comparison of tm:ylf and tm:yap in thermal analysis and laser performance

Comparison of Tm:YLF and Tm:YAP in thermalanalysis and laser performance

Bao-Quan Yao,* Pei-Bei Meng, Gang Li, You-Lun Ju, and Yue-Zhu Wang

National Key Laboratory of Tunable Laser Technology, Harbin Institute of Technology, Harbin 150080, China*Corresponding author: [email protected]

Received April 11, 2011; revised May 25, 2011; accepted May 30, 2011;posted June 8, 2011 (Doc. ID 145608); published July 8, 2011

The a-cut Tm:YLF and c-cut Tm:YAP laser performance for 1:94 μm in dual-end pump configuration are comparedin this paper. Higher slope efficiency and better beam quality are obtained for Tm:YLF lasers than Tm:YAP lasersin our present experiment. Theoretically, the temperature distribution and thermal focal length of Tm:YLF andTm:YAP with a dual-end pump structure are analyzed. The thermal focal length, which is deduced from the back-ward calculation with the measured M2 factor, is much longer for Tm:YLF than Tm:YAP, indicating a weakerthermal lens effect for the Tm:YLF laser, which is in agreement with the theoretical value deduced from the tem-perature distribution in the rod. In addition, a rate equation model is used to simulate the laser performance and isfound to have reasonable agreement with the experimental acquired data. © 2011 Optical Society of America

OCIS codes: 140.3480, 140.5680, 140.6810.

1. INTRODUCTIONSolid-state lasers emitting around 2 μm play an important rolein the fields of remote sensing, laser radar, and medical diag-nosis and surgery. The commonly used rare earth ions to ob-tain 2 μm laser radiations are Tm and Ho ions. Especially, theHo lasers can be resonantly pumped by 1:9 μm Tm lasers,which have the advantages of high slope efficiency and mini-mal heating owing to the inherent low quantum defect be-tween the pump and laser photons [1–3]. As a result, with thelaser diode pump technology growing up, high power 1:9 μmTm lasers have been widely investigated in the past few years[4–6]. Among these Tm lasers, the 1:94 μm radiation hasgood overlap with the absorption spectrum of Ho:YLF [7] andHo:YAG [8] so as to pump these lasers efficiently. Addition-ally, because of the strong absorption in water, the 1:94 μmlasers have wide applications in the medical region. So atpresent, a lot of laser materials have been used to generatethe 1:94 μm laser radiation, such as Tm:YLF, Tm:YAP,Tm:fiber, and so on.

Tm:YLF has attracted strong interest in recent years be-cause of its possibility to obtain high-efficiency output whenoperating in the mid-IR region, especially around 1:908 μm [9].However, wavelength selecting elements are required to ob-tain 1:94 μm (seen from the emission spectrum of Tm:YLF[1]). Using a Lyot filter, Dergachev and Moulton developeda cw Tm:YLF laser based on two atoms (at.) at % Tm:YLFslabs, each side pumped by two diode laser bars. As muchas 28W laser output at 1:94 μm was achieved with a pumpdiode laser power of ∼170W. The output beam profile wasdiffraction limited in the vertical plane and multimode(>10× diffraction limited) in the horizontal plane [10]. In2004, up to 30W output of a side-pumped Tm:YLF laser oper-ating at 1:94 μm has been obtained with a volume Bragg holo-graphic grating (VBG) in photothermorefractive glass as anoutput coupler [11]. However, experimental optimizationfor the transmission of the output coupler is too costly withVBG as an output coupler, since different transmissions of

VBG are required. Another attractive Tm-doped laser hostto obtain 1:94 μm radiation is YAlO3 (YAP), which has goodthermal property (thermal conductivity of 0:11W=ðcm · KÞand mechanical property (similar to that of YAG). Up tothe present, as much as 50W of output power from free run-ning b-cut composite Tm:YAP lasers at 1:94 μm was achievedby use of dual-end pumped structure [5]. For c-cut Tm:YAPcrystal, there are two emitting peaks located around 1.99and 1:94 μm [12]. The output wavelength for free running c-cut Tm:YAP lasers is usually at 1:99 μm [13] and hard to obtain1:94 μm laser oscillation due to the characteristics of large re-absorption losses for room temperature quasi-three-levellasers [14,15]. As a result, there are few reports on the c-cut Tm:YAP laser emitting at 1:94 μm, and primary analysisof the c-cut Tm:YAP laser emitting at 1:94 μm seems attractivefor researchers.

