Lüthy, W.

Pollnau, M.

Weber, H.P.

English

A computer simulation of the dynamics of the Er3+ 3 um cw crystal laser considering the full rate-equation scheme up to the 4F7/2 level has been performed. The influence of the important system parameters on lasing and the interaction of these parameters has been clarified with multiple-parameter variations. Stimulated emission is fed mainly by upconversion from the lower laser level and in many cases is reduced by the quenching of the lifetime of this level. However, also without upconversion a set of parameters can be found that allows lasing. For a typical experimental situation we started with the parameters of Er3+:LiYF4. In addition also the host materials YAG, YAlO3, YSGG, and BaY2F8 as well as the possibilities of codoping are discussed

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Influence of Normal and Inverse Upconversion Processes on the Continuous Wave Operation of the E P  3 pm Crystal Laser M. Pollnau, W. Liithy, and H. P. Weber Institute of Applied Physics, University of Bem, Sidlemtr. 5, CH-3012 Bem, Switzerland Abstract A computer simulation of the dynamics of the E$' 3 p cw crystal laser considering the full rate-equation scheme up to the 4F712 level has been performed. The influence of the important system parameters on lasing and the interaction of these parameters has been clarified with multiple-parameter variations. Stimulated emission is fed mainly by up- conversion from the lower laser level and in many cases is reduced by the quenching of the lifetime of this level. However, also without upconversion a set of parameters can be found that allows lasing. For a typical experimental situation we started with the parameters of E?':LiYF4. In addition also the host materials YAG, YAlO,, YSGG, and BaY2F, as well as the possibilities of codoping are discussed. Introduction In recent years there has been enonnous theoretical and practical interest in the E$' 3 p laser. Its possible application in surgery evoked large efforts to increase the power and efficiency of the laser and to reduce its size [1-6]. Several attempts have been made [l-91 to understand cw operation on a transition which is believed to be self-terminating due to the longer lifetime of the lower laser level. Possible reasons for the nevertheless OcCuIance of cw lasing proposed so far include 1) depletion of the lower laser level 4113/2 due to excited-state absorption, 2) cross relaxation from the 4S3/2 level and a subsequent fast multiphonon decay into the upper laser leve1 4~11/2, 3) upconversion from the 4~13/2 leve1 feeding the 41, 1/2 level, and 4) a relatively long lifetime of the 4111/2 level in combination with a low braching ratio fiom the 4~11,2 leve1 into the 4~1,12 level. ~ l l  these explanations, however, consider only a single aspect and cannot describe a complex system like E$'. In our paper we present a computer simulation of the E?' 3 p laser, which includes, to our knowledge for the first time, a11 excited levels up to 4~7 /2 ,  a11 lifetimes and branching ratios, ground-state depletion, excited-state absorption, three upconversion processes as well as their inverse processes, stimulated emission, and a real resonator design. Especially the inclusion of the inverse upconversion processes gives deeper insight into the population mechanisms of the system. Computer Simulation The standard parameters of our rate-equation model closely match the case of E$+:LiYF4 The labelling of the levels is indicated in Fig. 1. The 2Hll, level is thermally coupled with the 4~,,  level. The intrinsic lifetimes of the levels are taken as: z1 = 10 ms, z2 = 4.8 ms, z3 = 6.6 p, z4 = 100 p, z5 = 400 p, z6 = 20 