A diode-pumped efficient 2.05-µm Tm,Ho:GdVO4 laser with high beam quality is reported. The cavity configuration was optimized for weakening influence of thermal effect to resonator stability and mode-coupling. A conversion efficiency of 46% and a slope efficiency of 50% were obtained with continuous-wave (CW) output power of 10.5 W at 77 K. A repetitively Q-switched laser also achieved 10.1 W of output power at 10 kHz. A beam quality factor of M 2<1.1 was measured by the traveling knife-edge method. In addition, the energy per pulse of 1.9 mJ was obtained at 5 kHz, corresponding to the peak power of 0.14 MW.
©2006 Optical Society of America
High-power, high-energy holmium lasers are useful for a variety of applications such as remote-sensing and medical. Also, high-power quasi-continuous wave (QCW) 2-µm lasers are efficient pump sources of optical parametric oscillators (OPOs) and optical parametric amplifiers (OPAs) for the operation in 3-12-µm spectral region [1–3]. Tm:Ho lasers have achieved wide attention with a number of workers reporting laser emission and high efficiencies. Work by Hemmati  demonstrated a continuous-wave (CW) output power of 187 mW, corresponding to a 48% slope efficiency for the incident power in Tm,Ho:YLF at 77 K. Budni et al. reported an output power of 2.12 W corresponding to a 45.6% optical-to-optical overall conversion efficiency from a CW Tm,Ho:YLF TEM00 laser at 77 K . They also reported a repetitively Q-switched Tm,Ho:YLF oscillator followed by two amplifier stages with a total average output power of 23 W at 77 K . Elder et al. reported 270-mW output power and 14% absorbed conversion efficiency from a Tm,Ho:YAP laser at room temperature . Simultaneously, 660-mW output power and 30% absorbed conversion efficiency were obtained from a Tm,Ho:YLF laser. An output power of 585 mW and a slope efficiency of 42.4% were demonstrated in room-temperature Tm,Ho:YLF by Cornacchia et al., compared to 478 mW and 30.4% in Tm,Ho:BaYF . In addition, Morris et al. reported an output power of 4.6 mW with 135-mW absorbed pump power in room-temperature Tm,Ho:GdVO4 . Also, Sato et al. reported a side-pumping Tm,Ho:GdVO4 laser with an output energy of 31.2 mJ and a slope efficiency of 14.5% . However, the conversion efficiency and the average power of the side-pumping configuration were lower than that of the end-pumping configuration. The output power in room-temperature Tm:Ho laser was usually less than 1 W. Furthermore, the laser performance with a few hundred milliwatt output power was inefficient at room temperature.
Apart from the Tm:Ho co-doped lasers, diode-pumped thulium and then pumped holmium lasers were researched in recent years for reducing the holmium upconversion losses at room temperature. Lai et al. reported a 120-W CW diode side-pumped Tm:YAG with a conversion efficiency of 25.2% . Budni et al. reported 19 W of CW Ho:YAG output pumped by a Tm:YLF laser . The diode-to-Holmium optical conversion efficiency is about 18%. Bollig et al. reported a Ho:YAG laser intracavity pumped by a diode-bar-pumped Tm:YAG laser . The output power at 2.097 µm from the Ho:YAG laser was 2.1 W for 9.2 W of diode power. Shen et al. reported a Ho:YAG laser end pumped by a cladding-pumped tunable Tm-doped silica-fibre laser . The unpolarized output power was 6.4 W for 9.6 W of incident pump power, corresponding to a slope efficiency of 80% and an optical-to-optical efficiency of 67%. The output power of holmium lasers was limited by the thulium laser power due to the effects of thermal loading and the wavelength matched with the Ho absorption peak. Also, the diode-to-holmium optical conversion efficiency at the singly doped lasers was inefficient. In addition, the laser configuration was complex with diode-pumped thulium lasers pumping holmium lasers. Therefore, the Tm:Ho co-doped lasers still received considerable attention [14,15].
In this paper, we report a cryogenic 10-W Tm,Ho:GdVO4 laser with impressive efficiency and high beam quality pumped by 803-nm diodes. A conversion efficiency of 46% and a slope efficiency of 50% are recorded with a CW output power of 10.5 W. Also, CW-pumped Q-switched laser is operated with a beam quality factor of M 2<1.1 at a pulse repetitive frequency (PRF) of 10 kHz.
