Laroche et al. Vol. 16, No. 12 /December 1999 /J. Opt. Soc. Am. B 2269

Spectroscopic investigations of the 4f5d energylevels of Pr31 in fluoride crystals

by excited-state absorption and two-stepexcitation measurements

Mathieu Laroche, Alain Braud, Sylvain Girard, Jean Louis Doualan, Richard Moncorge, andMichel Thuau

Centre Interdisciplinaire de Recherche Ions Lasers Equipe Materiaux et Instrumentation Laser,Unite Mixte de Recherche 6637, Centre National de la Recherche Scientifique/Commissariat a l’Energie Atomique/

Institut des Sciences de la Matiere et du Rayonnement, 6 Boulevard Marechal Juin, 14050 Caen Cedex, France

Larry D. Merkle*

U.S. Army Research Laboratory, 2800 Powder Mill Road, Adelphi, Maryland 20783-1197

Received March 22, 1999; revised manuscript received August 9, 1999

Excited-state absorption spectra obtained by a pulsed pump–probe technique specially designed for thenear-UV spectral domain were recorded in three Pr31-doped fluoride crystals (KY3F10, LiYF4, and BaY2F8).These excited-state absorption spectra correspond to optical transitions from the 3P0 or the 1D2 metastablelevels of the 4f 2 configuration up to the first energy levels of the 4f5d electronic configuration. The position,the anisotropic behavior, and the line shape of the observed excited-state absorption bands are discussed andcompared with ground-state absorption (from level 3H4) or direct excitation spectra available in the literature.Subsequently, two-step excitation into the 4f5d high-lying energy levels of Pr3 by means of 3P0 and 1D2 isshown to be an efficient way to produce broadband UV fluorescence by use of pump beams in the blue and thenear UV. © 1999 Optical Society of America [S0740-3224(99)00712-2]

OCIS codes: 140.3580, 020.4180, 160.3380, 160.5690, 190.7220, 300.6540.

1. INTRODUCTIONSince the early 1980’s, it has been demonstrated that use-ful and reliable tunable all-solid-state lasers emitting inthe blue and the UV spectral domains can be obtainedwith the 4f n215d → 4f n interconfigurational transitionof trivalent rare-earth ions.1–10 Until now, the mostwidely studied trivalent RE ion for that purpose has beenCe31, which offers the advantage of possessing only oneelectron in the outer unfilled shell. This gives rise torelatively simple energy-level schemes for both theground electronic configuration 4f 1 and the first excitedelectronic configuration 5d1. The use of Ce31 results inlasers tunable from ;285 to ;325 nm, depending on thehost medium.8,10

However, only limited work has been devoted to otherinteresting ions such as Pr31 or Nd31 ions, which, in wide-bandgap dielectric crystals, also present strong UV emis-sion after direct excitation into the mixed configuration4f n215d (Pr31: n 5 2, Nd31: n 5 3). Only one lasertransition in the vacuum UV has been obtained, in Nd-doped LaF3 at l 5 172 nm by use of pump sources suchas Kr2 or F2 lasers.3

Tentative measurements of positive gain in Pr31-dopedfluoride crystals at a specific UV emission wavelength of;225 nm have been reported.11 According to the data inthe literature, no gain was observed in any of the crystalsstudied (at least at the emission wavelengths considered).

0740-3224/99/122269-09$15.00 ©

This result was attributed to pump-induced losses thatwere due, as in the case of Ce-doped materials,6,12,13 toexcited-state absorption (ESA) between the 4f5d and the4f6s electronic configurations and, more likely, betweenthe 4f5d emitting configuration and the conduction bandof the host material.11 However, a definitive assignmentis still a matter of discussion. Very few data are avail-able on the energy-level structure of the 4f5d and the4f6s Pr31 electronic configurations and of the conductionband of the materials or on their widths and their rela-tionship to the energy levels pertaining to the 4f 2 con-figuration. This lack of data is due mainly to the difficul-ties encountered when the materials need to be pumpedwith light sources in the vacuum-UV domain and whenabsorption spectra need to be recorded at wavelengthsshorter than 180 nm, such that these measurements needto be performed under vacuum.