In this paper, the laser performance at 1:94 μm and the ther-mal analysis of a-cut Tm:YLF and c-cut Tm:YAP are first indetail compared in experiment and theory. With VBG as a highreflector and an additional inserted Fabry-Perot (F-P) etalon,stable output at 1:94 μmwith a narrow linewidth (FWHM) wasobtained for both the Tm:YLF and Tm:YAP laser. For the Tm:YLF laser, up to 17:3W output was obtained with an incidentpump power of 59:5W, and for the Tm:YAP laser, as much as13:8W output was obtained under an incident pump power of61:5W. The temperature distribution within the crystal re-sulted because the ununiform pump was theoretically calcu-lated and compared. The measured beam quality M2 factorwas used to deduce the thermal focal length, which had rea-sonable agreement with the theoretical value. In addition, anumerical model [13], which was accounted for by spatial dis-tributions of pump and resonator fields, up-conversion,ground state depletion, and local temperature distribution inthe gain medium with dual-end pumped scheme, was adoptedto simulate the laser performance. The simulating results werefound to have reasonable agreement with the experimentaldata, and optimization of the output coupler transmission

1866 J. Opt. Soc. Am. B / Vol. 28, No. 8 / August 2011 Yao et al.

0740-3224/11/081866-08$15.00/0 © 2011 Optical Society of America

was performed which could give us valuable guidelines in ourfurther investigation of these Tm lasers.

2. EXPERIMENTAL RESULTSThe experimental setup of the 1:94 μm Tm:YLF/YAP laser isshown in Fig. 1. A total cavity length of 80mm was used withtwo 45° dichroic flat mirrors, a radius of curvature of 200mmoutput mirror with part of transmission at the laser wave-length, and a VBG as a high reflector. The diffraction effi-ciency of the VBG was greater than 99% at 1940:2 nm (at 22 °Cin air) with a FWHM of less than 1 nm. Table 1 shows the pa-rameters of the laser materials used in the experiment. Boththe crystals were antireflection (AR) coated on both flat-polished parallel facets at 790–800 nm and 1:9 μm. The crystalwas wrapped in indium foil and clamped in a copper heat sink,which was kept at 287K by a thermoelectric controller. Thepump source was fiber coupled and centered at a 790 nm laserdiode (nLIGHT Corp.) with a core diameter of 400 μm and aNA of 0.22, divided into pump 1 and pump 2, as shown in Fig. 1.The power ratio of pumps 1 and 2 was about 6∶4 because ofthe imperfect mirror coatings (experimentally measured). L1,L2, L3, and L4 were the collimating and focusing mirrors toreshape the pump beam radius. The pump waist (ωp0) was320 and 400 μm for Tm:YLF and Tm:YAP, respectively. Unfor-tunately, the wavelength near 1:94 μm has strong water vaporabsorption peak, which may easily damage the AR coatings ofthe laser crystal. In order to obtain high output power, an eta-lon (0:5mm in thickness YAG) with no coatings was insertedin the cavity to further stabilize the laser wavelength and avoidthe influences of water molecule absorption. In the experi-ment, the wavelength of the Tm:YLF laser was stable around1:94 μm (and also for the Tm:YAP laser), as shown in Fig. 2,measured by an EXFOWA-650 spectrum analyzer combinedwith an EXFO WA-1500 wavemeter (4GHz spectral resolu-tion). The linewidth (FWHM) of both the Tm:YLF and Tm:YAPlaser was about 0:15nm. In addition, the central wavelengthshift of only about 0:5 nm was observed for the two Tm lasers,changing from 1940:17nm around the threshold pump powerto 1940:64 nm at the highest pump power level for Tm:YLFlaser and from 1940.17 to 1940:68nm for the Tm:YAP laser inthe experiment.

