Passive Q-Switching by Cr4+:YAG Saturable Absorber of Buried Depressed-Cladding Waveguides Obtained in Nd-Doped Media by Femtosecond Laser Beam Writing

We report on laser performances obtained in Q-switch mode operation from buried depressed-cladding waveguides of circular shape (100 μm diameter) that were inscribed in Nd:YAG and Nd:YVO4 media by direct writing with a femtosecond laser beam. The Q-switch operation was realized with a Cr4+:YAG saturable absorber, aiming to obtain laser pulses of moderate (few μJ) energy at high (tens to hundreds kHz) repetition rate. An average power of 0.52 W at 1.06 μm consisting of a train of pulses of 7.79 μJ energy at 67 kHz repetition rate, was obtained from a waveguide realized in a 4.8 mm long, 1.1-at % Nd:YAG ceramics; the pulse peak power reached 1.95 kW. A similar waveguide that was inscribed in a 3.4 mm long, 1.0-at % Nd:YVO4 crystal yielded laser pulses with 9.4 μJ energy at 83 kHz repetition rate (at 0.77 W average power) and 1.36 kW peak power. The laser performances obtained in continuous-wave operation were discussed for each waveguide used in the experiments. Thus, a continuous-wave output power of 1.45 W was obtained from the circular buried depressed-cladding waveguide inscribed in the 1.1-at %, 4.8 mm long Nd:YAG; the overall optical-to-optical efficiency, with respect to the absorbed pump power, was 0.21. The waveguide inscribed in the 1.0-at %, 3.4 mm long Nd:YVO4 crystal yielded 1.85 W power at 0.26 overall optical efficiency. This work shows the possibility to build compact laser systems with average-to-high peak power pulses based on waveguides realized by a femtosecond (fs) laser beam direct writing technique and that are pumped by a fiber-coupled diode laser.


Introduction
The experiments performed by Davis et al. [1] demonstrated that a femtosecond (fs) laser beam can induce stable damages and changes of the refractive index in various glasses. The written tracks presented an increased index of refraction in comparison with that of the bulk medium, which allowed light propagation within the track itself; such an optical device is of interest for telecommunications, to build planar as well as three-dimensional photonic devices [2]. On the other hand, in the case of crystals the stress field induces an increase of the refractive index in the zones adjacent to that where laser irradiation is performed [3]. Based on this finding, wave-guiding was realized between two such written tracks that were positioned at a narrow distance (up to a few tens of µm) from each other; single-transverse mode operation was obtained in this way [4,5].
Power-scaling of a waveguide realized by an fs-laser beam can be achieved using a different approach, that is, the buried depressed-cladding waveguide. A tubular waveguide is obtained with this technique, by using a core of the crystal with unmodified properties around which many parallel power of 1.1 W at 1.06 µm was obtained from a 150-µm diameter waveguide that was inscribed in a 1.0-at % Nd:YAG/Cr 4+ :YAG (Cr 4+ :YAG SA with initial transmission T i = 0.70); the pulse energy and duration was 15.7 µJ and 3.9 ns, respectively, corresponding to a peak power of 4 kW. The use of a composite Nd:YAG/Cr 4+ :YAG medium can lead to a compact device, but it can also be an expensive choice. In addition, the use of discrete elements has the advantage of obtaining laser pulses with different characteristics by replacing only the Cr 4+ :YAG SA crystal, and not all of the system. In the present work we extend the previous investigations to Q-switch operation by discrete Cr 4+ :YAG SA of depressed-cladding waveguides that were inscribed in Nd:YAG ceramics and Nd:YVO 4 crystals. Average output power P ave = 0.52 W at 1.06 µm with laser pulses of energy E p~7 .8 µJ and peak power P p = 1.95 kW at 67-kHz repetition rate was obtained from a 100 µm diameter waveguide inscribed in a 1.1-at % Nd:YAG ceramics; the Cr 4+ :YAG SA initial transmission was T i = 0.89. A similar waveguide realized in a 1.0-at % Nd:YVO 4 crystal yielded pulses with energy E p = 9.4 µJ and peak power P p = 1.36 kW; the average power was P ave = 0.77 W. Characteristics of the laser pulses obtained from waveguides inscribed in other Nd:YAG and Nd:YVO 4 active media and employing Cr 4+ :YAG SA with different T i are given.

