Analysis of the fluorescence decay of MCVD Nd Al-codoped SiO2 fiber-preforms prepared by rare-earth chelate delivery

15 February 1999

Ž .Optics Communications 160 1999 235–239

Analysis of the fluorescence decay of MCVD Nd Al-codopedSiO fiber-preforms prepared by rare-earth chelate delivery2

A. Martınez ), L.A. Zenteno, J.C.K. KuoĆentro de InÕestigaciones en Optica, A.C., P.O. Box 1-948, C.P. 37150 Leon, Gto., Mexico´

Received 15 April 1998; revised 15 September 1998; accepted 23 December 1998

Abstract

The fluorescence decay of the 4F transition in neodymium-doped silica optical fibers is analyzed with respect to3r2Ž .neodymium concentration and temperature. New experimental data are compared with theoretical calculations based on i

w Ž . x Ž . w Ž . Ž .Grant’s supposition W.J.C. Grant, Phys. Rev. B 4 1971 648 and ii the Forster T. Forster, Ann. Phys. Paris 2 1948¨ ¨x w Ž . x55 and Dexter D.L. Dexter, J. Chem. Phys. 21 1953 836 model. Grant’s predictions are in reasonable agreement with the

data. The nonexponential decay predicted by Forster and Dexter is insufficient to explain the experimental data. q 1999¨Published by Elsevier Science B.V. All rights reserved.

PACS: 32; 42.50; 42.60B; 42.80Keywords: Fluorescence decay; SiO ; Rare-earth chelate delivery2

1. Introduction

Rare-earth doped optical fibers have been successfullyused as fiber lasers and fiber amplifiers. Such fibers can

w xalso be used as sensors 1 . The change of the fluorescenceof a small glass sample doped with neodymium – excitedby infrared radiation – has been used in the construction of

w xa fiber-optic temperature sensor 2 . This application relieson precise knowledge of the temperature dependence ofthe fluorescence decay. On the other hand, a novel ap-proach for realizing fast all-optical switches in rare earthdoped fibers by utilizing the biexponential nature of the

w xfluorescence decay has been demonstrated 3,4 . Further-more, co-dopants such as Al and P are introduced intosilica-based glass to enhance the solubility of the rare earthw x5 , allowing a variation of the ‘fast’ decay time which

) Corresponding author. E-mail: [email protected]

opens the possibility of choosing the optical switch fre-quency.

w xA previous investigation 6 on the dynamic fluores-cence spectroscopy of Al,Nd:SiO fiber glasses prepared2

by rare-earth chelate delivery showed that the fluorescencedecay is essentially exponential for Nd O concentrations2 3

from 0.035 to 0.114 mol%, and biexponential for Nd O2 3

concentration between 0.146 and 0.172 mol%.w xThis work together with Ref. 6 provides a detailed

study of the properties of rare earth oxides in preforms orŽfibers prepared by chelate delivery. Data not included in

w x. ŽRef. 6 on fluorescence decay as a function of time and. 4 3qNd-concentration from the F level of Nd are com-3r2

Ž .pared to theoretical calculations based upon: i Grant’sw x Ž . w xassumption 7 and ii the Forster and Dexter model 8,9 .¨

The contributions of this paper are two-fold: it comple-w xments the characterization presented in Ref. 6 , necessary

for the developments described at the beginning of thissection and second, the data of this paper set stringentconstraints on the theoretical calculations, providing de-tailed information on the characteristics of the decay. In

0030-4018r99r$ - see front matter q 1999 Published by Elsevier Science B.V. All rights reserved.Ž .PII: S0030-4018 99 00009-7

( )A. Martınez et al.rOptics Communications 160 1999 235–239´236

this respect, it is important to recall that the Forster and¨ŽDexter model predicts a nonexponential but not biexpo-

.nential! fluorescence decay.

