Transient population dynamics in flashlamp pumpedsensitized erbium glass lasers

Matjaz Lukac

Erbium population dynamics in ytterbium sensitized phosphate glass is studied by measuring transientchanges in laser probe transmission during flashlamp pumping. The influence of energy loss channels such asexcitation cumulation and nonlinear fluorescence quenching on the flashlamp pumping efficiency is observedto be relatively small. The decrease of the pumping efficiency at high input energies can be attributed mostlyto the blue shift in the flashlamp output radiation spectrum.

I. Introduction

Lasing from erbium doped glass provides a usefulcoherent source at the eye-safe wavelength of 1.54Mm.'Since the efficiency of direct flashlamp pumping ofEr3+ is low, codoping with sensitizer ions is necessaryto obtain lasing at room temperature. 2 3 The majorsensitizer ion is ytterbium, which absorbs in the spec-tral range of 850-1100 nm where the erbium ion isrelatively transparent. Additional sensitizers such asNd3+ and Cr3+ are also sometimes added to improvepumping in the visible spectrum.3 4

Investigations1 into inverse energy storage regulari-ties have shown that the dependence of the erbiumpopulation inversion vs specific absorbed energy dif-fers from the calculated dependence when only deple-tion of the erbium ground state is taken into account.In a phosphate glass, 1.5 times higher input energythan calculated had to be applied to achieve an inver-sion of 70% of Er3 + ions, while in germanate glasses a50% inversion could not even be reached. This effecthas been explained by the excitation cumulation trans-fer through the process Yb (2F5/ 2- 2F7 /2) - Er (WI13/2-4F9/2), where Yb3+ ions transfer their energy to thealready excited Er ions. Similarly, nonlinear quench-ing of the luminescence from the Er 4I13/2 level canoccur particularly at higher erbium concentrations be-cause of the interaction between erbium ions in the

The author is with ISKRA-Electrooptics, P.O. Box 59, LjubljanaY-61210, Yugoslavia.

Received 27 April 1990.0003-6935/91/182489-06$05.00/0.© 1991 Optical Society of America.

4I13/2 excited states.5 Other channels of energy lossthat have been identified are, for example, the erbiumto ytterbium energy back transfer through the processEr (I11/2-I15/2) - Yb (

2F 7 /2-2F 5 /2 ) (Refs. 1 and 6)

and the erbium 4I13/2 excited state absorption.6 7

To study the effect of energy loss channels on erbi-um phosphate glass lasers we carried out measure-ments of the erbium transient population dynamics ina flashlamp pumped (Nd,Yb,Er):phosphate glass. Weshow that in the studied sample excitation cumulationand nonlinear quenching have relatively low influenceon the erbium energy storage and that a simple theo-retical model is sufficient to describe the relativelycomplex process of erbium excitation.

11. Theory

The sample used in the experiment is a Nd3+ andYb3+ codoped erbium phosphate glass (Kigre QE-7).Our general measurements indicate that the glass sam-ple contains approximately 1 X 101 9-cm-3 Er 3 +, 1 X1019 -cm-3 Nd 3 +, and 1 X 102 1 -cm-3 Yb3 + ions. Theenergy level scheme relevant to the Er3+ pumping isshown in Fig. 1.3 The laser action of Er3+ at 1.54 ,m isproduced by the resonant transition 4I13/2-4I15/2.The fluorescence of higher states is practically fullyquenched by the process of nonradiative multiphononrelaxation, which has a rate of 105-107 s 1.1 Besidesdirect pumping of erbium absorption bands, the exci-tation of erbium is carried out through the sensitizerions Yb3+ and Nd3+. The Yb3+ ion absorbs into the2F5/2 band from where a transfer occurs to the 4I11/2band of Er 3 +. The Yb 2F 5/2 band can also be pumpedby the transfer (with a rate of 105 s1)1 from the 4F3/2band of Nd3 +, which has been populated by decay fromthe absorption bands of Nd3+ in the visible.3 Virtuallyall the transferred energy arrives in the 4I13/2 band of