The laser output power as a function of the pump power fordifferent transmissions of the output mirror (T) is illustratedin Fig. 3. The threshold of the Tm:YLF laser was lower thanthat of the Tm:YAP laser even with the largest output couplertransmission of 20%, as shown in Fig. 3. Although the thresh-old was slightly lower and the slope efficiency was a littlehigher with the output coupler transmission of 11.9% whenthe pump power was less than 35W for the Tm:YLF laser,

it was saturated more quickly than the other two transmis-sions, as shown in Fig. 3(a). With the transmission of 15.1%,as much as 17:3W output was obtained under a total incidentpump power of 59:5W for the Tm:YLF laser. For the Tm:YAPlaser, with the same transmission and a total incident pumppower of 61:5W, 13:8Wof output was obtained and saturationwas not observed with all the three different transmissions asshown in Fig. 3(b).

Figure 4 shows the evolution of the focused Tm:YLF laserand Tm:YAP laser beam at different laser powers after itpassed through a positive 100mm focal length lens which waspositioned approximately 180mm from the output coupler forTm:YLF and 102mm for Tm:YAP. In both cases, the beam pro-file was circularly symmetric. The beam quality factorM2 wasdetermined by fitting the standard Gaussian beam propaga-tion expression to the measured data. The M2 value of theTm:YLF laser kept almost the same (∼1:1) from the laser out-put power of 4 to 12W, as shown in Fig. 4(a), and the beamwaist radius after the lens was almost unchanged. This is ty-pical for the σ-polarization of Tm:YLF which has a very weakthermal lens effect, and our experimental measurement alsoshowed that the 1:94 μm transition for the Tm:YLF laser was σ-polarized. However, the M2 value of the Tm:YAP laser in-creased from ∼1:1 near the threshold (2W) to ∼1:9 at the laseroutput power of 12W, as revealed in Fig. 4(b), and the beamwaist radius after the lens was increased obviously.

3. THEORETICAL ANALYSIS ANDDISCUSSIONIn order to discuss the results, the thermal analysis of thea-cut Tm:YLF laser and the c-cut Tm:YAP laser is necessarybecause it not only influences the populations of upperand lower levels, thus the laser performance, but also relatesto the thermal lens, which will make the resonator unstableat high pump power levels and play one of the key roles in

Fig. 1. (Color online) Experimental setup of the dual-end pumped1:94 μm Tm:YLF/Tm:YAP laser.

Table 1. Parameters of Samples

Used in the Experiment

LaserMaterial Dimensions

DopedConcentration Orientation

Tm:YLF 3mm × 3mm × 12mm 3 at:% a-cutTm:YAP 3mm × 3mm × 12mm 3:5 at:% c-cut

Fig. 2. (Color online) Wavelength shift of a Tm:YLF/Tm:YAPlaser versus the pump power. Inset: typical output spectrum of theTm:YLF laser.

Yao et al. Vol. 28, No. 8 / August 2011 / J. Opt. Soc. Am. B 1867

limiting and degrading lasing performance in end-pumpedlaser systems.

