930 J. Opt. Soc. Am. B/Vol. 12, No. 5 /May 1995 Sennaroglu et al.

Efficient continuous-wave chromium-doped YAG laser

Alphan Sennaroglu* and Clifford R. Pollock

School of Electrical Engineering, Cornell University, Ithaca, New York 14853

Howard Nathel

Lawrence Livermore National Laboratory, Livermore, California 94551

Received May 25, 1994; revised manuscript received January 11, 1995

Continuous-wave power performance of a chromium-doped YAG laser pumped by a Nd:YAG laser is investi-gated as a function of crystal temperature, output coupling transmission, and emission wavelength. Usinga 2%-transmitting output coupler, we obtained as much as 1.9 W of cw output power at 1.45 mm with anabsorbed power slope efficiency of 42% when the gain medium was cooled at 3 ±C. Using the laser efficiencydata, we estimated the emission and excited-state absorption cross sections at 1.45 mm and compared themwith the previously reported values.

1. INTRODUCTION

Following the invention of the room-temperature alexan-drite laser1 in the late 1970’s, there have been extensivespectroscopic studies aimed at developing new tunablesolid-state laser sources that can be operated in variouswavelength regimes. Tunability is achieved by dopingtransition metal ions in suitably chosen host crystals withlow ligand field environments. Strong coupling betweenthe electronic and lattice vibration states then gives riseto broad absorption and emission bands.2 In searchingfor such new tunable laser materials, a number of otherimportant criteria have to be met to ensure reliable opera-tion and ready commercialization. These include chemi-cal and mechanical stability of the host crystal, repeatablecrystal growth process, sufficiently large gain cross sec-tion of the emission center, room-temperature operation,absence of absorptions in the lasing wavelength range,availability of pump sources that coincide well with theabsorption band of the laser-active centers, and good opti-cal quality of the crystal host to ensure fine beam quality.

Among the transition-metal ion candidates for tunablelaser operation, chromium has frequently been used be-cause of its chemical stability and broad pump bands.Tunable chromium lasers utilizing trivalent chromiumions as the lasing center include alexandrite,1 emerald,3

Cr:LiCAF,4 Cr:LiSAF,5 and chromium-doped garnets.6

These lasers have tuning ranges extending roughly be-tween 700 nm and 1 mm. A second category of tunablechromium laser believed to be based on the tetravalentchromium ion has also been developed; notable exam-ples include Cr:forsterite,7 Cr:YAG,8 and Cr:Y2SiO5,9

the last-named having been only cryogenically operatedto date.

The Cr:YAG laser, first reported by Angert et al.8 in1988, is unique as a source of coherent radiation be-cause it can be tuned over the 1.55-mm wavelength rangewhere the present-day low-loss fiber-optic transmissionsystems are operated. The market demand for compactrobust tunable sources in this wavelength region therefore

0740-3224/95/050930-08$06.00

makes the Cr:YAG laser potentially important. Further-more, this laser medium provides a readily commercial-izable, room-temperature alternative to the cryogenicallyoperated NaCl:OH2 laser10 that can be tuned in an over-lapping wavelength range.

To date, various modes of operation employing thechromium-doped YAG gain medium have been demon-strated. As a saturable absorber, having an absorptionband in the 0.9–1.1-mm region, it has been used for pas-sive Q switching of Nd:YAG lasers operated at 1.06 mm.11

As an optical gain medium in the near-infrared wave-length region, Q-switched,8, 12–14 continuous-wave14 (cw),cw mode-locked,15 and cw self-mode-locked16 operationshave been demonstrated. Recently dual-wavelength op-eration at both 1.06 and 1.44 mm was also demonstratedby use of a Cr:YAG crystal simultaneously as a Q switchand as a laser gain medium.17 We further note thatInGaAs laser diodes operating at 980 nm could also beused as pump sources to build compact, diode-pumpedCr:YAG laser systems.