20 June 1991 / Vol. 30, No. 18 / APPLIED OPTICS 2489

12

'111I2

10

'E 8

U

La

C)

C-aJ

2

0

I5I2

. 4 11/2lii4113/2-LZ19 /2

Nd

2F72

Yb

]I13/2

1.54,upmlasertransition

I 15/2

ErFig. 1. Energy level and transfer diagram for lower levels of Nd3+,

Yb3+, and Er3 + ions in a glass host.

erbium (the upper laser level), which has a spontane-ous emission lifetime of -8 ms.3 Our previous mea-surements8 have shown that, in the case of flashlamppumping, the excitation through Yb3+ ions is the majorerbium-ion pumping process and contributes -85% tothe total erbium inverse energy storage. The contri-bution of neodymium sensitizers to erbium energystorage was observed to be relatively small.

A number of simplifying assumptions will be madeto describe Er3+ upper laser level pumping. Sincemost of the Er3+ ions are excited via Yb3+ sensitizerions, either through the Yb:Er or Nd:Yb:Er chain weneglect direct erbium-ion pumping. We assume thatthe multiphonon relaxation between Er3+ states 4111/2and 4I13/2 is faster than the sensitization process. Inthis case all the Er ions are in either excited laser level 2or ground level 1 with corresponding population densi-ties n2 and n1. Since the 4I11/2 Er3 + level is assumed tobe empty, we ignore the Er (4I11/2-4I15/2) - Yb (2F7/2-2 F5 /2 ) back transfer process. 9 The Yb 2F5/2 and 2F7/2levels are represented by population densities N2 andN1, respectively. The evolution of the normalizedpopulation inversion densities n = (n2 - nl)/no and N= (N2 - N1)/No where no = n2 + n1 andNo = N2 + N1 , isdescribed by the following rate equations:

dn (1 + n)d t '

TEr

dN=-r W(1 + N)(1 -n)- (1+ N)dt Tyb

(lb)

sensitization rate W8(s-1 ). The last term in Eq. (lb)describes flashlamp pumping of ytterbium which isassumed to vary in time proportionally to the flash-lamp discharge current10; tp is the flashlamp currentpulse duration as measured at the 10% pulse height. Itis assumed that N2 << N 1 . The proportionality con-stant D measures the strength of the pumping anddepends, among other factors, on the flashlamp inputenergy and output radiation spectrum. Parameter rrepresents the ratio of Er3+ and Yb3+ ions, r = no/No.Note that in Eqs. (1) we ignored excitation cummula-tion as well as nonlinear quenching. This simplifica-tion will be justified by a relatively good agreementbetween experiment and model.

In our model a constant rate W, is assigned to theYb:Er energy transfer process. In reality, a wide dis-persion of collection rates by Er3+ sites from Yb3+donor surroundings exists.1" At large interionic dis-tances energy is transferred through the multipoleelectric interactions. On the other hand, our investi-gations12 into ion pair interactions in other rare earthdoped systems indicate that the coupling between theclosest ions is larger than expected from the simpledipole-dipole interaction, and probably is the result ofan exchange interaction. As a result of the dispersionin collection rates, the Er3+ ions with higher rates areexcited initially and then do not participate in thetransfer process because of lack of energy migration inthe erbium subsystem. This effect can lead to a fastdecrease in the sensitization rate.1

The value of interest in Q-switched lasers is themaximum inversion nmax that can be achieved in a lasermedium with a flashlamp pulse of specific input energyEin. When pumping processes are short compared toTEr, the change in n can be described by

dn =(2)

where Wp(s-1) is a time dependent pump rate. Notethat Wp(t) corresponds to the product W, (1 + N(t)] inEq. (1). Maximum inversion density nmax that can beobtained with a single pump pulse can then be ex-pressed as

nmax = 1 - 2 exp(-A), (3)

where A represents the pump integral defined as theintegral of the pump rate over the pump pulse duration

