Passive Q-switching of a Tm,Ho:KLu(WO4)2 microchip laser by a Cr:ZnS saturable absorber J. M. SERRES,1 P. LOIKO,1,2 X. MATEOS,1,3,5,* V. JAMBUNATHAN,4 A. S. YASUKEVICH,2 K. V. YUMASHEV,2 V. PETROV,3 U. GRIEBNER,3 M. AGUILÓ,1 AND F. DÍAZ1 1Física i Cristal·lografia de Materials i Nanomaterials (FiCMA-FiCNA), Universitat Rovira i Virgili (URV), Campus Sescelades, c/Marcel·lí Domingo, s/n., Tarragona E-43007, Spain 2Center for Optical Materials and Technologies (COMT), Belarusian National Technical University, 65/17 Nezavisimosti Ave., Minsk 220013, Belarus 3Max Born Institute for Nonlinear Optics and Short Pulse Spectroscopy, 2A Max-Born-Str., Berlin D-12489, Germany 4HiLASE Centre, Institute of Physics ASCR, Za Radnicí 828, Dolní Brežany 25241, Czech Republic 5e-mail: mateos@mbi‑berlin.de *Corresponding author: xavier.mateos@urv.cat Received 4 March 2016; revised 6 April 2016; accepted 6 April 2016; posted 7 April 2016 (Doc. ID 260487); published 3 May 2016 A diode-pumped Tm;Ho:KLuWO42 microchip laser passively Q-switched with a Cr:ZnS saturable absorber generated an average output power of 131 mW at 2063.6 nm with a slope efficiency of 11% and a Q-switching conversion efficiency of 58%. The pulse characteristics were 14 ns∕9 μJ at a pulse repetition frequency of 14.5 kHz. With higher modulation depth of the saturable absorber, 9 ns∕10.4 μJ∕8.2 kHz pulses were generated at 2061.1 nm, corresponding to a record peak power extracted from a passively Q-switched Tm,Ho laser of 1.15 kW. A theoretical model is presented, predicting the pulse energy and duration. The simulations are in good agreement with the experimental results. © 2016 Optical Society of America OCIS codes: (140.3070) Infrared and far-infrared lasers; (140.3540) Lasers, Q-switched; (140.3380) Laser materials. http://dx.doi.org/10.1364/AO.55.003757 1. INTRODUCTION The holmium (Ho3) ion is attractive for lasing due its wave- length-tunable emission at ∼2 μm (5I7 → 5I8 transition). Such an emission is eye-safe and of practical interest for remote sensing, metrology, and medical applications. Holmium lasers are also used for pumping mid-IR optical parametric oscillators [1]. An usual scheme to exciteHo3 is the energy transfer (ET) from Thulium (Tm3) ions, 3F4Tm3 → 5I7Ho3 by co- doping the host material [2]. This approach has the advantage of enhanced pump efficiency because the Tm3 ions strongly absorb the emission of commercial AlGaAs laser diodes at ∼0.8 μm. The ET in the Tm3, Ho3 pair is very efficient even at low Ho3 concentrations, achieved by efficient cross re- laxation between the Tm3 ions at high concentration whereas the Ho3 ions act as efficient traps [3]. Consequently, an opti- mum codoping ratio (NHo:N Tm, from 1∶5 to 1∶10) exists pro- viding both high Tm3 absorption and weak upconversion. Tm,Ho codoped materials are very suitable for the develop- ment of compact diode-pumped laser sources at ∼2 μm [4–6]. This is especially true by exploiting the microchip laser concept [7] with a gain material placed in a plano–plano cavity without air gaps. Such a compact, robust, and misalignment-free design provides low intracavity losses and high laser efficiency. Continuous wave (CW) Tm,Ho microchip lasers were realized with a number of hosts such as LiYF4, YAlO3, YVO4, and GdVO4 [8–12]. Recently, we studied potassium lutetium double tungstate, KLuWO42 or KLuW for short, which has proved to be very suitable host for rare earth doping [13]. This finding holds also for Tm,Ho doping because it provides high absorption and emission cross sections together with high ET efficiency [14]. A room-temperature CW Tm,Ho:KLuW microchip laser generated 451 mW at 2081 nm with a slope efficiency of 31% [15]. Passively Q-switched (PQS) microchip lasers containing a saturable absorber (SA) in the cavity [16] may generate very short pulses due to the reduced cavity round-trip time [17]. The stabilization of the laser mode in the microchip laser cavity is typically ensured by a positive thermal lens of the gain material [18]. The effect of the thermal lens