p. The values of the branching ratios [ lO]  are: pl0 = 1.000, p21 = 0.387, p20 = 0.613, f132 = 0.999, p31 = 0.000, /330 = 0.001, p43 = 0.903, p42 = 0.006, p41 = 0.004, p40 = 0.087, pS4 = 0.306, p53 = 0.012, p52 = 0.015, pSl = 0.179, p50 = 0.488, p65 = 0.941, p60 = 0.051. (4S3/3+2H1 1 4 2 9  41i5/2) f, ( '15/27 b/2)) and (4111/29 p64 = 0.000, fl63 = 0.002, = 0.002, fl61 = 0.004, Three ion-ion interactions are considered: (419~; 41i3/2)9 (41i3/~9 41~3/2) 11/2) f, (4115/2, 4F7/2)9 OSA Proccedings on Advanced So!id-Statc Lasca 1994. Vol. 20 Tso Yee Fon ond Bpce H. T. Cha~ (e&.) 01994 Opncd Socury of Amcnco 163 164 A dvanced Solid-Stare Larem parameters are Wso = 2.1W23m3s-1, Wll = 3.10-23m3s-1 [2], and W, = 1.8.10-23m3s-1 [2], reptively.  The E& ions are pumped cw with Pi, = 5 W at iz = 795 nm by ground-state absorption (GSA) 4fis12+419/2 (cross-section 003 = 5.10-21cm2) and excited-state absorption (ESA) 'Il3,,+ 2Hll, (ols = 1.10-20cm2). The laser transition is from the second Stark level of 4111/2 (Boltzmann population b,, = 0.200 at 300 K and degeneracy g2, = 2) into the fourth Stark level of 4113/2 (bl4 = 0.113, g14 = 2) at Ak = 2.81 pm with an emission cross-section = 3.10-20cm2. The pntaneous radiative fraction on the laser transition is y21 = 0.286. The crystal has a length t! = 2 mm and a dopant concentration N = 2.1021cm-3. The resonator data are: optical length topt = 0.1 m, incoupling efficiency of the pump light 7 = 0.56, average radius of the laser beam within the crystal rmode = 250 pm, transmission of the outcoupling mirror Tr = 2 %. Only the fraction P, / P = io-' of the spontaneous emission is emitted into the laser mode. c is the vacum speed of light and h is the Planck constant. The following rate equations for the population densities Ni and the photon density 4 are solved for the 795 nm pump wavelength in a Runge-Kutta calculation: The Influence of the Pump Leve1 Solving the rate equations for diEerent pump wavelengths provides deeper insight into the population mechanisms of the E$+:LiYF4 laser levels. The processes which are relevant for the cw operation of the E$+ 3 pn laser are indicated in the level scheme of Fig. 1. Pumping directly into the lower laser level at 1.53 pm leads to stimulated emission in both the simulation and experiments [3,4]. The calculation predicts that the slope efficiency is 18% with the threshold at 1.4 W. The excitation of the 4113/2 level is upconverted into the upper laser level via Wll and the subsequent multiphonon relaxation &. The 970 nm pump wavelength into the 4111.,2 upper laser level is the best choice for pumping the E?+:LiYF4 crystal, in agreement with experiments [5 ] .  The laser has a threshold of 0.5 W and a slope efficiency of 29 %. Pumping at 795 nm into the 4~9/2 leve1 leads to 0.9 W threshold and a slope efficiency of 19 %. "bis wavelength exhibits two disadvantages: The multiphonon relaxation fiom the 4b/z level reduces the quantum efficiency and results in the heating of the crystal and the higher population of the 4b,2 level enhances the inverse upconversion Wl1-l which populates the lower laser level and reduces stimulated emission. The Kr+ pump wavelength at 647 nm into the 4F9/2 level d e r s  from the m e  negative aspects as the 795 nm'wavelength, with additional losses being introduced by the multiphonon relaxation f143 and the ground-state fluorescence &. Advanced Solid-State h e r s  165 2 P60 P65 Figure 1. Es+:LiYF, level scheme indicating the processes which are relevant for the excitation of the laser levels. GSA R3) and ESA (Ris) are indicated only for the 795 nm pump wavelength. The application of a green a+ pump wavelength at 520 nm into the 2Hlln level leads to