PHYSICAL REVIEW B VOLUME 51, NUMBER 2 1 JANUARY 1995-II

Excited-state-absorption and upconversion studies of Nd +-doped single crystalsY3A15O t z, YLiF4, and LaMgA1» O t9

Y. Guyot, H. Manaa, J. Y. Rivoire, and R. Moncorge

N. Gamier, E. Descroix, M. Bon, and P. LaporteLaboratoire du Traitement du signal et de I'Instrumentation, Universite de St. Etienne, URA 842 CNRS, 42023 St. Etienne, France

(Received 10 May 1994; revised manuscript received 22 September 1994)

In this paper we derive expressions for the laser slope efficiency and the threshold absorbed pump

power which explicitly include excited-state absorption in the pump as well as in the laser-emission-

wavelength domains. They are applied to the case of the diode-pumped Nd +-doped laser systems and,

along with expressions allowing the calculation of excited-state-absorption (ESA) cross sections within

the framework of the Judd-Ofelt theory, they provide a theoretical framework for the second part in

which we present both experimental measurements and theoretical calibrations and an analysis ofexcited-state-absorption spectra in the stimulated emission as well as in the pumping domains of Nd

doped Y,A1,0», YLiF4, and LaMgA1»O» laser crystals. The results indicate that ESA in the infrared

metastable state of Nd + in these materials is negligible at the main laser wavelengths but can be more

significant if it takes place, following some energy-transfer induced-excitation process, in higher-lying ex-

cited states. The analysis of these ESA within the Judd-Ofelt formalism shows a general agreement

better than 50go between the experimental data and the theoretical predictions. This is used to estimate

the inhuence of ESA in the pumping domain on the laser performance of the materials. It is found that

it contributes but that it does not significantly perturb this laser performance, and that this effect is much

less than some upconversion energy transfers that limit the Auorescence excitation efficiencies and

reduce the energy-storage capacities by the reduction of the effective fluorescence lifetimes of the laser

metastable level.

I. INTRODUCTION

The study of excited-state-absorption (ESA) ormultiphoton-sequential-absorption phenomena generallyallows the completion of classical one-photon ground-state-absorption (GSA), ground-state-emission, anddynamical-fluorescence studies. ESA allows us to probehigh-energy-lying excited states drowned in continua,which are difficult to distinguish or to which the GSAtransition probability is too weak to be observed, and toknow more about the relaxation dynamics of the short-lived excited states, such as in plasma. '

The determination of the ESA cross sections in the ab-sorption and emission domains gives essential informa-tion about the operation mode and the performance oflaser systems based on the transition-metal ' and rare-earth ions emitting in the near-infrared spectral region.It is also very informative in the study of future laser sys-tems, so-called up conversion and photon-avalanche sys-tems, emitting in the visible range. The excited-stateabsorption of the pumping light, and the multiphonon re-laxations that follow, also could partly explain thethermal overloading processes observed at high pumpingpower in the laser rods when the operating regimechanges from a stimulated (lasing) to a spontaneous-emission regime.

No direct and quantitative study of ESA has been con-ducted so far in the case of the now well-known Nd +-

doped laser crystals Y3A1&O&2 (YACC) and YLiF& (YLF),either because no one realized the importance of it, or be-cause the experimental measurements it necessitates werenot easy to perform. To our knowledge, the only worksthat explicitly treat the ESA were conducted in glassymaterials. ' In the case of crystals, we note a nondirectmeasurement of an ESA cross section in YAG:Nd +

around 750 nm (Ref. 11) and an ESA spectrum inSrFz..Nd + around 1.06 pm. '

Thus, one did not know the real influence of thisphenomenon, so detrimental in the case of thetransition-metal-ion laser systems, ' on the laser perfor-mance of the Nd +-doped crystals and what perspectivesit could offer. One also did not know to what extent theexisting formalisms, such as the Judd-Ofelt theory, ' 'associated with the Einstein reciprocity law between theabsorption and stimulated-emission cross sections, wereable to give an account of the intrinsic cross sections ofthe optical transitions involved.

By testing a number of theoretical and experimentalmethods on well-known laser systems such asYAG:Nd + and YLF:Nd +, as mentioned above, and byapplying them to the less common and more complexLaMgA1&&O&9. Nd + (or LMA:Nd + or LNA) laser crys-tal, ' we 611 an important scientific vacancy. Moreover,by studying more carefully the relationships between theintrinsic spectroscopic properties of these materials (suchas stimulated emission and ESA cross sections, inhomo-

0163-1829/95/51(2)/784(16)/$06. 00 51 784 1995 The American Physical Society

EXCITED-STATE-ABSORPTION AND UPCONVERSION. . . 785

geneous versus homogeneous line broadening, etc.) andtheir laser performance, ' ' we are able to deduce someadditional information about their optical quality andabout the importance of eventual impurities. This can beuseful to the crystal grower spending time and money toimprove the fabrication processes.

The first part of this work is devoted to theoreticalconsiderations concerning the effect of ESA on the laserperformance and the Judd-Ofelt calibration or predictionof the ESA spectra. In the second part we first give theresults of experimental and theoretical calibrations inunits of cross sections of polarized ESA spectra that werepreviously reported in another article. ' The ESA spec-tra were recorded in the main regions of infrared-stimulated emission around 1.06 and 1.32 pm of Nd +-doped Y3AI&O&z (YAG), YLiF& (YLF), and LaMgAliiOi9(LMA) laser crystals. We then give for the same systemsESA data obtained in the blue and the red regions atwavelengths that can be important in the parametrizationof the photon avalanche process, which was enlightenedrecently, and also for the estimation of the importanceof ESA in the case of broadband flash-lamp pumping. Fi-nally, data are presented concerning the competitiveeffects of upconversion energy-transfer processes, in par-ticular when the systems are pumped by lasers, Ti-sapphire or semiconductor diode lasers, around 800 nm.

II. THEORETICAL CONSIDERATIONS

A. Effect of ESA on laser performance

In this subsection, we are going to treat the effect ofESA in the wavelength domains of laser emission (a casealready examined in the past' ) and of optical pumpingon the laser performance (threshold pump power andlaser efficiency) of a four-level laser system (for the case ofthe Nd +-doped systems emitting around 1.06 pm).

We first consider a laser crystal of thickness d within atwo-mirror symmetrical cavity with an output coupler oftransmission T and we assume stationary conditions.Then we introduce a simple model with a ground state 0and two excited states 1 and 2, in which we assume thatall of the photons absorbed in the excited state 1 are lostfor laser action, which is a pessimistic view of the prob-lem, and that there is negligible ground-state absorption(GSA) at the laser wavelength, which is justified in thecase of a four-level laser system. Of course, for a Nd +-doped laser system emitting around 1.06 mm, the levels 0,1, and 2 stand for levels I9/2 E3/2 and one of thehigher-lying excited states of the Nd + ion, respectively.o.

o and o.&

are the CAUSA and ESA cross sections at thepump wavelength; o.

&is the ESA cross section at the

laser wavelength; o., is the stimulated emission crosssection; W is the spontaneous emission rate; and ~ is theAuorescence lifetime of level 1. With these parameters,we solve, for a longitudinal pumping, the following equa-tions of evolution:

dI = —(o ~(@TO+o~iN, )Idz

G'"—1pth hvS,2o~~ 1 —eG' (4)

thlaser Pdiir( abs abs )

hvL T 2'& 1 1 eG2

Pdjff= hv 2 + G"—1 1 —e (6)

pdjff is the 1aser slope efficiency; h v~ and h vL are the ener-gies of the pump and laser photons; S is an averagecross-section area of the pump and cavity modes withinthe laser crystal; eo and e are the transparencies of thecrystal at the pump wavelength below and above laserthreshold, respectively; and G and I. are the single-passgain and losses. Knowing that,

o-~/(a —o. )—o~N d

(7)

P,„,-=(1—6 )P;„, ,

TG=L '= 1 ———52

where 6 gathers all the intracavity losses other than thatof the output mirror transmission and r is a dimensionlessparameter that measures the relative magnitude of theESA and of the stimulated-emission cross sections and isgiven by

LOem

(10)

If the losses and the output mirror transmission aresmall compared to 1, which is generally the case with cwlasers, expressions (4) and (6) for the threshold pumppower and the laser slope efficiency become

L~UL ~em 1 T (11)dif I + L T

ShvP'," = (T+25)(1 F)—

2(o, —o, )r(12)

with

(o~()+cr~i)( T+25)2(o, —cr, )

(13)

If we write S =a(co +col )/2 and assume that F is small,we find expressions close to those commonly used in theliterature. From these expressions it is clear that the

dIL =+(cr, —o i )NiILdz

dpi =o ONOI„(o—, +cr, )N, IL cr—,N, I~ —WN,dt

with N=NO+N& and IL=IL +IL N is the total iondensity, and IL+ and IL are the counter-propagating laserintensities in the cavity.