also strongly focused the laser mode in the SA resulting in its easy bleaching. Thus, PQS microchip lasers are also attractive for the genera- tion of high peak powers. We are aware of only one report on a PQS Tm,Ho microchip laser [19]. However, due to one par- ticular limitation of the SA used in [19] (single-layer graphene), namely, the lowmodulation depth, this laser generated 200 ns∕ 0.2 μJ pulses with a peak power of only ∼1 W. Several previous studies were devoted to PQS Tm,Ho bulk lasers using LiYF4, LiLuF4, YAlO3, and YVO4 host crystals and Cr2:ZnS or Research Article Vol. 55, No. 14 / May 10 2016 / Applied Optics 3757 1559-128X/16/143757-07 Journal © 2016 Optical Society of America carbon nanostructures as SAs [20–23]. However, in such lasers, the typical pulse durations were still a few hundred nano- seconds (ns) and the peak power did not exceed a few tens of watts (W). In this paper, the first Tm,Ho microchip laser PQS with a Cr2:ZnS SA is presented. Using a Tm,Ho:KLuW crystal as gain medium, peak powers exceeding the kilowatt level are achieved. Recently, Cr2:ZnS has been successfully applied for Q-switching of bulk [24] and microchip [25] Tm:KLuW lasers which operate at shorter wavelengths. 2. EXPERIMENT The studied crystal with composition 5.0 at. % Tm, 0.5 at. % Ho:KLuWO42 or Tm,Ho:KLuW for short was grown by the top-seeded solution growth slow-cooling method and potas- sium ditungstate K2W2O7 was used as a solvent; details about the growth procedure can be found in [13]. The starting materials were K2CO3, WO3, and Ln2O3 (Ln  Lu, Tm and Ho) with 99.99% purity. The actual ion densities in the crystal measured by electron probe microanalysis were N Tm  2.30 × 1020 at∕cm3 and NHo  0.53 × 1020 at∕cm3. Such doping levels for Tm3 and Ho3 ions provided high preva- lence of direct Tm3 → Ho3 energy transfer over the reverse Ho3 → Tm3 process [19] (expressed by an equilibrium constant, θ  0.089) which prevented unwanted colasing of both ions [26]. The latter, in turn, could be the main limitation for a stable Q-switched operation with this crystal. A rectangular sample was cut from the as-grown bulk in the frame of the dielectric axes with dimensions 2.86g mm× 2.86m mm × 2.94p mm. It was oriented for light propaga- tion along the Ng -axis. This crystal orientation was selected because it provides a positive thermal lens [15,27] required for stabilization of the laser mode in a plano–plano microchip cav- ity. Both m × p crystal faces were polished to laser quality and remained uncoated. The crystal was mounted in a water-cooled copper holder (kept at 14°C) and cooled from all four side faces. Indium foil was used to improve thermal contact. The laser cavity consisted of a plane pump mirror that was AR-coated for 0.7–1 μm and HR-coated for 1.8–2.1 μm and a plane output coupler (OC) providing a transmission of TOC  5% at the laser wavelength. The choice of this OC will be explained below. Two commercial SAs from polycrystalline Cr2:ZnS with thicknesses of 2.18 and 2.21 mm were studied (IPG Photonics). The SAs were AR-coated for the 1.8–2.2 μm range. The initial transmission at the laser wavelength, T SA, was 89% and 90.5%, respectively. Small-signal transmission of both SAs at ∼2.2 μm (i.e., outside of the Cr2 ions absorp- tion band) was 92.5%, representing 7.5% single-pass nonsatur- able loss. It is attributed to strong scattering and imperfect optical quality of this polycrystalline material and partially to residual Fresnel loss due to imperfect coating. Thus, the saturable absorption α 0SA was 3.5% and 2%, respectively. The passively cooled SAs were placed between the crystal and the OC and. The cavity contained no air gaps, and its total length was ∼5.06 mm. The crystal was pumped by a fiber-coupled AlGaAs laser diode (N:A:  0.22, fiber core diameter: 200 μm) operating at λp  805 nm (excitation wavelength for the 3H6 → 3H4 transition of Tm3 ). The unpolarized output from the diode was reimaged into the crystal by a lens assembly (1∶1 image ratio, focal length: 30 mm) resulting in a