somewhat Werent population mechmsms. A threshold of 1.1 W and a slope efficiency of 20 % is calculated, which is comparable to the 795 nm pump wavelength. The pump excitation is efficiently down-converted to the ,Igl2 level by the cross relaxation Ws0, and via the multiphonon relaxation p to the upper laser level. Pumping at 488 nm into the 4F,12 level leads to a threshold of 0.8 W and a slope efficiency of 23 %. Afler the multiphonon decay f165 the cross relaxation from the ,S3, level avoids further multiphonon relaxations. The higher population of the 4F712 level enhances the inverse upconversion W2i1 and reduces the net sum upconverted from 41,1, by WZ2 - W2;'. Parameter Variations and Discussion 32 In threedimensional parameter variations the dependence of severd parameters on each other and their influence on output power is investigated. We assumed pumping cw at 795 nmwith Ph = 5 W into the level. The varied parameters are the lifetimes of all levels, the upconversion patanreters and the ESA cross section at 795 nm from the 4~13/2 level. Pump ESA at 795 nm on the transition 4113/2+ 2H1 1/2 becomes relevant only at cross sections V 7,=400 ps ! ! W z4= 100 ps P43 i i ' Z3=6.6ps 1 r,=4.8 ms A r l = l O m s  I V V  of above 1.1o-l9cm2, w h i ~ .  are not present in crystals such as LiYF,, YAG, or YAlO, [ 111. The absence of this ESA does not sigmlicantly reduce laser output. In a three level system the ratio of the populations of the upper (2) and lower (1) excited level is not simply determined by the ratio of the intrinsic lifetimes z1 but is dependent on the feeding of level 1 through level 2 [7]. CW inversion is, therefore, obtained in LiYF, and BaY2F, in the complete absence of upconversion processes. Es+:LiYF, has lifetimes z2 = 4.8 ms and z1 = 10 ms and a low bmching ratio p21 = 0.387 from upper to lower laser level which leads to a ratio N2 / N1 = 1.24 of the multiplett-population densities. The ratio is even higher, if the Boltzmann populations of the lasing Stark sublevels are taken into account. E2+:BaY2F8 with T~ = 9.6 ms, z1 = 10.6 ms, and p2, = 0.35 [6] also exhibits cw inversion without upnversion. The situation in other crystals is Merent: higher phonon energies reduce the ,Illl2 lifetime and draw the branching ratio p21 towards unity. 1.2 Figure 2. Variation POut (z2, W,,, W22): (a) W2, = 1.8.10-24m3s-1, @) W22 = 1.8-10-23m3s-1. Explanations see text. 166 Advanced Solid-State b e m  In the presence of upnversion the lifetime of the 41,1/2 upper laser leve1 still has a large iduence on laser performance (Fig. 2). z2 should be as long as possible and in the E?':LiYF4 parameter configuration there is a lower limit for z2 of approximately 800 p for cw operation (Fig. 2, left hand side). This limit increases to several ms when reducing Wll, because this reduces the depletion of the lower laser level (Fig. 2, right hand side). E?':YAG d e r s  from high phonon energies. This results in a low lifetime z2 = 100 ps and a high branching ratio into the lower laser level due to multiphonon relaxation. The lower limit of z2 suppresses 3 pm cw lasing in E?+:YAG at 795 nm pumping. The ratios of the inverse to the normal upconversion rates in E?+:LiYF, with the given pump conditions are Wl1-l / W,, = 0.54 and W2i1 / W = 0.40. This demonstrates the necessity of considenng the inverse upconversion processes Wl1-l and W2i1  in the rate equations. The process W5t1 is very weak. 22 The upnversion Wll, which is mainly responsible for efficient 3 pn lasing, is in competition with the inverse upnversion Wl1-' and the 1.6 ptn fluorescence pio. If the parameter Wll is large (Fig. 3, left hand side), the 4b/2 lifetime should be short to prevent Wl1-' from increasing (Figs. 3a and b). Decreasing z1 by co-doping decreases the population of the 4~13/2 level, thus weakening the upconversion w,, and reducing the laser output (Fig. 3b). If the parameter Wll is small (Fig. 3, right hand side), z3 has no influence on lasing because Wl1-l decreases with Wll (Figs. 3a and b). Maintaining a long z,, thus preventing any depletion of the 411?