As a matter of fact, it is primarily for simplicity that wedecided to investigate an indirect technique, which usesonly visible and near-UV photons, based on the registra-tion of polarized ESA spectra starting from the meta-stable 3P0 and 1D2 energy levels of the 4f 2 configuration.Such a technique was recently used to determine the la-ser potential of Pr:YSO and Pr:GSO single crystals in theblue and the red spectral domains.14

This choice was also made, however, for more funda-mental reasons. As the ESA transitions should start

1999 Optical Society of America

2270 J. Opt. Soc. Am. B/Vol. 16, No. 12 /December 1999 Laroche et al.

from a spin singlet 1D2 or a spin triplet 3P0 , very inter-esting data should be obtained concerning the spin-orbitnature of the 4f5d electronic configuration. More par-ticularly, the ESA spectra recorded from level 1D2 shouldlead to the positions of singlet energy levels that havenever been observed inasmuch as they cannot be reacheddirectly by registration of regular ground-state (3H4) ab-sorption spectra because of the spin selection rule. Theuse of visible and near-UV photons should also lead tobetter-resolved spectra and hence to a better descriptionof the energy levels of the 4f5d electronic configurationresulting from the crystal field, the electrostatic, and thespin-orbit interactions.

Registration of ESA spectra starting from the 1D2 andthe 3P0 levels is also interesting because of the possibleupconversion pumping scheme that uses the two-step ex-citation processes 3H4 → 1D2 → 4f5d and 3H4→ 3PJ50,1,2 → 4f5d to reach the 4f5d UV emitting con-figuration. Such a pumping mechanism could be a favor-able alternative way to avoid or reduce the detrimentalsolarization effects.6,12,13 This solarization problem iscommonly explained by photoionization of the RE31 activeions under strong UV pumping and trapping of the freeelectrons at impurity or lattice defect sites having absorb-ing energy levels in the bandgap of the host medium.This then leads to the formation of color-center defectsthat can absorb in both the absorption and the emissiondomains of the active ions. This can lead to optical lossesthat reduce the efficiency of laser operation or even pre-vent any laser oscillation. The solarization effects arethus strongly dependent not only on the chemical purityof the crystal but also on the pump wavelength, since inmost cases the use of deep UV-laser excitation is a biggerproblem than the use of less energetic pump sources.Therefore the use of pump photons either in the near UVor in the blue spectral domain in a two-step excitationprocess could be very attractive in terms of photochemicalstability of these all-solid-state UV lasers.

In this paper, first we describe the experimental setupthat was used to record ESA spectra from both the 1D2and the 3P0 intermediate levels of Pr31 up to the first en-ergy levels of the 4f5d excited electronic configuration ina spectral domain between 220 and 450 nm. PolarizedESA spectra were registered and calibrated for three or-dered fluoride crystals: KY3F10, LiYF4, and BaY2F8,each doped with Pr31. The position and the structure ofthe observed ESA bands are then compared with the fewground-state absorption results already available in theliterature, giving the position of 4f5d energy levels andthe structure of the corresponding vibrational bands,which result mainly from the crystal field splitting of the4f5d configuration of Pr31. We complete this discussionby giving details about experiments showing the possibil-ity of using a two-photon excitation process to efficientlypopulate the 4f 15d1 lower energy level.

2. BASIC LUMINESCENCE PROPERTIES OFCRYSTALS STUDIEDThe basic luminescence properties of Pr:LiYF4 (4f 2

energy-level positions and intraconfigurational transitionintensities) can be found in Refs. 15–17. Concerning the

Fig. 1. Room-temperature polarized ground-state absorption(GSA) spectra of Pr-doped KY3F10 and LiYF4 in the region of the1D2 and of the (3P0,12, 1I6) energy levels.

Fig. 2. Room-temperature polarized GSA spectra of Pr:BaY2F8in the region of the 1D2 and the (3P0,12, 1I6) energy levels.

Laroche et al. Vol. 16, No. 12 /December 1999 /J. Opt. Soc. Am. B 2271

4f 2 –4f5d optical transitions, unpolarized data were re-ported in Refs. 11 and 18. In the case of Pr:BaY2F8, 4f 2

luminescence and stimulated emission data were re-ported in Refs. 19 and 20, and 4f 2 –4f5d unpolarizedspectra were reported in Refs. 11 and 21. As forPr:KY3F10, the only report of which we are aware is a1980 Harry Diamond Laboratories report22 that givesonly the positions of the 4f 2 energy levels. To our knowl-edge, nothing on the optical transitions between the 4f 2

