High-power, 0.83-GHz-repetition-rate tenth-order harmonic mode-locked GdVO₄/Nd:GdVO₄ laser under diode direct pumping

High-power, high-repetition-rate lasers generating picosecond pulses are needed in many fields such as telecommunications, high-speed electro-optic sampling and frequency conversion. The passively mode-locked diode-pumped solid-state laser is attractive due to its compactness and inherent simplicity. Short-cavity design with a semiconductor saturable absorber mirror (SESAM), which is called fundamental mode locking (FML), is often adopted to increase the repetition rate [1–8]. But the mode locking of such a cavity is mainly challenged by the strong tendency for Q-switched mode locking (QML) [9]. High-repetition-rate pulses can also be generated based on harmonic mode locking (HML), in which multiple pulses appear with equal spacing within a cavity round trip. HML preserves the simple cavity configuration, and can maintain a relatively good laser beam quality at high output power compared with FML. For HML femtosecond solid-state lasers, third-order HML has been observed in a passively mode-locked Cr⁴⁺:YAG laser with the use of a semiconductor saturable Bragg reflector (SBR) [10], and fourth-order HML pulses have been demonstrated in a soft-aperture Kerr-lens mode-locked (KLM) Ti:sapphire laser [11]. In these femtosecond lasers, the generation of the HML pulses was controlled by varying the total intra-cavity group-velocity dispersion (GVD) [10, 11]. For HML picosecond solid-state lasers, fourth-order HML corresponding to 360 MHz repetition rate was demonstrated in a diode-pumped KLM Nd:YAG laser using a Kerr medium [12], fourth-order HML with repetition rate of 312 MHz was observed in a passively mode-locked Nd:YVO₄ laser with a multiple quantum well (MQW) saturable absorber inserted in the cavity [13], and fifth-order HML with repetition rate of 576 MHz was demonstrated in a nonlinear mirror mode-locked Nd:GdVO₄ laser [14]; they all had nonlinear elements inserted in the cavity for mode locking. In [14], the HML pulses were due to the group-velocity mismatch between the fundamental and second-harmonic waves as well as cascaded second-order nonlinearity in the nonlinear crystal, while in [12, 13], the generation of the HML pulses were caused by the colliding pulse mode locking (CPM) mechanism—that is, the Nth-order HML is obtained by placing a saturable absorber at the position of 1/N cavity length [15]. Recently, using the large third-order nonlinearity of the laser crystal, Li et al reported a tenth-order HML Nd:YVO₄ laser with a high output power of 10 W at 1 GHz-repetition-rate based on the Kerr self-focusing effects in the gain medium and the CPM mechanism [16].

The Nd:GdVO₄ crystal has also a considerable value of third-order susceptibility, and self-starting KLM Nd:GdVO₄ lasers with multi-GHz-repetition-rate have been demonstrated experimentally [17]. Compared with Nd:YVO₄, the Nd:GdVO₄ crystal has larger conductivity for relatively weaker thermal effects and broader bandwidth benefit for shorter pulse width. In this paper, we demonstrate a tenth-order HML GdVO₄/Nd:GdVO₄ laser with diode direct pumping. By using the large third-order nonlinearity of Nd:GdVO₄ and a CPM cavity construction, the tenth-order HML pulses were attributed to the colliding of the counter-propagating pulses induced by the Kerr self-focusing effects in the laser crystal, and they could be further modulated by a SESAM. A maximum output power of 5.8 W in TEM₀₀-mode was obtained at the absorbed pump power of 23.1 W with the repetition rate of 0.83 GHz and the pulse width of 30 ps, corresponding to an optical–optical efficiency of 25.1% and a slope efficiency of 37.1%.

To reduce the thermal effects in the laser crystal, a grown-together composite GdVO₄/Nd:GdVO₄ crystal (Beijing Ke-Gang Electro-Optics) was used as the laser gain medium and an 880 nm fiber-coupled laser diode (LD, DILAS) was used as the pump source for direct pumping [16]. With the composite crystal, the undoped GdVO₄ section serves as a heat sink for the pumping surface. Compared with the traditional indirect pumping at 808 nm, direct pumping at 880 nm has a lower quantum defect, which could reduce the thermal load, minimize crystal stress and maximize optical efficiency.

