Energy transfer in Tm,Ho:KYW crystal and diode-pumped microchip laser operation

Abstraet: An investigation of Tm-Ho energy transfer in Tm(5at.%),Ho(0.4at.%):KYW single crystal by two independent techiqnes was performed. Based on flnorescence dynamics measnrements, energy transfer parameters Рц and P 28 for direct (Tm—>Ho) and back (Ho—>Tm) transfers, respectively, as well as eqnilibrinm constant 0 were evalnated. The obtained resnlts were snpported by calcnlation of microscopic interaction parameters according to the Forster-Dexter theory for a dipole-dipole interaction. Diode-pnmped continnons-wave operation of Tm,Ho:KYW microchip laser was demonstrated, for the first time to onr knowledge. Maximnm ontpnt power of 77 mW at 2070 mn was achieved at the fundamental TEM qo mode.


Introduction
Tm-sensitized Ho materials are considered to be among the most attractive solntions for lasers operating at wavelength slightly above 2 pm particnlarly when compact cavity design is reqnired [1]. Tm^^ ions possess strong absorption near 800 nm where commercially available AlGaAs laser diodes operate. Two-for-one qnantnm efficiency cansed by cross-relaxation process in thnlinm, and snbseqnent non-radiative energy transfer to Ho^^ ions enable efficient popnlation of holminm manifold [2]. When in addition microchip cavity design is implemented the final laser sonrce looks particnlarly compact and attractive for applications. Laser generation in microchip confignration has been achieved earlier with several Tm,Hocodoped crystals snch as: YAG [3], YLF [4][5][6], YVO4 [7], GdV04 [8], YAP [9] and KLnW [10]. It was shown that Tm,Ho materials can be snccessfully nsed for obtaining laser radiation on holminm transition in snch compact laser design. Recently efficient continnons-wave [11] and femtosecond pnlse [12] laser operation has been reported nsing Tm,Ho:KY(W04)2 (Tm,Ho:KYW) crystal nnder Ti-sapphire laser pnmping. These resnlts showed KYW crystal as an attractive host material for 2 pm lasers. There a description of the crystal growth, stractnre, spectroscopic properties and first resnlts of evalnation of energy transfer parameters were presented. However energy transfer processes were stndied incompletely and laser operation nnder diode-pnmping was not obtained. Thns in this paper an investigation of Tm-Ho energy transfer parameters in KYW crystal by two independent techniqnes was nndertaken and, for the first time to onr knowledge, continnons-wave laser operation nsing this crystal in a microchip cavity configmation nnder diode laser pnmping was demonstrated.