In this paper a detailed characterization of a cw Cr:YAGlaser is given. The experiments performed concentratedprimarily on a systematic study of the cw performanceof this gain medium as a function of crystal tempera-ture, output wavelength, and output coupling. Such dataclearly show the sensitivity of the output power to thevariation in a number of related operating parametersand will offer useful guidelines about how to design anefficient Cr:YAG laser system. For the sake of complete-ness, Section 2 gives a concise background on the spectro-scopic characteristics of the Cr:YAG gain medium. Thisis followed by the description of the experimental setupused in our measurements. In the sections that follow,performance data showing the variation of output poweras a function of output coupling, crystal temperature, andwavelength are presented. Using the data obtained fromthese measurements, in Section 7 we make estimationsof the stimulated emission and excited-state absorption(ESA) cross sections at 1.45 mm. Finally, it is noted thatthe cw output powers of the Cr:YAG laser obtained in our

1995 Optical Society of America

Sennaroglu et al. Vol. 12, No. 5 /May 1995/J. Opt. Soc. Am. B 931

Fig. 1. Unpolarized emission spectra of Cr:YAG at room tem-perature and at 77 K. The sharp peak is due to pump excitationat 1.06 mm.

experiments significantly exceeded all previously reportedresults in the literature of which we are aware.14,15

2. SPECTROSCOPIC BACKGROUNDHaving an absorption band in the 0.9–1.1-mm wavelengthregion, coinciding well with the Nd:YAG operating wave-length, the chromium-doped YAG medium has a broadfluorescence bandwidth extending over some 400 nm andpeaking close to 1.4 mm. Shown in Fig. 1 are the un-polarized emission spectra of this gain medium takenat room temperature and at 77 K, using excitation froma cw Nd:YAG laser operated at 1.06 mm. The sampleused in this study was a 1.3-cm-long, normal-cut YAGcrystal with 0.6% chromium doping, obtained from UnionCarbide, Inc. As is clearly illustrated, the fluorescenceintensity increases approximately an order of magnitudewhen the sample is cooled to 77 K because of a decreaseof phonon-assisted nonradiative decay processes from theexcited state.

Extensive spectroscopic studies have been performed toidentify the exact configuration of this laser-active centerin YAG.18–23 Like that in the chromium-doped forsteriteand yttrium silicate lasers, the near-infrared fluorescenceis attributed to the tetravelent chromium ions. Studiesalso suggest that the tetravelent chromium ions substi-tutionally replace trivalent aluminum ions in both octa-hedral and tetrahedral sites of the YAG lattice but thatonly those ending up in the tetrahedral sites give rise tothe 1.4-mm fluorescence.19

Because the preferred charge state of the substitu-tional chromium ions for laser action differs from thatof the trivalent aluminum ions, YAG crystals are si-multaneously codoped with divalent alkaline earth ions(magnesium or calcium) for charge compensation. Thechromium-doped YAG crystals codoped with magnesiumor calcium can be routinely grown by the Czochralski tech-nique, and the preferred tetravelent charge state of thechromium ions can be enhanced by subsequently anneal-ing the crystals in an oxidizing environment or by sub-jecting them to gamma radiation.18

Figure 2 shows the resulting energy levels of the tetra-hedrally coordinated Cr41 ion with 2d2 electron configu-ration and D2d point group symmetry.23 The pump bandabsorption in the 0.9–1.1-mm wavelength region corre-sponds to the transition between the states 3A2 and

3T2. The absorption cross section sa of this transition at1.06 mm was previously reported to be 7 3 10218 cm2.19

There is also ESA at 1.06 mm originating from the 3T2

state to the higher-lying 3T1 state with a cross section of5 3 10219 cm2 and a fast relaxation time of ,50 ps back tothe 3T2 state.19 The laser emission of the Cr:YAG centerin the 1.4-mm region occurs as a result of the transitionfrom the 3T2 state back to the 3A2 state with a relax-ation time of approximately 3.4 ms at room temperature.Previously reported data also show a drastic increase inthis lifetime from 3.4 ms at room temperature to 48 msat 77 K, as a result of a decrease in fast nonradiativetransitions.19 Polarized spectroscopy experiments previ-ously carried out also indicated that the maximum emis-sion intensity is obtained when the pump and the emis-sion electric fields are parallel to the [0, 0, 1] directionin the crystal.22 The presence of ESA, overlapping theemission spectrum of the center and originating from the3T2 state to the higher-lying 3T1 state, is a major draw-back for efficient laser operation, not only increasing thelasing threshold but also putting a fundamental limitto the highest efficiency attainable from the laser. InSection 7 the effect of ESA on the cw laser performance isdelineated, and we show that, based on the cw efficiencydata presented in this paper, the ESA cross section isapproximately 30% of the stimulated emission cross sec-tion, in reasonable agreement with previously reportedvalues.12