Figure 1 shows the scheme of the experimental setup. The temperature of the fiber-coupled LD was controlled by a water-cooling system. As the emitting center wavelength of the LD varies with its working current and temperature, the cooling water was set at 26 ° C to meet the absorption peak of Nd:GdVO₄ around 880 nm during the experiment. The core diameter and numerical aperture of the fiber were 400 μm and 0.22, respectively. The pump radiation from the fiber was imaged with 1:2 magnification into the laser crystal. The grown-together composite GdVO₄/Nd:GdVO₄ crystal was a-cut, and had dimensions of 3 × 3 × 25 mm³, consisting of one 2-mm-long undoped end cap and a 23-mm-long, 0.95 at.% Nd-doped section. The undoped end cap of the crystal was wedged 0.5°, and both end surfaces were antireflection coating at 1064 and 880 nm. The laser crystal was equipped in a copper heat sink and cooled by water at 19 ° C. The laser cavity was constructed to be a Z-folded resonator by three mirrors and a SESAM. The input and folding mirror M2 was a plane mirror with antireflection coating at 880 nm and with high-reflectance coating at 1064 nm. The folding mirror M3 was a 70 cm radius-of-curvature concave mirror with high-reflectance coating at 1064 nm. A flat wedged mirror M1 was used as the output coupler with 20% transmission at the laser wavelength. The distance L1 between M1 and the nearest end of the gain medium was about 18 cm. The arm length L2 between M2 and M3 was about 105 cm. The total cavity length was around 176 cm, and it could be changed by adjusting the position of the SESAM during the experiment.

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The leakage radiation from M3 was detected by an ultrafast InGaAs photodetector (ALPHALAS GMBH, UPD-40-UVIR-P, rise time < 40 ps), and the detected signal was shown on a digital oscilloscope (Agilent, DSO 80804B, bandwidth 8 GHz) throughout the experiment.

First, the laser cavity was aligned to obtain the maximum average output power with a plane end mirror coated of high-reflectance at 880 nm in place of the SESAM. When the pump power was increased, the detected signal shown on the digital oscilloscope exhibited sequentially in the continuous wave (CW) state, the irregular pulse state, the multiple-pulse state in which a single wavepacket per round trip included ten equal-spacing pulses, and then again in the irregular pulse state. The pulse-state performance of the laser was always accompanied by CW background. As there were no other nonlinear elements but the GdVO₄/Nd:GdVO₄ crystal which has large positive third-order nonlinearity, the pulses could only be induced by the Kerr self-focusing effects of the laser crystal combined with a soft gain aperture due to the finite transversal size of the active region [17], while the wavepackets with ten equally spaced pulses per round trip was attributed to the colliding of the counter-propagating pulses in the crystal [16]. The plane end mirror was then slightly moved to change the cavity length until the amplitudes of the ten pulses in the wavepackets were approximately equal, where the total cavity optical length was about ten times of the distance L1 between the output coupler M1 and the nearest end of the laser crystal. The adjacent pulses were separated about 1.2 ns which was approximately the round-trip time of the laser through the arm length L1. Thus, a CPM-like cavity configuration was satisfied and the tenth-order HML operation was obtained with the repetition rate being about 830 MHz, corresponding to the round-trip time of the laser through L1. The plane end mirror was then replaced by the SESAM, and it was observed that the ratio of the CW background in the tenth-order HML pulses decreased, which indicated that the pulses were further modulated by the SESAM. Figure 2(a) shows the pulse train with a time span of 20 ns, demonstrating tenth-order HML pulses at a repetition rate of 0.83 GHz; figure 2(b) shows the pulse train with a time span of 100 μs, demonstrating the amplitude stability.

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The average output power versus the absorbed pump power is plotted in figure 3. At the absorbed pump power of 23.1 W, an average output power of 5.8 W with stable mode-locked pulses was obtained, corresponding to an optical–optical efficiency of 25.1% and a slope efficiency of 37.1%, respectively. When further increasing the pump power, the output power still increased linearly with the pump, but the pulses start to become unstable. We measured the laser beam quality using a laser beam analyzer (Spiricon M²-200). At the output power of 5.8 W, the beam quality factors were Mx² = 1.17 along the horizontal direction and My² = 1.32 along the vertical direction, respectively, which indicated TEM₀₀-mode operation, while at the output power of 6.8 W, the beam quality factors were Mx² = 1.12 and My² = 1.64 along the horizontal and vertical directions, respectively, which showed relatively large beam distortion. Thus, the unstable tendency of the pulses at higher pump power over than 23.1 W might be caused by the beam distortion. Figure 4 shows the measured M² factor and the two-dimensional beam profile at the output power of 5.8 W.

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The second-harmonic autocorrelation trace of the mode-locked pulses was measured with a home-made autocorrelator, which is shown in figure 5. Assuming a sech²-shaped temporal profile, the FWHM (full width at half maximum) of the autocorrelation trace was fitted to be about 45.7 ps, corresponding to the pulse width of about 30 ps.

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In summary, we have demonstrated a high-power high-repetition-rate passively mode-locked GdVO₄/Nd:GdVO₄ laser with diode direct pumping based on tenth-order HML by combination of the large third-order nonlinearity of the laser crystal and a CPM cavity configuration. The HML pulses were induced by the self-focusing Kerr effects, as well as by the colliding of the counter-propagating pulses in the laser crystal. With the help of a SESAM, the pulses were further modulated. The maximum output power in TEM₀₀ mode was 5.8 W at the absorbed pump power of 23.1 W, corresponding to an optical–optical efficiency of 25.1% and a slope efficiency of 37.1%. The repetition rate was up to 0.83 GHz and the pulse duration was 30 ps.