GdVO4 used has some advantages in comparison with the other co-doped hosts. The large thermal conductivity of GdVO4 is favorable for efficiently cooling the crystal and reducing the thermal effect. The pump absorption band of GdVO4 host is stronger around 800 nm than that of YAP and YLF hosts. Additionally, the growth of Tm,Ho:GdVO4 crystal is easier than that of YLF host.
The liquid nitrogen refrigeration of the gain crystal was used for obtaining highly power laser operation at high beam quality in our experiments. There are five dominant energy level processes for Tm:Ho laser . These include energy absorption of pump light (3H6→3H4), cross relaxation between thulium ions (3H4, 3H6→3F4, 3F4), energy transfer between thulium and holmium ions (3F4, 5I8↔3H6, 5I7), emission of 2-µm laser (5I7→5I8), and upconversion of holmium ions (5I7, 3F4→5I5, 3H6). The upconversion losses of the Tm:Ho laser which influence the conversion efficiency seriously are sensitive to excited state densities. At room temperature, the quasi-three level nature of the Tm:Ho laser results in the necessity of very high excited state densities to achieve population reversion. High 5I7 upper level densities not only lead up to upconversion processes, but also decrease leaving holmium ions for the Tm 3F4→Ho 5I7 energy transfer. At 77 K, however, the quasi-four level nature decreases the upper level densities for fixed gain. The low excited state densities are useful to decrease upconversion losses remarkably. The output power at 77K is much higher than that at room temperature. Also, the beam quality in cryogenic laser can be improved by weakening thermal effect in the gain medium.
2. The thermal effect analysis
The thermal effects are decided by pump absorption, laser radiation and heat flow in the laser material, besides characteristics of material. They are critical problem in the design of solid-state lasers. The beam quality can be degraded due to the thermal-induced phase aberration . The resonator stability and the mode-coupling are also influenced by the thermal lens effect. The effective thermal focal length fth for CW end-pumped solid-state lasers  is given by the following equation:
where, Kc is the thermal conductivity, ξ is the thermal load ratio, η is the absorption ratio, Pin is the incident pump power of the gain medium, dn/dT is the thermal dispersion coefficient. In addition, is the square of the effective pump radius defined as:
where, P(x) is the pump power, l is the length of gain medium.
As the laser crystal is approximated to a thin spherical lens with focal length fth, the g-parameters  of a laser resonator can be shown as:
where, L 1 (L 2) is the distance between M 1 (M 2) and the centre of the laser crystal, R 1 (R 2) is the curvature radius of M 1 (M 2), and L 0=L 1+L 2-L 1 L 2/fth.
3. Experimental setup
The geometry of LD end-pumped Tm,Ho:GdVO4 laser is shown in Fig. 2. The laser crystal had dopant concentrations of 5 at% Tm, 0.5 at% Ho, and its dimensions were 4×4×7 mm. Both the crystal’s end faces were anti-reflection (AR) coated at 803 nm and 2 µm. The crystal was placed in a dewar which was used as the liquid N2 reservoir. The double end-pumped configuration facilitated the distribution of the thermal load. Both diodes outputs at wavelength of 803 nm were coupled by fibers with core-diameters of 400 µm and numerical apertures of 0.22. The coupling lenses with 35- and 50-mm focuses were used to re-focus the pump laser on the end faces of the laser crystal.
The resonator geometry used was plano-concave. The high reflector acted as a resonator mirror with a 40-cm radius of curvature and also transmitted the diode-pump radiation. The reflectivity at 2.05 µm was approximately 99.5%, and the transmission at the diode-pump wavelength was 96%. The dichroic mirror provided both high reflection (HR) at the resonated wavelength (99.5%) and high transmission (HT) at the diode pump (93%). The flat output coupler (OC) was coated for ~60% transmission at 2 µm. The optical length of L 1 and L 2 were approximately 26 and 146 mm, respectively. The power meter 1 was used to measure the output power of laser. A 30-cm focal length lens was located at 57.5 cm away from OC. The power meter 2 and the knife edge were used to analyze characteristics of laser beam.