The local temperature distribution can be obtained by solv-ing the heat transfer Poisson equation. With a cylindricallysymmetric laser crystal, the heat transfer equation is given by

1r

∂

∂r

�r∂ΔTðr; zÞ

∂r

�þ ∂2ΔTðr; zÞ

∂z2¼ −

Qðr; zÞk

; ð1Þ

if the anisotropy of the crystal is neglected. Here k is the ther-mal conductivity of the active medium, and ΔT ≈ T − Tb,where Tb is the boundary temperature. The heat sourceQðr; zÞ in the laser crystal relates to the pump beam waist(ωp0), crystal length (Lc), unsaturated absorption coefficient(α0), and the heat pump power (Ph) as described in [13]. Espe-cially, Ph ¼ Ppηh½1 − expð−α0LcÞ� is the fraction of the ab-sorbed pump power dissipated into the crystal as heat,mainly as a result of the quantum defect ηh. Because of themoderate doping concentration of Tm:YLF and Tm:YAP usedhere, the heat caused by the energy-transfer upconversion can

be ignored based on the [9,16]. For a paraxial coherent beampropagating in the z direction, the total radial optical path dif-ference OPDðrÞ for a rod is given by [17]

OPDðrÞ ¼ 2Z

Lc

0

�∂n

∂Tþ ðn − 1Þð1þ νÞαT

�ΔTðr; zÞdz: ð2Þ

The first term is caused by the thermal dispersion ∂n=∂T , andn is the refractive index of the crystal. The second term resultsfrom the laser rod end-surface deformation which relates toPoisson’s ratio (ν) and thermal expansion coefficient (αT ).Here, the OPD caused by strain-induced birefringence isneglected as the faces bulging and the natural birefringencedominate any thermally induced birefringence in YLF andYAP, respectively. Neglecting high-order aberrations, OPDðrÞis given by [18]

OPDðrÞ ¼ OPD0 −r2

f th; ð3Þ

where OPD0 is the optical path difference at the center ofpump and f th depicts the thermal focal length. For a laser crys-tal, f th is determined by fitting the calculated space-resolvedOPD of Eq. (2) with Eq. (3) over the extent of the beam radiusinside the rod (which depends on the resonator geometryunder consideration) with a least square fit.

Fig. 3. (Color online) Comparison of the measured and numericallycalculated output powers as a function of incident pump power for(a) the Tm:YLF laser and (b) the Tm:YAP laser. The solid curveswere theoretically modeled with nonuniform temperature distributionin the crystal, and the dot curves (T ¼ 11:9% for Tm:YLF andT ¼ 15:1% for Tm:YAP) were modeled with constant boundary tem-perature within the crystal.

Fig. 4. (Color online) Brightness determination at different outputpower levels for (a) the Tm:YLF laser and (b) the Tm:YAP laser.


The temperature distribution in the Tm:YLF and Tm:YAProd is first calculated. We emphasize that for simplifyingour calculation, the anisotropy for both YLF and YAP are ne-glected. This is reasonable for YLF since the thermal conduc-tivity along the a and c axis for YLF has nearly the same value[19]. For YAP, there is little report on its thermal conductivityalong the different crystal axis, and a lot of authors have trea-ted YAP as an isotropic crystal for its lasing and thermal mod-eling, such as Li et al. [13] , Boucher et al. [20], Shen et al. [21],and so on. As a result, we also treat YAP as an isotropic crystalhere. The parameters used in the numerical calculations aresummarized in Table 2. The value of Poisson’s ratio 0.3 is cor-rect for YAG and does not vary much for other materials [22].The pump quantum efficiency of Tm:YAP is assumed to be thesame as that of 3:5 at:%-doped Tm:YLF [4]. The pump powerused in the calculation is 60W, which corresponds to pump 1of 36W and pump 2 of 24W, respectively. The temperaturedistributions in the rods are shown in Fig. 5. While the peaktemperature in the Tm:YLF rod is 338K, the Tm:YAP rodexhibits the peak temperature of 324:5K. Even though the ab-sorbed pump power is less for Tm:YLF, the peak temperaturerise is higher than that for Tm:YAP (nearly 1:36× as that in theTm:YAP rod), which is mainly due to the smaller thermalconductivity (0:06W=ðcm · KÞ) compared with that of YAP(0:11W=ðcm · KÞ) and a smaller pump beam waist radius.