By using the emission data it is possible to come upwith a reasonably accurate estimate for the emission crosssection se. For a homogeneously broadened transitionthat has a Lorentzian line shape, the peak stimulatedemission cross section is given by

se ­l2

4p2n2tf Dn, (1)

where l is the wavelength, n is the index of refrac-tion of the host crystal, tf is the fluorescence lifetime,and Dn is the emission bandwidth (FWHM).24 FromFig. 1, Dn is approximately 41 THz for Cr:YAG. Becausenonradiative effects become dominant at elevated temper-atures, obscuring the true radiative strength of the tran-sition, the low-temperature (77-K) value of 48 ms is usedfor the fluorescence lifetime tf in Eq. (1).19 For n ­ 1.81,the peak emission cross-section value for se is calculatedto be 0.75 3 10219 cm2.

3. EXPERIMENTAL SETUPA schematic of the experimental setup used to character-ize the cw performance of the Cr:YAG laser is depicted

Fig. 2. Energy-level diagram of the Cr 41 ion with 2d2 electronconfiguration and D2d point group symmetry.

932 J. Opt. Soc. Am. B/Vol. 12, No. 5 /May 1995 Sennaroglu et al.

Fig. 3. Experimental setup of the cw Cr:YAG laser.

in Fig. 3. A symmetrical, astigmatically compensated,Z-fold cavity approximately 1 m in total length housedthe chromium-doped YAG crystal, positioned in the mid-dle of two curved high reflectors (M1 and M2), each with aradius of curvature of 10 cm. The laser cavity was com-pleted with a flat wedged high reflector (H.R.) and a flatoutput coupler (O.C.). Various output couplers having0, 1.0, 2.0, 3.1, and 8.1% transmission at 1.45 mm wereused. These 1.27-cm-diameter wedged mirrors, whichhad 20–10 scratch–dig surface quality and were broad-band coated to operate in the wavelength range from1.34 to 1.57 mm, were obtained from the optics division ofSpectra-Physics Lasers, Inc. The Cr:YAG laser setup inthis configuration was longitudinally end pumped by acommercial cw Nd:YAG laser (Quantronix Model 416) op-erated at 1.064 mm. The Nd:YAG pump beam was sentinto the Cr:YAG crystal through M1, which had 93%transmission at 1.06 mm.

The gain medium, a 2-cm-long, Brewster-cut Cr:YAGcrystal, was grown in IRE-POLUS, Moscow, Russia. Thechromium doping level in the sample was not known, butthe laser-active center concentration was estimated to be1.2 3 1018 cm23 based on the absorption data presentedin Section 4. The 5-mm-diameter cylindrical Brewster-cut Cr:YAG rod was wrapped with indium foil and tightlyclamped between two copper holders attached to a copperheat sink via a thermoelectric cooler. Closed-loop tem-perature control was established with the thermoelectriccooler. The crystal temperature could be controlled withpeak-to-peak temperature fluctuations of less than 0.2 ±Cover the temperature range from 3 to 36 ±C. For crys-tal temperatures below 20 ±C the crystal holder assem-bly was enclosed inside a Lucite compartment and purgedwith dry nitrogen to prevent water-vapor condensation onthe crystal surfaces. For relative humidity levels belowapproximately 30%, purging with dry nitrogen was notnecessary. In this temperature range (3–36 ±C) the low-signal absorption of the Cr:YAG crystal was measured tobe 95%. The measured round-trip reflective loss from thecrystal surfaces was 0.12%. The folding angle of the cav-ity was set at 34± to compensate for the astigmatism ofa 2-cm-long YAG crystal having an index of refraction of1.81. For some particular values of crystal temperature,output coupling, and pump power the cw performance ofthe Cr:YAG laser was also investigated for various foldingangles between 24± and 35±. The output power remainedessentially insensitive to this variation in the cavity fold-ing angle.