A = Wpdt. (4)

Note that when a laser is operating in a free oscillationmode the population inversion increases during pump-ing only until it reaches the laser threshold value nt.In situations when the total pump integral is largerthan threshold pump integral At defined by

= -In( - nt)

Here rEr and rYb are, respectively, the lifetimes of theEr 4I13/2 and the Yb 2F5/2 excited states. The processof sensitization is described by an average constant

(5)

the remaining difference (A - At) is used up for laseroscillation. It can be shown8 that when pump integralA is a function only of the flashlamp input energy but

2490 APPLIED OPTICS / Vol. 30, No. 18 / 20 June 1991

+ D(l - N) t exp0.4t 0.4t( P) (_ t J

not, for example, of the population inversion or laserphoton density, the following relation exists betweenthe total pump integral A and the output energy Eout ofthe laser oscillator:

Eo,(Ei.) = K[A(Ei.) - At],

where

K = 2 Vhvno0-1 (1 -no).

4

3. 5

3(6)

2. 5

(7) A 2

Here, V is the laser resonator volume, hv is the lasertransition photon energy, y is the total fractional pho-ton loss in a single round trip passage inside the resona-tor, and yl represents the fraction of photons emittedas useful output of the device. Both proportionalityparameter K and threshold pump integral At can becalculated from the basic laser material and resonatorproperties. The dependence of total pump integral Aon the input energy can thus be obtained by measuringthe laser output vs input energy characteristics.

When the strength of pumping D is a linear functionof Ein, our model assumes that the maximum inversionis related to the input energy by

nmax = 1 - 2 exp(- aEin), (8)

where a is a proportionality constant. By measuringmaximum inversion for different input energies it ispossible to check the validity of Eq. (8) which takesinto account only the depletion of the ground state. Adeviation of the experimentally measured relationfrom that assumed by Eq. (8) would indicate eitherthat D is a nonlinear function of Ein or that at highererbium inversions, loss processes occur, such as excita-tion accumulation or nonlinear quenching. To distin-guish between these two effects, we have recently car-ried out output energy measurements of the erbiumlaser operating in a free-oscillation mode. Because oflack of space, only some results are presented here,while the details are described elsewhere,8 where thesame flashlamp pumping conditions as in the presentstudy (see Sec. III) were applied. The laser resonatorconsisted of two flat mirrors separated by 14.5 cm withoutput mirror reflectivity of 85%. The dependence ofpump integral A on Eim as calculated from the laseroutput performance is for different pulse durationsshown in Fig. 2. No lasing below Ein = 60 J could beobtained for the shortest pulse duration in our experi-ment of tp = 0.1 ms. As can be seen, the pumpingefficiency drops at short pulse durations and at highinput energies. Note that the pump integrals shown inFig. 2 were calculated from the laser oscillation perfor-mance during which the erbium inversion is constant(i.e., n = nt)..

Therefore, the decrease in the pumping efficiencycannot be explained by the excitation cumulation ornonlinear quenching. We explain this effect by thedependence of the output radiation spectrum on theflashlamp power density. Namely, a total pulsedlamp's spectral output distribution is determined bypower density J, defined by J = Ein/(tpS), where S isthe internal surface integral of the lamp's discharge

0.5 / . .

0 10 20 30 40 50 60

Ei, J]Fig. 2. Dependence of the erbium pump integral on the flashlamp

pulse duration.

region.10 Both line radiation due to discrete transi-tions between bound xenon energy states and continu-um of radiation due to the recombination of free elec-trons and xenon ions are present in a pulsed xenonflashlamp spectral output. Line spectra in the nearinfrared are more dominant at lower power densities,while at high power densities the continuum radiationin the visible dominates. Our measurements, not de-scribed here, of the output radiation spectral distribu-tion of the particular flashlamp employed in our ex-periment have shown that the line spectrum in thenear infrared region is for the pulse duration of tp = 2.1ms approximately 2.5 times larger than in the case of tp= 0.1 ms.13 Since erbium ions are pumped mostlythrough Yb ions which absorb in the near infraredregion, low flashlamp power densities with outputspectrum shifted to longer wavelengths are more effi-cient.