Within this framework, the threshold absorbed pumppower and the laser output power are given by the follow-ing expressions:

786 Y. GUYOT et al. 51

effect of ESA in the stimulated-emission domain can bevery important since it can reduce the laser slopeefficiency and enhance the absorbed pump power atthreshold very significantly.

To understand the inhuence of the other parameters,particularly ESA in the pumping domain, we have ana-lyzed the threshold absorbed pump power and the lasers ope efficiency as a function of the output mirrortransmission by varying the value of the optical losses I.,the parameter r, and the transparency 80. The value ofthe ratio cry/(o, ~ o—, ) has been fixed to 0.15 because itis the value that generally applies in the case of thediode-pumped 1.06-pm Nd +-doped laser materials.Moreover, this ratio does not play a significant role sinceno difference could be observed between the curves forvalues larger than about 0.05. The output mirrortransmission has been varied from 0 to 25% (it is gen-erally less than 10%), the optical losses from 0 to 10%they are generally of the order of 1%), and we worked

with transparency values of 5 and 20%. Figures 1 —3show the dependences of the laser slope efficiency and thethreshoshold pump power on these parameters. From thecurves of Figs. 1 and 2, it can be concluded that ESA inthe pumping domain has a significant effect only for rvalues larger than 0.5 and for output mirror transmis-sions larger than 5%. In the case of a stimulated-

cm, it means thatemission cross section of a few 10 ', 'tESA in the pumping region will have to be of the sameorder of magnitude to significantly perturb the laser per-ormance of the system. This inhuence is more pro-

nounced as the optical losses and the transparency of thematerial are larger, but they are values for which the sys-tems are not generally operating. From the curves of Fig.3, it is found that ESA in the pumping domain is of littleimportance compared to that of the transparency eo.For an output mirror transmission T=10%, for instance,the absorbed pump power at threshold does not vary bymore than about 3% between r =0 and 2, that is, for avery unfavorable case corresponding to L =4% ande =20%. This ip Q. is is negligible compared to the experimen-tal uncertainties which are usually of the order of 10%.

B. Judd-Ofelt calibration of ESA spectra

The E&S. cross sections between the energy levels ofthe rare-earth ions in the materials can be theoreticallydetermined from an analysis of the classical GSA spectraby applying the well-known formalism developed b Juddand Ofelt. ' ' pe y u

Nd+mIn the case of ESA taking place in the

metastable state F3/2 the electric-dipole transition4

strengths will take the form

(14)+3/2 ~') =0.8

0.7-

0.6-

0.5-

0.4-

0.3-

0.2-

0.1-

00

0.80.05 0.1 0.15 0.2 0.2L

0.7-

0.6-

0.4-

0.3-CLC3

cn 02

~ 0.1-

00 0.250.05

r 1

0.1 0.15 0.2

OUTPUT MIRROR TRANSMISSION T

FICx. 1. Thheoretical variations of the laser slope eKciency,pd;&, as a function of the output mirror tra ' ' T fransmission T for vari-ous values of the optical losses L and for {a) r =0 with co=5 or20% and (b) r = 1 and eo= 5%%uo.

(n +2) 2' e

9n 3hc

and C(n)=0 0413 fo. r YAG (n =1.82), C(n)=0. 310 forYLF (n = 1.455), and C(n) =0.0397 for LMA (n = 1.77).

The Qdata

e, parameters obtained with our own absor t'solp ion

the Nd +-ata, as well as those found in the literature in th f'n e case oe -doped YAG, YLF, and LMA crystals studied

I. The disin the following, are given in units of 10

' T blcm ln a ee disagreements between the authors generally

come from two sources or error: (1) from the method ofcalculation which can give different results dependingon whether transition strengths S or oscillator strengths ftheare used; 2 from the choice of the transitions enter'ering in

e calculation (for example, previous authors ' foundso low values for the parameter 02 because they did notinclude the absorption transitions around 350 nm).

LMA(S) and LMA(NS) refer to two kinds of Nd +-

doped LaMgA1& |0» (LMA) single crystals, near-stoichiometric (S) crystals of formula LaMg Al 0g0. 7 11.2 19

and nonstoichiometric (KS) congruent crystals of formu-la Laa Lao 9Mgo 5A1» 433O19 that were recently studied' ' fortheir particular optical and laser properties. In the fol-lowing we shall use our own set of parameters (see Table

(16)

t=2, 4, 6

(t)where U are matrix elements that can be found in theiterature' and 0, are the so-called Judd-Ofelt parame-

ters. Then the ESA spectra can be calibrated in units ofcross sections by integrating them and writing

f o EsA(~)Scarc g

=C(n)S( F3y2~J') (15)

with

D UPCONyERSIOFXCITED--STATE ABSORPTION AN

0.8

787

0-8

Q.7-O.7-

0.6 0.6-

0.5-0.5-

p 4-p.4-

Q.3

U p2& O2-

I oi-

o

9 O8

Q5

GC& os-

II

0.15 0.p. 1Qos '

t ansml SS ionOutput mirror rap.25

4 p8

~ Q.7-

& os-

Q 4-

II

o.'1Sp.o5 Q.1

transml SSl oOutput mirror0.25

o.4-

0.3Q.3

0.20.2-

0.1-

O.2S

0.1

00

I

p. 1I

o.is~, r tranSmi SSlonOutput ml rr

0.250

0 0.2p.05I

Q. iS

mission T f various values

ml ss1 on T

t ut mirror transm'ut mirror transm

as a function of the ou pu'

mCutpu

p=%8=5%(b)L=1% =

. 2. Theoretical variationof r and for (a) L = 1%, Bo= o',

SULTS AND ANALYSISIII. EXPERIMENTAL RESULT

A. Excited-state absorption

can be often evidenced yb the observa-' 'blokes visi e u

g gs. Recording o exci c-

onee

ht }1n ossible anp pMp to investigate i

tu'

n domains.

( h o1 io i hh lk

resolved spectra ethe

f t}1 ESA th lative intensities o epositions and t crea '

lines.e infrared spectra, we have in rare, ve used two

dd-Of 1 fo 1' bme othods. We have app'

lied the Jusl descri e .'b d We also have

ain-ESA spectra directly.rocedure previou y

In this

b t d d 7-ocase,

d the samples to e s upummp chamber an ef6or7mmin iadiameter, depending

th o h h-cm-

he robe beams were

GNd dd 1periments: a pulsed YA: pn cell (with Exctton y

d DCM o d 1.32 ).h drogen Raman ce

590 around 1.06 pm and D ar

am assing rthrough the rod wasp o pMol ctron pyroele

SR 250 1'

1 b1 fed into a Standard Ssigna e-ESA spectra are then g'n iven bygain-

—o X*l,ln(I„/I )=(o.Es~—o,m &

0.25 /=2

0.2-

Lal

0.15-

C)CQ

0.1-CO

00 0.05

I

0.1 O. f 5OUTPUT MMIRROR TRANSMI SS ION T

0.2 0.25

a'

he threshold absorbedG 3. Theoretical vaariations o e rr transmission or

FIf the output mirrorer as a function o e

different values of0 =20%%u( ) dco=5% ( ' ' ) and Bo 0r and L.

Y. GUYOT et al. 51

TABLE I. Judd-Ofelt parameters (units of 10 cm ) of Nd'+-doped YAG, YLF, and LMA (near-

stoichiometric S as well as nonstoichiometric NS).

YAG

YLF

LMA(S)(NS)

0.370.200.32

1.90.360.93

1.231.121.34

2.292.73.23.0

2.74.022.56

1.751.791.84

5.9754.65.16

54.844.98

2.241.802.03

rms

0.16

0.17

0.100.11

Ref.

192021

This work

2223

This work

24This workThis work

where I and I„are the transmitted intensities of theprobe beam through the rod of length I with and withoutpumping, respectively.

Then, knowing the stimulated emission cross sectionspectra o., (A, ) and the shape of the ESE spectra, the in-tensity of which IEsE(A, ) is proportional to the ESA crosssection, i.e., IEsE(A, )=ao EsA(A, ), we can find o EsA(A, ) byadjustment of the value of N and by writing

cTEsA(A, ) =o,~(A, ) —ln(I /I„)/X*l =IEsE(A, )/a . (18)

»(I /I. ) =(oGsA oEsA)&*1 . (19)

This kind of spectra allows one to directly know theexcited-state-absorption cross section as soon as theground-state-absorption cross section, o.&sA, is known ata wavelength for which ESA is negligible.