2. Grant’s assumptions

Ž .The inverse of the 1re fluorescence decay time t isŽ .given by the sum of the radiative W and nonradiativeR

Ž .W rates where the contribution to the nonradiative rateNR

W comes from the ion–ion energy transfer W andNR ion – ion

from the multiphonon emission process, which is denotedas W :MP

ty1 sW qW , 1Ž .R NR

where

W sW qW .NR ion – ion MP

We define

W sW qW , 2Ž .RqMP R MP

In terms of W , the 1re decay time is rewritten as:RqMP

y1Wion – iony1

ts W 1qŽ .RqMP ž /WRqMP

t RqMPs . 3Ž .

1qW rWŽ .ion – ion RqMP

w xGrant 7 assumed that the ratio of transition probabilitiesŽ .entering Eq. 3 , has a power law dependence upon the

Nd O -concentration, and that those powers reflect the2 3

Fig. 1. 1re fluorescence decay time versus neodymium-concentra-tion. The solid curve is the theoretical calculation with Grant’sassumption.

Ž .Fig. 2. ln normalized emission decay versus time at room temper-Ž .ature for neodymium-concentration of 0.035 mol% data 1 and

Ž .0.1792 mol% data 2 . Dashed curves show the Forster and Dexter¨Ž Ž .. Žpredictions Eq. 8 with and t s569 ms and ks0.3261 dashed0

. Ž .curve 1 and ks1.4046 dashed curve 2 . Predictions from theŽ . Ž .biexponential decay solid curves are obtained from Eq. 6 with

Ž .t s534 ms, t s136 ms and ´ s0.90 solid curve 1 and1 2Ž .t s410 ms, t s113 ms and ´ s0.68 solid curve 2 .1 2

number of particles participating in the energy transferprocess.

nW rion – ion Nds , 4Ž .ž /W rRqMP 0

Thus, in this model, the 1re decay time is given by:t RqMP

ts . 5Ž .n1q r rrŽ .Nd 0

where r is the Nd O concentration and r is theNd 2 3 0

‘critical concentration’ which is defined as the concentra-Ž .tion for which tst r2. A least-squares fit of Eq. 5RqMP

Ž .Fig. 3. ln normalized emission decay versus time at 5008C forŽ .neodymium-concentration of 0.035 mol% data 1 and 0.1792

Ž .mol% data 2 . Dashed curves show the Forster and Dexter¨Ž Ž .. Žpredictions Eq. 8 with t s569 ms and ks0.3102 dashed0

. Ž .curve 1 and ks1.7624 dashed curve 2 . Predictions from theŽ . Ž .biexponential decay solid curves are obtained from Eq. 6 with

Ž .t s532 ms, t s132 ms and ´ s0.89 solid curve 1 and1 2Ž .t s400 ms, t s90 ms and ´ s0.67 solid curve 2 .1 2

( )A. Martınez et al.rOptics Communications 160 1999 235–239´ 237

Ž .Fig. 4. ln normalized emission decay versus time at room temper-ature for neodymium-concentration of 0.088 mol%. Dashed curve

Ž Ž ..shows the Forster and Dexter predictions Eq. 8 with t s569¨ 0Ž .ms and ks0.3987 dashed curve . Predictions from the biexpo-

Ž . Ž .nential decay solid curve is obtained from Eq. 6 with t s5281Ž .ms, t s128 ms and ´ s0.86 solid curve .2

to experimental data yielded, t s540 ms, r s0.232RqMP 0

mol% and ns2.4. Using these values, the curve in Fig. 1Ž .was generated, showing a quasi-quadratic ns2.4 de-

crease of the 1re fluorescence decay time with the concen-tration.

w xThe following two characteristics of Grant’s theory 7Ž .are worth noting: i The Nd-concentration dependence of

Ž .the ratio W rW is phenomenological. ii The nion – ion RqMP

dependence of the transition probability reflects the num-ber of interacting particles participating in the energytransfer process and not the spatial dependence of theinteraction. Thus, the value ns2.4 means that two parti-cle processes are by far the most probable followed bythree-particle processes.