/2 level, terminates cw laser action because WZ2 is sbll active (Fig. 3a). The quenching of the 4113/2 lifetime by codoping is now favorable (Fig. 3b). Promising co- dopants are P s +  [6] and Tb3+ [12]. There are combinations of the lifetimes z1 and z3, at which W,, and have the same rate and the laser performance becomes independent of the magnitude of the parameter Wll. When fiuther reducing z1 or increasing z3 the wl1-l process prevails over w,,, competing with f132, populating the lower laser level and reducing the laser output (Fig. 3b, front). The upconversion WZ2 is depleting the upper laser level, which reduces the laser output (Fig. 2b). The relation between z6 and W,, is the same as for z3 and W , but with the opposite effect on lasing: a long z6 mamtains a larger population in 4F7/2, which supports the cross relaxation W2;' and reduces the depletion of the 4~11/2 leve1 via the net sum w,, - w,;'. The cross relaxation Wso is fed by the upconversion W,, and the subsequent multiphonon relaxation &. In the standard configuration the depopulation of the upper laser level via W2, is redistributed via Wso into the 4113.,2 and 419/2 levels, regardless of the value of W,,. An increase of Wso has no effect. Decreasing Wso leads to its saturation, whereas a decrease of the lifetime z5 introduces a relaxation channel, which is in competition with Wso. In both cases the upconverted energy is mostly lost directly to the ground state via W2, (41,,/2 -k 4115/2) and to ground-state fluorescence (e.g. 4S,/2 -+ 4115/2) as well as multiphonon relaxations (4S3,2 -b 4F9/2 + 4h,2). "his leads to a decrease of the redistributed energy and a decrease of the laser output. The Merence in output power for a small and a large WsO is more signifícant, if a larger p m  of the excitation laves the upper laser level via WZ2 to be redistributed I! bY W50. Figure 3. Variation POM (zl, Wll, z3): (a) z1 = 10 ms, @) z1 = 1 ms. Explanations see text. Advanced Solid-Sfate Lasers 167 i m e  benefit of co-doping with cP+ is present ody in crystals with large W22 and small z5 like YSGG and YAG. In th is  case Wso cannot compensate for the depletion of the upper laser level via W22 and redistribute the lost energy. The energy transfer from the EP' 4S,/2 level via Cs' into the E?' 4111,2 and 4~9,2 levels takes over the role of v5,,. The E?':LiYF, laser pumped with 5 W cw into the 4h/2 leve1 h a ~  effective lifetimes ( ~ / T ~ + w ~ ~ N ~ ) - ~  = 1.4 ms in the 4111, level and ( ~ / T ~ + W ~ ~ N ~ ) - ~  = 0.89 ms in the 4113,2. level, and the 3 p laser is not self- terminating in this case. Since the populations of the laser levels also depend on the energy-feeding mechanisms of the laser levels, the ratio of the intrinsic lifetimes of 4111/2 and 411.31? has been misunderstood as an indication for the possibility of cw lasing. Conclusions We have developed a program for the full simulation of the Erbium laser including all relevant processes and a realistic resonator design. The evaluation shows that, in the frame of the available parameters, the fluorides LiYF, and BaYzFs are currently the best choice as host materials for the E?' 3 pm laser. The 970 nm pump wavelength has two advantages in comparison to 795 nm pumping: It avoids the multiphonon relaxation from the ,Igl2 level, thus increasing