1. Introduction

Efficient solid-state laser sources with linear polarization, high gain, high beam quality and picosecond pulse duration would benefit various research fields, such as nonlinear frequency conversion and nonlinear bio-imaging [1–4]. Excellent mode matching condition is essential in these sources to achieve large extraction efficiency. Meanwhile, thermal load must be well managed so that diffraction limited beam quality is not destroyed by harmful thermal effects.

A common configuration to achieve these goals is vanadate crystal end pumped by fiber coupled diode laser. It is attractive for its simple, compact, low cost characteristics. High gain and efficient pumping characteristics are governed by the large absorption and stimulated emission coefficient of vanadate crystal [5]. Due to its natural birefringence, linear polarized output could be achieved without additional intra cavity element. However, as an anisotropic material, vanadate’s absorption coefficients usually have a large difference between the two crystallographic axes [5]. When pumping with unpolarized light sources, the pump light with polarization direction parallel to c axes (π polarization) was absorbed much faster than the pump light with polarization direction parallel to a axes (σ polarization). According to Beer-Lambert law, to achieve a reasonable overall absorption efficiency, almost all of the π polarized pump light and most of the σ polarized pump light are absorbed in several millimeters near the entrance surface, while the absorbed pump power near the exit surface is very low. It would build a large thermal gradient along beam propagation direction in the crystal [6]. This large thermal gradient is one of the main reasons that result in high crystal temperature, large surface bulging, severe thermal lensing, and—eventually—crystal fracture. It prevents vanadate crystal from producing high average power output with diffraction limited beam quality.

Several techniques were proposed to lower the thermal gradient and scale the output power. Instead of pumping vanadate crystal at traditional 808 nm, in-band pumping technique with 880 nm is proven to be an attractive option [7–9]. It could directly pump the crystal into the emitting laser level, resulting in reduced quantum defect and less heat generation. The other technique is spreading the thermal load into multiple crystals, in which the output power can be linearly scaled at a price of adding system complexity [10].

Nd:YVO₄ is the most widely explored one among vanadate crystals in the past decades [11–13]. Its absorption coefficient along c axes is almost 4 times higher than that of a axes at 808 nm. McDonagh et al. proposed a technique for pumping Nd:YVO₄ with 888 nm, which makes absorption independent of the pump light polarization state. 56 W, 33 ps laser output was demonstrated by a passively mode locked oscillator with a 30 mm long Nd:YVO₄ bulk crystal [14]. This is, for almost a decade, the highest average power achieved with bulk crystal based picosecond oscillator. Unfortunately, absorption spectrum varies between different crystals; selecting similar spectroscopic property is tricky in other vanadate crystals. An alternative solution is pumping vanadate crystals with polarized light with polarization direction parallel to crystallographic axes. Thermal gradient could be significantly decreased by utilizing single absorption coefficient, therefore a higher pump power level is allowed.

Figure 1 shows the thermal conductivity of various vanadate crystals. It is seen that Nd:GdVO₄ has the highest thermal conductivity in vanadate family, which makes Nd:GdVO₄ a very promising candidate for high power laser operation [15–20]. In this paper, we report on a high power passively mode-locked picosecond oscillator based on Nd:GdVO₄ bulk crystal. Combining σ polarized pumping and in-band pumping technique, thermal gradient in the crystal was greatly decreased. At stable mode-locking operation, a maximum output power of 37 W was achieved at 73 W absorbed pump power, corresponding to a 51% optical efficiency. Pulse duration between 11.2 ps to 19.3 ps was achieved with different output coupling. Output beam quality maintained diffraction limited with M² < 1.05. Good beam quality confirmed low thermal aberration and refined thermal management with σ polarized in-band pumping. To the best of our knowledge, this is the highest output power based on single Nd:GdVO₄ bulk crystal. The output was presently limited by our current pumping source. With a more powerful pump and an optimized longer crystal, > 100 W output power would be feasible with a single bulk crystal laser head.

 

Fig. 1 Thermal conductivity of vanadate crystals.

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2. Experimental setup

The experimental setup of the laser oscillator is shown in Fig. 2. The crystal had a dimension of 4 mm (a) × 4 mm (c) × 14 mm (a) with 0.5% doping (CASTON Inc). Both facets of the crystal were antireflection coated at both 880 nm and 1064 nm. The crystal was wrapped with a thin layer of indium foil and mounted in a water-cooled copper heatsink. Cooling temperature of 25 °C was maintained during laser operation. The linear polarized pump was imaged into the center of the Nd:GdVO₄ crystal with 1200 μm diameter by coupling optics. The pump light polarization direction is parallel to the a axes, which is also referred as σ polarized pumping. The pumping wavelength was fixed at 880 nm. In a single pass through the crystal, ~80% of the pump radiation was absorbed.

 

Fig. 2 Schematic of the experimental setup.

