser diodes; F1, F2, F3, F4: lenses; M1, M2: folding mirrors; M3, focusing mirror; M4, M5: chirped mirrors; C: Yb-doped YLF crystal; OC: output coupler; SESAM: semiconductor saturable-absorber mirror.

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4. Mode-locked laser operation of Yb:YLF

Laser experiments were aimed to investigate mode-locking performance of the Yb:YLF crystal operating either with E‖c or E⊥c polarizations. In both cases, self-starting mode-locking operation was achieved using the setup of Fig. 3, with output couplings of 1% and 2%, and pulse repetition rate of 55 MHz. The chirped mirrors M4 and M5 provided the optimum group delay dispersion of -2600 fs² per round-trip, as needed to compensate for the positive dispersion introduced by cavity mirrors and propagation inside the laser crystal (refractive index dispersion and Kerr nonlinearity). Soliton mode-locking was recognized as the pulse generation mechanism because the pulse duration increased linearly with the negative intracavity dispersion and because approximately transform-limited, self-starting pulses ~50 times shorter than SESAM relaxation time were obtained. The best results were obtained with the E‖c polarization. In this case, the maximum average output power was 120 mW at 4.7 W incident pump power (1.7 W from LD1 and 3 W from LD2) using the 2% output coupler, and the pulse duration was 233 fs with a bandwidth of 5.4 nm centered at 1024 nm. Changing the output coupling to 1%, the spectral bandwidth of the pulse increased to 7.1 nm (centered at 1028 nm), and shorter pulse durations of 196 fs were observed with maximum average power of 54 mW at 3.9 W incident pump power (1.7 W from LD1 and 2.2 W from LD2). Figure 4 shows average output power versus incident pump power of the mode-locked Yb:YLF laser exploiting the E‖cpolarization.

 

Fig. 4. Average output power versus incident pump power of the mode-locked Yb:YLF laser with polarization E‖c, and output couplings of 1% (squares), and 2% (circles). Mode-locking thresholds are indicated by arrows.

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Fig. 5. Autocorrelation trace and optical spectrum (inset) of the mode-locked Yb:YLF laser with polarization E‖c: (a) 1% output coupler ; (b) 2% output coupler. Sech²- pulse shape is assumed.

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The incident pump power was limited to 4.7 W (3.9 W in the case of 1% output coupling) owing to the tendencies for multiple-pulse generation observed at higher pump rates. A small jump of the output power is observed in the transition from the pure Q-switching to the cw mode-locking regime due to saturation of the SESAM losses, in agreement with theoretical predictions [16]. The calculated pulse fluence incident on the SESAM corresponding to mode-locking threshold is 1800 µJ/cm² (20×SESAM saturation fluence). The autocorrelation traces and emission spectra of the mode-locked Yb:YLF laser operating with E‖c are reported in Fig. 5. Experimental autocorrelations are well fitted assuming a sech ²-pulse shape, yielding to estimation of the time-bandwidth product ΔvΔt of 0.39 and 0.36 (close to the Fourier-transform limit of 0.32), with 1% and 2% output couplings, respectively. Investigation of mode-locking performance of the Yb:YLF crystal operating with E⊥c polarization, lead to slightly worse results in terms of output power and pulse durations. In this case, the maximum average output power was limited to 70 mW at 4.7 W incident pump power using the 2% output coupler, and the pulse duration extrapolated from autocorrelation trace was 300 fs with bandwidth of 3.9 nm centered at 1021 nm. When the output coupling of 1% was used, the pulse duration reduced to 250 fs, with a 4.5-nm bandwidth centered at 1022 nm, and the maximum output power was 45 mW at 4.7 W incident pump power.

5. Conclusion

Passive mode-locking of an Yb-doped YLF laser has been successfully demonstrated. Laser pulse trains with minimum duration of 196 fs and 54 mW of average power were obtained exploiting the E‖c polarization with 1% output coupling. Increasing the output coupling to 2%, pulses with higher average power of 120 mW, but longer durations of 233 fs, were observed. Further progress in terms of efficiency and maximum output power are expected replacing the pump source LD2 with a laser diode coupled to a 50µm-core fiber to increase brightness, and optimizing the ytterbium doping level of the YLF crystal.