Waveguides Description
In the present experiments we used some of the waveguides realized and employed in our previous works [10,11]. For a better understanding, we remind the reader that the waveguides were inscribed with a Clark-MRX-2101 chirped-pulsed amplified system that delivers laser pulses at 775 nm with 200 fs pulse duration at 2 kHz repetition rate and up to 0.6 mJ energy. The fs-laser pulse energy suitable for writing each waveguide was chosen by an optical configuration comprising a half-wave plate, a polarizer, and several calibrated neutral filters. Typically, the beam was focused in the laser medium at a spot size of a few-µm diameter. The writing process was monitored with a camera. Figure 1 presents images of the exit surfaces of some waveguides while the pump radiation was coupled in each waveguide on the opposite side. Two waveguides, each with diameter of 100 µm, were inscribed in Nd:YAG ceramics (Baikowski Co., Ltd., Chiba, Japan). The first one was obtained in a 1.1-at % Nd:YAG ceramics of 4.5 mm length using a helical-moving technique developed in our group [28]; this waveguide, shown in Figure 1a, is denoted by DWG-YG-1. A second waveguide was written in a 4.8 mm long, 1.1-at % Nd:YAG ceramics by the classical writing technique developed by Okhrimchuck [6,15]. The waveguide consisted of an unmodified core of Nd:YAG around which many tracks were realized, at a distance of~5 µm between two consecutive tracks; this waveguide will be called DWG-YG-2 ( Figure 1b). An evaluation of the change of the refractive index induced in Nd:YAG by the fs-laser beam was made following the method described in Ref. [4]. Thus, a HeNe laser beam was coupled in each waveguide and the maximum incident angle at which no change of the transmitted power was occurring was determined. Following this technique of calculus it was concluded that the approximate change in the Nd:YAG refractive index ∆n, between the unchanged refractive index of waveguide core and the average refractive index of the waveguide wall, was around 1 × 10 −3 .

Laser Emission Experiments
In the laser experiments we used a plane-plane resonator. The resonator rear mirror (HRM) was coated for high reflectivity (reflectivity, R >0.998) at λem and for high transmission (transmission, T >0.98) at λp; this mirror was placed on a translation stage that has enabled its positioning very close to one surface of each waveguide. The pump was made through the HRM with a fiber-coupled diode laser (LIMO Co., Dortmund, Germany) that was operated in cw mode. The fiber end (100-μm diameter, numerical aperture NA = 0.22) was imaged into each waveguide with a collimating achromatic lens with focal distance of 50 mm and a focusing achromatic lens with 30 mm focal distance. The coupling efficiency of the pump beam into the waveguide was evaluated as a unit. Each laser medium was wrapped in indium foil and embedded in a copper holder; the holder temperature was kept at 20 °C by using a Peltier element cooled with re-circulated water. Uncoated Cr 4+ :YAG SA crystals (Cryslaser, Inc., Chengdu, China) with initial transmission Ti = 0.89, Ti = 0.84, and Ti = 0.79 were tested in the Q-switch experiments. Each Cr 4+ :YAG was placed (with positioning systems) as close as possible to the waveguide surface opposite to the one through which the pump was made, and was followed by the resonator out-coupling mirror (OCM). Several OCMs with transmission T between 0.01 and 0.10 were used for determining the optimum emission characteristics.
The laser emission performances measured in cw regime from the waveguides inscribed in Nd:YAG are shown in Figure 2 (in these experiments the Cr 4+ :YAG SA was removed from the resonator). With an OCM of T = 0.05 the waveguide DWG-YG-1 yielded maximum output power Pout = 2.05 W for an absorbed pump power Pabs = 6.65 W; this corresponds to an optical-to-optical efficiency, ηoa (with respect to Pabs) of ~0.31. The slope efficiency (with respect to Pabs) was ηsa = 0.38. In the case of waveguide DWG-YG-2 the output power was limited to Pout = 1.45 W for Pabs = 6.80 W (i.e., ηoa = 0.21); the laser operated with slope ηsa = 0.29 (OCM with T = 0.05). The differences in output performances between DWG-YG-1 (the waveguide written by helical moving techniques) and DWG-YG-2 (the waveguide inscribed by classical step-by-step method) can be explained by lower losses in the case of the first waveguide. Thus, based on a Findlay-Clay analysis [29] of cw emission characteristics it was concluded that the resonator round-trip loss was Li = 0.03 for waveguide DWG-YG-1, but much higher, Li = 0.10, for waveguide DWG-YG-2. We comment that in the case of laser emission in bulk Nd:YAG loss Li was evaluated, for both Nd:YAG media, to be lower than 0.01. On the other hand, losses Li for waveguides are in agreement with propagation losses determined at 632.8 nm, these being of 0.6 dB/cm for DWG-YG-1 and ~1.5 dB/cm for DWG-YG-2 [10]. In our previous investigations it was showed that laser emission from such waveguides has a high M 2 factor, indicating multimode transverse operation [28,30,31]. The inset of Figure 2 presents the 3D shape of the laser beam at the maximum output power (Pout = 2.05 W, the waveguide DWG-YG-1), suggesting similar multimode distribution of the laser beam.

