Judd±Ofelt intensity parameters and laser analysis of Pr3�

doped phosphate glasses sensitized by Mn2� ions

G. Ajithkumar a, P.K. Gupta b, Gin Jose a, N.V. Unnikrishnan a,*

a School of Pure & Applied Physics, Mahatma Gandhi University, Priyadarshini Hills PO, Kottayam, Kerala 686 560, Indiab Laser Fusion Laboratory, Centre for Advanced Technology, Indore 452 013, India

Received 18 December 1998; received in revised form 27 September 1999

Abstract

In this paper, we report the preparation and optical characterization of Mn2� activated Pr3� doped phosphate glasses

in four di�erent chemical compositions. The optical absorption spectra of Pr3� ions in phosphate glasses have been

recorded in the UV±VIS±NIR region. From the data available in the optical absorption spectra, various spectroscopic

parameters such as Slater±Condon (F2, F4, F6), Racah (E1, E2, E3), spin-orbit interaction (n4f ) and Judd±Ofelt (J±O)

(X2, X4, X6) parameters are derived. The calculated values of the J±O parameters are utilized in evaluating the various

radiative parameters such as electric dipole line strengths (Sed), magnetic dipole line strengths (Smd), radiative transition

probabilities (ARAD), radiative lifetimes (sRAD), ¯uorescence branching ratios (bR) and the integrated absorption cross-

sections (ra) for stimulated emission from various excited states of Pr3� ion. The principal ¯uorescence transitions of

interest are identi®ed by recording the ¯uorescence spectrum and measuring their stimulated emission cross-section and

optical gain. Quantum e�ciencies of the prominent lasing transitions are estimated by measuring their radiative and

¯uorescence lifetimes. The dependence of e�ective radiative lifetime on Pr3� ion concentration is discussed in the light of

non-radiative processes such as multiphonon relaxation and energy transfer between like and unlike ions. Ó 2000

Elsevier Science B.V. All rights reserved.

1. Introduction

In the development of optically pumped solidstate lasers rare earth materials play a very im-portant role. This is because of the multitude ofenergy levels possessed by these ions when in-corporated into a solid state matrix. A lot of rareearth doped optical materials can be suitablyprocessed so as to get laser action in the entire

visible and ultraviolet region. E�orts are beingmade to discover new laser materials for variousapplications and thus laser action has been ob-served in a large number of crystalline andamorphous media doped with rare earth ions. Insolid state rare earth doped laser materials, sev-eral energy levels capable of producing stimu-lated emission in the wavelength range of 500±3000 nm have been found amongst the rare earthions.

The ¯uorescence e�ciency of an active ion ina material depends on various spectroscopicparameters [1] such as the absorption andemission cross-sections, transition probabilities,

Journal of Non-Crystalline Solids 275 (2000) 93±106

www.elsevier.com/locate/jnoncrysol

* Corresponding author. Tel.: +91-481 597923; fax: +91-481

597731.

E-mail address: spapforum@vsnl.com (N.V. Unnikrishnan).

0022-3093/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved.

PII: S 0 0 2 2 - 3 0 9 3 ( 0 0 ) 0 0 2 4 4 - 1

lifetimes of the metastable levels, concentrationsof the dopant ions and also the e�ect of the li-gand ®eld on them. Glasses are promising hoststo investigate the in¯uence of microscopic envi-ronments on the optical properties of the rareearth ions [2]. In the last few decades, a plethoraof investigations has been carried out to under-stand the ¯uorescence e�ciency of trivalent rareearth ions in various glassy matrices [3]. Spec-troscopic studies of trivalent praseodymium ionshave received much interest because of theirgood ¯uorescence e�ciency in the visible andinfrared region. Laser action has been observedin several Pr3� incorporated crystalline andglassy systems [1,4±19]. The Pr3� ion exhibits anexceptional spectroscopic behaviour in compari-son with other trivalent rare earth ions. It wasfound that application of Judd±Ofelt (J±O) the-ory to Pr3� activated system yielded poor resultsin comparison with experimental observations.Absorption spectra of Pr3� also show certainunusual and unique features under the in¯uenceof dopant concentrations on transition intensities[20]. The optical properties of Pr3� ions havebeen studied in numerous glassy hosts [7±19]with particular interest on their radiative andnon-radiative transitions and their dependenceon the glass compositions. Divalent manganese(Mn2�) is considered as an e�cient energy sen-sitizer for almost all trivalent rare earth ions[21]. Due to the non-radiative energy transferfrom Mn2� to the rare earth ions the ¯uores-cence intensity and hence the optical gain of thetransitions can be enhanced too much. The aimof the present study is (i) to investigate the ra-diative properties of Pr3� ion sensitised by Mn2�

ion in phosphate glasses using the well-known J±O theory [22,23], (ii) to elucidate the variousnon-radiative mechanisms such as multiphononrelaxation of Pr3� ion and energy transfer be-tween Mn2� and Pr3� ions and (iii) to study thecross-relaxation between Pr3� ion pairs. Theaforesaid analyses clearly show that the radiativeand multiphonon relaxation rates are indepen-dent of the Pr3� ion concentration, while thenon-radiative relaxation rate due to energytransfer is largely dependent on Pr3� ion con-centration.

