Double-pass-pumped Tm:YAGlaser with a simple cavity configuration

Atsushi Sato, Kazuhiro Asai, and Toshikazu Itabe

For a double-pass-pumped cw Tm:YAG laser, we developed a theoretical model, taking into accountreabsorption loss and mode matching between the pumping light and the cavity mode. We also dem-onstrated that efficient operation can be obtained with a simple cavity configuration by using a dichroicoutput mirror, highly reflective at the pumping wavelength and partially reflective at the lasing wave-length. Experimental comparisons of this pumping method with single-pass pumping showed that thelongitudinally double-pass-pumped Tm:YAG laser performs as well at room temperature as the single-pass-pumped laser performs at 210 °C. © 1998 Optical Society of America

OCIS codes: 140.0140, 140.3480, 140.3580.

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1. Introduction

Since the first 2-mm solid-state lasers pumped by adiode laser were demonstrated using a rare-earth ion-doped crystal, Tm,Ho:YAG ~Ref. 1!, both the Tm:YAG~Ref. 2! and Tm,Ho:YLF ~Refs. 3 and 4! material sys-tems have been widely investigated with regard totheir possible use in lasers for medical applicationsand the coherent Doppler lidars used for measuringwind vectors. The main reasons these materials areespecially interesting are that their use might result ineye safety, high reliability, long lifetime, high overallelectrical efficiency, good thermal management, etc.

Inasmuch as these materials behave as quasi-three-level systems for the 5I7—5I8 transition in Ho31

~Ref. 5! and for the 3F4—3H6 transition in Tm31,reabsorption is a problem that leads to a reduction inpopulation inversion at room temperature owing to athermally populated lower laser level. This is also aproblem in the 4F3y2—4I9y2 transition in the Nd31,the 2F5y2—2F7y2 transition in Yb31. Researchershave designed many modeling approaches to under-stand and resolve this problem. The end-pumpedquasi-three-level laser with an equilibrium popula-

A. Sato and K. Asai are with the Tohoku Institute of Technology,35-1 Yagiyama-kasumi, Taihaku-ku, Sendai 982, Japan. T. Itabeis with the Communications Research Laboratory, Ministry ofPosts and Telecommunications, 4-2-1 Nukui-kita, Koganei, Tokyo184, Japan.

Received 24 November 1997; revised manuscript received 18May 1998.

0003-6935y98y276395-06$15.00y0© 1998 Optical Society of America

2

tion in the lower laser level was first modeled fortransitions to the manifolds 4I9y2 in Nd31.6,7 An-other model was proposed for optimization of thepumping efficiency and stored energy in a quasi-three-level model, and that model indicated thatdiode-pumped Yb:YAG lasers could be as efficient asdiode-pumped Nd:YAG lasers.8

A new pumping scheme with an active mirror wasintroduced to increase pump absorption, reduce upcon-version, and improve thermal management. Themethod was tested on the Tm,Ho:YAG laser pumpedby a titanium sapphire laser.9 A cw Ho:YAG laserhas been operated by using an end-pumping schemewith 1.9-mm diode lasers to improve the pumping ef-ficiency.10 The plane wave theory has been used in anew approach to modeling cw diode-pumped solid-state lasers and has yielded a model valid for arbitrarysaturation and outcoupling. Optimal crystal lengthsand reflectivities were estimated for Tm:YAG ~Ref. 11!nd Yb:YAG.12 Recently, a model that includes up-

conversion losses and ground-state depletion in bothTm and Ho as well as spatial dependencies of thepump and resonator modes was proposed from the rateequations for both cw and prepulse Q-switched opera-ion. Simulations of cw Tm- and Ho-doped lasershowed good agreement with experimental results.13

When one designs longitudinally pumped quasi-three-level lasers, it is important to consider both thereabsorption and the spatial mode matching betweenthe pump light and resonator modes. The lasercrystal cannot absorb all the pumping power. Onesolution to this problem is to use a double-pass pump-ing technique by which residual pump power, thatremaining after the pump beam passes through the