Thus, the next three subsections will present ESA re-sults in the three following interesting domains:

Concerning the ESA investigation in the visible andnear-infrared pumping domains, we have recorded cali-brated spectra more directly. The same kind of fiash-lamp pump chamber was used as a pumping source in thecase of Nd +-doped YAG and LMA but, because theYLF:Nd + laser rod was broken in the meantime andonly reduced samples were available, we had to useanother pulsed dye laser as pumping source for this sys-tem. The probe beam was that of a pulsed YAG:Ndpumped superradiant dye laser. Indeed the specialgeometrical shape of the dye cuvette used in this experi-ment allowed us to obtain a broadband amplified fIuores-cence the divergence of which was weak enough to becollected into an optical fiber and to be sent efficientlythrough the YAG or the LMA laser rod or the YLF sam-ple. At the output of the crystal, the transmitted lightwas collected by another fiber, sent onto the entrance slitof a Jobin-Yvon HRS1 monochromator and analyzedwith the help of a 512 pixels optical multichannelanalyzer from EG A G covering about 15 nm. Thisdetection system allowed us to register spectra with agood spectral resolution and also time-resolved spectrathanks to a synchronization system controlling the timeof triggering of the fIash pump and/or of the lasers.Then in the investigated pumping domains, we haverecorded transient absorption spectra:

(1) The infrared stimulated emission domains around1.06 and 1.32 pm for which we shall just complete the al-ready available data by experimental and/or theoreticalcalibrations of the ESA spectra in a cross-section unit.

(2) The visible domain around 470 and 610 nm becausethese wavelengths correspond to strong ESA transitions,F3/2~ H9/2 and F3/2 + D3/2 respectively, and also

because the GSA in these regions is relatively weak.These ESA transitions were already reported by Cairdet al. in a study about transient absorption due to colorcenters in YAG:Nd + and Nd +-doped phosphateglasses. As we shall see, we are reporting here muchbetter resolved spectra. Another reason to study the redF3/2 + D3/2 ESA transition is, as mentioned above, its

interest in photon avalanche processes which were re-ported recently.

(3) The laser diode pumping domain around 800 nm.As we shall see, because the GSA intensities were toostrong, we were unable to measure ESA experimentally inthis domain. Thus we have built ESA spectra theoreti-cally, knowing the ESA line positions, which can be cal-culated from the positions of the Stark components of theenergy levels involved in the transitions and which aregiven in the literature for each compound and usingthe Judd-Ofelt formalism, as described previously.

1. FSA in the infrared emission domainsaround 1.06 and 1.32 pm

In Ref. 15, we reported polarized excited-state-excitation spectra around 1.06 and 1.32 pm which corre-spond to

4F3/2 G 9/2 + ( 3/2 + 11/2 + + 15 /2 )

2 2 4 2

and F3/2 ~ G7/z ESA transitions, respectively. Themanifolds that appear between parentheses cannot be dis-tinguished from the G9/2 level in Nd +-doped YAG andLMA, whereas in YLF:Nd + the F3/2 + 69/2 transitionis well determined. Figure 4 recalls the energy levels ofthe Nd + ion and the transitions of interest here.

In each material, we had already noticed that the ESAintensities, for a given polarization, was very weak at thelaser wavelengths, around 1.06 ]Ltm ( F3/2~ I]]/2) aswell as around 1.32 pm ( F3/2~ I]3/2). Now we are go-

51 EXCITED-STATE-ABSORPTION AND UPCONVERSION. . . 789

S( F3/2~ G7/2 ) =0.106402+0.062904, (20)

where the JO parameters 0, are those reported in Sec. II.If E is the area of the polarization-averaged ESE spec-

tra IfsE(A, ) with p=a and o in the case of YLF andLMA, we have

f [2IEsE(A, )+IEsF(A, ) jdA,(21)

where k is the average wavelength of the transition.The ESA cross section is simply calculated for each po-

larization by using the expression

~fSA(A ) = (S„t,/E)IfsE(~ ) (22)

ing to give the maximum ESA peak cross sections andthe ESA cross sections at the laser wavelengths.

The calibration of the ESA spectra around 1.32 pmwas only made with the Judd-Ofelt (JO) formalism' ''because it was too dif5cult to extract information fromthe ESA-gain spectra that were disrupted by therotation-vibration water absorption in this region. Ac-cording to the literature' the strength of theF3/2~ G7/2 intermanifold transition should not depend

on the 06 parameter, the selection rule being~J—J'

~

~ t ~J+J' with J=—', , J'= —', and is given by

The peak ESA cross sections so calculated are gatheredin Table II. In the case of LMA, the large uncertainty onthe calculated values comes from the poor knowledge ofthe terminal levels, G7/2 or G9/2, of the ESA transitionsaround 1.32 pm. With these values we thus find that theESA cross sections at the laser wavelengths remain veryweak: less than 10 ' cm for YLF at 1.314 pm in o. and1.321 pm in m polarization and for LMA at 1.300 and1.378 pm in cr polarization, less than 0.5X10 ' cm. at1.318 pm and about 2.5X10 ' cm at 1.338 pm inYAG.

Around 1.06 pm the calibration with the Judd-Ofeltformalism is less accurate than around 1.32 pm becausethe terminal level of the ESA transition around 1.06 pmcan participate of several multiplets and also because therecorded ESE spectra do not cover the entire

4 2 2 4 23/2 9/2 3/2 + 11/2 + +15/2

ESA transitions. It is the case for YAG and LMA.Thus, the confrontation of the two methods of calibrationdescribed above was only really reliable in the case ofYLF because the observed ESA lines are assigned to theonly F3/2~ G9/2 ESA transition.

If we only take this F3/2 G9/2 ESA transition intoaccount for the three systems, we know that its strengthdoes not depend on the Q2 parameter and is given by'

where S„„is given by S„„=C(n)S and C(n) is given byexpression (16).

S("F3/2 ~ G9/2 ) =0.02130q+0.031606 . (23)

E(103c~1~

ji YLF:Nd

25l2

15

2ihhhh V 'A'wX'w& ~2

( 29Pxx x~vxxxxxwxx +g4

1

4

l

- F~

F~

7/2

+91

15'

F7/2

2F~

2 2

~2 2

17/2JI211Q15/l2%~%% X', X~ X~ %%4D

l5

25

Following the above procedure, the maxima of ESAcross sections in YLF were found to be 3.3 X 10 cmat 1.051 pm in ~ polarization and 1.75X10 cm at1.048 pm in a polarization. Using expression (18), theYLF-polarized gain-ESA spectra which are shown in Fig.5, and the values of the stimulated-emission cross sectionpeaks at 1.047 and 1.053 pm found in the m and cr polar-izations and which were reported in the literature, ' i.e.,3.7 X 10 ' and 2.6 X 10 ' cm, respectively, we havebeen led to maximum ESA cross sections of 7X 10 and4X10 cm at 1.051 and 1.048 pm in the ~ and o. po-larizations, respectively.

These values are about two times larger than those cal-culated with the first method. This factor cannot be ex-plained with only the experimental errors; two explana-tions can be considered: The Judd-Ofelt formalism is notreliable when high-energy levels are involved. This ex-planation is not completely satisfactory because the 69/2level is only lying at about 21000 cm ' and because, aswe shall see in the following, a good result has been ob-tained for an ESA transition terminating on an energylevel lying at about 28000 cm '. The calibration of the

TABLE II. Peak ESA cross sections (units of 10 cm ) inNd +-doped YAG, YLF, and LMA around 1.32 pm.

0

FIG. 4. Energy level diagram of Nd + (case of YLiF4) and

ESA transitions studied in this work.

System

YAGYLF (p=v)YLF (p =o )

LMA (p=~)LMA (p=~)

k (pm)

1.3521.3101.3281.310

1.310, 1.325

ops~ (10 cm2)

=1.0=1.9=0.7

0.9-2.00.5-1.1

790 Y. GUYOT et ai. 51

0.5-

YLF:Ndcross section at 1.049 pm in the m. polarization is estimat-ed to be about 1.2 X 10 cm by using the JO treatmentand 1.5 X 10

—zo cmz by using the gain-ESA spectra. The,stimulated-emission cross section that was used here wasan average of the values found in two kinds of LMA crys-tals' by other gain measurements, i.e., 5.9 X 10 cm atabout 1.0545 pm in the o. polarization. Here again ESAat the 1.0545-pm laser wavelength in the o. polarizationcan be neglected.

-0.51040 1045 1050 1055 1060 1065 1070

Wavelength (nm)

gain-ESA spectra is not good, leading us to reconsiderthe stimulated-emission cross sections found in the litera-ture. This appears to make sense since these values,which result from laser experiments, are certainly toolarge by comparison with the values obtained from thecalibration of the emission spectra I, (A, ) using the well-known expression

FIG. 5. Polarized gain-ESA spectra of YLF:Nd'+ recordedat T=300 K around 1.06 pm.