Laser Emission Experiments
In the laser experiments we used a plane-plane resonator. The resonator rear mirror (HRM) was coated for high reflectivity (reflectivity, R > 0.998) at λ em and for high transmission (transmission, T > 0.98) at λ p ; this mirror was placed on a translation stage that has enabled its positioning very close to one surface of each waveguide. The pump was made through the HRM with a fiber-coupled diode laser (LIMO Co., Dortmund, Germany) that was operated in cw mode. The fiber end (100-µm diameter, numerical aperture NA = 0.22) was imaged into each waveguide with a collimating achromatic lens with focal distance of 50 mm and a focusing achromatic lens with 30 mm focal distance. The coupling efficiency of the pump beam into the waveguide was evaluated as a unit. Each laser medium was wrapped in indium foil and embedded in a copper holder; the holder temperature was kept at 20 • C by using a Peltier element cooled with re-circulated water. Uncoated Cr 4+ :YAG SA crystals (Cryslaser, Inc., Chengdu, China) with initial transmission T i = 0.89, T i = 0.84, and T i = 0.79 were tested in the Q-switch experiments. Each Cr 4+ :YAG was placed (with positioning systems) as close as possible to the waveguide surface opposite to the one through which the pump was made, and was followed by the resonator out-coupling mirror (OCM). Several OCMs with transmission T between 0.01 and 0.10 were used for determining the optimum emission characteristics.
The laser emission performances measured in cw regime from the waveguides inscribed in Nd:YAG are shown in Figure 2 (in these experiments the Cr 4+ :YAG SA was removed from the resonator). With an OCM of T = 0.05 the waveguide DWG-YG-1 yielded maximum output power P out = 2.05 W for an absorbed pump power P abs = 6.65 W; this corresponds to an optical-to-optical efficiency, η oa (with respect to P abs ) of~0.31. The slope efficiency (with respect to P abs ) was η sa = 0.38. In the case of waveguide DWG-YG-2 the output power was limited to P out = 1.45 W for P abs = 6.80 W (i.e., η oa = 0.21); the laser operated with slope η sa = 0.29 (OCM with T = 0.05). The differences in output performances between DWG-YG-1 (the waveguide written by helical moving techniques) and DWG-YG-2 (the waveguide inscribed by classical step-by-step method) can be explained by lower losses in the case of the first waveguide. Thus, based on a Findlay-Clay analysis [29] of cw emission characteristics it was concluded that the resonator round-trip loss was L i = 0.03 for waveguide DWG-YG-1, but much higher, L i = 0.10, for waveguide DWG-YG-2. We comment that in the case of laser emission in bulk Nd:YAG loss L i was evaluated, for both Nd:YAG media, to be lower than 0.01. On the other hand, losses L i for waveguides are in agreement with propagation losses determined at 632.8 nm, these being of 0.6 dB/cm for DWG-YG-1 and~1.5 dB/cm for DWG-YG-2 [10]. In our previous investigations it was showed that laser emission from such waveguides has a high M 2 factor, indicating multimode transverse operation [28,30,31]. The inset of Figure 2 presents the 3D shape of the laser beam at the maximum output power (P out = 2.05 W, the waveguide DWG-YG-1), suggesting similar multimode distribution of the laser beam. For waveguide DWG-YG-1 the Q-switch regime was investigated with Cr 4+ :YAG of initial transmission Ti = 0.89, 0.84, and 0.79 and with an OCM of transmission T = 0.10 (for which the highest average output power was obtained). The results are shown in Figure 3. For the Cr 4+ :YAG with Ti = 0.89 the maximum average output power was Pave = 0.56 W (Figure 3a). At this level the laser ran at a repetition rate rp = 295 kHz, from which the laser pulse energy was evaluated as Ep = 1.89 μJ. A fast UPD-35-IR2-D photodiode (Alphalas, Göttingen, Germany) with a short (<35 ps) rise time and a Tektronix DPO7254 digital oscilloscope (2.5 GHz bandwidth, 40 GS/s sample ra1te) were used to measure the laser pulse duration, tp. The pulse duration was tp = 5.2 ns and therefore pulse peak power was calculated as Pp = 0.36 kW (Figure 3b). In the case of Cr 4+ :YAG with Ti = 0.84 the average power was limited to Pave = 0.37 W; the pulse energy was Ep = 1.55 μJ, and pulse duration narrowed to tp = 4.6 ns (i.e., Pp ~ 0.34 kW). A slightly shorter pulse, tp = 4.2 ns, was measured for the Cr 4+ :YAG SA with Ti= 0.79; the power decreased at Pave = 0.27 W, the laser ran at rp = 156 kHz with energy Ep = 1.71 μJ (or peak power Pp ~ 0.41 kW). It is noticeable that the duration of the laser pulse and its energy were nearly constant throughout the entire pump range (Figure 3b), in accordance with theory for such a passive Q-switch laser. Unfortunately damage of the waveguide coating was observed (this can be seen in Figure 1a); therefore further experiments were performed only for the Cr 4+ :YAG SA with Ti = 0.89.  For waveguide DWG-YG-1 the Q-switch regime was investigated with Cr 4+ :YAG of initial transmission T i = 0.89, 0.84, and 0.79 and with an OCM of transmission T = 0.10 (for which the highest average output power was obtained). The results are shown in Figure 3. For the Cr 4+ :YAG with T i = 0.89 the maximum average output power was P ave = 0.56 W (Figure 3a). At this level the laser ran at a repetition rate r p = 295 kHz, from which the laser pulse energy was evaluated as E p = 1.89 µJ. A fast UPD-35-IR2-D photodiode (Alphalas, Göttingen, Germany) with a short (<35 ps) rise time and a Tektronix DPO7254 digital oscilloscope (2.5 GHz bandwidth, 40 GS/s sample ra1te) were used to measure the laser pulse duration, t p . The pulse duration was t p = 5.2 ns and therefore pulse peak power was calculated as P p = 0.36 kW (Figure 3b). In the case of Cr 4+ :YAG with T i = 0.84 the average power was limited to P ave = 0.37 W; the pulse energy was E p = 1.55 µJ, and pulse duration narrowed to t p = 4.6 ns (i.e., P p~0 .34 kW). A slightly shorter pulse, t p = 4.2 ns, was measured for the Cr 4+ :YAG SA with T i = 0.79; the power decreased at P ave = 0.27 W, the laser ran at r p = 156 kHz with energy E p = 1.71 µJ (or peak power P p~0 .41 kW). It is noticeable that the duration of the laser pulse and its energy were nearly constant throughout the entire pump range (Figure 3b), in accordance with theory for such a passive Q-switch laser. Unfortunately damage of the waveguide coating was observed (this can be seen in Figure 1a); therefore further experiments were performed only for the Cr 4+ :YAG SA with T i = 0.89. For waveguide DWG-YG-1 the Q-switch regime was investigated with Cr 4+ :YAG of initial transmission Ti = 0.89, 0.84, and 0.79 and with an OCM of transmission T = 0.10 (for which the highest average output power was obtained). The results are shown in Figure 3. For the Cr 4+ :YAG with Ti = 0.89 the maximum average output power was Pave = 0.56 W (Figure 3a). At this level the laser ran at a repetition rate rp = 295 kHz, from which the laser pulse energy was evaluated as Ep = 1.89 μJ. A fast UPD-35-IR2-D photodiode (Alphalas, Göttingen, Germany) with a short (<35 ps) rise time and a Tektronix DPO7254 digital oscilloscope (2.5 GHz bandwidth, 40 GS/s sample ra1te) were used to measure the laser pulse duration, tp. The pulse duration was tp = 5.2 ns and therefore pulse peak power was calculated as Pp = 0.36 kW (Figure 3b). In the case of Cr 4+ :YAG with Ti = 0.84 the average power was limited to Pave = 0.37 W; the pulse energy was Ep = 1.55 μJ, and pulse duration narrowed to tp = 4.6 ns (i.e., Pp ~ 0.34 kW). A slightly shorter pulse, tp = 4.2 ns, was measured for the Cr 4+ :YAG SA with Ti= 0.79; the power decreased at Pave = 0.27 W, the laser ran at rp = 156 kHz with energy Ep = 1.71 μJ (or peak power Pp ~ 0.41 kW). It is noticeable that the duration of the laser pulse and its energy were nearly constant throughout the entire pump range (Figure 3b), in accordance with theory for such a passive Q-switch laser. Unfortunately damage of the waveguide coating was observed (this can be seen in Figure 1a); therefore further experiments were performed only for the Cr 4+ :YAG SA with Ti = 0.89.  