To converge rapidly to the optimum mode matching be-tween the pump and the laser cavity, a telescope con-sisting of two 5-cm focal-length lenses (L3 and L4 inFig. 3) with adjustable separation was used in conjunc-tion with the mode-matching lens L1. Once lasing was

achieved, we accomplished optimization in an iterativemanner by setting the telescope separation to a fixedvalue and then translating L1 until the best power out-put was reached. The calculated pump and laser beamprofiles established during the experiment are shown inFig. 4 as a function of the distance from the crystal edge.We performed the beam profile calculations without tak-ing into account astigmatic effects. For the particularcase shown in Fig. 4 the telescope lens separation was9.7 cm and the distance of mode-matching lens L1 frominput curved mirror M1 was 5.5 cm. As can be seen, thepump beam throughout the crystal falls inside the lasingvolume, giving rise to high pumping efficiency and lesslikelihood of higher-order transverse mode oscillations.Furthermore, from the pump and laser beam profiles de-picted in Fig. 4 the average pump and laser spot sizeswere calculated to be kvfcl ­ 54 mm and kvfpl ­ 46 mm,respectively.

4. ABSORPTION SATURATIONIN THE GAIN MEDIUMAs has been discussed in Section 1, Cr:YAG has been usedas a saturable absorber to passively Q-switch Nd:YAGlasers.11 In the cw performance of the Cr:YAG laser thesame pump absorption saturation plays a significant role,because the decreasing absorption with increasing pumppower leads to output power saturation. Figure 5 shows

Fig. 4. Calculated pump and laser beam radii as a function ofthe distance from the crystal edge.

Fig. 5. Variation of the measured fractional absorption as afunction of the incident pump power.

Sennaroglu et al. Vol. 12, No. 5 /May 1995/J. Opt. Soc. Am. B 933

the measured variation of the fractional absorption A,defined as

A ­ 1 2 T ; 1 2 sPtyPid , (2)

where T is the fractional transmission, Pt is the trans-mitted power, and Pi is the power incident upon the crys-tal. The data shown were taken at 3 and 20 ±C. Alsoshown are fourth-order polynomial fits made to the twosets of data. To extract the correct output power versusabsorbed pump power efficiency curves presented below,this pump saturation effect was taken into account.

These data can also be used to yield rough estimatesof the absorption cross section of the medium. Underthe assumption of a uniform beam profile and no power-dependent focusing effects taking place inside the gainmedium, the expression relating the incident power Pinc tothe fractional transmission T of a homogeneously broad-ened gain medium with a small-signal absorption coeffi-cient a0 can be derived to be

Pinc ­ Ps

"a0l 1 lnsT d

1 2 T

#, (3)

where l is the length of the crystal and Ps is the satu-ration power.24 Ps is defined in terms of the saturationintensity Is as

Ps ­ pkv2lIs , (4)

where kv2l is the mean-squared value of the laser spotradius in the absorbing medium.

Defining two new variables X ­ lnsT d and Y ­ Pincsl 2

T d establishes a linear relation between X and Y underthis model such that the gradient of the X–Y curve givesthe saturation power Ps and the ratio of the interceptto the gradient gives the small-signal absorption coeffi-cient a0l. These modified-variable plots for the absorp-tion data at 3 and 20 ±C, together with the best linearfits, are shown in Fig. 6. Deviations from the expectedlinear behavior observed in Fig. 6 may be due to a num-ber of simplifying assumptions made in our estimations.These include treating the Gaussian laser beam as a uni-form beam with a fixed spot size, ignoring the excited-state absorption of the pump photons from the 3T2 levelto 3T1 level, differences between the calculated and theactual pump spot sizes in the crystal, and most impor-tantly, neglecting temperature changes inside the crystal.At high pump power levels such thermal loading effects inthe crystal may give rise to nonlinearities that are due tothe temperature dependence of the absorption coefficientand the refractive index.

