A special up-conversion phenomenon of Sm3+ ion in fluoride glass — single-photon absorption followed by two-photon absorption

Optics Communications97 (1993) 69-73 North-Holland

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A special up-conversion phenomenon of S m 3+ ion in fluoride glass - single-photon absorption followed by two-photon absorption C h e n X i a o Bo ~ a n d C h e n Jin K a i Experiment Center, Fufian Normal University, Fuzhou, Fufian 350007, China Received 9 December 1991; revised manuscript received 21 July 1992

The first observationof a specialup-conversionfluorescencefrom the 4G5/2levelof Sms+ ions induced by 1.06 ~tmpulsed laser excitation is reported. Based on the one-photon and two-photon absorption theory, the transition probability and rate are estimated, the fluorescence process is modeled with rate equations. The dominating population of the 4Gs/2 state is attributed to a single photon excitation from ground state 6H5/2followedby two-photon absorption from excited state 6F~/2.Due to their much smaller transition probabilities,the other possibleup-conversionluminescenceprocessesare unobserved. 1. Introduction A very large number of so-called up-conversion phenomena has been described for rare earth ions in solid matrices [ l ]: through various mechanisms, the energies hop of several pump photons are added in the same ion, thus allowing emission at energies h/if noticeably greater than h Op. In some cases, up-conversion has useful applications, such as infrared viewer screens or lasers emitting at a wavelength shorter than the pump. The Ba-Zr-F fluoride glass is a pleasant optics fibre material, which has many advantages over oxide glass [2 ]. Recently, it became of interest to reduce the fibre loss by mixing suitable rare earth ions. This paper has just worked upon this background. According to selection rules, the singlephoton transition for trivalent free rare earth ions is forbidden. Their luminescence in solids results from mixing by the crystal field of excited configurations having opposite parity. So the magnitude of the oscillator strength for them usually is quite small ( < 10-6). However, two-photon transition (TPA) is allowed and has a rather high strength. Thus the TPA has its important position and role in the study of the spectroscopic properties of rare earths in solids [ 3 ]. In this paper we will report the first obserPost Doctor Station of Physics Department, NanKai University, Tianjin 300071, China.

vation of a special up-conversion phenomenon of Sm 3+ ions in fluoride glass - single-photon absorption followed by two-photon absorption. The yelloworange-red 4G5/2--*6Hs/2,7/2,9/2 emission of Sm 3+ ions is observed induced by 1.06 llm pulsed laser excitation. It is shown both by experimental and theoretical arguments that the main mechanism for this visible fluorescence is one-photon absorption from the ground 6Hs/2 level to 6F9/2, followed by non-radiative relaxation to 6F1/2, then by two-photon absorption to 6p3/2 and finally by non-radiative relaxation to the long-lived 4G5/2 level.

2. The experiment and results Figure 1 is a schematic diagram of the experimental set-up. The Sm3+:Ba-Zr-F fluoride glass in this study contains 0.6% (weight) of Sm 3+ ions. A YAG 1.06 ~tm laser of 8 ns pulsewidth, repeat-rate 10 Hz is used to excite the Sm 3+ ions. The fluorescence is conduced into the monochromator and received by a R456 photomultiplier, the signal is processed with a 4400 Boxcar signal processor. The obtained spectrum is shown in fig. 2. The peaks located at 560, 595 and 640 n m are assigned to the emission of 4Gs/2~6Hj ( J = 5 / 2 , 7/2 and 9/2) for Sm 3+ ions. The measured lifetime for these lines is ~ 4 ms, just the same as that of fluorescence excited by absorp-

0030-4018/93/$06.00 © 1993 Elsevier Science Publishers B.V. All rights reserved.

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~. ai '

L~

I~,F

'

monoGkromator

IO

IsPo |

"

F

. . . . . . . . . .

I=

Fig. 3. Dependence of fluorescence signal F on the laser energy

Fig. 1. Schematic diagram of the experimental set-up.

Po.