pump spot radius wp  100 μm. The M 2 parameter for the pump beam, esti- mated from the relation wp ×N:A:  λp∕π ×M 2, amounted to ∼86. Thus, the confocal parameter for the pump beam 2zR  2πw2pn∕λpM 2  1.8 mm. The absorption of the pump radiation in the crystal was 60%. The radius of the laser mode in the crystal and SA was calculated with the ABCD- method for the “hot” cavity to be wl  60 5 μm. The thermal lens was described as a thin astigmatic lens. For the pumped crystal, the following parameters of the thermal lens were used: M  24.9 and 24.1 m−1∕W for the mg- and pg-principal meridional planes, respectively [15]. Here, M  dD∕dPabs is the so-called sensitivity factor of the thermal lens, Pabs is the absorbed pump power, D  1∕f is the optical (refractive) power of the lens, and f is its focal length [28]. Thus, for the maximum studied Pabs of 1.9 W, f  21 and 22 mm for the mg- and pg-planes, respectively. The scheme for the PQS Tm,Ho:KLuW microchip laser is shown in Fig. 1(a). The transmission spectra of the used Cr:ZnS SAs are shown in Fig. 1(b). A fast InGaAs photodiode (rise time: 200 ps) and 2 GHz digital oscilloscope (Tektronix DPO5204B) were used for detection of the Q-switched pulses. 3. MODEL OF A Q-SWITCHED LASER First we modeled the pulse energy and pulse duration for the PQS Tm,Ho:KLuW microchip laser. This model is an adaptation of that presented in [29] for a Yb microchip laser. We consider a quasi-three-level laser system. PQS is realized by a “slow” SA, i.e., a SA with a recovery time much longer than the pulse duration. We introduce the following variables: (i) Φg  I g∕hνg , the photon flux density at the laser frequency (I g is the laser radiation intensity, h is the Planck constant, and νg is the laser frequency), (ii) N 2g  N 2 − βgNHo, the effective population of the upper laser level (N 2 is its actual population, βg  σgabs∕σ g SE  σgabs is the parameter characterizing the conditions for bleaching of the active medium at the laser frequency, and σgSE and σ g abs are the stimulated-emission and absorption cross sections for the active medium at the laser frequency, respectively), and (iii) Ngs, the population of the ground state of the SA. All these variables are averaged over the laser mode volume. For single-pulse generation, the system of rate equations is dΦg d t  cμ n σgN 2g − kL − kSAΦg ; (1a) Fig. 1. (a) Scheme of the passively Q-switched Tm,Ho:KLuW microchip laser. LD, laser diode; PM, pump mirror; OC, output cou- pler. (b) Transmission spectra of the used Cr:ZnS SAs. 3758 Vol. 55, No. 14 / May 10 2016 / Applied Optics Research Article dN 2g d t  −σgN 2gΦg ; (1b) dN gs d t  −ξσgsN gsΦg : (1c) Here, c is the speed of light, μ  lAMnAM∕l c is the resonator filling factor; lAM is the active element length; nAM is the refractive index of the active element; l c is the optical length of the resonator; σg  σgSE  σgabs; kL  −ln1 − TOC  ln1 − L∕2lAM is the resonator loss coefficient, where L is the coefficient of passive intracavity loss; kSA  σgsN gs  σesN esl SA∕lAM is the loss coefficient in the SA; σgs and σes are the ground- and excited-state absorption cross sections for the SA, respectively; Nes is the population of the excited state of the SA; lSA is the SA length; and ξ  Ag∕ASA is the ratio of effective areas of the lasing mode in the active medium (Ag ) and in the SA (ASA). The energy (Eout) and duration (Δt) of a single pulse are then determined as Eout  V gkacthνg 1 σg ln N i2 g Nf2g  ; (2a) Δt  Eout∕Ppeak; where Ppeak  V gkacthνgΦgN t2g: (2b) Here, N i2g  kLlAM − ln T SA∕σg lAM is the initial effective population of the upper laser level, and N t2g and N f 2g corre- spond to the moment when Φg reaches its maximum value (maximum of the pulse) and to the termination of the laser pulse, respectively. The solutions of Eq. (1) for ΦgN 2g, N t2g , and Nf2g parameters are given in Appendix A. The material parameters of Tm,Ho:KLuW and Cr:ZnS used for calculations [14,19,30] are listed in Table 1. From the point of view of the laser efficiency, the selection of the OC