Ill. Experimental

A cylindrical 3- X 50-mm erbium glass rod waspumped by a 3-mm bore, 40-mm arc length xenonflashlamp with a cerium doped quartz envelope. Theflashlamp pulse forming network provided criticallydamped pulses with adjustable pulse durations tpwithin a 0.1-2.1-ms range. Input energyEin was deter-mined by relation Ein = C X U2/2 where C is thedischarge capacitance and U is the initial voltage onthe capacitor. The glass cylindrical pumping cavitywith the outside dimensions of 15 X 43 mm, and wallthickness of 1 mm, was on the outer surface coated withchemically deposited silver. Population changes ofthe erbium 4I13/2 and 4I15/2 levels were monitored bymeasuring transmission changes at 488- and 473-mmargon laser lines. The transmission of the 488-nm lineundergoes a transient increase, and the 473-nm lineshows a transient decrease during flashlamp pumping.

20 June 1991 / Vol. 30, No. 18 / APPLIED OPTICS 2491

This is because the 488-nm line excites a transitionfrom the erbium ground state, and the 473-nm lineexcites a transition originating on the upper erbiumlaser level. We assign the absorptions at the 488- and473-nm wavelengths to the 4I 15/ 2 -4 F7 /2 , and 4I13/2-2K15/2 erbium transitions, respectively. It is assumedthat only these two transitions are excited and that thecontribution of other erbium lines to the laser probeabsorption is relatively small. From the observedtransmission changes it is estimated that the corre-sponding absorption cross sections for the two lines areapproximately a(488 nm) = 6 X 10-21 cm2, and a(473nm) = 20 X 10-21cm2. The applied probe argon laserpower was kept below 1 mW, which was found to be lowenough not to upset the erbium population apprecia-bly. The transmitted argon laser light was isolatedfrom the strong flashlamp light with a Spex Minimatesingle-grating monochromator. The light from themonochromator was detected with a Si photodiodecoupled to a waveform analyzer which could store andaverage transmission traces.

IV. Results

Figure 3(a) shows a typical transient change in thetransmitted intensities of the laser probe lights at 473and 488 nm after the onset of a flashlamp pulse. Forthe case shown in Fig. 3, a flashlamp pulse of durationtp = 0.15 ms was applied. As can be seen, the peaktransmission at 488 nm (which corresponds to theminimum of the erbium ground state population) andthe minimum transmission at 473 nm (correspondingto the maximum of the erbium 4I13/2 level population)occur within the experimental error of 50 ,us at thesame time. This is in agreement with our initial as-sumption that all Er3+ ions are on either the upper orlower laser level. The peak inversion is reached -0.7ms after the conclusion of the flashlamp pulse. Inagreement with this observation, it is at this time thatthe threshold output pulse is emitted when the erbiumrod is placed inside a laser resonator [see Fig. 3(b)].

When the population dynamics is monitored by the488-nm probe light, the inversion population n is relat-ed to transmitted intensity I of the probe laser light bythe following expression:

Imiln(t) =2 ,- 1 (9)

In( min \max /

where Imin is the measured minimum intensity throughan unexcited material (n = 1), while Imax represents themaximum transmitted intensity for the case when allEr3+ ions are in the upper laser level (n = 1). Ourmeasurements show that in the case of tp = 2.1 ms, thetransmission gets saturated for pump energies above-70 J. In our work we assume that this saturatedtransmission corresponds to the case when all Er ionsare excited. Note also that the inversion as deter-mined from the transmitted intensity variation repre-sents an average over the length of the laser rod.