'P,/~ 4"F~=

|;| *F,,/~

~. (Jm)

11 m

Fig. 2. Up-conversion fluorescence spectrum of Sm 3+ ions.

tion of a single shorter wavelength photon. The fact above mentioned shows that an up-conversion absorption of 1.06 ~tm laser produces population of the 4G5/2 state and its subsequent emission. The measured dependence of the fluorescence signal F on the laser energy Po is shown in fig. 3. The slope 7=2.75_+0.05 suggests that three photons are involved in this up-conversion process. The involved energy level structure is sketched in fig. 4. The barycenters of experimentally established lines are listed in table 1. Figure 5 is the fluorescence spectrum of Sm 3+ ions in the near-infrared region excited with 954.9 nm pulsed laser. Besides 1.58 ttm there are no other lines in fig. 5, which implies that the excitation above the 6Fl/2 and below the 6F11/2 states will primarily populate the 6F i/2 s t a t e due to the strong non70

6Fq/z 6FT/= 6F~ ~F~ 'H,s/= 6F,/. N,j/: 614,,/j ~H./= H,iI= tHrd2

Fig. 4. Energy level scheme 17~= 9391 cm - i.

radiative relaxation, therefore only a line emitted from it t o 6H5/2 is observed, and the others are completely quenched.

3. Analysis and discussion From the diagram of the energy level structure [ 4 ], it is found that the energy levels above the 4G5/2 s t a t e for Sm 3+ ions are close together and below it they are far away from it; our measurements for its emis-

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Table 1 Absorption barycenter position of Sm 3+ ions in Sm3+:fluoride

(6H5/2 IIU
(2)

glass.

(6F9/2 IIU (x) II4F3/2 )2 = 0 ,

(3)

Energy level

Barycenter (cm- i )

Energy level

Barycenter (era- i )

6F1/2

6327 6452 6711 7225 8091 9208 10571

4MI7/2

419/2

17857 18975 20000 20964

4G11/2

22727 22727 22727 24096 24096 24969 24969 24969 24969 25641 25641

4M15/2

20964

4DI/2

26738

4111/2 4113./2 4F5/2

20964 21598 22727

6P7/2

26738 26738 26738

6H 15/2

6F3/2 6Fs/2 6F7/2 6F9/2 6Fll/2

4Gs/2 4F3/2 4G7/2

4G9/2 4113/2 6ps/2 4ps/2 4L13/2 4F7/2

6P3/2 4K11/2 4L15/2

4L17/2 4K13/2

(6F1/2[IU(;OII6p3/2)2=(0.1920, 0, 0)

,

(4)

and then investigate the energy difference between the exciting laser beam and resulting transitions. From table 1, for one-photon absorption the energy of 1.06 ttm is 183 c m - ~ above the barycenter of the 6H5/2---~6Fg/2transition, for two-photon absorption it is 190 cm -1 under the 6Hs/2---,4F3/2 transition, and it is 140 cm-~ above the 6F]/2--,sP3/2 transition. They are in a near resonance with the 1.06 Ixm laser beam. According to Axe's theory of the two-photon absorption in second-order approximation [ 7 ], the line strenghth of the transition from l i) to IJ ) state is Sg-= ] (a[)2l (ill Ut2)IL/) 2 E~.

(5)

Because the linewidth for Sm 3+ ions in the glass at room temperature is rather broad ( F ~ 2 5 0 cm - ] ) and the exciting light source quite narrow, only a small part of the ions in the inhomogeneous width can be in reasonance with the 1.06 Ixm laser. Under this condition eq. (5) must be modified into

g

S~(17~)=!3(ot[)2 (iUU~Z)I[j)12E2g,j(O~) A0~,

O

I,o

~.z

1"4.

t.6

.S

(6)

~,qUM~

where go(0c ) is the lineshape of activator absorption of glass at exciting wavelength 0~ and can be expressed by

2~e

go(9~) = ~,42:-~ exp[ - 4 In 2 ( g o - 0~)2/F21 •

2

l/~-n2

Fig. 5. Infraredfluorescencespectruminducedby 954.9nm laser.

(7)

sion spectra and lifetime confirm that the nonradiarive rate from those levels above 4Gs/z to next lower states through multiphonon process is very small [ 5 ], the luminescence from those states are completely quenched and we can recognize them only by the excitation spectra. However, for the 4G5/2 state the multiphonon nonradiative transition rate is quite small and the quantum efficiency of the luminescence is nearly unity. The population of this level is destroyed only by the spontaneous radiation. To evaluate these processes, let us calculate the following matrix elements of irreducible tensor U~) [6] (2=2, 4, 6)

Usually the two-photon absorption is rather small. Therefore we can calculate the TPA transition rate d 2 by means of classical theory, i.e. we have QuPo

nPo P(gc)- c ATAS'

n2=ela~e,

(I0)

(6Hs/z l[ U(a)[[ 6F9/2)2----" (0, 0.0205, 0.3416) ,

E2=(4rt/~) p(~c) .