Study of energy transfer by fluoreseenee dynamies measurement
The study of energy transfer processes in Tm(5%),Ho(0.4%):KYW single crystal was implemented with an approach earlier described by B.M. Walsh in application to Tm,Hocodoped YAG and YLF crystals [13,14]. According to this approach energy transfer parameters could be easily evaluated by fitting experimental data on fluorescence dynamics from ^F4 energy level of Tm^^ ions and from level of Ho^^ ions to the solutions of rate equations set describing rates of change of energy levels population. Inspite the fact that this approach doesn't take into consideration up-conversion processes in the ions and can be used only at low excitation densities it was important to find the parameters earlier calculated for other Tm,Ho-codoped crystals to compare them and to understand place of KYW crystal among other host materials.
In our experiment OPO based on [3-BaB204 crystal and pumped by the third harmonic of actively Q-switched Nd:YAG laser was used as an excitation source of Tm and Ho fluorescence. The pulses had duration of 20 ns and repetition rate of 10 Hz. The fluorescence was collected by wide-aperture objective on entrance slit of monochromator MDR-12. The signal was detected by InGaAs photodetecor and processed by a digital oscilloscope with 500 MHz bandwidth. To eliminate inflnence of reabsorption on flnorescence dynamics a small piece of the crystal was grinded to crystalline powder and dilnted by liqnid silicone fonning homogeneons snspension which then was nsed as the sample. Pnlsed radiation at 1670 mn was nsed to selectively excite Tm^^ ions to ^p4 energy level, while the wavelength was changed to 1960 mn for excitation of Ho^^ ions to energy manifold. The flnorescence dynamics were measnred separately for Tm^^ ions at 1860 mn and for Ho^^ ions at 2056 mn. All the measnrements were carried ont at room temperatnre. The energy level transitions corresponding to absorption and emission wavelengths nsed in the experiment are shown in Fig. 1.  After Tm^^ ions excitation at 1670 mn fast decay of thnlinm flnorescence at 1860 mn is observed at early times ( Fig. 2(a)) with simnltaneons growth of flnorescence of holminm at 2056 nm ( Fig. 2(b)). This behaviour results froiu direct energy transfer from to Ho^^ ions, where fast decrease of ^p4 energy level population of accompaiued by an increase of ^І7 level population of Ho^^. At later times fluorescence from both ions starts to decay exponentially with the same time constant, which was estimated to be 2.4 ms. This can be explained by the fact that growth of holmium population intensifies back energy transfer from Ho^^ to Tm^^ ions and quickly brings the ions to the state of thermodynamic equilibrium when populations of ^p4 level of thulium and of holmium are detennined by Boltzmarm statistics as for a coupled system. It should be mentiond that this behavior is typical for Tm-Ho co-doped media [13]. Similar behaviour is observed when Ho^^ ions are excited at 1960 mn. Fast decay of holmium fluorescence at 2056 mn at early times ( Fig. 2(c)) goes along with simultaneous growth of thulium fluorescence at 1860 mn ( Fig. 2(d)), that is a consequence of back energy transfer from Ho^^ to Tm^^ ions. At later times fluorescence from both ions in similar marmer exponentially decays with the same time constant, which in this case was estimated to be 2.7 ms. This behaviour denotes setting of thermodynamic equilibrium between ions.
The experimental curves were then fitted by the solutions of rate equations set governing the rate of change of populations in Tm^^ ^p4 and Ho marufolds [14] in case of thulium excitation: n,{t) a n^(0) {^a+j3 and in case of holmium excitation: •e x p l-1 ■exp(-(«+p)t). (2) (4)

npO) \^a+P) ) \Gc+Py
Here the subscripts 1, 2, 7, and 8 denote the Tm ^He, Tm ^p4. Ho ^k, and Ho ^k marufolds, respectively (see Fig. 1). This indexing of the levels earlier was introduced by Bames [15] and is used through this paper to get an agreement with the results obtained with other hosts, и, is a population of / level, where / = 2, 7; x is the time constant of exponential decay, a, fi are the parameters determining direct and back energy transfer, respectively, which intrinsically are energy transfer probabilities with units of s ' . These parameters are concentration dependent. However if they are devided to concentration of corresponding ions the obtained values will be energy transfer parameters [13]: P28 = o/Nho and P71 = p/Nim, which are concentration independent and characterize host material itself. Nho and Nim are the holmium and the thulium concentrations. P28 and P71 are the energy transfer parameters for direct and back energy transfer, respectively, with uiuts of cm^/s. The best fitting for all experimental data both in case of thulium and holmium excitation was obtained with the same values of energy transfer probabilities: a = 7000 s ' and p = 6100 s '. The energy transfer parameters P28 and P71 were calculated to be 2.74 x ю '® cm^/s and 0.19 X 10'® cm^/s, respectively. We aslo found the ratio P71/P28, called equilibrium constant 0 [13]. In our case this value was estimated to be 0.069. The obtained results were tabulated in Table 1 in comparison with the data reported for other Tm,Ho-codoped laser crystals. Assuming that all the exitation resides in the ^p4 energy level of thulium and level of holimium we have also calculated a fraction of Ho^^ ion residing in the level at thermal equilibrium,/но = o/(a + (3) [14]. The obtained value was to be 53.4%, which shows that more than a half of excitation energy in Tm(5at.%),Ho(0.4at.%):KYW crystal at low excitation densities transfers to Ho^^ ions. Additionaly we found the value of /но after increasing of holmium concentration up to 1 at. % with unchanged thulium concentration. The result was to be 74.2%. Further increase of holmium content up to 2 at.% leads to /ко = 85.2%. So Tm,Ho:KYW crystals with higher doping level of holmium could be of interest for future investigation.
Fluorescence dynamics of Tm,Ho:KYW single crystal were also measured under excitation of thulium ions at 802 mn to higher laying ^H4 energy manifold The obtained results are shown in Fig. 3. Fast growth of thulium fluorescence notable at early times is attributed to cross-relaxation process in Tm^^ ions, leading to population of ^p4 energy manifold. The time constant of this process was evaluated to be 6.5 ps. The further behavior of fluorescence is similar to the case of thulium ^p4 excitation with setting of thermodynamic equilibrium at later times ( Fig. 3(b)).