and the 4f5d configurations was reported. Conse-quently, for clarity, we have reported in Figs. 1 and 2 the4f 2 absorption spectra corresponding to the 1D2 and the(3P0,1,2 , 1I6) manifolds, and in Fig. 3 we show the 4f5d→ 4f 2 emission spectra (corrected from the spectral re-sponse of our experimental setup) for the three systems.To aid in our discussion of the ESA results, which are re-ported in Section 3, we also present an illustration (Fig. 4)of the energy-level scheme of Pr:LiYF4. As shown in Fig.1, because of the spin selection rule, the oscillatorstrength of the GSA transition to the (3P0,1,2 , 1I6) mani-fold, and more particularly of that corresponding to the3H4 → 3P2 transition around 445 nm, is significantlylarger than that associated with the 3H4 → 1D2 transi-tion around 600 nm. For this reason (but also because ofreduced nonradiative multiphonon relaxations), the life-time of the fluorescence from this 1D2 singlet state is al-ways significantly longer than that from the emittingtriplet state 3P0 . The positions of the 1D2 and the 3P0energy levels and their fluorescence lifetimes measured atroom temperature are reported in Table 1. Conse-quently, absorption in the triplet state is more efficient,but more energy can be stored into the singlet, so both

Fig. 3. Room-temperature 4f5d UV emission spectra of Pr-doped KY3F10, LiYF4, and BaY2F8.

metastable levels can be interesting as intermediatestates in the two-step pumping process considered above.

3. EXPERIMENTAL CONDITIONSA. CrystalsSingle crystals of Pr31-doped KY3F10, LiYF4, and BaY2F8were grown by the Czochralski technique in a homemadepulling apparatus according to an experimental processdescribed in a previous paper.23 The nominal dopantconcentration added to the melt was typically 1 at. %, andit led to final dopant concentrations ranging between0.2% and 0.5% because of the strong segregation effect at-tributed to the difference of size between Pr31 and Y31

ions. The samples were then oriented by x-ray diffrac-tion.

B. Excited-State Absorption MeasurementsESA measurements were performed by use of the pump–probe experimental setup shown in Fig. 5. The pumpsource was provided by a broadband optical parametricoscillator (GWU-Lasertechnik Model C355) widely tun-able in the visible and the infrared domains. It ispumped by the third harmonic of a Q-switched Nd:YAGlaser (Spectron Model 404G) and emits nearly 10 mJ/pulse, with a pulse duration of 4–5 ns at a repetition rate

Fig. 4. Energy-level scheme of Pr31:LiYF4.

Table 1. Approximate Positions and FluorescenceLifetimes of the 1D2 and the 3P0 Metastable

Levels in Pr-Doped KY3F10, LiYF4, and BaY2F8

Materials Pr:KY3F10 Pr:LiYF4 Pr:BaY2F8

n(3P0) 20 730 cm21 20 860 cm21 20 840 cm21

t(3P0) 33.5 ms 43.5 ms 42.5 ms

n(1D2) 16 670 cm21 16 740 cm21 16 650 cm21

t(1D2) 92.5 ms 205 ms 175 ms

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of 10 Hz. The output wavelength of the signal wave wastuned either around 450–480 nm (3H4 → 3PJ , 1I6) oraround 590 nm (3H4 → 1D2). The pump beam diameteron the sample was adjusted with a 22-cm focal-length lensand was limited to a value of 500 mm with the aid of asmall aperture on the crystal mount. The pulse energy ofthe pump beam passing through this aperture was re-duced to less than 1 mJ to avoid any optical damage, andthe pump fluence was typically of the order of 0.15–0.25J/cm2. The probe beam was provided by a CW high-pressure Xe arc lamp (Osram Model 100W). It propa-gated collinearly to the pump beam through the sample,but in the opposite direction, and it was collimated andfocused successfully onto the sample and onto the en-trance slit of a monochromator, thanks to two UV silicatelenses of 12-cm focal length. The probe beam was spec-trally analyzed with a 0.25-m monochromator (OrielModel 77200) equipped with a 600-grooves/mm gratingblazed at 200 nm. The opposite propagation directions ofthe pump and the probe beams help to ensure that the de-tector will not be blinded by pump light directly focusedonto the entrance slit of the monochromator and permit agood overlap between the pump and the probe beams intothe sample. The detection system consisted of a photo-multiplier tube (Hamamatsu Model R3896, with a photo-cathode extended into the UV), a fast digitized oscillo-scope (Tektronix Model TDS 350), and a boxcar integrator(Princeton Applied Research Sciences Model 162) inter-faced to a PC.