In both cases a best-fit value of approximately 1.5 cm21

has been obtained for a0, in excellent agreement with themeasured low-signal absorption coefficient of the sample.In addition, Ps values of 2.6 and 2.9 W have been cal-culated at 3 and 20 ±C, respectively. Using an averagepump spot size of approximately 46 mm, as has been cal-culated in Section 3, we calculated the absorption satura-tion intensity for the Cr:YAG medium to be 43 kW/cm2 at20 ±C. Saturation intensity Is, in turn, is related to theabsorption cross section sa, the lifetime tf , and the pumpphoton energy hnp through24

Is ­hnp

satf

. (5)

Assuming the previously reported value of 3.4 ms forthe lifetime at 300 K,19 we thus calculated the absorp-tion cross section to be 1.3 3 10218 cm2. This value isapproximately a factor of 5 smaller than what was re-ported by Zverev and Shestakov19 and comes closer tothat reported by Spariosu et al.17 Using our estimate ofthe absorption cross section, we estimated the laser-activecenter concentration in the Cr:YAG gain medium to be1.2 3 1018 cm23, using the relation

N0 ­ 21

lsalnfT0g , (6)

where T0 is the small-signal transmission of the sample(5%).

5. LASER EFFICIENCY DATAOnce lasing and final mode matching of the pump andlaser cavities were accomplished, efficiency measure-ments were carried out with the Cr:YAG laser operatedin free-running mode with no intracavity elements otherthan the gain medium. We obtained the efficiency databy measuring the output power as a function of the in-put pump power, using a calibrated thermopile detector(Coherent Model 210). The pump power was varied bya commercial variable attenuator (Newport Model 935-3)consisting of two pairs of counterrotating parallel glassplates. This procedure was repeated for each output cou-pler and at two different temperatures, 3 and 20 ±C. Ineach case we also carefully measured the threshold pumppower required for observation of lasing by reducing thepump power to the point where only flashing output ofthe laser could be seen on a highly sensitive phosphores-cence card (Quantex Model Q-42-R). From the raw datathus obtained we deduced the actual output power versusabsorbed pump power efficiency curves by taking intoaccount the saturable absorption of the gain medium asdescribed in Section 4. Having obtained the efficiencycurves, we made a linear best fit to each data set andcalculated the absorbed pump power slope efficiency habs,defined according to

habs ­ DPoutyDPabs , (7)

Fig. 6. X–Y plots at 3 and 20 ±C to calculate the saturationintensity.

934 J. Opt. Soc. Am. B/Vol. 12, No. 5 /May 1995 Sennaroglu et al.

Fig. 7. Efficiency curves for the Cr:YAG laser at (a) 3 ±C and (b)20 ±C with various output couplers.

where Pout is the measured output power and Pabs is theabsorbed pump power, from the slope of the linear bestfits. The peak wavelength and the linewidth of the oscil-lation were measured with a Jarrel-Ash 1/4-m monochro-mator having a pair of 25-mm slits and equipped witha dc-coupled germanium detector. The resolution of themonochromator was approximately 0.2 nm.

Figures 7(a) and 7(b) show the variation of the outputpower as a function of the absorbed pump power for thedifferent output couplers used at 3 and 20 ±C, respectively.The laser emission in the free-running mode peaked atapproximately 1.45 mm with a measured linewidth of0.8 nm. We obtained the best results at 3 ±C, using the2% transmitting output coupler. In this case, as muchas 1.9 W of cw output power was obtained at 1.45 mmwith an absorbed pump power slope efficiency of 42% anda threshold absorbed pump power of 1.08 W. As can beseen from Fig. 7(b), the absorbed pump power slope effi-ciencies decreased and the threshold absorbed pump pow-ers increased going from 3 to 20 ±C, believed to be due to adecrease in the fluorescence lifetime, resulting in reducedpopulation inversion.

All the data presented were taken with the laser oper-ating in the cw mode, except for data for the 8.1% trans-mitting output coupler at 20 ±C, where the poorest powerperformance was observed. In this case, 50% duty-cycledata were recorded because chopping the pump powerresulted in doubling of the power efficiency. The poorpower performance observed with the 8.1%-transmittingoutput coupler could be attributed to the fact that the

intracavity intensity was not sufficiently large to satu-rate the gain effectively during laser oscillation. Thisresult clearly puts an upper limit to the output couplertransmission that should be used in designing practicalCr:YAG laser systems with comparable cavity geometriesand pump power levels.