If the thermal lens in a thermally loaded material inside alaser resonator under operation can be assumed to be an idealthin lens, a useful method to determine the thermal focallength is based on the use of a supplementary focus lens withthe known focal power and the position of the test beam waist[23]. The beam propagates as illustrated in Fig. 6. On one

hand, the TEM00 Gaussian beam waist radius ω0 at positiond2 (shown in Fig. 6) could be denoted as

ω0 ¼ωffiffiffiffiffiffiffiM2

p ; ð4Þ

where ω is the measured beam waist in practice, namely themultimode laser beam radius, and M2 is the beam quality fac-tor. Thus the TEM00 Gaussian beam parameters q2 at positiond2 can be defined and with the Gaussian beam propagationtheory, the TEM00 beam radius ωM at the output mirror can

Fig. 5. (Color online) Temperature distribution in one-halfof an axial cross section of an edge-cooled (a) Tm:YLF rod and(b) Tm:YAP rod.

Fig. 6. (Color online) Transformation of the output beam for a stableresonator containing a thermal lens f th.

Table 2. Parameters Used in the Thermal Numerical

Calculation and Laser Modeling

ParameterTm:YLF Value

[Ref.]Tm:YAP Value

[Ref.]

Crystal radius (Rc) [mm] 1.5 1.5Thermal conductivity (k)

[W=ðcm · KÞ]0.06 [32] 0.11 [16]

Heat fraction (ηh) 0.22 0.22Poisson’s ratio (ν) 0.3 [22] 0.3 [22]Thermal expansion

coefficient (αT ) [K−1]13 × 10−6 [19] 11:9 × 10−6 [24]

Thermal dispersion(∂n=∂T) [K−1]

−2 × 10−6 [32] 10:08 × 10−6 [33]

Refractive index (n) 1.44 [27] 1.92 [33]Location of pump beam

waist (z0) [mm]4 4

Pump beam quality (M2p) 175 175

Pump quantum efficiency (ηp) 1.84 [9] 1.88 [4]Pump wavelength (λp) [nm] 790 790Laser wavelength (λl) [μm] 1.94 1.94Unsaturated pump absorption

coefficient (α0) [cm−1]1.3 (measured) 1.8 (measured)

Effective stimulated emissioncross section (σemðλlÞ)

[cm2]

1 × 10−21 [1] 3:8 × 10−21 [12]

Upper level lifetime (τ2) [ms] 14 [27] 4.4 [34]Total up-conversionrate (kΣ) [cm3=s]

0 0

Resonator round-trip loss (Δ) 1.5% (estimated) 5.5% (estimated)


be calculated. On the other hand, with a given thermal lensinside the resonator, the fundamental mode beam radius atthe output mirror can be written as

ω2M ¼ λL0

π

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffig02

g01ð1 − g01 · g02Þ

s; ð5Þ

with the modified resonator lengths L0 and g-parametersgiven by

L0 ¼ l1 þ l2 −l1 · l2f th

; g01 ¼ 1 −L0

R1−

l2

f th;

g02 ¼ 1 −L0

R2−

l1

f th; ð6Þ

where R1 is the radius of curvature of the high reflector andset as ∞ here, R2 is the radius of the curvature of the outputcoupler and equal to 200mm, l1 and l2 are the distance fromthe thermal lens to the high reflector and the output coupler,which is 22 and 58mm, respectively, as shown in Fig. 1. Withthis calculated, ωM compared with the value deduced from theM2 backward calculation method as mentioned above, thethermal focal length can be deduced as shown in Fig. 7.We can get the parameters d2, ω, and M2 from Fig. 4. Thesolid curve is the analytical result from Eqs. (2) and (3).