The ESA spectra could be recorded from 450 to 220 nm.Below 220 nm, ESA measurements were not possible be-cause of direct 4f 2(3H4) → 4f5d absorption. PolarizedESA spectra were recorded with the aid of a Glan–Taylorprism made of a barium borate specially designed for theUV spectral domain between 200 and 400 nm. TheseESA spectra were calibrated in the following way.

When the pump beam was switched off, the only popu-lated multiplet is the ground-state multiplet 3H4 , andthe population density is NT , the chemically measuredPr31 dopant concentration inside the crystals. The probebeam intensity transmitted throughout the sample in thisunpumped case, denoted Iu , is then given by the Beer–Lambert law for small incident intensities I0 :

Iu 5 I0 exp@2NTsGSA~l!#, (1)

where sGSA is the GSA cross section and l is the length ofthe sample. When the crystal is pumped and if the probebeam intensity is measured immediately after the pumppulse (by opening of the gate of the boxcar a few micro-seconds after this pump pulse), the only populated excitedlevel is the one directly excited, i.e. (depending on the se-lected pump wavelength), the 3P0 or the 1D2 level in thepresent situation. So, if N* stands for the populationdensity in this excited level, the probe beam intensity Ipin this pumped case then becomes

Ip 5 I0 exp@2~NT 2 N* !sGSA~l!l

1 N* sSE~l!l 2 N* sESA~l!l#. (2)

Here the subscript p indicates the pumped case, sSE rep-resents the stimulated emission (SE) cross section, andsESA indicates the ESA cross section. Then Eqs. (1) and(2) can be combined to yield

sESA~l! 2 sSE~l! 2 sGSA~l! 51

N* llnS Iu

IpD . (3)

In Pr-doped fluoride crystals the stimulated emission andthe GSA cross sections are zero for wavelengths between220 and 450 nm, and therefore the ESA cross sectionstarting from the metastable level is the only term re-maining in Eq. (3). One can obtain sESA just by writing

sESA~l! 5 21

N* llnS 1 2

DI

IuD . (4)

Here DI 5 Iu 2 Ip stands for the intensity change of theprobe beam.

Calibration of the recorded spectra [DI(l) and Iu(l)]therefore requires some experimental determination ofthe population density N* . This can be done by directmeasurement of the absorbed excitation energy in thepumped and probed portion of the sample. For that pur-pose, pump energy is measured successively before andafter the samples, and for Pr-doped and undoped crystals,to account for the Fresnel as well as for the scatteringlosses, since both effects become quite important in the

Fig. 5. ESA experimental setup.

Laroche et al. Vol. 16, No. 12 /December 1999 /J. Opt. Soc. Am. B 2273

UV domain. If we denote as Eabs the measured absorbedenergy, the excited-state ion density can be obtained byuse of the expression

N* 5Eabslp

hcSl, (5)

where S is the area of the small hole drilled into the crys-tal mount, h is Planck’s constant, c is the speed of light,and lp is the pump wavelength. One further verifies thiscalibration method by measuring the bleaching effect ex-perienced by the GSA transition 3H4 → 3PJ after directpumping into level 1D2 . The absorption line strengthassociated with the 3H4 → 3P2 transition of the Pr31 ionis the strongest one and hence is particularly useful fordetection of small variations in the ground-state popula-tion after optical pumping.

4. EXCITED-STATE ABSORPTIONEXPERIMENTAL RESULTSThe polarized ESA spectra recorded after excitation intothe 3P0 and the 1D2 levels for the three different crystalsinvestigated here are presented in Figs. 6–8. These spec-tra are reported in units of wave numbers (inverse centi-meters) and have been shifted by the energies of the re-spective absorbing excited levels, 3P0 and 1D2 (see Table1), by use of the expressions

n~4f5d ! 5 n~3P0! 1 n~3P0 → 4f5d !,

n~4f5d ! 5 n~1D2! 1 n~1D2 → 4f5d ! (6)

to yield the real positions of the 4f5d energy levels.

Fig. 6. ESA spectra for Pr:KY3F10, shifted by the energies of the3P0 and the 1D2 absorbing excited states.