The main results obtained with waveguide DWG-YG-2 and the Cr 4+ :YAG of T i = 0.89 are given in Figure 4. One could see that due to high losses (L i~0 .08) lasing was obtained only from a quite high pump power at threshold, of about 4 W. The laser yielded P ave = 0.52 W at a repetition rate r p = 67 kHz ( Figure 4a); thus, at this point the laser pulse energy was calculated as E p = 7.79 µJ. The pulse duration was t p = 4 ns (Figure 4b) giving a pulse peak power P p = 1.95 kW. There is a wider variation of laser pulse parameters with the pump power (Figure 4b), most likely due to the thermal effects induced by the pump in the laser medium and the variation with them of the waveguide properties. The main results obtained with waveguide DWG-YG-2 and the Cr 4+ :YAG of Ti = 0.89 are given in Figure 4. One could see that due to high losses (Li ~ 0.08) lasing was obtained only from a quite high pump power at threshold, of about 4 W. The laser yielded Pave = 0.52 W at a repetition rate rp = 67 kHz ( Figure 4a); thus, at this point the laser pulse energy was calculated as Ep = 7.79 μJ. The pulse duration was tp = 4 ns (Figure 4b) giving a pulse peak power Pp = 1.95 kW. There is a wider variation of laser pulse parameters with the pump power (Figure 4b), most likely due to the thermal effects induced by the pump in the laser medium and the variation with them of the waveguide properties. The characteristics of cw laser emission yielded by the waveguides inscribed in Nd:YVO4 crystals are given in Figure 5; the best performances were obtained with an OCM of transmission T = 0.10. The waveguide DWG-YV-1 delivered maximum power at 1.06 μm, Pout = 2.90 W for Pabs = 6.75 W (i.e., ηoa ~ 0.43); a good slope efficiency ηsa = 0.44 was determined. The results obtained in cw regime with all the waveguides investigated in this work are summarized in Table 1. It can be seen that power Pout = 2.0 W and Pout = 1.85 W were measured from waveguide DWG-YV-2 and DWG-YV-3, respectively; the corresponding slope efficiency ηsa was 0.34 and 0.30. As in the case of Nd:YAG, a Findlay-Clay analysis concluded that the resonator round-trip loss was Li ~ 0.06 for the waveguide DWG-YV-1 and nearly the same, Li ~ 0.10, for the other two waveguides inscribed in Nd:YVO4. The laser beam at the maximum output power was polarized The characteristics of cw laser emission yielded by the waveguides inscribed in Nd:YVO 4 crystals are given in Figure 5; the best performances were obtained with an OCM of transmission T = 0.10. The waveguide DWG-YV-1 delivered maximum power at 1.06 µm, P out = 2.90 W for P abs = 6.75 W (i.e., η oa~0 .43); a good slope efficiency η sa = 0.44 was determined. The main results obtained with waveguide DWG-YG-2 and the Cr 4+ :YAG of Ti = 0.89 are given in Figure 4. One could see that due to high losses (Li ~ 0.08) lasing was obtained only from a quite high pump power at threshold, of about 4 W. The laser yielded Pave = 0.52 W at a repetition rate rp = 67 kHz ( Figure 4a); thus, at this point the laser pulse energy was calculated as Ep = 7.79 μJ. The pulse duration was tp = 4 ns (Figure 4b) giving a pulse peak power Pp = 1.95 kW. There is a wider variation of laser pulse parameters with the pump power (Figure 4b), most likely due to the thermal effects induced