We emphasize that for the Tm:YLF laser, it was much moredifficult to obtain the thermal focal length from the M2 back-ward calculation than the Tm:YAP laser since the good beamquality of the Tm:YLF laser and measurement errors. To ob-tain the thermal focal lengths for Tm:YLF, the measurementson each power point were done repetitively for at least threetimes and averaged in our experiment. As can be seen inFig. 7(a), the thermal focal length of Tm:YLF is in the rangeof 200–400mm when the incident pump power is changedfrom 21 to 43:4W. The thermal focal length of Tm:YAP is cal-culated in the range of 60–100mm, corresponding to the rangeof the incident pump power from 25.2 to 56:4W, as shown inFig. 7(b). Obviously, the thermal lens effect in the Tm:YAP la-ser is more severe than that in the Tm:YLF laser. Also shownin Fig. 7 is that the thermal focal length deduced from the tem-perature distribution and M2 backward calculation are in thesame quantity level and have reasonable agreement witheach other, indicating that the M2 backward calculationcan give other researchers a simple method to estimate thethermal focal length. As the anisotropy of the YAP crystal, itshould be pointed out that a thermal expansion coefficient of6:5 × 10−6 K−1, rather than the value given in [24], is used togive the reasonable theoretical repeat of the experimentalthermal focal length of Tm:YAP.

For the measured range of the thermal focal length of theTm:YLF and Tm:YAP rods, using the well-known ABCDmatrix method, the radius of the TEM00 mode on the lasercrystal with different cavity length Lc can be calculated asshown in Fig. 8 when l1 is fixed to be 22mm. It can be seenthat for the present cavity length used in our experiment, theTEM00 mode radius on the Tm:YLF laser crystal was around230 μm and did not vary much when the thermal focal lengthwas larger than 200mm. For the Tm:YAP laser, the cavitywould become unstable when the thermal focal length wasless than 60mm, and further power scaling of the Tm:YAP la-ser was limited by the severe thermal lens effect in our presentresonator design although no saturation of the laser outputwas observed at the highest pump power level as shown inFig. 3(b). Taking the severe thermal lens effect of the Tm:YAP crystal into account, we adopted a larger pump beam ra-dius for the Tm:YAP laser compared with the Tm:YLF laser,and further power scaling of the Tm:YAP laser requires aspecial cavity design considering the compensation of the

Fig. 7. (Color online) Focal length f th of the thermal lens versus in-cident pump power: (a) Tm:YLF and (b) Tm:YAP.

Fig. 8. (Color online) Dependence of the beam size on the thermalfocal length at different total cavity length.


thermal focal length [5], which is out of the scope of this pa-per. Also the much more severe thermal lens effect of Tm:YAPcan explain the worse beam quality of the Tm:YAP laser com-pared with the Tm:YLF laser [25,26].

In this study, we adopt the rate equation model first pro-posed by Schellhom and Hirth[27] and further developed byLi et al. [13] to simulate the laser performance. The rate equa-tion for the local population densities of the Tm 3F4 manifoldis written as

dN2

dt¼ c0

nσabsðλpÞηp½Pf þ Pr �N1 − kΣ½N2�2 −

N2

τ2

−c0

nσemðλlÞ½Sf þ Sr �

�N2 −

f 1

f 2N1

�; ð7Þ

where N2 and τ2 are the population and the spontaneous de-cay time of the upper level, respectively; N1 is the populationof the lower level; kΣ is the total up-conversion rate; c0 is thevelocity of light in the vacuum; σabsðλpÞ is the effective absorp-tion cross section at the pump wavelength λp; σemðλlÞ is theeffective stimulated emission cross section at the laser wave-length λl; ηp is the total pump quantum efficiency; Pf ;r and Sf ;r

are the local photon densities of the pump and laser fields,respectively. f 1 and f 2 are the Boltzmann thermal occupationfactor of the lower and upper laser level, respectively,