2. ESA spectra around 610 and 470 nm

(a) Case of YAG:Nd +. Figure 6 shows the room-temperature difference absorption spectra ln(I„ /I )

which were recorded in YAG:Nd + from 590 to 625 nmand from 440 to 480 nm for the same excitation pumppower. As in the case of the ESE spectra in the infrareddomain, these spectra are made up of several lines the po-sitions of which are in very good agreement with the onescalculated from the Nd + energy level diagram for thismaterial. In the first range, we clearly distinguish the

F3/2 D5/2 from the F3/p + D3/2 ESA transitions.The most intense line is lying at 619.4 nm and the shoul-der on its short-wavelength side well corresponds to an

1.0C!YAG:Nd

3~'P I~ (A)o~ (A, )=

g~n «„~ f [2I, (A, )+I, (A, )]dA,(24)

0.80-

0.60-

4F3/2-& 4D3/2 (l)

where r„z is the radiative lifetime and /3 the branchingratio of the considered emission transition. Indeed, byusing this expression, the maximum stimulated-emissioncross sections at 1.047 and 1.053 pm are found to beequal to 1.8X10 ' and 1.4X10 ' cm in the m. and cr

polarizations, respectively (if the Boltzmann factors aretaken into account, however, we again find values close tothe previous ones, i.e., 4. 1X10 ' and 2.4X10 ' cm ).With these values the calibration of the gain-ESA spectraleads to ESA cross sections, o EsA (1.051pm)=3. 7X10 cm and crEsA (1.048 pm)=1. 9X10cm, in much better agreement with those obtained withthe help of the Judd-Ofelt formalism. At any rate, in-dependently of the chosen stimulated-emission cross sec-tions of the laser transitions at 1.047 and 1.053 pm inNd +-doped YLF, they are about 60 and 100 timesstronger than the ESA cross sections at the same wave-lengths in the same polarizations.

In the case of YAG:Nd +, depending on the terminallevels of the ESA transitions which are taken into ac-count ( G9&z alone or with G»&2) in the Judd-Ofelttreatment, the estimated maximum ESA cross section at1.074 pm is found between 3 and 11X 10 cm . On theother hand, by using a stimulated-emission cross sectionof 7.4X 10 ' cm at 1.064 pm, the gain-ESA calibra-tion gives an ESA cross-section value at 1.074 pm of10X10 cm, in good agreement with the Judd-Ofeltprediction. As a consequence ESA at the 1.064-pm laserwavelength is negligible.

In the case of LMA:Nd +, the maximum peak ESA

0.2o- 4F3/2 -& 4D5/2 (+)

0.00-

e

%so 565 ado 665

Wavelength (nm)0.3C

YAG:Nd

625

0.25- F3/2 -& H9/2 (1)

0.20-

& 0.35-

3/2 - D5/2 + H11/2 (+)

0.05-

0.00-

4 40NI 4 OO ~ X)NXI ~ I ~ I ~

Co 4/0Wavelength (nm)

FIG. 6. Difference absorption spectra of YAG.Nd'+ record-ed at T=300 K around 620 and 470 nm.

51 EXCITED-STATE-ABSORPTION AND UPCONVERSION. . . 791

o EsA(470. 9 nm) =(3.6+1.2) X 10 cm

o Es&(619 nm) =(10.8+3.3) X 10 cm

As in the previous section the difference absorptionspectra also can be calibrated with the help of the JO for-malism, but it is a little less direct than in the case of theESE spectra because GSA has to be taken into account.The ESA cross-section spectra can now be obtained byusing the expression

TABLE III. Wavelengths of the main F,/, ~ D3/2 and

F3 /2 + H9 /2 ESA transitions found or expected around 620and 470 nm in YAG:Nd + and positions of the involved energylevels.

/2 11427 cm 11512 cm

32613 cm32662 cm32745 cm32802 cm32840 cm

/2

472.01 nm470.92 nm469.08 nm467.83 nm467.01 nm

473.91 nm472.81 nm470.96 nm469.70 nm468.86 nm

27571 cm27670 cm

619.43 nm615.65 nm

622.70 nm618.89 nm

expected line. In the second range, we observe the fol-lowing ESA transitions: F3/2 —+ D3/2+ H»/2 around

4 nm F3/2~ Ds/2 a ound 465 nm, and F3/2~ H9/24 2 4 2

around 470 nm. For this last transition, six lines over tentheoretically expected can be clearly observed. The onesexpected at 467.0 and 467.8 nm are certainly too weak tobe observed. On the other hand, the most intense line at470.9 nm is in fact made of two overlapping ones and aline at 468.87 nm is probably also overlapping with thatfound at 469.08 nm. The wavelengths of both theF3/2 ~ D 3/2 and F3/2 + H9/2 ESA transitions and

their assignments are gathered in Table III.The negative parts of the spectra correspond to GSA

lines or backgrounds; they express bleaching processesdue to depletions of the number of ions in the groundstate. Most of these GSA lines are saturated (at 459 nmfor instance), which means that the probe beam at thesewavelengths is almost fully absorbed by the rod (1=8cm) and that the ratio I„/I is not reliable. However atsome other weak GSA wavelengths k, for which ESA isnegligible, we can estimate the product N*I by using theGSA cross section oos~(A, , ) and the expression derivedfrom expression (19):

—ln(I„/I )(A,, )N*I =os (A,, )

Then we can use this factor to "directly" calibrate thedifference absorption spectra ln(I„/I ) in cross-sectionunits. In our experiment, the number of excited Nd +

ions was about 10' ions/cm, which corresponded toabout 0.75% of the total density of Nd + ions in our 1

at. % Nd -doped YAG crystal. The peak ESA crosssection is found

oEs~(A ) = (S~

2 )Ag(A, )/G +oosA(A ) (26)

where bg =in(I„/I ), 6 = fAg(k)d A/, X, anda = foos„(~)d~/X, the limits of integration for G and3 being the same and being chosen so as to cover theconsidered ESA transition, and where S„&, is calculatedby using expression (15) and the JO parameters given inSec. II.

In the case of the YLF and LMA uniaxial crystals, wealso have to take into account for expression (26) theweights of —', and —,

' of the polarizations o. and ~ in the in-

tegrals G and A. If the oscillator strength of theF3/2 —+ H9/2 ESA transitions does not depend of the Q2

parameter, the oscillator strength of the F3/2 + D3/2ESA transition only depends on this parameter and S„&,are given by

S( F3/2 ~ H9/2 ) —0.016804+0.006406 (27)

S( F3/2~ D3/2)=0. 146202 . (28)

The peak ESA cross sections in YAG:Nd are nowfound to be equal to 1.1X10 and 1.7X10 cm at470.9 and 619.4 nm, respectively. Thus, these "theoreti-cal" values are about three and six times weaker than theexperimental ones. If the first disagreement can be ex-plained in part by the experimental errors, especially inthe determination of N*l from the very weak intensity ofthe GSA lines, the reason for the second one must prob-ably be found in the error made in the derivation of theQ2 parameter, especially in YAG:Nd + in which it isabout 50% according to Krupke, but it is probablymore important.

(b) Case of LMA:Xd +. Concerning LMA:Nd +, wehave proceeded in the same way, but contrary to the caseof YAG and YLF (presented below), the theoretical posi-tions of the high-lying energy levels thus of the corre-sponding ESA lines are not well known. Furthermore, asis shown in Fig. 7, the lines in this material are muchbroader. Nevertheless, in each region, we can distinguishten lines (numbered 1 to 10) which correspond to thenumber of expected lines for each F3/2~ D3/2+ D5/2and F3/2~ H9/2 intermanifold ESA transition around605 and 465 nm, respectively. These spectra allow us todetermine a repetitive energy level spacing of about 120cm ' which we assign to the energy splitting of the twoStark components of the F3/2 multiplet. This value issmaller than that usually reported in the literature butthis disagreement can be explained by the width of theESA lines (b,v=50 cm ') and also by the multisite na-ture of this LMA system. '

Assuming a F3/2 energy splitting of the order of 120cm ' the positions of the ESA lines can be used in turnto determine the energies of the terminal levels of the as-sociated ESA transitions, of D3/2 and D, /2 for ESAaround 605 nm and of H9/2 (and probably D3/z) forESA around 465 nm. These energies are all gathered inTable IV.