2. Experimental

The glasses were prepared using 99.9% puritysodium dihydrogen phosphate, manganese car-bonate and 99.99% purity praseodymium oxide.The following batch compositions were taken formelting:

Here NaH2PO42H2O functions as the networkformer, while Pr2O3 acts as the network modi®er.Also MnCO3 is added as an energy sensitizer toPr3� ions [24]. Calculated quantities of the chem-icals were mixed in an agate mortar and heated atabout 900°C in an electric furnace for 5 h in silicacrucibles so that a homogeneously mixed melt isobtained. The melt was quickly transferred on to apreheated brass mould and was pressed by a sim-ilar brass disc to obtain glass discs of 2-mmthickness having a diameter of 2 cm. The glassdiscs thus obtained were annealed at a temperaturebelow the glass transition temperature for 3 h andthen taken out and polished well. Glass formationwas con®rmed by X-ray di�raction analysis. Therefractive indices of the glasses were measuredusing an Abbe refractometer. The densities ofthese glasses have been measured at room tem-perature using xylene as the immersion liquid. Thedopant concentrations in the glasses were deter-mined from the starting batch composition anddensity of the glass samples.

Absorption spectra of the glasses were recordedin the UV±VIS±NIR region on a spectrophotom-eter. The systematic errors associated with thespectrophotometer are 50 cmÿ1 for the x-axis and0.00001 Abs. for the y-axis. The excitation, emis-sion and decay time measurements were carriedout using a spectro¯uorimeter with the 488-nmexcitation from an Ar� ion laser. The systematicerror for the spectro¯uorimeter is �0.2 nm (x-axis)

Glass A 94NaH2PO42H2O5MnCO3 1Pr2O3

Glass B 94.4NaH2PO42H2O5MnCO3 0.6Pr2O3

Glass C 94.8NaH2PO42H2O5MnCO3 0.2Pr2O3

Glass D 94.25NaH2PO42H2O5MnCO3 0.75Pr2O3

94 G. Ajithkumar et al. / Journal of Non-Crystalline Solids 275 (2000) 93±106

and the signal to noise ratio for the y-axis is2000:1. All the spectra were taken at laboratorytemperature.

3. Results

3.1. Spectroscopic parameters

From the absorption spectra (Fig. 1) the energycan be computed theoretically using either theTaylor series expansion method [25] or the 4f2

energy matrix diagonalization procedure [26].Following the Taylor series expansion method, wehave calculated the Slater±Condon and spin-orbitinteraction parameters [27] which contain param-eters relevant to the radiative properties of the ion.By employing a computerized least square analysis[28] the values of the interaction factors DFk andDn4f were evaluated. These were then added to thezero-order parameters to obtain the F2, F4, F6 andn4f parameters of the Pr3� ion in the respectiveglass compositions [29,30]. Knowing the values ofthe Fk parameters, the Racah parameters (E1, E2,E3) can be evaluated using standard equations [30].A convenient way of representing the intensity ofan absorption band is to measure the oscillatorstrength of the transition, which is found to beproportional to the area under the absorption lineshapes. Oscillator strength (f) can be expressed interms of the molar extinction coe�cient (e), and

the energy of the transition in wave number (m) bythe relation [31]

f exp � 4:32� 10ÿ9

Ze�m�dm �1�

The electronic transitions of the trivalent lantha-nides can be electric dipole, magnetic dipole orelectric quadrupole in nature [32]. Electric dipoletransitions between the states of the 4fN con®gu-ration of an isolated trivalent rare earth ion areprohibited by the parity selection rule [27]. Thisprohibition can be more or less avoided due to thenon-centrally symmetric interactions of the ionswith its surroundings, which mix states of oppositeparity and thus relaxing the parity restriction.Electric dipole transitions may also occur as a re-sult of the symmetries produced by means of thevibronic coupling of the central ion with its ligands[33]. In contrast to this parity restriction, electricquadrupole and magnetic dipole transitions areparity allowed [27]. Neglecting higher multipolemechanisms such as electric quadrupole transi-tions, oscillator strength (f) can be regarded as asum of the electric dipole (fed) and magnetic dipole(fmd) contributions. The J±O theoretical analysis[22,23] of the absorption spectra yielded the J±Oparameters. The matrix elements and the 6j sym-bols required for the analysis have been takenfrom the literature [34,35]. The matrix elementswere then transformed from the LS basis state tothe physical coupling scheme prior to being used inthe calculation [26]. Table 1 summarizes all therelevant spectral parameters computed by thisanalysis. The experimental oscillator strengths(fexp) and theoretically calculated oscillatorstrengths (fthe) are given in Table 2.

3.2. Radiative transition parameters

Radiative transition parameters such as totalradiative transition probability (AT), radiativelifetime (sRAD), and the ¯uorescence branchingratio (bR ) are calculated using the known expres-sions [36,37].The integrated absorption cross-sec-tion or e�ective cross-section (ra) for stimulatedemission is estimated using the Fuchtbauer±Ladenberg equation [38]. The e�ective cross-sec-

Fig. 1. Room temperature absorption spectrum of Pr3� ion in

phosphate glass (Glass A composition).

G. Ajithkumar et al. / Journal of Non-Crystalline Solids 275 (2000) 93±106 95

tion which is the stimulated emission cross-sectionintegrated over the total band gives a measure ofthe peak stimulated emission cross-section fortransition under the assumption that the bands donot contain sharp emission peaks.

The emission spectra of all the glasses arefound to be almost identical in nature except intheir bandwidths and peak intensity values andtherefore a representative spectrum correspondingto the glass A composition is shown in Fig. 2. Bymeasuring the frequency width (Dm) and thepeak wavelength (kp) of the various ¯uores-

cence transitions, the stimulated emission cross-sections re can be evaluated using the equation[39]

re � k2pA��W0J 0;WJ�=4p2n2Dm: �2�

The quantum e�ciency (g) of the emission statewas computed from [4]

g � sLUM=sRAD; �3�where sLUM is the measured lifetime and sRAD isthe radiative lifetime.