by the pump in the laser medium and the variation with them of the waveguide properties. The characteristics of cw laser emission yielded by the waveguides inscribed in Nd:YVO4 crystals are given in Figure 5; the best performances were obtained with an OCM of transmission T = 0.10. The waveguide DWG-YV-1 delivered maximum power at 1.06 μm, Pout = 2.90 W for Pabs = 6.75 W (i.e., ηoa ~ 0.43); a good slope efficiency ηsa = 0.44 was determined. The results obtained in cw regime with all the waveguides investigated in this work are summarized in Table 1. It can be seen that power Pout = 2.0 W and Pout = 1.85 W were measured from waveguide DWG-YV-2 and DWG-YV-3, respectively; the corresponding slope efficiency ηsa was 0.34 and 0.30. As in the case of Nd:YAG, a Findlay-Clay analysis concluded that the resonator round-trip loss was Li ~ 0.06 for the waveguide DWG-YV-1 and nearly the same, Li ~ 0.10, for the other two waveguides inscribed in Nd:YVO4. The laser beam at the maximum output power was polarized The results obtained in cw regime with all the waveguides investigated in this work are summarized in Table 1. It can be seen that power P out = 2.0 W and P out = 1.85 W were measured from waveguide DWG-YV-2 and DWG-YV-3, respectively; the corresponding slope efficiency η sa was 0.34 and 0.30. As in the case of Nd:YAG, a Findlay-Clay analysis concluded that the resonator round-trip loss was L i~0 .06 for the waveguide DWG-YV-1 and nearly the same, L i~0 .10, for the other two waveguides inscribed in Nd:YVO4. The laser beam at the maximum output power was polarized E||c axis (π polarization) with extinction ratio better than 100:1, similar to the results reported in Ref. [11]. The average power, P ave outputted in Q-switch regime (Cr 4+ :YAG SA with T i = 0.89) by the waveguides inscribed in Nd:YVO 4 and the resonator with an OCM of T= 0.10 is plotted in Figure 6a versus P abs . The highest power P ave = 0.77 W was delivered by waveguide DWG-YV-3 at a repetition rate r p = 83 kHz (Figure 6b). The pulse energy reached E p = 9.4 µJ and the pulse peak power was calculated as P p = 1.36 kW (the pulse duration was t p = 6.8 ns). Finally, the characteristics of the Q-switch laser pulses obtained in this work with the Cr 4+ :YAG SA of T i = 0.89 are summarized in Table 2. One can see that the waveguide DWG-YV-1 yielded laser pulses with E p = 4.15 µJ at high repetition rate, r p = 178 kHz and quite low peak power P p = 0.29 kW (pulse duration, t p = 14 ns). The use of a shorter DWG-YV-2 waveguide decreased the pulse duration at t p = 8.2 ns whereas the repetition rate was r p = 152 kHz; the laser pulse energy and peak power was E p = 3.68 µJ and 0.45 kW, respectively. E||c axis (π polarization) with extinction ratio better than 100:1, similar to the results reported in Ref. [11]. The average power, Pave outputted in Q-switch regime (Cr 4+ :YAG SA with Ti = 0.89) by the waveguides inscribed in Nd:YVO4 and the resonator with an OCM of T= 0.10 is plotted in Figure 6a versus Pabs. The highest power Pave = 0.77 W was delivered by waveguide DWG-YV-3 at a repetition rate rp = 83 kHz (Figure 6b). The pulse energy reached Ep = 9.4 μJ and the pulse peak power was calculated as Pp = 1.36 kW (the pulse duration was tp = 6.8 ns). Finally, the characteristics of the Q-switch laser pulses obtained in this work with the Cr 4+ :YAG SA of Ti = 0.89 are summarized in Table 2. One can see that the waveguide DWG-YV-1 yielded laser pulses with Ep = 4.15 μJ at high repetition rate, rp = 178 kHz and quite low peak power Pp = 0.29 kW (pulse duration, tp = 14 ns). The use of a shorter DWG-YV-2 waveguide decreased the pulse duration at tp = 8.2 ns whereas the repetition rate was rp = 152 kHz; the laser pulse energy and peak power was Ep = 3.68 μJ and 0.45 kW, respectively.