Figure 8 shows the variation of the output power as afunction of the output coupling for a fixed incident pumppower of 5.6 W at 1.45 mm for the same two tempera-tures. In this case, cubic spline fitting was done to eachdata set. It is seen that the optimum coupling at 3 ±C is2% and shows a slight decrease to lower values with in-creasing temperature. The fact that the optimum outputcoupling is so low stems from the relatively small stimu-lated emission cross section of this gain medium comparedwith that of, say, a color-center laser10 and makes the cwoperation very susceptible to even small amounts of lossesintroduced into the cavity. This fact is further delineatedin Section 8, which describes the tuning characteristics ofthe Cr:YAG laser. For pump powers well above thresh-old, stable quiet operation with less than 2% peak-to-peakpower fluctuations could be obtained. In most cases thenoise arose primarily from pump power fluctuations.

6. EFFECT OF TEMPERATURE ONLASER PERFORMANCEThe effect of crystal temperature on the cw Cr:YAG laserperformance has also been investigated in detail in thetemperature range from 3 to 36 ±C. Strictly speaking,the temperature inside the crystal is higher than thecopper holder temperature because of thermal loadingcaused by the unused pump beam. However, becauseof the complicated axial and radial variation of tempera-ture inside the longitudinally pumped crystal, we choseto characterize the thermal effects by measuring the tem-perature of the copper holder. Figure 9 shows the vari-ation of the output power as a function of the crystaltemperature for a fixed incident pump power of 5.6 Wat 1.45 mm. Note that there is a fairly linear decreaseof the output power with increasing temperature, the ef-fect becoming more pronounced the higher the outputcoupler transmission is. As noted in Section 5, such de-grading of power performance is possibly due to a de-

Fig. 8. Variation of the output power as a function of the outputcoupling transmission for a fixed incident pump power of 5.6 Wat 1.45 mm.

Sennaroglu et al. Vol. 12, No. 5 /May 1995/J. Opt. Soc. Am. B 935

Fig. 9. Variation of the output power as a function of the crystaltemperature at a fixed incident pump power of 5.6 W for differentoutput couplers.

crease in the upper-state lifetime, resulting in reducedinversion. In the case of the 8.1%-transmitting outputcoupler, where again the poorest results were obtained,laser operation at this pump power level was observedonly up to ,25 ±C. Even though no higher-transmittingoutput couplers were tested, it can easily be deducedfrom the trends in the obtained data that laser operationshould be difficult to achieve for output coupler trans-missions greater than 10%. Furthermore, as the crys-tal temperature is increased, a decrease in upper-statelifetime also causes a shift of the optimum output cou-pling to smaller values, giving rise to the crossover be-tween the 1% and the 3% data near 20 ±C, as shown inFig. 9.

Because attaining lower crystal temperatures at thesame time necessitates more aggressive cooling require-ments, there is a trade-off between obtaining better powerperformance and increased complexity of the laser setup.What is more, lower-temperature operation calls for theneed to purge the crystal surfaces with dry nitrogento prevent water condensation. A recommended oper-ating temperature where fully satisfactory laser perfor-mance can be expected with modest cooling is 20 ±C,which is above the dew point of water under normalconditions. The mode-locking work carried out with theCr:YAG laser and reported earlier was therefore done at20 ±C.16

7. ESTIMATION OF THE EMISSIONAND EXCITED-STATE ABSORPTIONCROSS SECTIONSThe presence of ESA is a serious limiting factor of ef-ficient laser operation. Using the laser data presentedabove, one can estimate the absolute magnitude of thestimulated emission cross section se and the ESA crosssection sESA. To do so, we used the model of a cw laseraccounting for ESA and ground-state absorptions reportedby Payne et al.4 Assuming that the pump and laser spotsizes remain unchanged inside the gain medium, the ex-pressions for the slope efficiency habs and the thresholdabsorbed pump power Pabs

th become

habs ­lp

lchp

√1 2

sESA

se

!√T

T 1 L

!, (8)