The calibration of the LMA:Nd spectra was madeby using two methods: (1) From the determination of

792 Y. GUYOT et aI. 51

N l, knowing that it was very delicate because it wasdifficult to find a wavelength at which there is no ESAand not too strong GSA. The chosen wavelength was475 nm where the GSA cross section is 4. 1 X 20 and2.4X 10 cm in the o. and ~ polarizations, respective-ly. Then, the ESA cross sections are calculated by usingthe expressions (19) and (25) and it is found

11580 cm 11700 cm

TABLE IV. %'avelengths of the main F3/2~ D3/2+ Ds/2and F3/2~ 09/2( D3/2) ESA transitions found experimentallyaround 605 and 465 in LMA:Nd + and tentative positioning ofthe corresponding energy levels.

o EsA(468. 8 nm) =2. 8 X 10 ' cm

o Es&(603.3 nm) =8.3 X 10 ' cm

oEs~(463. 6 nm)=1. 1X10 ' cm

oEs&(599.8 nm)=5. 8X10 ' cm

27923 cm27989 cm28160 cm28370 cm28427 cm

616.4 nm (1)609.5 nm (4)603.3 nm (6)596.5 nm (6)593.7 nm (10)

611.9 nm (3)613.9 nm (2)607.4 nrn (5)599.8 nrn (7)597.9 nm (8)

Here, the experimental error is estimated to be 50% espe-cially on the factor N'l and also because of the choice ofthe level of zero intensity of the difference absorptionspectra. (2) From the Judd-Ofelt formalism, we havecalibrated the polarized spectra by totally integratingeach band, between 590 and 625 nm and between 450 and475 nm. The oscillator strength of the ESA transitioncorresponding to the first range is:

32960 cm33030 crn33150 cm33220 cm33340 cm33450 cm33540 cm

467.8 nrn (2)468.8 nrn (1), 466.3 nrn (3)466.3 nm (3), 463.6 nm (5)464.8 nrn (4), 462.0 nm (6)462.0 nrn (6), 459.6 nm (7)459.6 nm (7), 457.4 nm (9)457.9 nm (8), 455.4 nm (10)

S( F3)2~ D3)2+ D5~2)=0.222102+0.246004 (29)and using expression (10), the results are

o Es&( 603.3 nm ) = 14.7 X 10 cm2

0.15

4F3/2 -) 4D3/2 + 4D5/2LMA:Nd

and

o Es&(599.8 nm) = 10.6 X 10 ' cm

0.10.

0.05-C

thus in good agreement with the previous values, consid-ering the approximations made and the experimental un-certainties.

Around 465 nm, the F3/2 ~ H9/2 ESA transitionstrength is given by expression (27) and that of4F3/z D3/2 b2

0.00-;S ( F3yp~ D3y2 ) =0.00720' (30)

0.04

0.03-

sos ebs 635Wavelength (nm)

4F3/2-& H9/2

EJC

625

0.01-

0.00-~:=:=~t

1a

4.01 .Wavelength (nm)

4&O 475

FICx. 7. Polarized difference absorption spectra ofLMA:Nd + recorded at T= 300 K around 605 and 465 nm.

So, even if the latter is taken into account in thecalibration —it represents about 15% of the former —wehave found that the difference (S„~,—A ) which is in-volved in expression (26) remains negative. So, in orderto compare the results of the two methods we have pro-ceeded in another way. We have first calibrated the spec-tra with the cross-section values found above and then wehave compared the integrated cross sections. The in-tegration of the difference absorption spectra from thevalue of X*l leads to a value of 1.8 X 10 cm and that—23of the GSA spectra in the same domain to 2. 5 X 10cm which results in an ESA integrated cross section of4.3 X 10 cm, a value about 2.5 times that of1.7X10 cm derived by the JO formalism. It is not sogood as around 605 nm but it remains acceptable, takinginto account the experimental uncertainties.

(c) Case of YLF:Xd +. As mentioned previously theYLF:Nd + crystal was excited by a pulsed YAG:Ndpumped dye laser instead of a Gash lamp. The samplewas a parallelepipedic crystal (1.5X4X6 mm ) of YLF:1.5% Nd and it was excited at 585.3 nm (Exciton dyeRh 610). The resulting difference absorption spectrarecorded in the m and o. polarizations around 595 and465 nm are reported in Fig. 8.

EXCITED-STATE-ABSORPTION AND UPCONVERSION. . . 793

Though these spectra are much more noisy than in thecase of YAG:Nd +, especially around 465 nm, all the ob-served lines could have been identified. Only three linesat 464.5, 465.7, and 466.9 nm among ten could have beenobserved and assigned to F~/2~ H9/2 ESA transitions,probably because GSA is more intense than ESA at theother wavelengths. Similarly, among the four lines which

xpected for the Fs/2~ Ds/2 ESA transition around602 nm, only two of them at 601.62 and 603.64 nm havebeen distinguished. The expected line at 599.31 nm isprobably hidden in the band corresponding to thebroader Fz/2 —+ D5/z ESA transition located around 595nm, and the intensity of the line expected at 605.59 nm isprobably too weak to be detected. The positions of theselines and the energies of the levels involved in the ESAtransitions are gathered in Table V.

4F~(Z -~ 4D5]2

CO -50

-100

-150.

580 585 590 595 600

Wavelength (nm)605 610

YLF: Nd

E//C

E J.C (x4)

465 470Wavelength (nm)

FICx. 8. Polarized diferent absorption spectra of YLF:Nd +

at T= 300 K around 595 and 465 nm.

TABLE V. Wavelengths of the main F3/2 ~ D3/2 andF3/2 ~ H9/2 ESA transitions found experimentally around 605

and 465 nm in YLF:Nd + and positions of the involved energylevels.

3/2 11543 cm 11598 cm

28109 cm28220 cm

603.64 nm(599.31 nm)

(605.59 nm)601.62 nm

3/2

33016 cm33072 cm

465.7 nm464.5 nm

466.9 nm465.7 nm

Because the sample does not absorb too much, theGSA lines corresponding to the I9/2 —+ G7/2+ G»2transition appear distinctly and are not saturated. So it iseasier to estimate the factor N*l. Moreover the resultingcalculated density of excited ions, X*= 1.3 X 10'ion/cm, is in good agreement with the value which iscalculated by knowing the absorbed energy in the crystal,i.e., &*= 1.05 X 10' ions/cm . Knowing the GSA crosssections o, =o., =2X10 cm, the ~ and o. polarizedESA cross sections at 603.6 nm are

and

o Es~(603.3 nm ) =0.65 X 10 cm

o.EsA( 603.6 nm ) = 1.6 X 10 cm

For this ESA transition, the calibration with the Judd-Ofelt formalism gave ESA cross sections in very goodagreement with these values, i.e., 0.84 and 1.9X10cm in the ~ and o polarizations, respectively.

As we mentioned previously, it is precisely the"F~/2~ D3/2 ESA transition which is involved in thephotoavalanche process recently evidenced inYLF:Nd +. This process is operating at low temperatureand necessitates the presence of a very efficient ESA at awavelength where GSA is very weak. According to Fig.8 and the previous calculations, we note that at roomtemperature this ESA should be more efficient in ~ polar-ization than in o. , whereas the avalanche mechanism wasoperating at low temperature in o. polarization. It seemsthat between low and room temperature, there is an in-version between the ESA intensities at 603.64 nm. Thesame temperature effect is known to occur on theF3/2 ~ I» /2 emission transition and very recently we

recorded ESA spectra around 600 nm which confirmedthis effect. Moreover, Joubert et al. worked out a sim-ple rate equations model which was previously proposedin the case of Ni -doped CsCdC1~ (Ref. 36) and they es-timated that the ESA cross section at 603.64 nm in o. po-larization at 9 K is 3.2X10 cm, that is about fivetimes larger than our experimental value at room temper-ature. Our recent results seem to confirm this but furtherexperiments are necessary and are underway to evaluatethis cross section accurately. A subsequent article will bedevoted to these measurements and their analysis.