Table 1

Values of the various spectral parameters derived for Pr3� ions in the four glass compositions studieda

Parameters Glass A Glass B Glass C Glass D

F2 318 318 318 318

F4 56 56 55 54

F6 5.32 5.32 5.33 5.31

F2 71 550 71 550 71 550 71 550

F4 60 984 60 984 59 895 58 806

F6 39 164 39 164 39 237 39 090

E1 5094 5094 5066 5040

E2 20.8 20.8 21.1 21.4

E3 480.6 480.6 478.3 477

E1/E3 10.59 10.59 10.59 10.56

E2/E3 0.04 0.04 0.04 0.04

F4/F2 0.85 0.85 0.83 0.82

F6/F2 0.54 0.54 0.54 0.54

X2 ´ 1020 cm2 0.25 � 0.03 )1.81 � 0.24 1.31 � 0.16 )0.07 � 0.02

X4 ´ 1020 cm2 7.47 � 0.44 11.18 � 2.2 19.37 � 2.15 3.17 � 0.32

X6 ´ 1020 cm2 5.37 � 0.36 12.95 � 1.02 18.68 � 3.12 3.93 � 0.18

n 1.536 1.495 1.452 1.523

n4f 764 764 765 737

Ionic concentration (1020 ions/cm3) 6.07 3.64 1.21 4.8

a All the F and E parameters are in cmÿ1. Free ion parameters : F 02 � 305 cmÿ1, F 0

4 � 51:88 cmÿ1, F 06 � 5:321 cmÿ1, n4f � 730.5 cmÿ1.

Table 2

Experimentally and theoretically observed oscillator strengths of Pr3� ion

Levels from 3H4 Glass A Glass B Glass C Glass D

fmeas fcal fmeas fcal fmeas fcal fmeas fcal

3P2a 14.32 � 1.7 ± 21.49 � 1.4 ± 34 � 5.2 ± 6 � 0.97 ±

3P1 6.3 � 1.5 4.53 8.6 � 1.2 6.5 12.7 � 5.3 10.9 3 � 0.95 3.73P0 5.2 � 1.5 4.49 5.16 � 1.2 6.5 9.72 � 0.8 10.7 1.5 � 0.93 3.71D2 5.68 � 1.4 1.14 5.67 � 1 2.3 6.2 � 0.42 3.3 2.6 � 0.91 0.713F4 1.77 � 0.8 3.42 3.54 � 0.2 7.6 6.63 � 0.5 10.75 1.7 � 0.6 4.63F3 6.0 � 1 6.7 13 � 0.6 13.3 17.7 � 3.3 20 3.5 � 0.71 8.13F2 4.67 � 1.2 3.2 5.19 � 0.78 4.1 12.3 � 3.3 8.7 2 � 0.67 2.8

RMS (10ÿ6) �3.1 �3.4 �3.9 �3.6

a Hypersensitive transition.

96 G. Ajithkumar et al. / Journal of Non-Crystalline Solids 275 (2000) 93±106

In order to determine the gain property of thematerial quantitatively, the gain coe�cient, a(m)can be evaluated using the expression [40]

a�m� � N Pre�m�� ÿ �1ÿ P �ra�m��; �4�where P stands for the population of the upperlaser level divided by the total ionic concentrationand ra is the absorption cross-section. Optical gainof an emission component can be evaluatedknowing the gain coe�cient and the length of theexciting material. In fact, we obtained the radiativeparameters for all the glass compositions and as arepresentative case the various parameters of theprincipal ¯uorescence transitions originating fromthe 3P0, 3P1 and 1D2 manifolds of Glass A com-position are summarized in Table 3. The opticalgain values and stimulated emission cross-sectionsfor all the four compositions are collected inTable 4.

3.3. Non-radiative decay processes

In the case of non-radiative multiphonon re-laxation process, the excitation energy of the ion istransformed into a discrete number of phonons.Given the energy of the phonons mediating themultiphonon relaxation process, it is possible toevaluate the non-radiative multiphonon relaxationrate. This can be done by using an approximateexponential energy gap law [41]

Wmp � W �0��1� n�p; �5� Ta

ble

3

Rad

iati

ve

para

met

ers

of

the

pri

nci

pal

emis

sio

ntr

an

siti

on

sfr

om

the

3P

0,

3P

1an

d1D

2m

an

ifo

lds

of

Pr3�

ion

inG

lass

Aco

mp

osi

tio

na

Pa

ram

eter

s3P

0!

3H

51D

2!

3H

43P

0!

3H

63P

0!

3F

23P

1!

3F

33P

1!

3F

41D

2!

3H

53P

0!

3F

3

k p5

70

.68

59

0613

648.5

689.7

5710.3

699.1

770.3

7

Dk p

(nm

)6

.87

9.3

811.2

710.3

17.5

25.6

13.1

511.2

5

AT

(sÿ1

)9

74

4�

10

68

78

�2

39744

�104

9744

�98

21522

�155

21522

�160

878

�25

9744

�108

s RA

d(sÿ1

)1

02

�5

11

38

�48

102

�8

102

�6

46

�2

46

�3

1138

�52

102

�9

b R(c

alc

)(%

)0

40

.616.4

2.7

90

10.5

2.0

50

b R(e

xp

t)(%

)1

.02

11

.162

1.7

15.3

10.8

514

3.7

7

r a´

10

18

(cm

2)

00

.73.4

0.6

35.9

0.5

0.0

50

aT

he

esti

ma

ted

erro

ris6

5%

.