0 September 1998 y Vol. 37, No. 27 y APPLIED OPTICS 6395

fiaPnlap

aTfi

es

icf

s

pp

P

6

laser crystal, is reflected back to the same opticalpath.8,9,12 Double-pass pumping can increase the ef-

ciency with which pump power is absorbed and canlso result in better population inversion profiles.revious studies of the double-pass pumping tech-ique, however, have not used a quasi-three-level

aser model, including the effect of reabsorption lossnd the effect of spatial mode matching between theump light and the resonator mode.Here we describe both a theoretical analysis of

nd experimental results for the cw operation of am:YAG laser with the simplest possible cavity con-guration14 for double-pass pumping. We experi-

mentally compare double-pass and single-passpumping techniques. In Section 2 we provide thetheoretical treatment needed to obtain more rigor-ous and accessible rate equations. In Section 3 wepresent and discuss the experimental results andsummarize our study in Section 4.

2. Theory

A quasi-three-level laser model, including the effectof a reabsorption loss, has been developed by Fan andByer6 and Risk.7 Their model takes into account theeffect of an overlap between the pump and lasermodes. We theoretically derive the threshold pumppower and the slope efficiency for the end-pumpedTm:YAG laser under double-pass pumping by usingsome modifications of Risk’s model.7

Figure 1 shows an energy level diagram for Tm:YAG when the 0.78-mm pump light from the diodelaser is absorbed into the 3H4 manifold, and the 3F4manifold is efficiently populated through the well-known two-for-one cross-relaxation process. The la-ser emission at 2.01 mm is due to a transition betweenthe lowest Stark level in the 3F4 manifold and a highlevel in the 3H6 ground-state manifold. Reabsorp-tion, however, takes place because of the Tm ions inthe lower laser level, which are thermally pumped.We assume here that the cross-relaxation efficiency isunity, which is a reasonable assumption when Tmdopant concentrations are above 3–4%.13 A ratequation for a population inversion density DN in theteady state is given as follows:

dDN~x, y, z!

dt5 2fRrP~x, y, z! 2

DN~x, y, z! 2 DN0

t

2fcsDN~x, y, z!

nFf0~x, y, z! 5 0, (1)

where rP~x, y, z! is the normalized spatial distributionof the pump light, f0~x, y, z! is the normalized spatialdistribution of the laser photons, t is the upper statelifetime, c is the speed of light in a vacuum, s is thestimulated emission cross section, n is the refractivendex of the laser medium, x and y are the transverseoordinates, z is the coordinate along the optical axis,~5f1 1 f2! is the sum of Boltzmann thermal occupa-

tion factors of the lower and upper laser levels, andDN0~5N2

0 2 N10! is the unpumped population inver-

ion density, which at thermal equilibrium can be

396 APPLIED OPTICS y Vol. 37, No. 27 y 20 September 1998

resumed to be 2N10. The pump rate R and total

hoton number F in the laser cavity are given by

R 5ha PP

hnP, (2)

F 52nlPL

chnL, (3)

where ha is the fraction of pump power absorbed bythe crystal, PP is the incident pump power, h is

lanck’s constant, nP and nL are the pump and laserfrequencies, l is the crystal length, and PL is the laserpower that travels in one direction in the cavity. Totreat the longitudinally double-pass pumping case,we consider the following normalized spatial distri-bution of the pump light:

rP~x, y, z! 52a

pwpxwpyhaexpF22S x2

wpx2 1

y2

wpy2DG

3 @1 1 RP exp~22al 1 2az!#exp~2az!, (4)