+ GUYOT et aI.

crE&~ (A. ) =AS„r,(J~J')

1 AA/2. . 2J'+J+1 ~ (X—X,, )'+(aX/2' ' (31)

an expression in which we have assumedsitions between th Sen e tark components

h8

e same polarization and where ~; is the

multiplet J of the ESAe tark level No. '. i of the starting

e transition and that wproximated by 1/(2J+ 1); b, A. is the lineis the linewidth of the ESA

linewidth as the GSA nm~ ~

e wit a Lorentzian rofie lines around 800 nm

and 3 nn1 in YAG, YLFnm, i.e., 1.5, 2,

the expected wavel t, and LMA, res ectivel

cause of the poor kno 1 d feng positions of the ESA lines {be-

LMA, wehaven tnow e ge of the L Sf )7/p tark levels in

sition)' /(, is the avera e wve not reported the correesponding ESA tran-

ge g o a tcm; and S (J~J'

ansi ion

again expression (15). Thus') is calculatedted by using

S[ I' ~2D3/2 ~ D5/~( 1 ) j =0.001002+0.000704

and

(32)

4G 2G7 /2 ~ I.i 7/2 ) =0.019206 '

The resultin g ESA cross-section s ectra ap ra are repor ed in

domain.e spectra inp in the same wavelength

The GSA tr ansition lines more stron 1o g y overlap w'tht an with the 6

~

"dh e cross sections of th

tions differ b ordthese various transi-

y or ers of magnitude with hi muc smaller

(33)

ES~ sPectra around 800 nm

When the crystals are pum ed arish white ti e race appears in the cr stal

pumpe around 800 nm, a green-1 e

'e crystal, especially in the

These are anti-Stoissued from the G 1

okes fluorescencese 7/2 level located around 19 000

1 d d 27000we s a see in the followi

another kind ofllowing section, from

in o upcon version rocessP gin o t ese high-lyin en

analysis of ESA- y ng energy levels. An

o was thus necessar . Unfwe already ment' den ione at the be innin

y. n ortunately, as

wavelength dom' '

yomain is very stron andginning, GSA in this

g ga cou ave been extracted. Con

built calibrated ESA sConsequently, we

malism hoping th tspectra by usin the

'g e Judd-Ofelt for-

'ng at we could reach, as in tregions investi ated riga e previously, ESA cross section

ood eno gh recision t d 'd

mechanism on th 1

' 'n o ecide the imd importance of this

on e aser performance.From the anal ysis of the energy level dia r 3+

after pumping around 800un nm the first ESA

(24000 cm ') th b ue ween t e levels I' 2

en, ecause of fast mul'

tions, between the 67 emie 7/z emi«ing level and the levelcm ). Thus we have built the E~

tra corresponding to the SA spec-

used for th t tho ese two transi

'

a e expressionnsitions and we have

19/2 -) F5/2 + 289/2YAG Nd

~ 5-

C0

~ 4-O

OOCDCA 3CoCOOO

0 2-2-CO

)Irrrr

lI

4G7/2 ")2L$7/2

x50I

iI

II

{

r

r

j

tiI

I I

t

lIr pI r'tlr

r

tI r

r

I

I

I III

r

,'I

rrrr

I

Ir

I r

I r

rr

II (

rI

r

I

i)l

F3/2 -& D5/2

x 500

76O 7'to 760 760 sbo 8& oWavelength (nm)

800 83O 84O SSO

4.5-

E 4-

o 35

19/2 ) F5/2 + 2H9/2 YLF:Nd

r E//C

0OCDco 2.5-COOo 2O~ 1.5-1O

I

4G7/2 -& 2L17/2:„'r 4F3/2 -& 205/2

0.5-

50 76o 7&0 740 760 860 810 8 0 $0 840 850Wavelength (nm)

FIG. 10. Polarized GSA and calculated (non olarized8a aroun 800 nrn in YLF:Nd'

4I9/2 -& 4F5/2 + 289/2 LMA:Nd

2 0.8-

o O.7

~o 0.6-

COco 0.5-

o o4-O= 0.3-

~ 0.2-

950 760 7/0 7(r0 76 6 8407 0 8 0 810 800 $0 840Wavelength (nm)

840 850

FIG. 11. Polarized GSA and calculated (non olarizt' t d 800a aroun 800 nm in LMA:Nd'+.

FIG. 9. GGSA and calculated ESA cross-around 800 nm in YAG:Nd'+

cross-section spectra

EXCITED-STATE-ABSOSORPTION AND UPCONVERSION. . .

~ ~

he ESA than for the GSA transitions. Wevalues for theh t the relative posi-shall see in the fo

'

gfollowin section t aities of these spectra canno g't ive accounttions and intensities o

excitation spectraalone of t e an i-h t'-Stokes fluorescence exci a'

which have been recorded in this domain.

1.2YAG:Nd

B. Up-conversion effects

l. Anti Sto-kesguorescence exci 'pitation s ectra

around 800 nm0.4-

O

d anal ze excitationsubsection we report an yIn this sud d by monitoring thespectra which

'h have been recor e y

d above and by scan-ants-Stokes flu orescences mentione a oveTi:sapphire lasern with a homema e cw i:sning the excitation w

ber of similar studies haveh 800-nm region. A numint ebeen a yalread devoted in the pa

Nd +-doped materials, buYLF:Nd and other N - opeour knowledge, that some results

been re orted for an excitation around

d blue fluorescences aroundnd 590 an4 2p

an ue

I ) emission transitions, respec'

blue fluorescence, howowever, was o serve'

h Jobin Yvons were analyzed wit a o inThese fluorescences'

h HamamatsuHR250 monochromator andand detected wit amics of the stud-lier. Depending on the dynamics o t e s u

h t unting system or aied fluorescence,e an Ortec p o on cou led with a computerStanford boxcar integrator coup e wi

completed the detection system.f the intensity ofd first that the dependence o t e in en

'We noted rson the excitation pumpran e and blue fluorescences on

d b respectively as it is ex-as uadratic and cu ic, reh t excitation processes.o- and three-p o on e

dFi s. 12—14 poj.arize exce po gs.d b monitoring ewhich were obtained y

coming from the infrafrared emitting leve 3/2 avels G (orange) an 3/pd 2P (blue)from the high-lying leve s 7/2

'h the or-he sha e of these spectra wit ein order to follow the s ape

h' oint of view,d rocesses. From t is poine same behavior was observe in e

f YLF.Nd+ 11 b 1 dtems, so only the case of YL

~ ~

s ectra of the three fluorescences ongi-p4n t g of th th e F3/2y 7/2

the same positions. It means apresent peaks at t-ecences are not very sensi ive't' to the ex-anti-Stokes fluorescences a

as is expected for an pESA ro cesscitation wavelength, as pOn the otheris assisted by phonons. n eprovided that it is

r with widths of abouth lines become narrower, wit wi shand, thed f the excitation process

a t spectra extend froIDnd 1.6 nm, as the or er o e

all these excitation s ecd h780 up to 810 nm wh'while, accor ing o

ESA should be significant only a oveanalysis, s'd the occurence of up-This has led us to consi er

f which is morecitation by energy trans ers wco ersion e cita ion y

h lt b using a fouriven the doping leve s o e

are thus tempted t y ho anal ze the resu s yd id multipho-e in which we have assume rapi

d3 dnon relaxations from levels 2 an an

0770 780 790

I

800 810Wavelength (nm)

820 830

of the Stokes and anti-StokesFIG. 12. Excitation spectra ofGrom the levels F3/2 and G7/2 influorescences coming from e

YAG:Nd

1.2YLF:Nd EJ c

~ 0.8-~~

0.6-

0.4-O

0.2-

0 M~~c770 ?80

FIG. 13. a -polarizedan i-t'-Stokes fluorescences

d3+and 'P3/2 in YLF:Nd

I

790 800Wavelength (nm)

excitation spectra of thet e Stokes andcoming rofrom the levels F3/2 G7/2,

820810

LMA:Nd EJ c

1.2

0.8-

O

~ 04-

0770 780

I

790 800Wavelength (nm)

810 820

'n s ectra of the Stokes andIG. 14. o.-polarized excitation spec ra

in from the levels F3/2 7/2,anti-Stokes fluorescences coming romand P3/2 in LMA:Nd'+.

796 Y. GUYOT et al.

ergy transfers between adjacent ions bringing one ion instate 2 or state 3 from another one in state 1, and whereo o is the GSA cross section, cr, and cr2 are the (phonon-assisted) ESA cross sections from levels 1 and 2, respec-tively, &2 and w3 are the fluorescence lifetimes of levels 2and 3, O'I i and 8'I2 are the energy-transfer rates(1,1)~(0,2) and (1,2)~(0,3), respectively. InYLF:Nd + the energy-transfer processes which can be in-volved are

Wll' . ( F3/2, F3/2 )~( I„/2& G9/2 )4 4 4 2

of N3 should vary like the cube of the spectral profile ofN i . On the other hand, if the ESA cross sections o.

i ando.

2 are not negligible, this profile will be modulated by thespectral shape of o. i and o.2. The best fits of the excita-tion spectra of the anti-Stokes Auorescences issued fromthe 67/2 and P3/2 levels, with a power function of theexcitation spectrum of the fluorescence coming from theF3 /2 metastable level, is obtained for

N2(z) =N, (X)'"

F3/2& F3/2 ( 13/2& G7/2 ) &

4 4 4 4

4 4 4 4W12' ( F3/2& G7/2) ( I9/2& D7/2)&

4 4 4 43/2 & G7/2 ) ( 11/2 & 3/2

and

( F3/2 G7/2 )~( I13/2 P3/2 ) .4 4 4 2

N3(&(, ) =N1(A, )

As these values only slightly differ from 2 and 3, theupconversion energy transfers probably play an impor-tant role; it seems however ESA is far from being negligi-ble. Thus we have tried to determine more particularlythe contribution of ESA to the feeding of level 67/2 bylooking for the best set of parameters a and P such as

The population equations for levels 2 and 3 can thus bewritten

N2(A, ) =aN, (A, )+PN1(&(, )

with

(40)

aI1d

dN3 + S [2NIN2 N3 /7 3dt (34)

and

Nl maxCX

=~2O. iIN2max

dN2o iNI+ 8'i]NI —N2/w2 —O2FN2 —KI2NIN2,dt

Nl max

N2max

where F is the excitation pump power.In the steady state, the populations become

N3 =r3(a2FN2 + W12N'1 N2 )

(35)

(36)

The best fit was obtained for a=0. 3 and P=0.7. Thismodel assumes that a, i.e., ESA, is independent of A, ,which means, as mentioned above, that ESA is phononassisted.