Discussion
The spectroscopic properties of interest for the Q-switch regime differ for Nd:YAG and Nd:YVO 4 . Thus, for Nd:YAG the emission cross-section, σ g in the 1 µm range is moderate, σ g = 2.6 × 10 −19 cm 2 and the luminescence lifetime of the 4 F 3/2 emitting level at 1.0-at % Nd-doping level is long, τ f~2 25 µs [32]. In case of Nd:YVO 4 the emission-cross section is much larger, σ g = 14.1 × 10 −19 cm 2 (in πpolarization), whereas the lifetime is shorter, τ f~8 4 µs for 1.0-at % Nd:YVO 4 . Thus, due to their spectroscopic characteristics, Nd:YAG can provide Q-switch laser pulses of high energy at tens to hundreds of kHz repetition rate, while Nd:YVO 4 is expected to yield pulses with lower energy, but at much higher repetition rate.
Several experiments performed in all bulk Nd:YAG ceramics and Nd:YVO 4 crystals confirmed these statements. For example, the Q-switch laser built with the 4.5 mm long, 1.1-at % Nd:YAG, the Cr 4+ :YAG SA with T i = 0.89, and an OCM with T = 0.05 delivered P ave = 2.3 W for the pump P abs = 6.65 W; the laser ran at r p = 312 kHz, indicating a pulse energy E p~7 .4 µJ. Furthermore, average power P ave = 1.6 W (at P abs = 6.75 W) was obtained from the 6.9 mm long, 0.5-at % Nd:YVO 4 crystal, the Cr 4+ :YAG SA of T i = 0.89 and an OCM of T = 0.10. The repetition rate was r p = 1720 kHz and therefore the laser pulse energy amounted to E p = 0.93 µJ. These results could be easily modeled by the theory of the passive Q-switch regime [33,34]. However, the waveguides used in the experiments, both those inscribed in Nd:YAG or in Nd:YVO 4 , yielded laser pulses with comparable (µJ level) energy. Therefore, further analysis is necessary in order to understand this behavior. The influence of thermal effects on the waveguide dimensions; an accurate determination of each waveguide and resonator losses; the impact of the pump radiation that is not absorbed in the waveguide on the properties of the Cr 4+ :YAG SA medium [35], or the variation with temperature of Nd:YAG and Nd:YVO 4 emission cross sections [36,37], which was shown to have a great impact on the emission performances of such lasers passively Q-switched by the Cr 4+ :YAG SA [38,39], could be considered in modeling.

Conclusions
In this work we reported on the Q-switch laser pulse characteristics obtained from circular (100 µm diameter) buried depressed-cladding waveguides that were inscribed in Nd:YAG ceramics and Nd:YVO 4 single crystals by direct writing with an fs-laser beam. Compared to a previous paper [27], in which Nd:YAG and Cr 4+ :YAG SA media were bonded in a composite structure, in the present investigations we considered discrete elements in order to obtain a greater variety of laser pulses, mainly by changing the Cr 4+ :YAG SA. For the pump level used in the experiments (close to or slightly below P abs = 7 W), the average power at 1.06 µm reached P ave = 0.52 W from a waveguide inscribed in a 1.1-at % Nd:YAG ceramic of 4.8 mm length. This device, which was built with a Cr 4+ :YAG of T i = 0.89 and a resonator OCM of T = 0.05, delivered pulses with energy E p = 7.79 µJ and short 4.0 ns duration; the pulse peak power was P p = 1.95 kW. Laser pulses with close peak power, P p~1 .36 kW at 83 kHz repetition rate were yielded by a waveguide that was written in a 3.4-mm long, 1.0-at % Nd:YVO 4 crystal, and that was placed in a resonator with the Cr 4+ :YAG of T i = 0.89 and an OCM with T = 0.10; the pulse energy was high, E p = 9.4 µJ. Worthy of mention is that the pump was made with a fiber-coupled diode laser; this proves the potential to build compact laser systems with average-to-high peak power pulses based on waveguides realized by fs-laser beam direct writing technique. Further work could consider modeling of such passively Q-switch Nd:YAG-Cr 4+ :YAG systems.