The pump wavelength was adjusted for each system byoptimization of the fluorescence intensity coming fromthese metastable levels (3P0 and/or 1D2) to the 3H4

Fig. 7. ESA spectra for Pr:LiYF4, shifted by the energies of the3P0 and the 1D2 absorbing excited states.

Fig. 8. ESA spectra for Pr:BaY2F8, shifted by the energies of the3P0 and the 1D2 absorbing excited states.

2274 J. Opt. Soc. Am. B/Vol. 16, No. 12 /December 1999 Laroche et al.

ground state. KY3F10 is cubic, LiYF4 is uniaxial, andBaY2F8 is biaxial, so the ESA spectra for each crystalwere recorded either with an unpolarized probe beam orwith a probe beam polarized along or perpendicular to theprincipal axis or parallel to the three principal axes of theoptical indicatrix. BaY2F8 is a biaxial crystal with mono-clinic structure (we used the notations given in Ref. 24).Therefore a complete knowledge of the absorption spectraof Pr31 in this crystal should necessitate the registrationof ESA spectra with a polarization varying continuouslyin the plane perpendicular to the twofold axis (010). Thisis due to the noncorrespondence between the principalaxes deduced from the real and from the imaginary partsof the dielectric tensor. However, because of the doublerefraction, spectroscopic measurements are almost al-ways limited to beams propagating along the principalaxes of the real part of the dielectric tensor (the principalaxes of the optical indicatrix), labeled 1, 2, and 3 (see Ref.24). However, because of the electric dipole nature of theinterconfigurational optical transitions, only three polar-izations have to be considered (two in the case of theuniaxial crystal LiYF4).

As can be seen in Figs. 6–8, the ESA cross sections areof the order of 10218 cm2, which is typical for 4f –5dparity-allowed electric dipole transitions [see, e.g., the ab-sorption cross section of Ce31 ions in LiCa(Sr)AlF6 (Ref.6)].

Concerning Pr:KY3F10, there are no available data inthe literature on the absorption bands characterizing the3H4 → 4f5d transitions. According to our near-UV ab-sorption spectra, UV absorption rises rapidly at ;230 nm,which corresponds to an energy of ;43 500 cm21. Thiscoincides well with the onset of the 3H4 → 4f5d absorp-tion band deduced from the ESA spectra associated withthe 3P0 → 4f5d and the 1D2 → 4f5d transitions and re-ported in Fig. 6. According to these spectra, the 4f5delectronic configuration splits into various componentswith a more or less pronounced spin character (spin selec-tion rule for transitions starting from 3P0 or 1D2). The3P0 → 4f5d ESA spectrum probably indicates at leastfour bands peaking around 210 nm (47 500 cm21), 198 nm(50 500 cm21), 188 nm (53 000 cm21), and 182 nm (55 000cm21), respectively. The 1D2 → 4f5d ESA spectrum it-self leads to five bands peaking around 215 nm (46 500cm21), 205 nm (48 700 cm21), 195 nm (51 200 cm21), 187nm (53 500 cm21), and 177 nm (56 500 cm21), respec-tively. Note that both sets of energy levels are clearlydistinct and that the lowest 4f5d energy level would bepredominantly a spin singlet. For clarity, we have re-ported the positions of these energy levels in Fig. 9.

In the case of Pr:LiYF4 and Pr:BaY2F8, absorption orexcitation spectra corresponding to the GSA transition3H4 → 4f5d have already been reported in theliterature.22,25,26 These unpolarized spectra were re-corded up to 70 000 cm21 and are made of two groups ofbands: two well-resolved and well-separated broad ab-sorption bands around 47 000 and 54 000 cm21, and threeoverlapping ones between ;60 000 and ;67 000 cm21, re-spectively. These bands result from the crystal-fieldsplitting of the 4f5d electronic configuration22 into a well-resolved orbital doublet and a triplet. In this regard, onecan also refer to the case of Pr:LiLuF4, an isomorphic sys-

tem of LiYF4, for which a very clear absorption spectrumis reported in Ref. 27. Note that similar band splittingscould be observed, for example, in the case of BaY2F8,