for the Tm,Ho:KLuW laser is limited by a strong upconversion loss for high TOC [15] due to a high inversion ratio and, hence, high population of the upper laser level of Ho3. Consequently, low transmittance of the OC and high transmission of the SA are desirable. Considering the latter, we have calculated the pulse duration and energy for the PQS Tm, Ho:KLuW microchip laser for TOC  1%…9% and α 0SA  6%, 4%, or 2%, as shown in Fig. 2. The model indicates that with an increase in the modulation depth of the SA, the pulse duration will be shortened from ∼13 to 7 ns and there exists an optimum range of TOC, namely, 4%…6% corresponding to the shortest pulses. The pulse energy is expected to increase with the increase in α 0SA. Concerning its dependence on the OC transmittance, it is nearly saturated for TOC > 4%. All these considerations led to the selection of TOC  5% as the one close to optimum for our designed microchip, and a peak power >1 kW is expected. 4. RESULTS AND DISCUSSION In the CW regime, we achieved 225 mW at ∼2063 nm with a slope efficiency η  16% (with respect to the absorbed pump power); see Fig. 3. The laser threshold was at Pabs  0.5 W, and the optical-to-optical efficiency amounted to 12%. Further power scaling of this laser was limited by strong thermal effects observed at Pabs > 2 W, leading to a roll-off of the output power due to a strong upconversion. The output emission from this laser was linearly polarized, E‖Nm, naturally selected by the anisotropy of the gain. Stable Q-switching was achieved for the two studied SAs for Pabs ≤ 2 W. Within this range of absorbed power, the Table 1. Material Parametersa of the Tm,Ho:KLuW Laser Crystal and Cr:ZnS SA Used for the Calculations [14,19,30] Parameter Notation Value AM: Tm,Ho:KLuWb Absorption cross section σgabs 0.7 × 10 −20 cm2 Stimulated-emission cross section σgSE 2.4 × 10 −20 cm2 Lifetime of Ho3ions∕Tm3− Ho3 pair τHo5I7∕τTm−Ho 4.8 ms∕2.1 ms Refractive index nAM 1.9852 SA:Cr2:ZnS Ground/excited-state absorption cross section σgs∕σes 0.1 × 10−18 cm2∕≈0 Saturation fluence FS  hνl∕σgs 1.07 J∕cm2 Recovery time τ5E 5 μs Nonsaturable loss 7.5% Refractive index nSA 2.2647 aAt the laser wavelength, λl  2.06 μm. bFor light polarization E‖Nm. Fig. 2. Modeling of (a) the pulse duration and (b) energy for the Tm,Ho:KLuW microchip laser passively Q-switched by a Cr:ZnS SA. α 0SA , modulation depth of the saturable absorber; TOC, transmis- sion of the output coupler. Fig. 3. Output characteristics of CW and passively Q-switched Tm,Ho:KLuWmicrochip lasers, where TOC  5%, and η is the slope efficiency. Research Article Vol. 55, No. 14 / May 10 2016 / Applied Optics 3759 input–output dependence of the PQS Tm,Ho:KLuW micro- chip laser was linear. The laser output was also linearly polarized, E‖Nm. The maximum output power achieved corresponded to the SA with α 0SA  2%. It was 131 mW at 2063.6 nm with a slope efficiency of 11%. The laser threshold was at ∼0.7 W of absorbed pump power, and the optical- to-optical efficiency was ∼7%. The Q-switching conversion efficiency with respect to the CW regime was then 58%. For α 0SA  3.5%, we extracted 85 mW at 2061.1 nm with a re- duced slope η  6%. This is attributed to higher upconversion loss due to lower T SA. The Q-switching conversion efficiency was only 38%. The laser spectra of the PQS Tm,Ho:KLuWmicrochip laser are shown in Fig. 4(a). The spectra consisted only of a single emission peak. These laser wavelengths are in agreement with the maxima in the gain cross-section spectrum ofHo3 ions in KLuW; see Fig. 4(b). For light polarization E‖Nm, the gain spectrum exhibits two local maxima centered at ∼2060 and 2076 nm. For high inversion ratios (β > 0.25) associated with high TOC and small T SA, the laser is expected to oscillate near the short-wavelength peak at ∼2060 nm. By increasing the pump power, the duration of the single Q-switched pulse (FWHM) decreased only slightly from 16 to 14 ns (α 0SA  2%) and from ∼11 to 9 ns (α 0SA  3.5%). This reduction was accompanied by a near-linear increase in the