the quantum efficiency, and the lower population of the 4~ leve1 reduces the inverse level. CW inversion can be obtained in the absence of upconversion processes because of a long lifetime of the upper laser level and a favorable low branching ratio into the lower laser level. The strong upconversion from the 4~13/2 leve1 has a major effect on stimulated emission by efficiently depleting the lower and feeding the upper laser level. In the presence of upconversion the lifetime of the lower laser level should be as long as possible. The quenching of t h i s  level by codoping decreases the upconversion Wll without simultanmusly decreasing the inverse process Wl1-l and thus reduces the output power of the laser. Upconversion from the upper laser level is detrimental to stimulated emission but may be compensated by cross relaxation from the 4S, level. The lifetime of the upper laser level must be longer than 800 p for cw-laser operation. Despite the influence of upconversion t h i s  lifetime is the most crucial parameter for the efficient cw-laser operation ofthe E?' 3 p Iaser. upconversion from the 9P I,,, level into the lower laser Acknowledgement s We thank H. J. Weder for his help with the figures. This work was supported in part by the Swiss Priority Program Wptique" . References [l] K. S .  Bagdasarov, V. I. Zhekov, V. A. Lobachev, T. M. Murina, and A. M. Prokhorov, "Steady-state stimulated emission from Y3Al5Ol2:E2+ laser (X = 2.94 pm, T = 300 K)", Kvant. [2] H. Chou and H. P. Jenssen, "Upconversion processes in Er-activated solid state materials", in Tunable Solid State Lasers, Vol. 2 of the OSA Proceeding Series, M. L. ShandandH. P. Jenssen, eds. (Opt. SOC. Am., Washington,D.C., 1989), pp. 167-174. [3] P. Xie and S .  C. Rand, "Continuous wave, pair-pumped [4] S .  A. Pollack, D. B. Chang, M. Birnbaum, and M. Kokta, YJpconversion-pumped 2.8-2.9 pm lasing of E?+ ion in garnets", J. Appl. Phys. 70(12), 7227 (1991). [SI R. C. Stoneman, J. G. Lynn, and L. Esterowitz, "Direct upper-state pumping of 2.8 pm E2':YLF Laser", IEEE J. QuanhnElectron. 28(4), 1041 (1992). [6] D. S .  Knowles and H. P. Jenssen, "Upconversion versus Prdeactivation for Efficient 3 pm Laser Operation in Er", IEEE J. Quantum Electron. 28(4), 1197-1208 (1 992). [7] R. S. Quimby and W. J. Miniscalco, "Continuous-wave lasing on a self-tenninating transition", Appl. Opt. 3(1), 14 (1989). [SI W. LUthy and H.P. Weber, "The 3 pm erbium laser", Mared Phys. 283 (1991). [9] V. Lupei, S .  Georgescu, and V. Flora, "On the dynamics of population inversion for 3 pm E?' lasers", IEEE J. Quantum Electron. 29(2), 426 (1 993). [lO] C. Li, Y. Guyot, C. Linarès, R. Moncorgé, and M. F. Joubert, "Radiative transition probabilities of trivalent rareearth ions in LiYF,", in Advanced Solid- State Lasers and Comuact Blue-Green Lasers Technical Dieest, 1993 (Optical Society of America, Washington, D.C., 1993), V01.2, pp.423425. [11] M. Pollnau, E. Heumann, and G. Huber, "Time- resolved spectra of excited-state absorption in E2' doped YAlO,", Appl. Phys. A 54(5),  404 (1992). [12] M. Pollnau, E. Heumann, and G. Huber, "Stimulated emission and excited-state absorption at rmm temperature on the 550 nm-laser transition in E?' doped YA103", to appear in J. Lumin. (1994). Elektr.lO, 452 (1983). la~er", Opt. Lett. u( 1 5), 848-850 (1 990). 

Influence of normal and inverse upconversion processes on the continuous wave operation of the Er<sup>3+</sup> 3 µm crystal laser

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Influence of normal and inverse upconversion processes on the continuous wave operation of the Er<sup>3+</sup> 3 µm crystal laser

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