Fig. 2. Emission and excitation spectra of Pr3� ion in glass A

composition at room temperature. kexc� 445 nm. (Excitation

peaks: (1) 3H4 ® 3P2, (2) 3H4 ® 3P1, (3) 3H4 ® 3P0. Emission

peaks: (1) 3P0 ® 3H5, (2) 1D2 ® 3H4, (3) 3P0 ® 3H6, (4)3P0 ® 3F2, (5) 3P1 ® 3F3, (6) 1D2 ® 3H5, (7) 3P1 ® 3F4, (8)3P0 ® 3F3).

G. Ajithkumar et al. / Journal of Non-Crystalline Solids 275 (2000) 93±106 97

where W �0� � Bexp�ÿaDE�. Here B and a areconstants which are typical of the glass host, n isthe thermal occupation of the phonon mode offrequency, x.

Assuming B � 5:4� 1012 sÿ1 and a � 4:7� 10ÿ3

cm for the phosphate glass matrix [42,43] the non-radiative multiphonon relaxation rate, Wmp valueswere evaluated for the four glass compositions.

As the concentration of the impurity ions isincreased the average distance between the ionsdecreases which in turn causes greater interactionbetween the ions. Consequently, the excitationenergy residing on one ion (donor) can non-radi-atively be transferred to another ion (acceptor).This type of energy transfer can take place betweenlike and unlike ions and the energy transfer be-tween like ions is usually known as cross-relax-ation.

According to the well-known Forster±Dextertheory [44,45] of multipole interaction, energytransfer can occur between a donor and an ac-ceptor provided the emission transition of thedonor overlaps with the acceptor absorptiontransition. Mathematically, the transfer probabil-ity can be expressed as

WMn±Pr � R1=ss�R0=R�ss�6;8;10

; �6�

where s� 6, 8, 10 for dipole±dipole, dipole±quad-rupole and quadrupole±quadrupole interactionsrespectively and ss is the decay time of the sensi-tizer in the absence of the activator, R the sepa-ration between the donor and acceptor and R0 thecritical separation. Also the critical separation, R0

is given by

R60�d±d� � 3h4c4

4pn4QA

ZfS�E�FA�E�dE

E4

�dipole±dipole�;

R80�d±q� � 135ph9c8

4n4QA

ZfS�E�FA�E�dE

E8

�dipole±quadrupole�;

R100 �q±q� � 225ph11c10

2n6

ZfS�E�FA�E�dE

E10

�quadrupole±quadrupole�;�7�

where fS�E� is the normalized emission line shapefunction of the sensitizer, fA�E� the normalizedlineshape function of the activator, n the refractiveindex of the host medium, QA is the oscillatorstrength of the absorption transition of the acti-vator which is in resonance with the sensitizeremission transition and E is the average energy ofthe overlapping transition. In the emission spectra,Mn shows a broad band transition in the 600 nmregion and this corresponds to the a4F ® 6Semission transition of Mn2� ion. Since this tran-sition is in resonance with the 3H4 ® 1D2 absorp-tion transition (585 nm) of Pr3� ion, there is astrong overlap between these transitions andthereby a strong non-radiative transfer betweenthese ions. In addition to the aforesaid energytransfer process, energy transfer can also occurdue to the cross-relaxation between two Pr3� ions.For energy transfer to occur by cross-relaxationthere should be two pairs of energy levels withidentical energy mismatch between them. When

Table 4

Optical gain values and stimulated emission cross-sections in Glass A, B, C and D compositions

Glass A rE ´ 1020 (cm2) 5.49 4.51 271.1 10.2 123.3 29.7 7.99 41.2

G (dB/cm) 144.72 101 3955 268.8 1815 782.9 210.6 542

Glass B rE ´ 1020 (cm2) 24.3 9.3 804.2 33.8 250.6 63 16 123.6

G (dB/cm) 384 139.4 6931 534 2172 995 252 978

Glass C rE ´ 1020 (cm2) 52.2 31 1420 116 597.2 78 30.2 317.7

G (dB/cm) 274 161.8 4114 609 1452 409 158 1027

Glass D rE ´ 1020 (cm2) 10.2 4.8 401.5 15.7 130.54 30.5 8.5 62.1

wG (dB/cm) 212.6 91.8 4567 327.2 1522 635 177.1 841

98 G. Ajithkumar et al. / Journal of Non-Crystalline Solids 275 (2000) 93±106

energy matching for resonance is too bad, phononassisted energy transfer may take place. For agiven decay channel, the cross-relaxation rates dueto Pr3�:Pr3� interaction [WPr:Pr] can be obtainedfrom the equation [42]

1=s � ARAD � Wmp � WMn:Pr � WPr:Pr; �8�

where s is the measured decay time of the con-cerned level.

4. Discussion

All the spectroscopic parameters, viz. theSlater±Condon (F2, F4, F6), spin-orbit (n4f ), Racahparameters (E1, E2, E3) and the hydrogenic ratios(E1/E3, E2/E3, F4/F2, F6/F2), are found to be con-stants irrespective of the matrix compositions.These parameters are therefore considered to befundamental constants for trivalent praseodymiumin a given matrix. The Slater±Condon parameters(Fk) generally represent the radial integral part ofthe electrostatic interaction matrix elements oftrivalent rare earth ion while the spin-orbit inter-action parameter (n4f ) represents the radial integralpart of the spin-orbit interaction matrix element[26]. For a free ion these interaction parametersare constants. But, when the ion is under the in-¯uence of another interacting ®eld (ligand ®eld orcrystal ®eld) these parameters change due to theoverlapping of the 4f wave functions of rare earthion with that of the surrounding ligand ion. As aresult of this overlapping e�ect, the distance be-tween the nucleus and the electron of the rare earthion changes slightly, which in turn a�ects the en-ergy levels and spectroscopic parameters [28].