pulse repetition frequency (PRF), from 4.5 to 14.5 kHz (α 0SA  2%) and from 3 to 8.2 kHz (α 0SA  3.5%); see Fig. 5. By using the data on the average output power, PRF, and pulse duration, we calculated the pulse energies (Eout  Pout∕PRF) and peak powers (Ppeak  Eout∕Δt) for the studied PQS Tm, Ho:KLuW microchip laser; see Fig. 6. For both SAs, the pulse energy was nearly independent of the pump level, 9.0 0.2 μJ (α 0SA  2%) and 10.2 0.3 μJ (α 0SA  3.5%), and the maxi- mum peak power amounted to 0.65 and 1.15 kW, respectively. The use of a SA with α 0SA  3.5% was superior with respect to the pulse duration and energy mainly due to an increased modulation depth. The criterion for efficient passive Q-switching by a slow SA is [31] X  σgs σgabs  σ g SE Ag ASA ≫ 1: (3) For the Tm,Ho:KLuW microchip laser, the sizes of the laser mode in the active medium and in the SA are nearly the same (Ag≈ASA), so that the value of X is determined solely by the spectroscopic parameters of the Tm,Ho:KLuW and Cr:ZnS materials. For a laser wavelength of ∼2.06 μm, X is ∼3 which means that although this combination of materials facilitates efficient Q-switching, the pulse energy and duration may show slight dependence on the pump power with saturation well above the laser threshold; see Figs. 5 and 6. The experimental values of pulse duration and energy agree well with the theo- retical predictions for TOC  5%; see Fig. 2. For α 0SA  4% and 2%, the model predicted generation of 9.8 ns∕11 μJ and 13.6 ns∕8.4 μJ pulses which correlates well with Figs. 5 and 6. No damage of the Cr:ZnS SA was observed in our experi- ments. Indeed, the maximum axial peak intensity on the SA, I in  X 2Eout∕πw2l Δt (where X  1 R∕1 − R and R is the reflectivity of the OC, wl is the radius of the laser mode, and the term “2” indicates that it has a Gaussian spatial profile corresponding to a TEM00 mode) was ∼0.5 GW∕cm2 (α 0SA  2%) and 0.8 GW∕cm2 (α 0SA  3.5%), which is well below its damage threshold (>10 GW∕cm2 for picosecond- long pulses [32]). Figure 7 shows the oscilloscope traces of the shortest Q-switched pulses for α 0SA  2% and 3.5% and a typical pulse train for α 0SA  2% (in all cases, Pabs  1.9 W). The intensity instabilities in the pulse train are ∼15% . They are attributed to the heating of the SA by the residual nonabsorbed pump. The output beam of the Tm,Ho:KLuWmicrochip laser cor- responded to a TEM00 mode with an almost circular profile and M 2x;y < 1.1 (x ≡ p, y ≡ m), as can be expected from the very low astigmatism of the thermal lens (S∕M  4%) [15] and the symmetrical four-side cooling of the laser crystal. Fig. 4. (a) Typical laser emission spectra of the passivelyQ-switched Tm,Ho:KLuW microchip laser. (b) Gain cross sections, σg , of the Ho3 ions in KLuW for light polarization E‖Nm; β, inversion ratio. Fig. 5. Pulse duration and pulse repetition frequency for the passively Q-switched Tm,Ho:KLuW microchip laser. Fig. 6. Pulse energy and peak power for the passively Q-switched Tm,Ho:KLuW microchip laser. 3760 Vol. 55, No. 14 / May 10 2016 / Applied Optics Research Article So far, active and passive Q-switching of Tm,Ho bulk lasers have been intensively studied. Because Tm,Ho-codoped mate- rials suffer from strong upconversion losses limiting their output performance, previous studies with active Q-switching were mainly performed with cryogenic cooling of the active material (typically at liquid nitrogen temperature, 77 K). By using an acousto-optic modulator (AOM) or a RTP Pockels cell, PQS Tm;Ho:YVO4, GdVO4, LiYF4, and YAlO3 lasers have been demonstrated generating typically 1–2 mJ/ 20 ns pulses with a multiwatt-level output [33–36]. Room- temperature AOM Q-switched Tm,Ho:YLF lasers were also reported, however, with much worse output characteristics [37]. Passive Q-switched laser operation at room temperature is more favorable to benefit from the compactness of the cavity. A comparison of passively Q-switched Tm,Ho bulk lasers re- ported so far [19–23] is presented in Table 2. Two types of SAs were employed in these