22

with Ce31 (5d), Pr31 (4f5d), and Nd31 (4f 25d) as well,indicating the predominant effect of the crystal field onthe 5d orbitals. These UV GSA/excitation bands do notshow any really distinct fine structures (at least at roomtemperature), a result that could be due to the 4f –5delectrostatic interaction and/or the spin-orbit coupling.Our ESA spectra (Figs. 7 and 8) for Pr:LiYF4 andPr:BaY2F8, as well as for Pr:KY3F10, however, look morecomplex—and thus more informative. Indeed, thesespectra are recorded in a more restricted domain, be-tween 240 nm (41 500 cm21) and 420 nm (23 800 cm21),which corresponds to 4f5d energy levels between;62 500 cm21 (160 nm) and ;44 000 cm21 (224 nm), andhence to energy levels associated with the above-mentioned doublet. Also, they are polarized spectra (Eicor p ; E'c or s for LiYF4; and Ei1, Ei2, and Ei3 forBaY2F8), and they correspond to transitions from spin-singlet and spin-triplet states 1D2 and 3P0 instead offrom the only ground-state triplet 3H4 .

In the case of Pr:LiYF4, the 3P0 → 4f5d ESA spectrum(shifted by 20 860 cm21, the energy of the 3P0 absorbingstate) consists of at least two groups of bands: one withpeaks around 208 nm (48 000 cm21) and 250 nm (50 000cm21), and the other around 190 nm (52 500 cm21) and180 nm (55 500 cm21). As to the 1D2 → 4f5d ESA spec-trum, it also consists of two groups of bands around 213nm (47 000 cm21) and 202 nm (49 500 cm21), and at ;188,;183, and ;175 nm (53 000, 54 500, and 57 000 cm21, re-spectively). As above, the corresponding 4f5d energylevels are reported in Fig. 9. According to these results,the lowest level of the 4f5d configuration might have amore pronounced spin-singlet character.

In the case of Pr:BaY2F8, for which the UV GSA spec-trum can be found in Ref. 26, similar results are obtained,and the resulting 4f5d energy-level positions are also re-ported in Fig. 9 (we determined these positions as above,by shifting the ESA spectra by the energies of the 3P0 and1D2 absorbing states). As with Pr:LiYF4 and Pr:KY3F10,

Fig. 9. 4f5d energy levels according to the 3H4 → 4f5d GSAand according to the 3P0 → 4f5d and the 1D2 → 4f5d ESAspectra.

Laroche et al. Vol. 16, No. 12 /December 1999 /J. Opt. Soc. Am. B 2275

the lowest level of the 4f5d configuration in Pr:BaY2F8

would have a stronger spin-singlet character.

5. ENERGY-LEVEL ANALYSISFrom Fig. 9 it is clear that the observed ESA transitionsend on 4f5d energy levels. According to Ref. 22, in par-ticular, between ;45 000 and ;58 000 cm21, these tran-sitions would end on the two lowest (and well-separated)components of the 4f5d electronic configuration that ap-pear in the GSA spectra. These components must be duepredominantly to the effect of the local tetragonal crystal-field distortion on the low-energy E component, which it-self results from the cubic splitting of the 5d electronic or-bitals. Indeed, as previously recognized by several otherauthors (see, e.g., Refs. 28 and 29), this crystal-field effectcan be so large compared with that experienced by the 4felectron and compared with the electrostatic interactionbetween the 4f and the 5d electrons that the 4f and the5d electrons can be considered as separate systems. Inthis hypothesis the mixed states can be constructed fromthe separate states of the 4f and the 5d electrons withinthe crystal. Since, in KY3F10, LiYF4, and BaY2F8 as well,the Pr31 ions substitute for Y31 ions in tetragonally dis-torted cubic sites of C4n , S4 (or D2d), and C2 symmetry,respectively, the 5d orbitals split first, in Td symmetry,into two—E and T2 , with E being lower. Then the E or-bitals split into two components, and the T2 orbitals splitinto two or three components, depending on the local dis-tortion (see Table 2).

Although a discussion of many details must be deferredto a future paper, a little more can be set forth here tohelp one understand the complexity of the problem to besolved. We first consider the energy levels of the 4f5delectronic configuration for the free ion. As reported inRef. 30, the energy spacings (a few thousand inverse cen-timeters) among the different spectral terms resultingfrom the 4f –5d electrostatic interaction have a magni-tude comparable with that produced by the local crystalfield on the 5d orbitals. Consequently, it is likely thatthe electrostatic and the local distortion Hamiltoniansshould have to be treated together. At the moment,without knowing the energies of the resulting states, wecan only predict their nature and their symmetry. Let usconsider the case of Pr:LiYF4, for which complete GSAdata are available.16 The local site symmetry is S4 , sothe 5d(e) orbital component of lower energy (in Td sym-metry), state 5d(2E), splits into two spin doublets 2G1and 2G2 (in Bethe notation,31 for example). However, ifwe neglect spin-orbit interaction with respect to electro-static interaction, the orbital wave functions of the 4felectron, i.e., of the 4f(2F) state, transform as follows(through decomposition of the reducible representationD3 for l 5 3): G1 1 2G2 1 2G3,4 (or A 1 2B 1 2E, in