The experimentally measured oscillatorstrengths of various absorption transitions of Pr3�

ion in the present glassy systems are found to be ingood agreement with that of other oxide systems.An examination of these oscillator strengthsclearly shows that the oscillator strength of the3H4 ® 3P2 transition is extremely large in com-parison with all other transitions. These hyper-sensitive transitions are observed in many otherrare earth ions also and show anomalous natureirrespective of the matrix environments [29]. This

hypersensitive transitions satisfy the selection ruleDS� 0, DJ��2. Because of the anomalous natureof this transition it is usually excluded from thecalculation of the J±O parameters. A close obser-vation of the absorption transition matrix ele-ments of Pr3� ion shows that the value of X2

parameters entirely depends on the 3H4 ® 3F2

transition because of the high value ofh3H4kU2k3F2i. Even though this matrix element iscomparatively larger, the oscillator strength of thistransition is comparable to all other transitionsexcept the hypersensitive transition 3H4 ® 3P2

transition. Therefore the value of X2 entirely de-pends on the nature of the 3H4 ® 3P2 transition. Ifthis transition is excluded in the calculation, thevalue of X2 will be extremely small in comparisonwith X4 or X6 and in some cases it assumes anegative value [13±15,18,19,46,47]. In the presentanalysis, even-though this hypersensitive transitionis excluded from the calculation it was found thatfor glasses B and D compositions, X2 is still neg-ative. The quality of ®t between the experimentaland theoretical oscillator strength can be expressedby the root mean square (RMS) deviation (Table2). These values are comparable to the RMS de-viations found by other investigators in manyother glassy matrices [8,9,13,19]. The larger RMSdeviation between the calculated and observedoscillator strengths in the case of Pr3� arises be-cause of the strong 4f±5d mixing [18] which isknown to bring about contributions to intensitiesthrough the matrix elements with odd values of kwhich are usually neglected in the J±O model. Anenergy level diagram for rare earth ions, reportedby Dieke [48] shows that the energy gap betweenthe centers gravity of 5d-electron energies and 4f-electron energies is the smallest for Pr3� ions. Thissuggests that strong mixing between the 4f and 5dorbitals can occur in this ion and this f±d mixinge�ect accounts for the negative nature of X2 inPr3� ion and its anomalous spectroscopic behav-iour. This has been discussed in detail by Riedet al. [49,50].

The X2 parameter in the J±O analysis is an in-dication of the extent of covalent bonding betweenthe rare earth ion and the surrounding ligand at-om. An increase in the value of X2 representsstronger covalent bonding with the host matrix.

G. Ajithkumar et al. / Journal of Non-Crystalline Solids 275 (2000) 93±106 99

Generally it is noted that X2 is higher in glassesthan in crystals [43]. In glassy systems, the dopantsare randomly distributed over non-equivalent siteswith a distribution in the crystal ®elds. A largenumber of impurity sites will thus occupy siteswith non-centrosymmetric potential, which isknown to contribute signi®cantly to X2 [43]. Thelarger values of X2 parameter in glassy hosts arisefrom this random distribution of dopant sites andlower site symmetry. A comparison of the X2 pa-rameters of various glasses (Table 5) shows that,for ¯uorides X2 parameter is the least showing thatthe covalency is least in ¯uoride glass matrix.

For Pr3� ion the various metastable levels fromwhich appreciable radiative transition can takeplace are 3P2, 3P1, 3P0, and 1D2 levels. Out of thevarious radiative parameters given in Table 3, the

three most important parameters of interest for alaser designer are the radiative lifetime, ¯uores-cence branching ratio and the stimulated emissioncross-section. The values of the various radiativeparameters derived for Pr3� ion in the presentphosphate matrix are almost in agreement withthat of other Pr3� doped glassy systems [13±19].The radiative lifetimes resulted from the presentanalysis, in general, show the tendency3F3 > 1G4 > 1D2 > 3P0 > 3P2 > 3P1 consistent withthose reported for other glassy materials (Table 6).

Fig. 2 shows the room temperature excitationand emission spectrum of Pr3� ion in glass Acomposition in the wavelength range of 300±800nm. The excitation spectrum (dotted line) displays®ve bands at 360, 411, 444, 469 and 482 nm. Thelatter three bands coincide in energy with the ab-sorption transitions 3H4 ® 3PJ (J� 0,1,2) and areeasily identi®ed. The excitation spectrum alsoshows two broad band transitions in the 360 nmand 411-nm region. These transitions cannot beassigned to any 4f ® 4f intra-con®gurationaltransition, since it is too broad and is located farfrom any 4f state (the 1S0 state should be muchmore higher). In fact, they could be identi®ed asinter-con®gurational 4f ® 5d transitions. Theanalysis of these two bands cannot be performedin the absorption spectrum because it overlapswith the absorption edge and contributes to itsanomalous rising at 25 777 cmÿ1 (Fig. 1).