1.3

LU7-

0 1 2 3 4

TIME (msec)

Fig. 3. (a) Transient change during flashlamp pumping in thetransmitted intensities at 488- and 473-nm laser probe wavelengths.The transmission curves represent the average of thirty-two traces.(b) Flashlamp pulse output radiation intensity as measured with aGe photodiode. The arrows indicate the time when the laser thresh-old output pulse is emitted when the erbium rod is placed inside a

resonator.

The evolution of n as obtained from the measuredtransmitted intensity variations are for several flash-lamp input energies and for the pulse duration of tp =150 ,us shown in Fig. 4. The solid lines represent thetheoretical fit on n(t) obtained by numerical integra-tion of Eqs. (1). The following values were used in thefit: 1rYb = 3 ms (Ref. 3) and r = 1/80. The bestagreement with the data for all pumping strengths wasobtained with rEr = 7.5 + 0.1 ms and W, = 2.3 (1 + 0.1)105 s1. Note that the population decay at differenterbium inversions is adequately described by a singleerbium 4I13/2 level decay time indicating that nonlinearquenching is not important at erbium concentrationsof 1 X 1019 cm- 3 . A slightly lower decay time thanobserved in other erbium glasses with no Nd sensitizermight indicate that a back transfer to the 4I15/2 of Ndoccurs. 3

Our data are not exact enough to confirm any exis-tence of higher initial sensitization rates resulting fromthe nearest Er:Yb neighbor interactions. However,Fig. 3 shows that the sensitization process can be de-scribed quite adequately by the average constant sen-sitization rate W Approximately 10-2 Yb3+ ionsneed to be excited to achieve full erbium populationinversion. The rate of the erbium inversion changeWp is, therefore, of the order of 103 s-1.

As can be seen from Fig. 2, the functional depen-dence of pumping area A can be approximated by alinear function only at low power densities. In partic-ular, for the input energy range of 0-50 J the linear

2492 APPLIED OPTICS / Vol. 30, No. 18 / 20 June 1991

1

1

0 -

0 2 4 6 8 10

Time (msec)

Fig. 4. Measured (circles) and calculated (line) temporal evolutionof the erbium inversion during flashlamp pumping of pulse duration

tp = 0.15 ms for several flashlamp pumping levels.

0.5

nmxo

-0.5

10 20 30 40 50 60

E,, [J]Fig. 5. Measured maximum erbium inversions as a function of theinput energy for the flashlamp pulse durations of tp = 2.1 ms (circles)and tp = 0.1 ms (triangles). Solid lines represent the theoreticalcurves for pumping with flashlamp pulse durations of t, = 2.1 ms (a),0.9 ms (b), and 0.3 ms (c) as calculated from the measured pumpintegrals. The dashed line represents the laser threshold inversion

of nt = 0.4.

relationship exists only for the long pulse duration of tp= 2.1 ms. It is only for these pumping conditions thatthe maximum inversion is expected to increase withthe input energy according to Eq. (8). The measuredmaximum inversions, as obtained from transmissiontransients, are for pulse duration of tp = 2.1 ms and tp= 0.1 msec, as shown in Fig. 5. Also shown are thepredicted maximum inversion curves as calculatedfrom Eq. (3) with the measured pump integrals shownin Fig. 2. It is evident that the measured values for tp= 2.1 ms agree well with those predicted by Eq. (8).Within the experimental error, no appreciable devi-

ation can be observed at high inversions, indicatingthat the effect of excitation cumulation is relativelysmall. On the other hand, the shift of the pump spec-trum to lower wavelengths at high power densitiesresults in much less efficient pumping with tp = 0.1 mslong pulses. For this pulse duration, the measurederbium maximum inversion is for input energies up to50 J below the particular laser resonator thresholdinversion of nt = 0.4. This is in agreement with theobservation that no lasing could be obtained with tp =0.1 ms long pulses.