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The cavity was formed by four plane mirrors (M1, M3, OC, SEAM) and two curved mirrors M2 (R = 200 mm) and M4 (R = 500 mm) with a total length of 1.85 m. M1 was antireflection coated at 880 nm and high reflection coated at 1064 nm. The curvature and the distances between mirrors were optimized regarding to stability and mode matching of the laser and pump beam. SESAM (BATOP GmbH) was used as the passive mode-locking device, which had a modulation depth of 3%, relaxation time of 10 ps. Copper heatsink of the SESAM was cooled by the chiller to minimize possible thermal effects.

3. Results

Like other vanadate crystals, Nd:GdVO₄ possesses very different absorption coefficients between two axes [21]. Using the same method as in [6], we calculated the absorbed power per length with unpolarized pump and σ polarized pump, where the absolute values of absorption coefficients had been adjusted to achieve the same total absorbed power (95% in this case). The only condition being set was α_c = 11α_a [21]. As shown in Fig. 3(a), thermal load on the crystal entrance face with unpolarized pumping is almost 3 times higher than that with σ polarized pumping. Therefore, thermal effects and risk of crystal fracture is considerably decreased with σ polarized pumping.

 

Fig. 3 (a) Calculated normalized absorbed power per length with unpolarized pump (dashed curve) and σ polarized pump (solid curve) at 880 nm for the same 95% total absorption efficiency. (b) Experimental continuous wave output power versus absorbed pump power with different output coupling.

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Continuous wave operation was demonstrated prior to mode-locking to confirm optimum cavity performance. Figure 3(b) illustrates continuous wave output power versus absorbed pump power with different output coupling, in which the SESAM was replaced by a high reflection coated plane mirror. The curvature and the distances between mirrors were optimized for best beam quality and highest optical efficiency at full pump power. Maximum output power of 38 W was achieved at 73 W absorbed pump power with a output coupling of 30%, corresponding to a 52% optical efficiency.

SESAM was inserted into the cavity for mode-locking operation. The oscillator went into Q-switched mode-locking regime before stable continuous wave mode-locking was achieved. In continuous wave mode-locking regime, 37 W of average power at a repetition rate of 81 MHz was achieved at 73 W absorbed pump power with 30% output coupling, corresponding to a 51% optical efficiency. The output power was slightly decreased due to the presented loss of SESAM. The pulse duration was measured to be 19.3 ps with an intensity autocorrelator assuming a Gaussian fitting. No damage to the saturable absorber was observed throughout the operation, even in Q-switched mode-locking regime.

While the absorbed pump power remained as 73 W, pulse duration and output power were investigated with different output coupling. As shown in Fig. 4(a), the output power decreased from 37 W to 25 W and the pulse duration was shortened from 19.3 ps to 11.2 ps, when the output coupling was changed from 30% to 13%. The curve reflects the general behavior that pulse shortening happens at higher intracavity power intensity [22]. Figure 4(b) illustrates the autocorrelation traces at different output coupling. Inset in Fig. 4(b) shows the typical RF spectrum, illustrating stable mode locking behavior of the oscillator.

 

Fig. 4 (a) Pulse duration and output power versus output coupling efficiency. (b) Autocorrelation traces at different output coupling. The inset shows the RF spectrum of the oscillator.

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The oscillator always delivered a TEM₀₀ beam profile throughout the operation, and the beam quality is identical regardless of the output coupling. Characteristics of the output beam presented a diffraction limited beam quality with M²_x = 1.02 and M²_y = 1.05 at full pump power (shown in Fig. 5). Inset in Fig. 5 illustrates the far field beam profile at the focus.

 

Fig. 5 Beam quality and far field beam profile.

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Stable long term performances were observed at each output coupling. Full pump power was applied throughout the measurement. As shown in Fig. 6, the system presented excellent long term stability. A standard deviation of 0.6% was shown in a period of one hour. Long term stability of the pump power was also measured with a 0.24% standard deviation. The standard deviation of the peak power fluctuations in the output was measured to be < 1.5% (shown in the inset of Fig. 6). Better performance could be achieved with an improved power supply and a housing of the system.

 

Fig. 6 Power stability of the pump source and oscillator output at full pump power. The inset shows the temporal evolution of the output pulses.

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4. Conclusion

In conclusion we have demonstrated a high power passively mode-locked picosecond oscillator based on an end-pumped Nd:GdVO₄ bulk crystal. Excellent thermal management was achieved with σ polarized in-band pumping. 37 W, 81 MHz, 19.3 ps laser output was achieved at 73 W absorbed pump power with 51% optical efficiency. Pulse duration was measured between 11.2 ps to 19.3 ps at different output coupling. The output beam quality maintained diffraction limited with M² < 1.05. This is to the best of our knowledge the highest output power based on single Nd:GdVO₄ bulk crystal. Power scaling with this configuration is feasible by adopting higher power pump source and longer crystal. Future oscillator has a potential to deliver over 100 W output power with a single Nd:GdVO₄ bulk crystal.