f iðr; zÞ ¼gi exp

�−Ei

KTðr;zÞ�

Pmi

j¼1 gj exp�

−Ej

KTðr;zÞ� ; ð8Þ

where i ¼ 1; 2, mi is the number of levels in the manifold i, giis the degeneracy of the energy level Ei, K is the Boltzmannconstant. From Eq. (7), it can be seen that the ratio of the twoBoltzmann occupation factors f 1ðr; zÞ and f 2ðr; zÞ influencethe calculated output power. For Tm:YLF and Tm:YAP, theenergy level corresponding to the 1:94 μm laser radiation is3F4 (5599 cm−1) to 3H6 (419 cm−1) [28], and 3F4 (5631 cm−1)to 3H6 (472 cm−1) [29], respectively. Assuming that the wholecrystal’s temperature is kept at 287K, f 1 and f 2 of Tm:YLF arecalculated to be 0.0273 and 0.2817, respectively. For Tm:YAP,f 1 ¼ 0:0284 and f 2 ¼ 0:2544. The ratio f 1=f 2 of Tm:YLF issmaller than that of Tm:YAP, which is beneficial to the popu-lation inversion accumulation. Considering thermal distribu-tion, the distribution of ratio f 1=f 2 in the z direction andaxial cross section of the edge-cooled crystal is revealed inFig. 9. The maximum value of f 1=f 2 has risen by as muchas 36% in Tm:YLF and as much as 26% in Tm:YAP under apump power of 60W compared with that calculated with theconstant boundary temperature of 287K. Thereby, it is neces-sary for laser performance analysis to take the thermal distri-bution in the crystal into account. As can be seen from Fig. 9,the ratio f 1=f 2 of Tm:YLF is smaller than that of Tm:YAP at thesame point of the whole crystal, even though the temperaturewithin Tm:YLF is higher than that within Tm:YAP, as shown inFig. 5, which indicates the Tm:YLF crystal may have betterlaser performance than the Tm:YAP crystal.

The modeling results in the form of output power versustotal incident pump power are presented in Fig. 3, togetherwith the measured data. The parameters used in the numeri-cal calculations are summarized in Table 2. It should bepointed out that the resonator round-trip losses are estimatedto be 1.5% and 5.5% for the Tm:YLF and Tm:YAP lasers,

respectively. The difference of the losses can be explainedby the following three reasons: first, due to the good beamquality and small beam divergence, the diffraction lossescaused by the VBG were smaller for the Tm:YLF laser thanthat for the Tm:YAP laser [30]; second, the thermo-induceddiffraction losses of the Tm:YLF laser were smaller than thatof the Tm:YAP laser because of the weaker thermal effects asdiscussed above [31]; finally, the Tm-doped concentration wasslightly higher for Tm:YAPð3:5 at:%Þ than Tm:YLFð3 at:%Þ,which indicated that the self-absorption losses of the laserwavelength were slightly higher in Tm:YAP. The numericalsimulation of the laser performance is in good agreement withthe measured data for the Tm:YAP laser with all the threedifferent output mirror transmissions, as shown in Fig. 3(b).For the Tm:YLF laser, the theoretical results are in goodagreement with the experimental data with the transmissionsof 15.1% and 20%. With the transmission of 11.9%, the laser

Fig. 9. (Color online) Ratio of the lower and upper laser level Boltz-mann occupation factors in the z direction and axial cross section ofthe edge-cooled (a) Tm:YLF crystal and (b) Tm:YAP crystal.


output seems saturated more quickly although the theoreti-cal results indicate the transmission of 11.9% is better thanthe other two output mirror transmissions. However, in theDergachev et al. investigation, with the 10% transmission ofVBG as an output coupler, no saturation of the laser was ob-served even at the highest pump power of 170W [11]. The rea-son of saturation in our Tm:YLF laser is unclear, and furtherinvestigation is needed. Figure 10 shows the theoretical slopeefficiency and maximum output power under 60W total inci-dent pump power as a function of the output mirror transmis-sion for the Tm:YLF and Tm:YAP lasers assuming the Tm:YLFlaser would not saturate (the laser parameters used in the cal-culation are taken from Table 2, and the slope efficiency isdetermined to make sure all the linear fitted data are on astraight line considering the characteristics of quasi-three-level lasers). As can be seen from Fig. 10(a), the optimumtransmission of the Tm:YLF laser is around 10%, which hasgood agreement with the experimental result of Dergachevet al. [11]. For the Tm:YAP laser, although the theoretical high-est slope efficiency is achieved at the transmission around35%, the maximum output is achieved at the transmissionaround 25% under the assumed 60W total incident pumppower, as shown in Fig. 10(b). In our experiment, better per-formance was achieved with the 15.1% transmission of theoutput coupler for the Tm:YAP laser rather than 20% as shownin Fig. 11. The slope efficiency of the 20% transmission (33%)