Pabsth ­

psvp2 1 vc

2dhnpsT 1 Ld

4se

√1 2

sESA

se

!tf hp

, (9)

respectively. In Eqs. (8) and (9), vp and vc are the av-erage pump and the laser spot sizes, respectively, hnp isthe pump photon energy, T is the fractional transmissionof the output coupler, L is the fractional round-trip pas-sive cavity loss, se is the stimulated emission cross sec-tion, sESA is the ESA cross section, tf is the fluorescencelifetime of the transition, hp is the pumping efficiency,and lp and lc are the pump and laser wavelengths, re-spectively. The role of ESA in this model is accountedfor by replacement of the emission cross section se withan effective cross section seff given by seff ­ se 2 sESA.The pumping efficiency hp, defined as the fraction of theabsorbed pump photons that populate the upper laserlevel, is approximated to be unity because the excited-state absorption of the pump photons has a fast relax-ation time compared with that of tf and the pump modeprofile, calculated in Section 3, is completely contained in-side the laser mode volume in the crystal. Also note thatassuming the pumping efficiency to be unity gives an up-per bound to the ratio of the ESA to emission cross sec-tions. In writing these equations we have also ignoredthe presence of the ground-state absorptions present inthe original form of the equations in Ref. 4, as no suchsignificant process exists in the case of the Cr:YAG gainmedium. The values of the known parameters appearingin Eqs. (8) and (9) are listed in Table 1. The small varia-tion in lifetime between 3 and 20 ±C was also neglected inthe following calculations.

By multiplying Eqs. (8) and (9) together one can solvese solely in terms of the fractional transmission, the ab-sorbed threshold pump power, the slope efficiency, andother known parameters appearing in Table 1 as

se ­p

4hclc

svp2 1 vc

2dtf

TPabs

thhabs

­ 16.21 3 10219sW cm2dT

Pabsthhabs

. (10)

Column 5 of Table 2 lists the various values of se

thus calculated. The first four columns consist of experi-mentally measured parameters from the laser efficiencydata of Section 5. The calculated value of the stimulatedemission cross section, averaged over all the measureddata points, is se ­ s0.95 6 0.1d 3 10219 cm2. This es-timation is approximately three times smaller than thepreviously reported value.19 This result compares favor-ably with the value of 0.75 3 10219 cm2 calculated withthe emission spectroscopy data in Section 2. More inter-estingly, the calculated emission cross section from only

Table 1. Values of the KnownParameters Appearing in Eqs. (8) and (9)

vp s mmd vc s mmd lp s mmd lc s mmd hp s1d tf s msd

47 54 1.06 1.45 1 3.4

936 J. Opt. Soc. Am. B/Vol. 12, No. 5 /May 1995 Sennaroglu et al.

Table 2. Values of the Emissionand ESA Cross Sections Calculatedwith the cw Laser Efficiency Data

Temp T Pabsth habs se

(±C) (%) (W) (%) s310219 cm2d sESAyse

3 1.0 0.755 0.293 0.733 0.1213 2.0 1.085 0.421 0.692 0.0733 3.1 1.290 0.405 0.962 0.2343 8.1 2.980 0.292 1.511 0.543

20 1.0 0.844 0.259 0.700 0.22320 2.0 1.215 0.342 0.718 0.24720 3.1 1.543 0.305 1.009 0.42320 8.1 3.665 0.269 1.258 0.579

Fig. 10. Variation of the output power as a function of theemission wavelength for various intracavity tuning elements.

the 1% and 2% output coupler data is within 5% of thespectroscopically determined value.

Before the ESA cross section is calculated, the passiveround-trip cavity loss needs to be estimated. We do thisby using the fact that the absorbed threshold pump poweris proportional to the sum of the output coupler transmis-sion and round-trip passive cavity loss [Eq. (9)]. Usingthe cw laser data presented in Section 5, we calculate anaverage value of 1.2% for the round-trip cavity loss. Withthe stimulated emission cross section and the cavity lossthus determined, we can then calculate the ESA cross sec-tion by using Eq. (8) and by assuming that the pumpingefficiency is approximately unity. Column 6 of Table 2shows the values of the sESAyse calculated in this way.The average value obtained is 0.31 6 0.07, in reasonableagreement with what was reported earlier.12

After correcting for the measured 0.12% Brewsterlosses from the crystal surface, we concluded that theloss that was due to the crystal was approximately 1.1%.By further assuming that the estimated round-trip crys-tal loss of 1.1% was distributed over the crystal length,one can deduce the figure of merit (FOM) of the Cr:YAGgain medium, defined according to

FOM ­ a1.06ya1.45, (11)

where a1.06 is the low-signal absorption coefficient of thepump photons (1.5 cm21 in our case) and a1.45 is relatedto the cavity loss L through

a1.45 ­ 212l

lns1 2 Ld , (12)

with l being the crystal length. We calculated a figure ofmerit of 540 for the crystal, using Eqs. (11) and (12).