Table 2. Splitting of the Levels withCrystal-Field Symmetry

Orbital KY3F10 (C4v) LiYF4 (S4) BaY2F8 (C2)

E A1 1 B1 A(G1) 1 B(G2) A(G1) 1 B(G2)T2 B2 1 E B(G2) 1 E(G3,4) A(G1) 1 2B(G2)

Mulliken notation). So, electrostatic coupling4f(2F)5d(2E) should result in two sets of spin singletsand spin triplets, which we can label 1,3GE1 and 1,3GE2 ,respectively, with

GE1 5 G1~G1 1 2G2 1 2G3,4! 5 G1 1 2G2 1 2G3,4 ,

GE2 5 G2~G1 1 2G2 1 2G3,4! 5 G2 1 2G1 1 2G3,4 .

Then the same decompositions can be done for the 3H4ground state and for the 3P0 and the 1D2 excited states.With the electric dipole selection rules for the differentcrystal symmetries, attempts can then be made to pro-pose some order in the 4f5d energy levels, but it is pref-erable to wait for more data (low-temperature data andspectra recorded over a more extended wavelength do-main) and for more-specific calculations to flesh out theproposal. It is interesting, however, that the GSA spec-tra alone certainly cannot reveal all the 4f5d energy lev-els and that many different energy levels can be reachedby means of ESA transitions, as we have actually ob-served.

6. EXCITED-STATE EXCITATION ANDTWO-STEP PUMPING MODELThe different ESA spectra reported above confirm thattwo-step excitation should be an efficient upconversionprocess for population of 4f5d energy levels in Pr-dopedfluoride crystals. Compared with other ESA’s betweenenergy levels that all result from the same 4f n configura-tion, which is the usual case encountered for upconver-sion in rare-earth-doped laser materials, the second stepis here greatly enhanced because of the high value of the4f 2 → 4f5d ESA cross sections (sESA is 3 orders of mag-nitude higher than for intraconfigurational ESA transi-tions). Even if the excited-state ion density obtained af-ter the first pumping step is limited to only a few percentof the dopant concentration, the second step can effi-ciently bleach the intermediate metastable level andgives rise to a final 4f5d population that has significantdensity compared with a direct 4f 2 → 4f5d excitation.To demonstrate such a two-photon effect experimentally,we simultaneously sent onto our Pr:LiYF4 sample the sig-nal wave of the optical parametric oscillator at approxi-mately l1 5 450 nm and part of the pump residue atl2(3P0 → 4f5d) 5 355 nm (third harmonic of theNd:YAG laser). According to Fig. 7, the ESA cross sec-tion at n(4f5d) 5 n(3P0) 1 n(3P0 → 4f5d) 5 49 030cm21 (with a value of approximately 0.4 3 10218 cm2 in spolarization) is far from being maximum, but the use ofthe pump residue has the advantage of facilitating thetemporal and the spatial overlap of the two pulsed pumpbeams. A schematic representation of the two-steppumping process can be found in Fig. 4. As expected,though the second pump source is not perfectly adequate,the stepwise excitation gives rise to a strong UV emission,and the registered fluorescence spectrum is exactly thesame as the one reported in Fig. 2. Similar results wereobtained for Pr:KY3F10 and Pr:BaY2F8.

We further investigated the efficiency of this two-steppumping process by estimating the single-pass gain thatcan be obtained from such a potential UV laser system.

2276 J. Opt. Soc. Am. B/Vol. 16, No. 12 /December 1999 Laroche et al.

We assumed two pulsed laser beams, each with time du-ration tp1 5 tp2 5 5 ns and energy E1 5 E2 5 1 mJ andfocused on cross sections s1 5 s2 5 2 3 1023 cm2 of asample of length l 5 2 mm [which indicates pump flu-ences of 0.5 J/cm2, which is generally enough, for ex-ample, to achieve laser threshold with Ce-doped lasercrystals (see, e.g., Refs. 6 and 10)].