The input pump power affected the thermal focal length and thus the mode-coupling. It was the effective means to minimize the thermal influence to the mode-coupling efficiency by placing the gain medium near the concave mirror. The laser radius in the gain medium as a function of the thermal focal length is shown in Fig. 3. The broken line indicated the laser radius without thermal effect. The excursion of the laser radius was less than ±3%, when the thermal focal length was varied from infinity to 40 cm. From Eq. (1), the calculation of thermal focal length was about 61 cm with an incident pump power of 21 W. The corresponding parameters values were: Kc=11.7 W/m·K, , ξ=33%, η=94%, dn/dT=4.7×10-6/K. The thermal effect was little influence to the laser radius in the gain medium and thus the mode-coupling efficiency. Also, the resonator was stable unless the thermal focal length less than 24 cm.
4. Experimental Results
The output power of Tm,Ho:GdVO4 laser as a function of the pump power is illustrated in Fig. 4. The maximum CW output power was 10.5 W at 2.05 µm for total pump power of 22.6 W, corresponding to a conversion efficiency of 46%. If both the pump reflection loss of the dichroic mirrors and the pump transmission loss of the gain crystal were considered, corrections for absorbed pump power yielded a conversion efficiency of 52%, and a slope efficiency of 56%. Operating at a CW pumped and repetitively Q-switched mode, the Tm,Ho:GdVO4 laser achieved 10.1 W of output power at 10 kHz, with corresponding conversion efficiency of 45%. The energy per pulse was 1.0 mJ with a pulsewidth of 22 ns. In addition, the highest energy per pulse of 1.9 mJ in 14 ns was obtained at 5 kHz, corresponding to a peak output power of 0.14 MW.
The Q-switched output power was lower than the CW output power. The Tm 3H4 and Ho 5I7 manifolds were thermal equilibrium in CW operation. Their relative populations and therefore net energy transfer from Tm to Ho satisfied a Boltzmann distribution . The energy transfer time from Tm to Ho was about a few microsecond. Thus, the stimulated emission rate exceeded the energy transfer rate largely in our Q-switched operation; in this case, the Boltzmann approximation was no longer valid. Therefore, the excited density of Tm ions was little contributing to the stimulated emission when the pulse was bringing out. The available excited density of Ho ions in Q-switched operation was less than that in CW operation. As a result, there was a little decline of the conversion efficiency when the laser operation is QCW.
Figure 5 shows the intensity profile of the laser beam at 10 kHz which is measured by a knife-edge method  at about 130 cm away from the lens. The solid curve represented a Gaussian fit to the data, from which it was apparent that the profile exhibited a Gaussian distribution.The radiuses of the laser beam were also calculated by the knife-edge method. The 1/e2 radius of a Gaussian laser beam is given by:
where X 10% (X 90%) is the place in which the power falls to 10% (90%) of the full value. Figure 6 shows the measured beam radiuses at various distances from the lens with full laser power at 10 kHz. By fitting Gaussian beam standard expression to these data, we estimated the beam quality to be M 2=1.04±0.02, clearly indicating nearly diffraction limited beam propagation. The waist diameter of 0.629 mm and the full-angle divergence of 4.33 mrad were calculated after the output coupler.
To summarize, we have demonstrated diode-pumped 10-W Tm,Ho:GdVO4 laser with near-diffraction limited beam quality. The influence of the thermal effect to the laser performance was analyzed. The cavity configuration was optimized for weakening influence of thermal effect to resonator stability and mode-coupling. We obtained CW output power of 10.5 W and conversion efficiency of 46% with total pump power of 22.6 W. Corrections for absorbed pump power yielded conversion efficiency of 52%, with corresponding slope efficiency of 56%. Also, the average output power of 10.1 W was obtained at 10 kHz, corresponding to conversion efficiency of 45%. The laser operated at a single mode (TEM00) with a beam quality factor of M 2<1.1 which was demonstrated by a knife-edge method. Finally, the highest energy per pulse of 1.9 mJ in 14 ns was achieved at 5 kHz, corresponding to the highest peak power of 0.14 MW.
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