8. TUNING CHARACTERISTICSOF THE Cr:YAG LASERThe cw Cr:YAG laser, having only a few percent saturatedround-trip gain during oscillation, is highly susceptibleto even small amounts of loss introduced into the cav-ity. Because of this, it is extremely difficult to mapthe intrinsic tuning profile of the cw laser as a functionof wavelength because any intracavity element in prac-tice has some small amount of residual loss. Figure 10shows the variation of the output power as a functionof the resonator emission wavelength for a fixed inci-dent pump power of 5.6 W and 1%-transmitting outputcoupler at 20 ±C when a number of different intracavitytuning elements are used. For comparison, the outputpower obtained under identical conditions from the free-running cavity is also included. In the case of the SF-14and fused-silica prisms, wavelength-dependent materiallosses in the prisms severely affect the cw performance ofthe laser, shifting the peak emission wavelength out toapproximately 1.5 mm. These material losses stem fromthe OH2 content. The prisms provide coarse tuning ofthe laser, the measured linewidth being ,1 nm. We ob-tained the broadest tuning range of the laser by employingthe Brewster-cut SF-14 prism, positioned at minimumdeviation on the high-reflector side of the cavity. Thetuning range, which extended from 1.34 to 1.57 mm, wasessentially optics-coating limited. In the case of thefused-silica prism, even though the overall efficiency atthe peak emission wavelength was higher, the laser hadmore limited tuning range owing to greater losses ap-proaching the 1.4-mm region. For the SF-14 and thefused-silica prisms the additional loss introduced into thecavity was estimated to be 1.4 and 0.2%, respectively.

A grating (Bausch & Lomb), having 830 groovesymm,with a blaze angle of 30± (blaze wavelength of 1.2 mm),was placed at Littrow configuration to replace the high re-flector for tuning the laser. In this case, there was negli-gible wavelength-dependent loss in the wavelength regionof interest but considerable fixed loss owing to scatter-ing off the surface, amounting to an estimated 3.8% addi-tional intracavity loss. Because of the higher dispersionof the grating, a narrower linewidth (0.4 nm) could be ob-tained. As can be seen from Fig. 10, the linewidth wasnarrow enough to resolve local dips in the tuning range ofthe laser, believed to be due to atmospheric absorptions.Even though this has not been attempted, we believe thatthis structure in the tuning curve could be eliminated bypurging the laser cavity with dry nitrogen gas.

9. CONCLUSIONSIn this paper a detailed characterization of a cw Cr:YAGlaser, pumped by a cw Nd:YAG laser and operatedbetween 3 and 36 ±C, has been described.25,26 The sen-sitivity of the output power to variations in output cou-pling transmission, crystal temperature, and emissionwavelength was studied. At 3 ±C, where the best cwperformance was obtained, as much as 1.9 W of use-ful output power was obtained at 1.45 mm with a 2%-

Sennaroglu et al. Vol. 12, No. 5 /May 1995/J. Opt. Soc. Am. B 937

transmitting output coupler. The broad cw tuning rangedemonstrated between 1.34 and 1.57 mm should make theCr:YAG laser useful in several optical communication ap-plications. We also believe that the tuning range, whichwas essentially optics limited in our experiments, can beextended to beyond 1.57 mm by use of different mirrorsets. Finally, using the cw laser data, we made estima-tions of the emission and ESA cross sections at 1.45 mmand compared them with the previously reported results.To the best of the authors’ knowledge, the wavelengthdependence of the ESA cross section across the lasertuning range is not known. However, with a low-lossintracavity tuning element it may be possible to obtainthis information by performing the cross-section calcula-tions outlined in Section 7, using cw laser data gatheredat different wavelengths.

ACKNOWLEDGMENTSWe thank Dennis Peressini of Union Carbide, Inc., forproviding the Cr:YAG sample used in the fluorescencestudies. This research was supported by the MaterialsScience Center of Cornell University and the U.S. Depart-ment of Energy under the auspices of contract W-7405-Eng-48.

*Present address, Department of Physics, Koc Univer-sity, Istinye, Istanbul 80860, Turkey.

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