2. Infrared fluorescence decay behavior

~,FN, +W»N,-'o2F+8'I2N) +1/ 2

or by combining the previous expressions,

(37)

o. ,FNi + 8'iINiN3 =~3 I+ 1 i(o2F+ W, 2N1" .

)r2(38)

and, in the case of weak excitation pump power, i.e.,cr2~2F &&1 and 8'i2~2NI &&1,

QON3 =r2r3[cr1o2F N1 +(W» .+oW2, 2o, )FN1

QO+W„W, N 2]1. (39)

So, as expected, if N, varies linearly with the excita-tion pump power (in the case of weak dopant concentra-tion and not too strong excitation power), the dependencewith the excitation power of the intensity of the anti-Stokes fluorescence corning from the third emitting levelwill be cubic.

Moreover, if only the upconversion processes are in-volved in the feeding of levels 2 and 3, the spectral profile

dNI = —NI /~+ 8'iiNI . (41)

The solution of this Bernouilli equation is

The upconversion energy-transfer processes can alsoaffect the Auorescence lifetime of the infrared metastablelevel. On the other hand, laser experiments have shownthat the effective fluorescence lifetime ~, of this level isshorter than the expected value and shortens as the exci-tation pump power is increased. So we have studied thevariation of this infrared fIuorescence decay with the ex-citation pump power and have tried to relate the resultswith the upconversion energy-transfer mechanism dis-cussed previously. First, we find that the fluorescence de-cay mode is exponential at weak excitation pump powerbut becomes more and more nonexponential when thisexcitation po~er increases. This is shown in Fig. 15 inthe case of YLF:Nd +. To analyze this behavior, wehave used again the energy level scheme worked above,but by only considering the three lower levels and by as-suming no ESA. With these conditions the rate equationfor the infrared emitting level No. 1 is

51 EXCITED-STATE-ABSORPTION AND UPCONVERSION. . . 797

4.5

4.0

3.5

3.0

2.5Ck

CJ

O 2.0

FIG. 15. Decay of the in-

frared fluorescence coming fromlevel "I'3/2 in YLF Nd fordifferent excitation pump powersP «P1&P2 and fits with ex-pression (42) in the text.

1.5

1.00 200 400 600 800

Time (p,s)1000 1200 1400

1N (t) = —rW„+ +rW„exp(t /r)

N1(0)

(42)From this expression, we deduce the ratio between theeffective lifetime r, for which N, (r, )=N, (0)/e and thefluorescence lifetime r (at low pump power):

re1

(e —1)1+N, (0)W„r (43)

o 0.6-

04

0.4-

0.2-

01

I I I I I I III I I I I I I I II I I I I I IIII I I I I I I II I I I I I I 1&I

10 102 103 1O4 105N1(0)W11

FICx. 16. Theoretical evolutions of the ratio ~, /~ as a func-tion of the parameter 8'»%1(0) in the case of YAG'Nd + andYLF:Nd +.

Thus the decrease of the effective lifetime only dependson the product N&(0) W»r, i.e. , of the pumping and up-conversion rates and of the fluorescence lifetime. We re-port in Fig. 16 the variation of ~, /~ as a function ofW»N&(0) in the case of YLF and YAG for which v=550and 240 ps, respectively.

Knowing the excited ion density and the effective life-time which is calculated from the decays, thus the ratior, /r, we have estimated from Fig. 16 the upconversion

1.2

rates in YLF and YAG, W» =(1.7+1)X 10 ' and

(2.8+1)X10 ' cm s ', respectively. In the end, we

have fitted the decays according to expression (42) and

adjusting 8'». The result is shown in Fig. 15 and the ad-

justed 8'&& values agree well with that found previously.

IV. DISCUSSION/CONCLUSION

In the first part of this work we developed a very sim-ple model to examine the inhuence of excited-state ab-sorption, in the pumping as well as in the emissiondomains, on the laser performance of a four-level lasersystem in order to apply it in the case of Nd +-dopedlaser crystals. The effect of ESA in the emission domainis clearly detrimental for laser action. The effect of ESAin the pumping domain is less evident. In particular, themodel shows that ESA will significantly perturb the laserperformance of the Nd +-doped laser crystals if its crosssection is of the same order of magnitude as that of thestimulated emission.

The second part of this work has been devoted to anexperimental and theoretical analysis of ESA in Nd +-doped crystals of YAG, YLF, and LMA in the laserwavelength domains around 1.06 and 1.32 pm and insome specific excitation wavelength domains, around 460,600, and 800 nrn, because of their intervention in Aash-lamp and diode laser pumping and also in some particu-lar photon-avalanche process. The experimental resultshave shown first that ESA in the infrared metastable level

F3&2 of Nd + in these crystals at the main laser wave-lengths is negligible. So it cannot be invoked in these ma-terials to account, for instance, for discrepancies thatsome authors could find between the net gain cross sec-tions derived from laser experiments and the stimulated-emission cross sections determined from emission spec-tra. Then, the analysis of the ESA data in the laser aswell as in the pumping domains within the framework ofthe Judd-Ofelt theory have shown that the ESA cross sec-tions could be estimated, in most cases, to better than

798 Y. GUYOT et al. 51

(44)&,*=Paw/h v,where a is the absorption coefficient at the pump wave-length and w the Auorescence lifetime at low excitationpump powers. By using ~=540 ps and P=800 W/cmwe find with our model r, /r=(0. 7+0. 15), thus r, =385

50%, which is very satisfactory, considering the experi-mental uncertainties and the approximations made in thistheory. Knowing that, we have found that ESA in theF3/2 metastable state in the laser diode-pumping domain

around 800 nm could occur but with much weaker crosssections than for GSA in the same domain, the latter be-ing already much weaker than the stimulated-infrared-emission cross sections around 1.06 pm, with o Gs~(800nm) =0.15o, (1.06 pm) approximately. This is very im-portant because, as stated above, ESA in the metastablestate at the pumping wavelength can perturb the laserperformance of the systems only if its cross section is ofthe same order of magnitude as that of the stimulatedemission. Since it is not the case, we can conclude thatESA around 800 nm, at least in the metastable state,should not inhuence the laser performance significantly.Moreover, concerning ESA in the visible domain, whichmight be important for Aash-lamp pumping, we have es-timated theoretically that the integrated ESA cross sec-tion between 400 and 900 nm should not exceed 10% ofthe integrated GSA cross section in the same domain.So, the inAuence of ESA should be notable only for highexcitation densities, as is the case in the high powerHash-lamp-pumped system. In this case we could haveshown indeed the existence of increasing thermaleffects —thermal lensing, thermal birefringence —whengoing from a stimulated-emission to a spontaneous-emission regime which can be explained for about one-third by the ESA mechanisms and the subsequent heatingby the multiphonon relaxations.

ESA not being the essential mechanism for the reducedlaser performances of the systems, we have invoked exci-tation and loss processes by upconversion energytransfers, first in the F3/2 metastable state. This possi-bility has been analyzed and confirmed by recording inthe 800-nm wavelength domain excitation spectra ofanti-Stokes Auorescences coming from higher-lying emit-ting levels of Nd +, by discussing their profiles, and bycomparing them to the ones expected theoretically. Ithas been invoked too to account for the reduction of theinfrared metastable lifetime, as by Seelert et al. to ex-plain the reduced laser performance of their high-powerYLF:Nd + laser. They determined a fluorescence life-time of 410 ps, instead of 540 ps, for a cw excitation den-sity of 800 W/cm at around 800 nm. If we analyze theproblem within the framework of the model that we havedeveloped in the second part of our work, and which ap-plies for pulsed excitation, the equivalent number of ex-cited ions N,' is related to the pump power by the expres-sion

ps, in very good agreement with the above values.Concerning the energy transfers which are involved for

these upconversion phenomena we also have remarkedfrom the ESA spectra recorded in the infrared domainthat the only ESA transitions taking place in the metasta-ble state which overlap with emission transitions arethose terminating on the G9/2 and G7/2 levels around1.06 and 1.32 pm, respectively; There is no overlap of anyESA transition from state F3/2 with the emission transi-tion F3/2 ~ I9/2 around 0.9 pm. Consequently the ener-

gy transfers are the following:

+3/2r +3/2)~( Ill/2, G9/2)4 4 4 2

and

4 4 4 4+3/2~ +3/2 ) ( 13/2 ~ G7/2 )

To illustrate this point we have calculated the spectraloverlaps of the respective ESA and emission cross sec-tions in YAG and YLF:Nd + (averaging over polariza-tion in the latter) and we have foundjtTEs&(A, )o', (A, )dA, =3.2 and 2. 5X10 cm s, know-

ing that the contribution of the overlap around 1.06 pmis about 30 and 210 times larger than that around 1.32pm, in YAG and YLF, respectively. The overlap inYAG is thus 1.2 times larger than that in YLF, whichagrees well with the ratio of 1.6 found between theenergy-transfer rates derived from the decay data.