where a is the absorption coefficient at the pumpwavelength and RP is the fraction of unabsorbedpump power reflected back into the crystal. For fur-ther general considerations, here we introduced anelliptical Gaussian pump beam with the radii wpx andwpy because the beam patterns of a high-power diodelaser are not circular even when the beam is opticallyshaped. For simplicity, we also assume that the ra-dii of the pump beam are constant within the lasercrystal, and that the second pass of the pump beam isin the same path as the first one. In this case, thefraction ha of the pump power absorbed can be writ-ten as

ha 5 @1 2 exp~2al !#@1 1 RP exp~2al !#, (5)

which, for RP 5 1, becomes ha 5 1 2 exp~22al !. Ifwe assume a circular Gaussian mode for the laserbeam, the normalized spatial distribution of the laserphotons would be given by

f0~x, y, z! 52

pwL2l

expF22Sx2 1 y2

wL2 DG , (6)

Fig. 1. Energy level diagram for Tm:YAG.

Table 1. Parameters Used for Numerical Simulations

PT

T

where wL is the radius of the laser beam waist. De-fining the parameters

B 52sN1

0lL 1 T

, (7)

S 54stPL

pwL2hnL

, (8)

F 54stha PP

pwL2hnP~L 1 T!

, (9)

and using the procedure derived by Risk,7 we obtain

8pwL

2wpxwpy

3 *0

`

*0

`2fFwL

2 expF22S x2

wpx2 1

y2

wpy2DG 2 Bwpxwpy

1 1 fS expF22Sx2 1 y2

wL2 DG

3 expF22Sx2 1 y2

wL2 DGdxdy 5 1, (10)

where L is the round-trip loss, T is the transmissionof the output mirror at the laser wavelength, B is theratio of reabsorption loss to cavity losses, S is thenormalized laser power in the cavity, and F is thenormalized pump power. Introducing

rx 52x2

wpx2 , (11)

ry 52y2

wpy2 , (12)

ax 5wpx

wL, (13)

ay 5wpy

wL, (14)

we then obtain the relation

Setting S 5 0 in Eq. ~15! and using Eq. ~9!, we canwrite the laser threshold power Pth as

Pth 5

phnPÎwL2 1 wpx

2 ÎwL2 1 wpy

2 ~L 1 T 1 2sN10l !

8stfha.

(16)

20

Equation ~16! becomes the same as the threshold-pump-power equation in Ref. 7 when RP 5 0, wpx 5wpy, and the cross relaxation is negligible. It shouldbe noted that it is possible by double-pass pumping toincrease ha without increasing the reabsorption lossterm 2sN1

0l and that this pumping method is there-fore useful for reducing the threshold of quasi-three-level lasers. Furthermore, the slope efficiency hrelative to the incident pump power is given by

h 5T

L 1 TnL

nPha

dSdF

, (17)

where dSydF is the normalized slope efficiency ob-tained by differentiating Eq. ~15! with respect to S:

dSdF

5

2 *0

`

*0

` exp~2rx 2 ry!

Îrxry @exp~ax2rx 1 ay

2ry! 1 fS#drxdry

*0

`

*0

` 2fF exp~2rx 2 ry! 2 Bax ay

Îrxry @exp~ax2rx 1 ay

2ry! 1 fS#2drxdry

.

(18)

We used Eqs. ~16! and ~18! to evaluate the effects ofdouble-pass pumping on the performance of the Tm:YAG laser, and the parameters we used in the sim-ulations are listed in Table 1. The threshold pumppowers calculated for single-pass pumping anddouble-pass pumping are shown in Fig. 2 as a func-

Tm dopant concentration 4 at. %Absorption coefficient ~at 0.78 mm! a 3 cm21

Crystal length l 3 mmRound-trip loss L 1%Transmittance of output mirror T 1.5%Stimulated emission cross section s 0.5 3 10220 cm2

Upper state manifold lifetime t 11 msLaser beam waist wL 100 mm

ump beam waist wpx, wpy 100 mm, 140 mmhermal occupation factor in theupper laser level

f2 0.46

hermal occupation factor in thelower laser level

f1 0.018

tion of temperature. Although the stimulated emis-sion cross section and the absorption cross sectiondecrease slightly with increasing temperature, thesechanges are neglected in this calculation becausethey are small.6 It is obvious that at any tempera-ture the threshold pump power for double-passpumping is approximately 70% of the threshold pumppower for single-pass pumping. For example, when

F 5

1 1Bax ay

p *0

`

*0

` exp~2ax2rx 2 ay

2ry!