Ž .Fig. 5. ln normalized emission decay versus time at 5008C forneodymium-concentration of 0.088 mol%. Dashed curve shows

Ž Ž ..the Forster and Dexter predictions Eq. 8 with t s569 ms and¨ 0Ž .ks0.4776 dashed curve . Predictions from the biexponential

Ž . Ž .decay solid curve is obtained from Eq. 6 with t s623 ms,1Ž .t s251 ms and ´ s0.60 solid curve .2



Ž . Ž .nential decay solid curve is obtained from Eq. 6 with t s5201Ž .ms, t s126 ms, and ´ s0.85 solid curve .2

Before concluding this section, we should mention thatw xthe rate equation model 7 predicts a biexponential decay:

w x w xI t s´ exp ytrt q 1y´ exp ytrt . 6Ž . Ž . Ž .1 2

A brief discussion on the physical interpretation of Eq.Ž . w x6 has been given in Ref. 6 . Figs. 2–9 illustrate the

Ž .fluorescence decay – plotted as ln I t versus t – forNd O concentrations between 0.172 and 0.035 mol%, at2 3

room temperature and 5008C. The solid curves shown inFigs. 2–9 correspond to curves fitting the data using ´ , t1

and t as free parameters. We observe that the prediction2Žfrom the biexponential decay deviates at large times t)

.600 ms from the nonexponential decay predicted byŽ .Forster and Dexter to be discussed in Section 3 . Al-¨

though both models properly fit the data at short times, the




( )A. Martınez et al.rOptics Communications 160 1999 235–239´238

predictions of the biexponential decay are in better agree-ment with data at large times.

3. Forster and Dexter model¨

w xA previous investigation 6 revealed that for Nd O -2 3

concentration )0.114 mol%, the dominant effect in thedecrease of the 1re decay time is the concentrationquenching by ion–ion resonant cross relaxation. The en-ergy transfer from a donor to an acceptor is, in general,nonradiative. The theory for this type of transfer has beenextensively studied beginning with the papers of Forster¨w x w x8 and Dexter 9 . Two important characteristics of this

Ž .model are: 1 The nonexponential nature of the predictedŽ .intensity. From Eq. 7 below, we see that the exponential

decay is obtained only in the case of zero Nd-concentra-Ž . Ž .tion r s0 . 2 Although the model predicts a nonex-Nd

ponential decay, it involves one decay time only.The assumptions in the Forster and Dexter theory, as¨

w x Ž .developed by Hinokuti and Hirayama 10 are: a thedonors and acceptors in the glass are uniformly and inde-

Ž .pendently distributed, and b the ion–ion interaction, onw xaverage, is constrained to nearest neighbors 7 .

Under these assumptions and after statistical averaging,the time dependent normalized emission intensity is givenas follows:

1r2yt r tNd'I t sexp y p , 7Ž . Ž .ž /t r t0 0 0

w xwhere, following Hinokuti and Hirayama 10 , t is called0

the decay time at very low concentrations. This equation is



Ž . Ž .nential decay solid curve is obtained from Eq. 6 with t s5201Ž .ms, t s124 ms and ´ s0.79 solid curve .2




obtained assuming that the exciting source is a Dirac d

function and a dipole–dipole interaction.The experimental data we consider in the present work 1

was obtained using as exciting source a square-wave mod-ulated semiconductor. Taking the time average of thefluorescence intensity over the time according to the excit-ing source characteristics we obtain:

wI t s exp y trt yk trt'Ž . Ž½ 0 0

2'y p kr2 exp kr2Ž . Ž .

= 1yerf kr2 q trt'Ž . 50

=2'1y p kr2 exp kr2Ž . Ž .½

=y1

w x1yerf kr2 8Ž . Ž .5' Ž .where ks p r rr . The dashed curves shown inNd 0

Figs. 2–9 correspond to curves fitting the data using r0Ž .and t as free parameters Forster and Dexter . We ob-¨0

serve that at room temperature and low Nd-concentrationthe Forster and Dexter model accounts satisfactorily for¨the experimental data, whereas that for Nd-concentrationof 0.146 and 0.172 mol% the agreement is poor. On theother hand, at Ts5008C, even at a Nd-concentration of0.088 mol%, the Forster and Dexter model cannot repro-¨duce the trend of the experimental data. This disagreementbecomes more pronounced with increasing Nd concentra-tion.