Energy transfer mieroparameters aeeording to the Forster-Dexter theory
To support the results obtained from fluorescence dynamics measurement we calculated microscopic interaction parameters for our Tm,Ho:KYW single crystal according to Forster-Dexter theory of resonant energy transfer [18]. According to the theory mieroparameters of energy transfer from donor (D) to acceptor (A) ions can be calculated with the expression: -|гту(2)<(2)гіА \6k n ' Here c is the velocity of light in vacuum, n -refractive index of the crystal, <ryemission cross-section of donor ion, of' -absorption cross-section of acceptor ion, is a factor describing the relative orientation in space of the transition dipoles of the donor and acceptor. When the relative orientation of donors and acceptors in a medinm is random, bnt fixed and do not change dnring excited state lifetime of the ions, as it is in case of crystalline matrix, the orientation factor can be taken as 0.476 [19,201 • So the valne of microparameter according to Forster-Dexter theory is basically detennined by the overlap of absorption and emission spectra of donor and acceptor ions. To calcnlate direct energy transfer microparameter стт^ш, one mnst have emission spectram of Tm^^ ions and absorption spectram of Ho^^ ions in KYW crystal. Whereas to calcnlate back energy transfer microparameter сно^тт, one mnst have emission spectram of Ho^^ ions and absorption spectram of Tm^^ ions in the crystal. The absorption spectra of the ions in KYW host where measnred for singly doped crystals nsing spectrophotometer Cary 5000 at room temperatnre for polarization of light along principal axes N^, TV p and TV g of the crystals. The emission cross-section spectra where calcnlated for each polarization by reciprocity method.
Polarization averaged absorption and emission cross-section spectra of Tm^^ and Ho^^ ions in KYW crystal are shown in Fig. 4. With Eq. (5) we calcnlated the valnes of interation microparameters for direct and back energy transfers: стт^ш = 35.1 x cm®-s"' and сно^тт = 2.16 x cm®-s"\ respectively. The energy transfer probabilities for a dipole-dipole interaction can be fonnd by dividing microparameter to the six power of the distance between interacting ions. So the ratio сно^тт/стт^но will Ьо oqnal to the ratio of energy transfer probabilities, which is analogons parameter to eqnilibrinm constant &, that was calcnlated for this crystal from flnorescence dynamics measnrements. After calcnlations сно^тт/стт^ш was fonnd to be 0.061. This valne is in a good agreement with the valne of eqnilibrinm constant (0 = 0.069), that coirfirms the resnls of flnorescence dynamics analysis. The obtained resnlts were tabnlated in Table 2 in comparison with the data reported for other Tm,Ho-codoped hosts. One can see from the table that the energy transfer coefficient Стт^ш for Tm,Ho:KYW crystal is higher than that for the most of the other laser hosts. Also KYW shows a low valne of the ratio Сно^тт/стт^ш that is lower than that observed in BNN (Ba2NaNb50i5), YAG (Y3AI5O12) and YLF (LiYp4), and slightly higher than for CaSGG (Ca3Sc2Gc30i2) and Gd3Ga50i2(Ca,Zr). However in these latter hosts, the valne of the direct energy transfer process is mnch smaller than that of KYW.