It is quite evident that most of the ¯uorescencetransitions are occurring from the 3P0, 3P1 and 1D2

excited states. According to J±O theory, a total ofsix ¯uorescence transitions are allowed from 3P0

levels by the dipole mechanism: (3P0 ® 1D2, 1G4,3F4, 3H4;6). Since the matrix elementsh3P0kUkk3F3i, h3P0kUkk3H5i are zero, these twotransitions are not accounted by J±O theory in

Table 5

Comparison of J±O parameters of Pr3� ion in various glassy

matrices

Matrix X2 ´ 1020

cm2

X4 ´ 1020

cm2

X6 ´ 1020

cm2

K2O, B2O3 2.14 2.91 1.67

Na2O B2O3 0.77 4.13 3.07

Li2OB2O3 0.77 3.84 3.58

ZnOTe2O3 2.59 7.26 5.45

Na2OTe2O3 2.83 6.5 4.64

BaOTeO2 4.95 6.46 5.44

ZBLA 0.24 4.51 5.37

K2SO4 ZnSO4 )4.61 12.48 5.13

Fluorozirconate 2.5 5.4 6.0

Fluoroindate 3.2 4.5 6.5

Fluoride

phosphate

2.7 5.3 5.0

PbOPbF2 0.02 7.88 4.81

CaOB2O3 Al2O3 3.3 8.28 14.0

Fluoroborate )0.8 3.45 1.55

Borate )6.01 8.29 10.26

ZBLAN )7.7 18.45 1.43

Table 6

Radiative lifetimes (srad) (ls) of Pr3� ion in some glassy matrices

Matrix 3P03P1

3P21D2

3F31G4

ZBLA 41.1 41.1 40 605 1815 2695

K2SO4 ZnSO4 18 15 452

PbO PbF2 14 15 252 7813 813

Ca Pb2O3 Al2O3 16 15 198 600

Fluoroborate 27 26 467 1794

Borate 36.4 34.6 1934 1261

100 G. Ajithkumar et al. / Journal of Non-Crystalline Solids 275 (2000) 93±106

Pr3� ion. The existence of such transitions in theexperimentally observed spectrum is thus a failureof the J±O theory in the case of Pr3� ion. Anotheremission band from the 3P1 manifolds, viz.3P1 ® 3F3, could also be against the J±O theory.The presence of these bands can be accounted byconsidering the J±J mixing [51].

The linewidths (DkP) of various emission bandsof Pr3� ion in the present case are comparable withthe values reported for other phosphate and ¯uo-ride glasses [9,52]. A comparison of the experi-mental branching ratio (bexp), obtained from thearea under the ¯uorescence lineshapes, with thecalculated branching ratio (bcal) shows wide devi-ation which is also a result of the extremely lowvalue of X2 parameter in the present case. Thevalues of stimulated emission cross-sections (re)obtained in the present phosphate system are ex-tremely larger than the values reported in other¯uoride systems [43]. It should also be noted thatthe emission cross section is maximum for the3P0 ® 3H6, transition while minimum for the1D2 ® 3H5 transition (Table 4). The values ofthese maximum and minimum cross-sections arerespectively 92 and 14 times larger than that of¯uoride matrix. Since the stimulated emissioncross-section is maximum for 3P0 ® 3H6 transition,as expected, optical gain (G) is found to be thehighest for this transition. The variation of opticalgain coe�cient with the emission wavelength isgraphically shown in Fig. 3 for the four investi-gated glass compositions. From the ®gure, it can beseen that as the concentration of Pr3� ion increasesoptical gain of the emission components starts to

decrease and the reason for this ¯uorescencequenching is discussed by invoking cross-relaxation process between Pr3� ion pairs and thepresence of molecular impurities.

In most cases of our investigations, the quantume�ciency of the levels 3P0, 3P1 and 1D2 are alwaysfound to be less than unity, which is clearly amanifestation of the non-radiative processes takingplace in the system. Out of all the non-radiativeprocesses, the multiphonon relaxation processtaking place between adjacent levels has a non-negligible contribution in the case of Pr3� ion. Ithas been established that the multiphonon decayrates vary inversely as the energy gap between theparticipating levels [42]. Table 7 summarizes thedecay rates resulted from the analysis of the levels.The analysis favours an appreciable ¯uorescenceemission for the 3P0 and 1D2 levels, while it isconsiderably less for 3P1 level (Fig. 2). Fig. 4 illus-trates the multiphonon emission rate vs energy gapfor the four glass compositions. Since neither the

Fig. 3. Calculated gain coe�cient (a) vs emission wavelength in

the four glass compositions.

Table 7

Probabilities of non-radiative transitions of Pr3� ions by multiphonon relaxation in the four glass compositions studied

Transitions Glass A Glass B Glass C Glass D

DE

(cmÿ1)

Wmp

(sÿ1)

DE

(cmÿ1)

Wmp

(sÿ1)

DE

(cmÿ1)

Wmp

(sÿ1)

DE

(cmÿ1)

Wmp

(sÿ1)

3P2 ! 3P1 1082 3.9 ´ 1010 528 428 ´ 1011 1128 3.1 ´ 1010 756 1.69 ´ 109

3P1 ! 3P0 503 5.4 ´ 1011 503 5.4 ´ 1011 550 4.3 ´ 1011 400 8.6 ´ 1011

3P0 ! 1D2 3987 7.3 ´ 104 3987 7.3 ´ 104 4000 6.7 ´ 104 3900 10.9 ´ 104

1D2 ! 3F4 7220 30.6 ´ 10ÿ3 10 040 8.2 ´ 10ÿ8 10 097 6.4 ´ 10ÿ8 10 247 32.7 ´ 10ÿ9