(II)

( 1)

Bd = 87r3e2 ( n 2 + 2 ) 2 l Sd(9~) 3h 2 9n 2 2Ji+ 1 '

(8)

(9)

AT, AS are the duration and cross-section of the laser beam. Assuming /t ~ 1 (non-magnetic material), then

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By eqs. (5) to ( 11 ), we finally obtain

AT

IC3(t)12= ( A T ) -1 J IC3(t) l 2dt

Q~_321t4e2(1......~'~Z(n2+2)21 'J-

9h 2 \ c A T A S }

9n 2

0

2Ji+l

47t3 S]3(ge)e 2

Xgij(ge) Age (Or'2) I ( illUt2)llJ)12 1

oc ~-7-7-7, , gu(go) I ( i[IUt2)llJ)12 . Zdi-l- I

-

(12)

The ratio of the transition rates for two kinds of TPA, one starting from the 6El/2 excited state to the 6P3/2 state and the other from the 6H5/2 ground state to the 4F3/2 state, is

P(ge) (AT) 2 ,

3n2h 2

(15)

and the transition rate per second (referred to as "stimulated" absorption transition rate Q]3Po) is a ] 3 ( t ) P0= ~d I C3(t) 12 •

(16)

The average transition rate is AT

d d =0.52 X 104 Q26/Q15

(13)

Q]3Po= (AT)-~ ] QI3( s t)

Podl

0

where we use the numbers 1 to 6 to represent the 6H5/2, 6F1/2, 6F9/2, 4G5/2, 4F3/2 and 6p3/2 states, respectively. As for the one-photon absorption of the 6H5/2~ 6F9/2 transition, the near resonance and high exciting power will make it quite strong and a notable population of the 6F1/2 state will occur. Therefore we can use the Rabi-solution of a two-level system in the semi-classical theory to calculate its transition rate [8 ]. Let us neglect the damping term and consider only the population part resonating with the laser. If the system is entirely in the 6H5/2 state at the initial moment t=0, i.e. IC~(0)12=l, IC3(0)12=0, then at moment t the probability of finding the system in the 6F9/2 state is

=

4n3 S]a(ge) e 2 n2h 2 P(ge) AT.

(17)

Under the condition AT~ 8 ns, Po = 104~ 105 erg, I C3(t)12=5X 10-3~ 5X 10 -2<< 1 ,

(18)

which corresponds to the case of Rabi-solution in first order approximation. The transition probability of single-photon absorption from 6H5/2 tO 6F9/2 is then Q]3Po= 1 × 106~ 107

(s-l).

(19)

Now, we turn to evaluate transition rates for other ways of populating 4G5/2. For the stepwise one, such as 6H5/2-~ 6F9/2--~4F3/2, it is zero, because [ (6F9/21 [ U(2)114F3/2) 1 2 = 0 . F o r a d i r e c t o n e like t h e

IC3(/) 12= ~z2e2E2 h2 S]3(ge) t 2 ,

(14)

where, according to Judd-Ofelt theory of rare earth ions [9,10], S]3(ge) =gl3(ge) Age ~.. g2al( 6H5/2 IIUta)ll 6F9/2 )12 2

is the line intensity of the single-photon absorption resonating with the 1.06 ~tm laser. The ~2a are intensity parameters, which are calculated by a linear regressive method from the measured linear absorption: ~22=2.5×10 "2° cm 2, Q 4 = 3 . 4 × 1 0 -2° cm 2, ~26=2.0× l0 -2° cm 2. During the laser irradiating time AT, the average probability of finding the system in ~F9/2 state is 72

6H5/2 to 4F3/2 transition it is small. However, the twophoton absorption from the excited state 6Fl/2 tO the 6P3/2 state has a rather large transition rate and, due to the large population of 6F I/2 under these pumping conditions, it will become a quite efficient process. Therefore, even though several TPA happen simultaneously, the two-photon absorption from 6F~/2 following a single-photon absorption from the ground state will be a leading process, which makes the observed fluorescence signal from 4G5/2 have a dependence on the third power of the laser energy. The process above mentioned can. also be described with rate equations. Let us assume that: (i) The nonradiative relaxation rate from 6P3/2 and 4F3/2 to 4G5/2 is quite large, so that the efficiency of the population transfer for

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dN6/ dt = Qd26p2N2 -- W64N6,