Microchip laser experiment
To demonstrate a potential of Tm,Ho:KYW crystal for nsing in microchip laser devices we have carried ont laser experiment with a laser diode (LD) as a pnmp somce. Ng-cnt Tm(5 at.%),Ho(0.4 at.%):KYW crystal with thickness of 2.98 mm was nsed as an active element. It was earlier shown that snch orientation of the crystal is favorable for arising of positive thermal lens in the crystal that enables stability of plane-plane microchip cavity confignration [24]. The experimental setnp of Tm,Ho:KYW laser is shown in Fig. 5.  Fiber-conpled (0 = 105 pm, N.A. = 0.15) AlGaAs laser diode with maximnm available ontpnt power of 3 W at 802 mn and = 20 was nsed as a pnmping sonrce. The diode wavelength was shifted to the absorption peak of the ^H4 level (Tm^^) by temperatnre tniung of LD. The laser diode radiation was collimated and focnsed into the active element to a spot of 120 pm diameter with two spherical lenses (fi = 70mm, f2 = 80mm). The laser resonator was formed by two plane mirrors which were positioned in close proximity to the ends of the active element. The HR plane inpnt mirror M l was AR coated for pnmp radiation (802 mn). Two ontpnt conplers with transmission of 0.8 and 1.8% were nsed. The crystal faces were AR-coated for the pnmp (802 mn) and laser (2.07 pm) radiations as well. The lateral sides of the laser crystal were in thermal contact with the alnminnm heat sink whose temperatnre was precisely maintained with a thermoelectric cooler which temperatnre was to be 16°C.
CW laser operation was relized at the fundamental TEMqo mode and lasing radiation was polarized along Np principal axis of the crystal. The laser performance characteristics are demonstrated in Fig. 6. The highest output power of 77 mW was obtained with 0.8% output eoupler. The laser emission speetrum was eentered at 2070 nm. This matehes with a loeal maximum in the gain speetrum of Ho:KYW, see Fig. 6, dashed line represents losses (Tqc = 0.8%). The eorresponding slope effieieney of the laser with respeet to ineident pump power was estimated to be 8.5%. The laser threshold was about 0.8 W of ineident pump power. The slope effieieney for output eoupler Tqc = 1.8% at low pump power was higher than 9%, however maximum output power was limited by 46 mW. In the last ease the laser wavelength shifted to 2058 nm that is attributed to higher level of eavity losses. Nonlinear dependenee of the output power with respeet to ineident pump power and visible fluoreseenee was observed during lasing. Roll-over in input-output eharaeteristie with higher output eoupler transmission value (1.8%) was evident at 1.4 W of ineident pump power. Sueh behavior ean be eaused by the higher up-eonversion losses whieh inerease heat release in the erystal. It's evident that higher transmission of the output eoupler requires greater population inversion of the Ho^^ upper laser level ^ly and this leads to inerease in up-eonversion losses in the Tm, Ho:KYW. Similar behavior of Tm,Ho-laser was observed in [11].

Conclusion
Energy transfer in Tm(5at.%),Ho(0.4at.%):KYW single erystal has been investigated by two independen teehniques. With an analysis of fluoreseenee dynamies of the erystal eoneentration independent energy transfer parameters for direet P71 and baek transfer P28 proeesses were determined, whieh were 2.74 x 10"'® emVs and 0.19 x 10"'® emVs, respeetively. Equilibrium eonstant 0 = P28/P71 was ealeulated to be 0.069. These results demonstrate domination of direet energy transfer in the erystal and in eomparison with other host materials provides favourable eonditions for population of ®І7 energy level of holmium. A fraetion of Ho^^ ions residing at ®І7 energy manifold in the erystal at equilibrium eonstant was ealeulated to be 53,4%. An inerease of this fraetion was predieted with further growth of holmium eontent. The results obtained from fluoreseenee dynamies measurement were eonfirmed by independent ealeulation of interaetion mieroparameters in aeeordanee with Forster-Dexter theory. The mieroparameters were ealeulated to be Схт^но = 35.1 x 10"""' em®-s"' and Сно^тт = 2.16 x 10"""' em®-s"'. The ration Сно^тт/ Wm^Ho was to be 0.061, that is in a good agreement with the equilibrium eonstant obtained from fluoreseenee dynamies. CW laser operation with Tm,Ho:KYW in mieroehip eonfiguration with LD pumping was realized for the first time to our knowledge. Maximum output power of 77 mW at 2070 nm was obtained with slope effieieney of 8.5% with respeet to ineident pump power. The laser was operating at the fundamental TEMqo mode.