lasers, namely, Cr:ZnS and carbon nanostructures (graphene and single-walled carbon nanotubes, SWCNTs). However, they provided similar output character- istics with a pulse duration of hundreds of ns and a pulse energy of a few microjoules. Although the results in the present work do not present any record in terms of average output power or pulse energy, they represent a substantial reduction in the pulse duration and, consequently, a few orders of magnitude increase in the peak power, from a few W to the ∼1 kW level. Further improvement of the developed laser can be expected by decreasing the intracavity losses, i.e., applying AR-coatings on the laser crystal or improving the ratio of the saturable to the nonsaturable SA losses. The use of Cr:ZnSe, which demon- strates a higher ground-state absorption cross section at the Ho3 laser wavelength (σgs  2.5 × 10−18 cm2 at ∼2.06 μm) as compared with its Cr:ZnS counterpart [38], seems to be useful for increasing the modulation depth of the SA which is important for obtaining shorter duration and higher energy pulses. In this way, according to our model, the generation of peak powers up to ∼10 kW from a room-temperature Tm,Ho:KLuW microchip laser is expected. 5. CONCLUSIONS We report on the first, to the best of our knowledge, passively Q-switched Tm,Ho-codoped double tungstate microchip laser using polycrystalline Cr2:ZnS as saturable absorber and a 5 at. % Tm, 0.5 at.% Ho:KLuW crystal cut along the N g -axis as the gain medium. This laser generated a maximum average out- put power of 131 mW at 2063.6 nm with a slope efficiency of 11% (α 0SA  2%). With higher modulation depth of the SA (α 0SA  3.5%), a pulse duration of 9 ns was achieved, the short- est ever reported for a PQS Tm,Ho-doped laser. At a pulse energy of 10.4 μJ, this corresponds to a record peak power of 1.15 kW, the highest ever extracted from a room-temperature PQS Tm,Ho laser, exceeding >50 times the previous results [19–23]. A theoretical model of a quasi-three-level laser system PQS with a “slow” SA is developed. It agrees well with the experimental results. Further improvement of the output characteristics of the compact ∼2 μm Tm,Ho PQS room- temperature microchip can be expected by use of Cr:ZnSe SA and optimization of intracavity losses. APPENDIX A Solutions of Eq. (1) for the photon flux density at laser fre- quency (Φg ), effective population of the upper laser level at the moments when Φg reaches its maximum value (N t2g ), and the termination of the laser pulse (Nf2g ) are given by ΦgN 2g  cμ n 8< : N i2g − N 2g − kLlAMβ ln1∕T SA lAMσg ln  N i2g N 2g  − − 1−β ln1∕T SAlAMσgα h 1 −  N i2g N 2g  α i 9= ;; (A1) Fig. 7. (a) Records of the shortest laser pulses achieved with α 0SA  2% and 3.5%, and (b) a typical pulse train for the Tm,Ho:KLuW microchip laser Q-switched with Cr2:ZnS SA; α 0SA  2%, TOC  5%, and Pabs  1.9 W. Table 2. Summary of PQS Near-Room-Temperature Tm,Ho Lasers Reported So Far Crystal, Tm,Ho: SA Pout, mW Δt , Ns PRF, kHz Eout, μJ Ppeak, kW T , K Ref. KLuW A 85 9 8.2 10.4 1.15 287 This work A 131 14 14.5 9 0.65 287 KLuW B 74 200 340 0.2 0.001 285 [19] LiYF4 A 10 1250 2.6 4 0.003 283 [20] LiLuF4 A 68 1200 5.2 13 0.01 283 [21] YAlO3 C 660 135 245 2.7 0.02 285 [23] Pout, average output power; Δt, pulse duration; Eout, pulse energy; PRF, pulse repetition frequency; Ppeak , peak power. SA: A—Cr:ZnS, B—graphene, C—SWCNTs. Research Article Vol. 55, No. 14 / May 10 2016 / Applied Optics 3761 N t2g N i2g  N 2g ° N i2g   1 − N 2g ° N i2g N t2g N i2g  α ; (A2) Nf2g N i2g  1 N 0 2g N i2g ln Nf2g N i2g  − 1 α  1 − N 02g N i2g  1 − N t2g N i2g  α  ; (A3) where α  ξσgs∕σg , β  σes∕σgs, and N 02g  kLlAM − β ln T SA∕σg lAM. Funding. Spanish Government (MAT2013-47395-C4-4- R, TEC2014-55948-R); Generalitat de Catalunya (2014SGR1358); ICREA Academia for Excellence in Research (2010ICREA-02); European Commission: Marie Skłodowska-Curie (657630). REFERENCES 1. P. A. Budni, L. A. Pomeranz, M. L. Lemons, C. A. Miller, J. R. Mosto, and E. P. 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