1 1 fS exp~2ax2rx 2 ay

2ry!

1

Îrxry

drx dry

2fp *

0

`

*0

` exp@2~1 1 ax2!rx 2 ~1 1 ay

2!ry#

1 1 fS exp~2ax2rx 2 ay

2ry!

1

Îrxry

drx dry

. (15)

September 1998 y Vol. 37, No. 27 y APPLIED OPTICS 6397

d

eppm

6

we use the single-pass pumping scheme the crystalmust be cooled to 225 °C if we want to get the samethreshold power that we get at 125 °C when we usethe double-pass pumping scheme. The calculatedthreshold pump power at room temperature is shownin Fig. 3 as a function of crystal length l. We ob-tained the optimum crystal length to minimize thethreshold pump power by differentiating Eq. ~16!with respect to l and setting it equal to zero. Theoptimum length for double-pass pumping is shorterthan for single-pass pumping because the pump lightis efficiently absorbed under double-pass pumping.According to our calculations, the optimum lengthsfor the single-pass and the double-pass cases are,respectively, 3.5 and 2.3 mm.

The normalized slope efficiency dSydF calculatedwith Eq. ~18! is shown in Fig. 4 as a function ofincident pump power. Given the model and as-sumptions presented above, the optimum normalizedslope efficiency, which can be obtained by substitut-ing B 5 ax 5 ay 5 0 into Eq. ~18!, is 2. The values of

SydF increased with increasing incident pumppower PP, and all the values calculated for double-

Fig. 2. Calculated threshold pump power versus temperature.

Fig. 3. Calculated threshold pump power as a function of crystallength.

398 APPLIED OPTICS y Vol. 37, No. 27 y 20 September 1998

pass pumping are higher than those calculated forsingle-pass pumping. It can be estimated, for exam-ple, that, when the incident pump power is 300 mW,double-pass pumping increases h by a factor of 1.45.

3. Results and Discussion

A resonator configuration for double-pass pumping isshown in Fig. 5. The laser crystal was a 4%-dopedTm:YAG crystal 3 mm long, which was the optimumlength for our experiments because it is near theaverage of optimum values calculated for single-passand double-pass pumping. An AlGaAs diode laser~Spectra Diode Laboratory SDL-2432! was used asthe pump source and was temperature tuned to 0.78mm, which is the wavelength of an absorption peak inTm. The diode laser was capable of operating with acw output power of as much as 560 mW at that wave-length. After the diode laser light passed through acollimating lens with a focal length of 8 mm andthrough an anamorphic prism pair, the pump beamwas focused into the laser crystal with a lens havinga focal length of 48 mm. One end face of the lasercrystal was coated for high reflection ~HR! at 2.01 mmand high transmission ~HT! at 0.78 mm. The othernd face was coated to be antireflective at both theump wavelength and the laser wavelength. Ap-roximately 60% of the incident pump power at 0.78m was absorbed during the single-pass through the

Fig. 4. Comparison of simulations of normalized slope efficiencyas a function of incident pump power.

Fig. 5. Schematic diagram of the double-pass-pumped Tm:YAGlaser.

laser crystal. The hemispheric resonator consistedof the pump-side surface of the laser crystal and theoutput mirror, which had a 100-mm radius of curva-ture. The cavity length was thus approximately 100mm. The transmittance of the output mirror was1.5% at 2.01 mm. The double-pass pumping resultedfrom the output mirror having an additional HR coat-ing ~at 0.78 mm! that returned the unabsorbed pumplight to the crystal. Two three-stage thermoelectriccoolers controlled the crystal temperature at levelsbetween 210 °C and 25 °C.