In the end we can examine the solution which has beenproposed recently to identify the process responsible forthe increasing inefficiency of a diode-pumped Q-switchedNd: YLF laser with decreasing pulse repetition rate. Theproposition is an ESA transition at the laser emissionwavelength taking place in the 67/2 excited state afterpopulation of this state via the above upconversion ener-

gy transfers and subsequent multiphonon relaxations.We have calculated first the integrated cross section ofthe involved ESA transition and we have foundS„),( 67/2~ D5/2)=9. 6X10 cm, which is of thesame order of magnitude as the F3/p —+ G9/2 transition.So this could lead to ESA peaks with cross sections of theorder of several 10 cm, which indeed could be detri-mental for laser action at high pumping levels if one ofthese peaks coincided with a laser transition, and consid-ering the energy scale of Nd in YLiF„(Ref. 29) this mightbe possible.

ACKNOWLEDGMENTS

Thanks are expressed to Dr. J. Y. Gesland (Universitedu Maine, Cristallogenese, France), Dr. Ch. Wyon(LETI/CEA, Grenoble), and CRISMATEC S.A. for pro-viding us with the YLF, LMA, and YAG crystals, re-spectively, and B. M. Industries for the fIash-lamp pumpchamber used in this study.

M. Hemici, S. Mottin, M. Bon, J. Y. Roncin, and P. Laporte, J.Phys. III (France) 1, 2061 (1991).

R. Moncorge and T. Benyattou, Phys. Rev. B 37, 9177 (1988);37, 9186 (1988).

3H. Manaa, Y. Guyot, and R. Moncorge, Phys. Rev. B 48, 3633(1993).

4J. S. Chivian, W. E. Case, and D. D. Eden, Appl. Phys. Lett.35, 124 (1979);A. W. Kueny, W. E. Case, and M. E. Koch, J.

51 EXCITED-STATE-ABSORPTION AND UPCONVERSION. . . 799

Opt. Soc. Am. B 6, 639 (1989); M. E. Koch, A. W. Kueny,and W. E. Case, Appl. Phys. Lett. 56, 1083 (1990).

5W. Lenth and R. M. Macfarlane, J. Lumin. 45, 346 (1990).M. F. Joubert, S. Guy, and B.Jacquier, Phys. Rev. B 48, 10031

(1993).~Y. Guyot, R. Moncorge, X. Banti, P. Laporte, and E. Mottay

(unpublished).R. R. Petrin, M. L. Kliewer, J. T. Beasley, R. C. Powell, I. D.

Aggarwal, and R. C. Ginther, IEEE J. Quantum Electron.27, 1031 (1991}.

S. Zemon, B. Petersen, G. Lambert, W. J. Miniscalco, B. T.Hall, R. C. Folweiler, W. A. Thompson, and L. J. Andrews,IEEE Phot. Tech. Lett. 4, 244 (1992).P. R. Morkel, M. C. Farries, and S. B. Poole, Opt. Commun.67, 349 (1988).

~~M. L. Kliewer and R. C. Powell, IEEE J. Quantum Electron.25, 1850 (1989).S. A. Payne, J. A. Caird, L. L. Chase, L. K. Smith, N. D.Nielsen, and W. F. Krupke, J. Opt. Soc. Am. B 8, 726 (1991).B.R. Judd, Phys. Rev. 127, 750 (1962).G. S. Ofelt, J. Chem. Phys. 37, 511 (1962).Y. Guyot and R. Moncorge, J. Appl. Phys. 73, 8526 (1993).N. Mermilliod, R. Romero, I ~ Chartier, C. Garapon, and R.Moncorge, IEEE J. Quantum Electron. 28, 1179 (1992).Y. Guyot, C. Garapon, and R. Moncorge, Opt. Mater. (to bepublished).W. T. Carnall, H. Crosswhite, and H. M. Crosswhite (unpub-lished).A. A. Kaminskii and L. Li, Phys. Status Solidi A 26, K21(1974).

~cW. F. Krupke, IEEE J. Quantum Electron. 7, 153 (1971).D. Knowles, A. Cassanho, and H. P. Jenssen, in Tunable SolidState Lasers, Vol. 5 of the OSA Proc. Series, edited by M. L.Shand and H. P. Jenssen (Optical Society of America,Washington, D.C., 1989),p. 139.W. F. Krupke, in Proceedings of the IEEE Region IV Conference (Institute of Electrical and Electronics Engineers, NewYork, 1974), p. 17.J. R. Ryan and R. Beach, J. Opt. Soc. Am. B 9, 1883 (1992).B. Viana, D. Saber, A. M. Lejus, D. Vivien, R. Romero, andC. Wyon, in Advanced Solid State Lasers, Vol. 15 of the OSAProc. Series, edited by A. Pinto and T. Y. Fan (Optical So-ciety of America, Washington, D.C., 1993),p. 242.

25C. Li, Doctoral thesis, University of Lyon 1, 1992.2 J. Y. Roncin and H. Damany, Rev. Sci. Instrum. 52, 1922

(1981).2~J. Caird, P. R. Staver, and K. S. Jancaitis (unpublished).

J. B. Gruber, M. E. Hills, T. H. Allik, C. K. Jayasankar, J. R.Quagliano, and F. S. Richardson, Phys. Rev. B 41, 7999(1990).A. A. S. da Gama, G. F. de Sa, P. Porcher, and P. Caro, J.Chem. Phys. 75, 2583 (1981).D. Saber, J. Dexpert-Ghys, P. Caro, A. M. Lejus, and D.Vivien, J. Chem. Phys. 82, 5648 (1985).N. P. Barnes, D. J. Gettemy, L. Esterowitz, and R. E. Allen,IEEE J. Quantum Electron. QE23, 1434 (1987).

3~T. M. Pollack, W. F. Wing, R. J. Grasso, E. P. Chicklis, andH. P. Jenssen, IEEE J. Quantum Electron. QE18, 159 (1982).W. F. Krupke, M. D. Shinn, J. E. Marion, J. A. Caird, and S.E. Stokowski, J. Opt. Soc. Am. B 3, 102 (1986).M. D. Shinn, F. P. Milanovich, and J. N. Roe (unpublished).

35Y. Guyot, H. Manaa, R. Moncorge, N. Gamier, E. Descroix,and P. Laporte, J. Phys. (Paris) Colloq. 4, C4-529 (1994).U. Oeliker, M. J. Riley, P. S. May, and H. U. Gudel, J. Lumin.53, 553 (1992).J. Mares, B. Jacquier, P. Pedrini, and G. Boulon, Mater.Chem. Phys. J 21, 237 (1989).

3sG. E. Venikouas, G. J. Quarles, J. P. King, and R. C. Powell,Phys. Rev. B 30, 2401 (1984); G. J. Quarles, G. E. Venikouas,and R. C. Powell, Phys. Rev. B 31, 6935 (1985).

39M. A. Kramer and R. W. Boyd, Phys. Rev. B 23, 986 (1981).4 T. Y. Fan and R. L. Byer, J. Opt. Soc. Am. B 11, 1519 (1986).

J. H. Schloss, L. L. Chase, and L. K. Smith, J. Lumin. 48-49,857 (1991).

42R. Buisson, J. Q. Liu, and J. C. Vial, J. Phys. 45, 1533 (1984).R. B. Barthem, R. Buisson, J. C. Vial, and H. Harmand, J.Lumin. 34, 295 (1986).

~T. Chuang and H. Verdun, in Advanced Solid State LasersTechnical Digest, 1994 (Optical Society of America,Washington, D.C., 1994), p. 239.

4~F. Auzel, J. Lumin. 31-32, 759 (1984).W. Seelert, H. P. Lortz, and W. M. Yen, in OSA Proceedingson Advanced Solid State Lasers, edited by L. L. Chase and A.Pinto (Optical Society of America, Washington, D.C., 1992},Vol. 13, p. 209.

4~Y. Guyot, Doctoral thesis, University of Lyon I, 1993.