Nevertheless, in relation to the time-resolved fluores-cence decay measurements, we should mention that thevalues obtained from the actual curve fits range from

1 Details about the experimental techniques and setup can bew xfound in Ref. 6 .

( )A. Martınez et al.rOptics Communications 160 1999 235–239´ 239

r s0.195 mol% for r s0.035 mol% to r s0.4010 Nd 0

mol% for r s0.114 mol%. In all cases the value ob-Nd

tained for t is approximately 569 ms. Thus, r is far0 0

from being constant, indicating that the Foster and Dexteräpproximation is inadequate to describe the rare earth-doped system under consideration.

The Forster and Dexter model predicts also the¨Nd O -concentration dependence of the 1re fluorescence2 3

Ž Ž ..decay time, which is obtained from ln I tst sy1,Ž . Ž .where I t is given in Eq. 8 . It is not possible to get an

analytical expression for the lifetime; however, the numeri-cal solution using for r and t the results of the previous0 0

Žfit t s569 ms and r s0.195 mol% or r s0.4010 0 0.mol% leads to incorrect predictions. Whereas the experi-

Ž .mental data follows a concave curve Fig. 1 , the Forsteränd Dexter theory leads to a convex curve.

The failure of the model discussed in the previoussections is interpreted as a need for a second decay timewhich is associated to the biexponential nature of thefluorescence.

4. Conclusions

The Nd O -concentration dependence of the 1re fluo-2 3Žrescence decay time as well as measurements not included

w x.in Ref. 6 of time-resolved fluorescence decay ofneodymium aluminosilicate glasses for different tempera-tures and Nd O -concentration are compared to theoretical2 3

calculations using Grant’s model and the Forster and Dex-¨ter model.

Forster and Dexter approximation is inadequate to de-¨scribe the Nd O -concentration dependence of the 1re2 3

fluorescence decay time whereas the theoretical calcula-tions using Grant’s hypothesis are in reasonable agreement

with the experimental data, except for the highest 0.172mol% Nd-concentration.

The Forster and Dexter model properly describes the¨time-resolved fluorescence decay at room temperature andlow Nd-concentration. The discrepancy between Forsteränd Dexter predictions and experimental data increases asthe temperature and Nd-concentration rise. Thus, the onetime nonexponential predictions of Forster and Dexter¨cannot account for the data. On the other hand, predictionsfrom biexponential fluorescence decay describe the trendof the data both at room temperature and at 5008C.

Summarizing, the time-resolved fluorescence decay isdescribed by both models, although Grant’s predictions forlarge times are closer to the data. On the other hand, theNd-concentration dependence of the 1re decay time isproperly accounted for by Grant’s model but not by Forsteränd Dexter model.

References

w x1 P.L. Scrivener, P.D. Maton, A.P. Appleyard, E.J. Tarbox,Ž .Electron. Lett. 13 1990 873.

w x2 K.T.V. Grattan, A.W. Palmer, C.A. Wilson, J. Phys. E 20Ž .1987 1201.

w x3 R.W. Sadowski, M.J.F. Digonnet, R.H. Pantell, H. Shaw,Ž . Ž .Opt. Lett. 18 11 1993 927.

w x4 M.J.F. Digonnet, R.W. Sadowski, H.J. Shaw, R.H. Pantell,Ž .Opt. Fiber Technol. 3 1997 44.

w x5 K. Arai, H. Namikawa, K. Kumata, T. Honda, J. Appl. Phys.Ž .59 1986 3430.

w x6 A. Martınez, L.A. Zenteno, J.C.K. Kuo, Appl. Phys. B 67´Ž .1998 17.

w x Ž .7 W.J.C. Grant, Phys. Rev. B 4 1971 648.w x Ž . Ž .8 T. Forster, Ann. Phys. Paris 2 1948 55.¨w x Ž .9 D.L. Dexter, J. Chem. Phys. 21 1953 836.

w x Ž .10 M. Hinokuti, F. Hirayama, J. Chem. Phys. 43 1965 1978.

Documents

Analysis of the fluorescence decay of MCVD Nd Al-codoped SiO2 fiber-preforms prepared by rare-earth chelate delivery