3F4 ! 3F3 520 4.9 ´ 1011 511 5.1 ´ 1011 394 8.9 ´ 1011 450 6.9 ´ 1011

3F3 ! 3F2 1285 1.2 ´ 1010 1402 9.1 ´ 109 1388 9.7 ´ 109 1308 1.1 ´ 1010

3F2 ! 3H6 705 2.1 ´ 1011 708 2.0 ´ 1011 700 2.1 ´ 1011 690 2.3 ´ 1011

3H6 ! 3H5 2170 2.8 ´ 108 2180 2.6 ´ 108 2150 3.0 ´ 108 2140 3.2 ´ 108

3H5 ! 3H4 2320 14.2 ´ 107 2340 12.9 ´ 107 2300 14.3 ´ 107 2285 16.7 ´ 107

G. Ajithkumar et al. / Journal of Non-Crystalline Solids 275 (2000) 93±106 101

multiphonon emission process nor the radiativedecay process is found to be concentration inde-pendent, the ¯uorescence quenching at higheractive ion concentration is attributed to be due tothe concentration dependent energy transfer pro-cess.

Since the emission spectrum of Mn2� ion is al-ways found to overlap with the 3H4 ® 1D2 ab-sorption transition, according to Forster±Dextertheory the chance of non-radiative energy transferfrom Mn2� to Pr3� through multipole interactionis immense. This transfer probability, WMn:Pr canbe evaluated using Eqs. (6) and (7) and more de-tails about these calculations can be found in ourearlier communication [53]. Results show that theMn2�® Pr3� energy transfer probability is maxi-mum for glass A composition. Analysis also showsthat the values of the overlap integralR

fS�E�fA�E�dE varies only slightly from onecomposition to another and hence it will notcontribute much to the energy transfer process. Onthe other hand, the interionic separation, R, is themain parameter controlling the energy transferprocess. As the concentration of the active ions (N)increases, the average interionic separation de-creases �R � �3=4pN�1=3� which in turn increasesthe energy transfer as is clear from the glass Acomposition.

The other important process of energy transferis cross-relaxation between Pr3� ion pairs. This canhappen either by resonant cross-relaxation (whenenergy mismatch is small) or phonon assistedcross-relaxation (when large energy mismatch ex-ists) process. On analyzing the various experi-mental energy levels it can be seen that thefollowing cross-relaxation processes can bepossible.

Process 1. Cross-relaxation involving level 3P0

�a� 3P0�A� � 3H4�B� ! 1G4�A� � 1G4�B� � Nhx

DEÿ � 1267 cmÿ1

�;

�b� 3P0�A� � 3H4�B� ! 1D2�A� � 3H6�B� � Nhx

DEÿ � 895 cmÿ1

�;

�c� 3P0�A� � 3H4�B� ! 3H6�A� � 1D2�B� � Nhx

DEÿ � 895 cmÿ1

�:

Process 2. Cross-relaxation involving level 1D2.

�d� 1D2�A� � 3H4�B� ! 1G4�A� � 3F4�B� � Nhx

DEÿ � 190 cmÿ1

�;

�e� 1D2�A� � 3H4�B� ! 3F4�A� � 3F4�B� � Nhx

DEÿ � 3100 cmÿ1

�:

Process 3. Cross-relaxation involving level 3P1.

�f� 3P1�A� � 3H4�B� ! 1D2�A� � 3F2�B� � Nhx

DEÿ � 705 cmÿ1

�;

where A and B represent a pair of Pr3� ion im-purities participating in the cross-relaxation pro-cess. Out of these six cross-relaxation processes,process (d) can be considered as a resonant cross-relaxation process as the energy mismatch betweenthe interacting levels are comparatively smaller.All the rest of the processes are phonon assistedcross-relaxation processes. Assuming the maxi-mum phonon energy of phosphate matrix to be1300 cmÿ1, processes (a) and (e) can be identi®edas one phonon and two phonon processes respec-tively. Knowing the ¯uorescence decay time of therespective level and its radiative- and non-radiative

Fig. 4. Multiphonon emission rates of Pr3� ion as a function of

the energy gap to the next lowest level.

102 G. Ajithkumar et al. / Journal of Non-Crystalline Solids 275 (2000) 93±106

rates, its cross-relaxation rate can be evaluatedusing the Eq. (8). Our calculation shows that cross-relaxation rates for the phonon assisted processes(a, b, c, e and f) are negligibly small, while it hasgot a considerable contribution from the resonantprocess (d). The resonant cross-relaxation rate isfound to vary linearly with the ionic concentration(Fig. 5). It is also seen that the cross-relaxationrate [WPr:Pr] is thousand times larger than thetransfer rate WMn:Pr. Since this is the major cross-relaxation process occurring in our system it isexpected that this is responsible for the concen-tration quenching of the 1D2 emission. It shouldalso be noted that a similar cross-relaxation pro-cess satisfactorily explains the concentrationquenching of 1D2 emission from many crystallinesolids [4,5]. A schematic illustration of the cross-relaxation process [1D2, 3H4] ® [1G4, 3F4] betweentwo Pr3� ions (A and B) is shown in Fig. 6. Takinginto account of all the non-radiative processes, thee�ective decay time (seff ) of the 1D2 level can beplotted as a function of the ionic concentration asshown in Fig. 7.