(20)

dNs/dt=Qdsp2 N~ - W54Ns ,

(21)

sition rates, Sm 3+ behaves as if it had only three levels (1, 2 and 4). Level 2 is populated from level 1 with the rate Q] 3PoN~ and depopulated toward level 1 with the rate Q2N2. Hence, far from saturation, N I ~ N o and N2=Q]3PoNo/Q2. With the much smaller rate Q'~6p2N2, level 2 is depopulated toward level 4, the lifetime of which is 1/A 4. Thus,

dN4/dt= W64N6 + W54N5-A4N4 ,

(22)

N4 ~ Q26PoN2A/4d2

dN3/dt=Q~3PoN1 - W32N3 - Q [ I P o N 3 ,

(23)

dN2/dt= W32N3 - Q~6p2 N2 - Q2N2 ,

(24)

6 E N,=No,

(25)

In fact, the estimation of eqs. (28), (29) is not strict. Under the condition that the influence of the Q~3Po or Q d5Q2 term in eq. (27 ) can not be entirely neglected, the population of the 4G5/2 level should have a less than third power dependence on the 1.06 I~m laser energy, which is in agreement with the results of the experiments.

them can be taken as 1. (ii) The nonradiative relaxation rate from 4G5/2 to states below is quite small and can be taken as 0. Then we have

i=l

where Q2 is the relaxation rate for the 6F1/2 state and W# is the nonradiative relaxation rate from i t o j state. Usually the transition rate of TPA is much smaller than that of one-photon from 6H5/2 to 6F9/2, therefore eq. (25) can be simplified into N~ +N2 +N3 = N o .

(26)

Under stationary conditions (dNi/dt = 0) and because of W32 >> Q2, Q26 d >> Q d15, the solution for these equations is N, -

Nop2 Q26QI3Po d S d +QIsQ2 - A4 Q2 + QIaPo

(27)

From fig. 5, we find that the luminescence from 6Ft/2 is not completely quenched even if its energy gap away from the nearest lower state is rather small ( 1300 c m - t ), therefore we can believe that is has a quite short lifetime and it is reasonable to estimate Q2 of the order of magnitude of 10s~ 109 (s -~ ), and so by eq. (19) we have

Q2/Q]~Po ~ 102 • From

d d ~0.5× Q26/QIs

(28) I0 4 and from (28), w e have

d s d Q26QIaPo/QtsQ2 ~ 50.

(29)

Finally, cq. (27) can be reduced into d

s

N4",~, N°Q26Qt3 P30,

(30)

A4Q2 which indicates that the emission from level 4Gs/2 will have a dependence on the exciting laser energy in third power. Equation (30) has a simple physical meaning. With the orders of magnitude of the various tran-

~ Q26dQ sl3eoNo/A 4 3

Q2.

4. C o n c l u s i o n

Under 1.06 ttm laser excitation, the observed upconversion fluorescence of Sm 3+ ions in a fluoride glass can bc described as follows: a strong one-photon absorption from 6H5/2 to eF9/2 results in a rather large population in 6F1/2 and creates a convenient condition for subsequent TPA from 6Fl/2 tO 6p3/2 which through nonradiative relaxation finally populates the 4G5/2 state, the other possible up-conversion luminescence processes will be unobserved due to much smaller transition probabilities.

References

[ 1] G.D. Gilliland, R.C. Powell and L. Esterowitz, Phys. Rev. B 38 ( 1988 ) 9958, and referenceswithin. [2] Fuxi Gan and Haixing Zheng, J. Non-Crystalline Solid. 95&96 (1987) 771. [3] B.G. Wybourne, Spectroscopicpropertiesof rare earths (Wiley,New York, 1965). [4] W.T. Carnall,P.R.Fieldsand K. Rajnak,J.Chem. Phys.49 (1968) 4424. [5] Chen Jin Kai and Chen Xiao Bo, The three-photon fluorescence phenomena of Sin3+: fluoride glass, to be published in J. Lumin. (chinese). [6]W.T. Carnall, Energy level structure and transition probabilities of the trivalent lanthanides in LaF3 (Argonne National Laboratory, 1978). [7] J.D. Axe Jr, Phys. Rev. A 136 (1964) 42. [8 ] M. Sargent IIl, Laserphysics (Addison-Wesley,1974). [9] B.R. Judd, Phys. Rev. 127 (1962) 750. [ 10] G.S. Ofelt, J. Chem. Phys. 37 (1962) 511. 73