With a system such as Pr:KY3F10, the first excitationstep is realized with a laser tuned at l1 5 445 nm (3H4→ 3P2 GSA cross section s1 5 3.75 3 10220 cm2); thesecond step, with a laser tuned at l1 5 355 nm (3P0→ 4f5d ESA cross section s2 5 0.4 3 10218 cm2). De-noting by N1 , N2 , and N3 the instantaneous populationsof the 3H4 ground state, the 3P0,1,2 excited multiplet, andthe 4f5d electronic configuration, respectively, we cancalculate the single-pass gain, given by

G 5 exp$@N3sSE~lg! 2 N2sESA~lg!#%, (7)

by solving the following system of rate equations:

]N1

]t5

N2

t2b21 1

N3

t3b31 2

E1s1l1

tp1hcs1f1~t !N1 ,

]N2

]t5 2

N2

t21

E1s1l1

tp1hcs1f1~t !N1 2

E2s2l2

tp2hcs2f2~t !N2 ,

]N3

]t5 2

N3

t31

E2s2l2

tp2hcs2f2~t !N2 . (8)

Here the branching ratios for the 3P0 and the 4f5d emis-sions down to the ground state b21 and b31 are set equalto 1. Their fluorescence lifetimes are given by t25 30 ms and t3 5 26 ns, respectively, and f1 and f2 standfor the normalized Gaussian shapes of the pump pulses.sSE 5 1.2 3 10218 cm2 and sESA 5 0.05 3 10218 cm2 arethe cross sections of the 4f5d stimulated emission and ofthe 3P0 → 4f5d ESA transition, respectively, at the cho-sen probe emission wavelength lg 5 266 nm.

The result of this simulation is reported in Fig. 10.The second pump pulse was intentionally delayed by ;6ns after the first, and, in these conditions, gain reaches amaximum some 17 ns later, with a value G 5 1.2, whichindicates 20% gain per pass. It is worth remembering,however, that one achieves this simulation by assumingnegligible ESA of the pump and emitted photons in the

Fig. 10. Temporal evolutions of the 3H4 ground state, the3P0,1,2 excited multiplet, and the 4f5d electronic configurationpopulations N1, N2, and N3 after two-step excitation pumping.

4f5d emitting state and that, while this assumptionmight be warranted at particular wavelengths and/or forparticular polarization conditions, it has not yet beenproved.

7. CONCLUSIONThis paper reports, for the first time to our knowledge, de-tailed 4f n –4f n215d interconfigurational ESA spectra fora trivalent rare-earth ion, here Pr31 (n 5 2), in variousfluoride crystals, KY3F10, LiYF4, and BaY2F8, crystalsgrown in our laboratory. The complex electronic struc-ture of the first excited electronic configuration 4f5d forPr31 is thus clearly demonstrated. Because they areboth polarized and better spectrally resolved, ESA spectrareveal many more structures than do unpolarized ground-state absorption or excitation spectra performed in thevacuum-UV domain. Though ESA spectra associatedwith the absorbing spin singlet and spin triplet, 1D2 and3P0 , respectively, differ significantly with the appearanceof distinct energy levels, it is difficult to say at this timewhether this distinction is linked with any spin orangular-momentum selection rule, as in the case of a pureL –S coupling. A definitive assignment will have to bedeferred until there are low-temperature data and spe-cific calculations that thoroughly consider crystal-fieldand electrostatic interactions.

These ESA measurements enable us to predict an opti-mized wavelength for the second step under two-photonexcitation, using a step-by-step mechanism. This upcon-version process is a possible way to alleviate the solariza-tion problems and to overcome the lack of practical pumpsources in the near UV. The simulation of such upcon-version pumping reported here is encouraging. Assum-ing negligible ESA in the emitting level, which is probablytoo optimistic, 20% laser gain per pass is demonstrated.Gain measurements by synchronized pump laser radia-tion and by use of a probe beam that can be tuned to thevarious emission peaks are under way.

ACKNOWLEDGMENTSThis work was partially supported by the European Re-search Office of the U.S. Army under Contract N68171-97-M-5764.

Address correspondence to M. Laroche atmoncorge@spalp255.ismra.fr.

*Present address, Department of Natural Sciences,University of Houston–Downtown, One Main Street,Suite N-813, Houston, Texas, 77002-1001.

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