We point out that as the 2F5 /2 manifold of Yb fills,there may be an upconversion back transfer to Nd,which could also lead to lowered pumping efficiency inEr at high pumping levels. However, measurementsof the lifetime of the Yb fluorescence for various Ndconcentrations have shown that the back transfer timeis too long (of the order of 10-2 s) to have an apprecia-ble effect on the population of the 2F/ 2 manifold ofYb.3

VI. Conclusion

The energy transfer dynamics from Yb3+ to Er3+ in aphosphate glass was studied by measuring transientchanges in laser probe transmission during pulsedflashlamp pumping. Measurements show that a sim-ple rate equation model where the sensitization pro-cess is described by a single constant rate of W, = 2.3 X105 s-1 adequately describes the pumping process. Noevidence of the nonlinear fluorescence quenching wasobserved.

In the studied erbium glass the contribution of theexcitation cumulation and nonlinear fluorescencequenching to the efficiency decrease at high inputenergies is relatively small. The decrease in thepumping efficiency can be attributed mostly to theblue shift in the flashlamp output spectrum at highflashlamp power densities.

The author also works at the Josef Stefan Institute.

References

1. V. P. Gapontsev, S. M. Matitsin, A. A. Isinev, and V. B. Krav-chenko, "Erbium Glass Lasers and Their Applications," Opt.Laser Technol. 14, 189-196 (Aug. 1982).

2. E. Snitzer and R. Woodcock, "Yb 3 +-Er3 + Glass Laser," Appl.Phys. Lett. 6, 45-46 (1965).

3. J. G. Edwards and J. N. Sandoe, "A Theoretical Study of theNd:Yb:Er Glass Laser," J. Phys. D, 7, 1078-1095 (1974).

4. S. G. Lunter, A. G. Murzin, M. N. Tolstoi, Yu. K. Fedorov, and V.A. Fromzel, "Possibility of Improving the Efficiency of LampPumping of Erbium-Glass Lasers," Opt. Spectrosc. USSR 55,345-347 (1984).

5. T. T. Basiev et al., "Radiative and Nonradiative TransitionsExhibited by Er3+ Ions in Mixed Yttrium-Erbium AluminumGarnets," Sov. J. Quantum Electron. 6, 796-799 (1976).

6. V. P. Gapontsev, S. M. Matitsin, and A. A. Isineev, "Channels ofEnergy Losses in Erbium Laser Glasses in the Stimulated Emis-sion Process," Opt. Commun. 46, 226-230 (1983).

7. R. I. Laming, S. B. Poole, and E. J. Tarbox, "Pump Excited-State Absorption in Erbium-Doped Fibers," Opt. Lett. 13,1084-1086 (1988).

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8. M. Lukac and M. Marincek, "Energy Storage and Heat Deposi-tion in Flashlamp Pumped Sensitized Erbium Glass Lasers,"IEEE J. Quantum Electron. 26, 1779-1787 (Oct. 1990); M. Lu-kac and M. Marincek, "Effect of Sensitizers on FlashlampPumping Efficiency and Heat Deposition in Er Glasses," Proc.Soc. Photo-Opt. Instrum. Eng. 1277, 40-47 (Mar. 1990).

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10. ILC Technology, "An Overview of Flashlamps and CW ArcLamps," Technical Bulletin 3.

11. W. Q. Shi, M. Bass, and M. Birnbaum, "Investigation of theInteractions Between Dissimilar Ions in (Er,Nd): Y3A560 1 2," J-Opt. Soc. Am. B 6, 23-29 (1989).

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13. M. Lukac, "Energy Storage and Population Dynamics in Flash-lamp Pumped Sensitized Erbium Glass Laser," in Proceedings,OE/Lase 91, Symposium on High Power Lasers (Los Angeles,Jan. 1991), paper 1419-07.

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