was slightly higher compared with the 15.1% transmission out-put coupler (32.9%), which had qualitative agreement with thetheoretical curve shown in Fig. 10(b). However, due to themuch higher threshold, about 18W compared to 15W, the ex-perimental maximum output power of the 20% transmissionwas lower than that of the 15.1% transmission. Note thatthe rate equation used here has ignored the reabsorptionlosses which would significantly increase the threshold pumppower but had little influence on the slope efficiency for quasi-three-level lasers if operating far above threshold since itcan be saturated with high circulating cavity power density[14,15]. This indicated that with higher transmission of theoutput coupler, thus lowering the circulating cavity powerdensity, would lead to a more slowly saturated reabsorptionlosses. As a result, it was reasonable that the laser perfor-mance with the 20% transmission output coupler had a slightlypoor performance compared with the 15.1% transmission inour present experiment. Nevertheless, our theoretical resultshas reasonable agreement with the experimental data to alarge extent, which are very helpful for our further optimiza-tion of the laser performance and also are useful for otherresearchers who are interested in the 1:94 μm a-cut Tm:YLFand c-cut Tm:YAP lasers. Taking the thermal lens effect intoaccount and for the purpose of maximizing the laser outputunder the given pump power, the a-cut Tm:YLF laser is morefavorable to obtain high power 1:94 μm output compared withthe c-cut Tm:YAP laser presented here.

4. CONCLUSIONTo our knowledge, it is the first time to report a detailed the-oretical and experimental study of Tm:YLF and Tm:YAP laserslasing at 1:94 μm. Although different pump beam diametersand doping concentrations were used in our experiment, thisprimary comparative investigation may provide some gui-dance for other researchers and our further work. Experimen-tally, with VBG as a cavity mirror and an additional F-P etaloninserted in the cavity, the output wavelength of both theTm:YLF and Tm:YAP laser was stable around 1:94 μm. Up to17:3W was achieved for the Tm:YLF laser under a pumppower of 59:5Wwith a pump beam radius of 0:32mm. For theTm:YAP laser, as much as 13:8W was obtained with an inci-dent pump power of 61:5W and a pump beam radius of0:4mm. In theory, for the dual-end pumped structure, the

Fig. 10. (Color online) Simulation of the slope efficiency andmaximum output power under 60W total incident pump power asa function of output mirror transmissions: (a) the Tm:YLF laser and(b) the Tm:YAP laser.

Fig. 11. (Color online) Comparison of the Tm:YAP laser performancewith the transmission of 15.1% and 20%.


temperature distribution and thermal focal length in Tm:YLFand Tm:YAP are analyzed. At the same pump power and edgetemperature, the peak temperature in Tm:YLF is higher thanthat in Tm:YAP. In addition, from the backward calculationwith the measured M2 factor, the thermal focal length ofTm:YLF is deduced to be in the range of 200–400mm. ForTm:YAP, it is in the range of 60–100mm, much shorter thanthat of Tm:YLF, which has reasonable agreement with thetheoretical value. A rate equation model was further used tosimulate the laser performance and found to have reasonableagreement with the experimental acquired data. The theore-tical analysis presented here can be easily applied to otherTm or Ho-doped laser systems such as Tm:YAG, Tm:LuAG,Ho:YLF, and so on.

ACKNOWLEDGMENTSThis work is supported by the National Natural Science Foun-dation of China (NSFC) (60878011 and 61078008) and theProgram for New Century Excellent Talents in University(NCET-10-0067).

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comparison of tm:ylf and tm:yap in thermal analysis and laser performance

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