Figure 6 shows the 2-mm output power for the end-pumped Tm:YAG laser under both single-pass anddouble-pass pumping conditions. The lines in Fig. 6are the best least-squares fits. The cavity lengthwas adjusted to obtain a maximum output power andwas nearly the same for both pumping methods.With single-pass pumping, the output power of 62mW and a slope efficiency ~relative to the incidentpump power! of 27% were obtained at room temper-ature, and the corresponding values at 210 °C were81 mW and 30%. In contrast, with double-passpumping the output power was 82 mW at 25 °C and100 mW at 210 °C. The threshold pump powers atboth temperatures were obviously reduced by double-pass pumping, which at 210 °C resulted in an outputpower of 100 mW and a slope efficiency of 35% ~whichcorresponds to a slope efficiency of 45% relative to theabsorbed pump power!. When we measured outputfluctuations, owing to the relatively low pump powerin our experiments, we found no influence of thepump beam propagating in the backward direction.The ratio of the curvature of the output mirror to thefocal length of the focusing lens is well known to be animportant design parameter in establishing a goodoverlap between the pump and laser modes in end-pumped lasers. The design parameters in our sys-tem were nearly optimum for the double-passpumping scheme.

For evaluation of laser performance, it is necessaryto compare the effects of double-pass pumping withthose predicted by the model. We compared the

Fig. 6. Output power at 2 mm versus incident pump power.

20

above experimental results with numerical simula-tions based on the model derived in Section 2 ~Fig. 7!.Although RP is essentially zero for the single-passcase, the output mirror in our single-pass pumpingexperiment had a reflectance of 27% at 0.78 mm. Forthe simulations it was necessary for us to take intoaccount the slight effect of double-pass pumping byusing RP 5 0.27 even for single-pass pumping. Thisresulted in good agreement between the experimen-tal results and the numerical simulations, but theoutput power actually observed with double-passpumping was somewhat lower than that in our sim-ulations. The slight disagreement seems to be dueto imperfect spatial overlap between the cavity modeand the pump beam propagating in the second pass.

Optical-to-optical conversion efficiency is shown inFig. 8 as a function of temperature. As a result ofthe lower threshold and higher slope efficiency owingto double-pass pumping, the optical-to-optical conver-sion efficiency at temperatures between 210 °C and25 °C was increased by a factor of 1.3. At 210 °C,the double-pass pumping scheme yielded a conver-

Fig. 7. Comparison of experimental results and simulations.

Fig. 8. Optical-to-optical conversion efficiency as a function oftemperature.

September 1998 y Vol. 37, No. 27 y APPLIED OPTICS 6399

3. B. T. McGuckin and R. T. Menzies, “Efficient cw diode-pumped

6

sion efficiency of 29% for the incident pump power of340 mW. In our system, the double-pass pumpingat room temperature results in an optical-to-opticalconversion efficiency equivalent to that obtained un-der single-pass pumping at 210 °C. This meansthat double-pass pumping can sufficiently improvethe system efficiency even without cooling.

4. Conclusion

We have discussed the cw operation of the longitu-dinally double-pass-pumped Tm:YAG laser with asimple cavity configuration using a dichroic outputmirror. A more general model was developed bytaking into account the effect of double-pass pump-ing in addition to the reabsorption loss and modematching between the pump and laser modes. Acomparison of the experimentally observed laserperformance of a double-pass-pumped laser withthat of a single-pass-pumped laser revealed thatdouble-pass pumping increased the system effi-ciency by a factor of 1.3. Furthermore, the reason-able agreement between the experimental resultsand the results of the theoretical analysis indicatesthat the model we derived is valid for an end-pumped Tm:YAG laser under double-pass pumping.

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