In addition to the above described quenchingprocesses, molecular impurities present in thematrix will also a�ect the ¯uorescence. The onlymolecular impurity that has been studied to anyextent is OHÿ whose high vibration frequencygives it a strong e�ect on the non-radiative decayof the rare earth ion. The water content of phos-phate glasses can be very high because the OHenters the structure easily by converting a P ¸ Odouble bond to a single P±OH bond. The presenceof a small amount of water in our sample is con-

®rmed from the two OH bands observed in the3400 cmÿ1 and 1640 cmÿ1 regions of the IR spec-trum shown in Fig. 8. The quenching rates due toOH groups are usually expressed in terms of theabsorption coe�cient at the OHÿ fundamentalvibrational frequency and is directly proportionalto it [54].

A characteristic feature of the emission from3P0;1;2 manifolds is that their intensities are tem-perature dependent. As expected due to the rapid

Fig. 5. Cross-relaxation rates of 1D2 emission as a function of

ionic concentration.

Fig. 6. Schematic illustration of [1D2, 3H4] ® [1G4, 3F4] cross-

relaxation process in a Pr3� ion pair.

Fig. 7. E�ective decay rates of 1D2 level as a function of ionic

concentration.

G. Ajithkumar et al. / Journal of Non-Crystalline Solids 275 (2000) 93±106 103

non-radiative relaxation of the 3P2 level no ¯uo-rescence emission was observed from this level. Atlow temperature the population density will bemaximum in the 3P0 level, which results in an en-hanced emission intensity from this level. Since the3P1 level is lying very close to 3P0 with an energyseparation of � 550 cmÿ1, as temperature in-creases the enhanced Boltzmann population ofhigher Stark components of the ground state 3H4

facilitates direct excitation to 3P1 or the thermalexcitation from 3P0 to 3P1 level results in an en-hanced ¯uorescence from this level. The interpre-tation of the thermalization process involving 3P0

and 3P1 levels was given in detail by Shinn et al.[55]. A clear evidence for this interpretation theexperimental ¯uorescence spectra of Pr3� in manyglassy systems recorded at 77 K show that most ofthe e�cient transition occurs from the 3P0 excitedstate.

The measured ¯uorescence decay time (sLUM)and hence the quantum e�ciency (g) of the emis-sion from the 3P0, 3P1 and 1D2 excited metastable

levels are given in Table 8. Out of the four glasssamples, e�ciency is always found to be maximumin the batch C composition. For certain transitionsLUM is greater than sRAD and hence the quantume�ciency exceeds unity. The radiative life-timecalculated from the J±O intensity parameters is thesum of contributions from ions in sites havingdi�erent number densities, thermal level popula-tions, microscopic environment and line strengths.Therefore, the calculated radiative lifetime repre-sents some averaged time rather than the extremevalue. This is the case with all glassy systemsstudied and it accounts for the extremely highervalues of quantum e�ciency in some cases [56].

5. Conclusion

Spectroscopic approach using the optical ab-sorption and emission spectra of Pr3� ion inphosphate glassy matrices sensitized with Mn2�

ion yielded some of the important parameters ofradiative and non-radiative processes. The com-paratively small RMS deviation between the ex-perimental and theoretical oscillator strengthsshows the applicability of Taylor series expansionmethod in obtaining the theoretical spectroscopicparameters. Some of the most important spectro-scopic parameters, viz. Slater±Condon, spin-orbitinteraction and the associated spectroscopic pa-rameters, can also be derived using this approach.Applications of J±O theory to Pr3� ion in analyz-ing the radiative properties yielded poor agreementbetween theory and experiment and are attributedto the strong f±d mixing which is not accounted bythe theory. In order to identify the potential lasertransitions of interest the emission spectrum isanalyzed in detail and found that most of the ef-

Table 8

Experimental decay time (sLUM) and quantum e�ciencies of ¯uorescence transitions from the 3P0, 3P1 and 1D2 levelsa

Transitions Glass A Glass B Glass C Glass D

slum (ls) g (%) slum (ls) g (%) slum (ls) g (%) slum (ls) g (%)

3P0 40 39.2 43 113 44 191 42 59.11D2 120 10.5 165 25.7 300 78.1 150 12.53P1 20 43.4 23 85.1 27 168 21 43.7

a The random error is estimated to be 65%.

Fig. 8. Typical IR spectrum of the investigated glass showing

various vibrational band assignments.

104 G. Ajithkumar et al. / Journal of Non-Crystalline Solids 275 (2000) 93±106

®cient transitions are from the 3P0 and 1D2 mani-folds. Also stimulated emission cross-section, ¯u-orescence branching ratio and optical gain valuesare found to be maximum for the 3P0 ® 3H6

transition. When the concentration dependence ofthe emission intensity from various levels is stud-ied, it was observed that the 1D2 ® 3H4 emission ishighly a�ected with concentration quenching.Since multiphonon relaxation rate is concentrationindependent and Mn2�® Pr3� non-radiative en-ergy transfer has a negligible contribution infeeding the 1D2 level of Pr3� ion, the concentrationdependent cross-relaxation process [1D2,3H4] ® [1G4, 3F4] was responsible for the quench-ing of 1D2 emission at high-active ion concentra-tion. It is also observed that the high rate ofmultiphonon relaxation is primarily responsiblefor the reduction of ¯uorescence emission from the3P1 level. Hence we conclude that quenching of¯uorescence will be minimum in glass C compo-sition and hence this composition is quite ideal forlaser applications.

Acknowledgements

The authors are grateful to Dr D.D. Bhawal-kar, Director, CAT, Indore for extending thespectro¯uorimeter facility. G.J. gratefully ac-knowledges the award of a fellowship by CSIR,New Delhi. The authors are particularly thankfulto the referees for the critical reading of themanuscript and for many useful suggestions.

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