LINE NARROWING CAPABILITIES OF Nd3+ PAIRS IN LiYF4

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LINE NARROWING CAPABILITIES OF Nd3+ PAIRS

IN LiYF4

J. Vial, R. Barthem, F. Madeore

To cite this version:

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JOURNAL DE PHYSIQUE

Colloque C7, supplément au n°10, Tome 46, octobre 1985 page C7-555

LINE NARROWING CAPABILITIES OF Nd

3 +

PAIRS IN LiYF

4

*

J . C . V i a l , R.B. Barthem and F . Madeore

Laboratoire de Speotrometrie Physique (L.A. C.N.R.S.), Universite Soientifique et Medicale de Grenoble, B.P. 27, 38402 Saint-Martin d'Heres Cedex, France

Résumé - Les paires d'ions Nd

3+

dans UYF4 sont u t i l i s é e s pour mesurer la

corrélation entre les d i s t r i b u t i o n s inhomogènes des deux t r a n s i t i o n s

succes-sives nécessaires à leurs doubles e x c i t a t i o n s . Les p r o f i l s e t les intensités

des raies sont bien i n t e r p r é t é s . Nous déduisons une f a i b l e largeur hoiroçène

qui est proche de c e l l e qui peut être déduite du temps de vie des états

e x c i t é s .

Abstract - Pairs of Nd

3+

ions in UYF4 are used to test the c o r r e l a t i o n

between the inhomogeneous d i s t r i b u t i o n s of the two successive t r a n s i t i o n s

needed f o r t h e i r double e x c i t a t i o n . The experimental l i n e shape and l i n e

i n t e n s i t i e s are well accounted for by a single model. We measure a small

homogeneous linewidth which can be connected to the l i f e t i m e of the

exci-ted l e v e l s .

I - INTRODUCTION

Optical transitions in condensed matter or in gas are always homogeneously broa-dened, so that structures of physical importance are unobservable. The fluorescence line narrowing effect is very effective for the resonant fluorescence transition, for the other transitions in spite of some "accidental coincidences" /l/ their inhomogeneous distributions are not correlated to the resonant one and their widths remain partially inhomogeneous. For the same reason the A.L.N, technique is not suitable for the extraction of small homogeneous linewidth from inhomogeneously broadened transition. Rare earth ion pairs in ionic crystals are systems for which previous experiment / 2 / have shown they are suitable for line narrowing effects. We want to show here that both theoretical arguments and new experimental results obtained with a new technique allow the extraction of small homogeneous width from inhomogeneously broadened transitions.

I I - THEORY

As a f i r s t step we consider t r i v a l e n t rare earth ions (R.E.) subtituted to some

t r i v a l e n t anions in a perfect ionic c r y s t a l . The spectroscopic properties of pairs

has been given previously / 2 / . At f i r s t sight a pair made up with two ions a and

b can be doubly excited by the e x c i t a t i o n of the ion a followed by the e x c i t a t i o n

of the ion b and conversely. However, due to the proximity of the too ions, the

coulombic i n t e r a c t i o n perturbs the energy levels of each i o n , t h i s perturbation

being d i f f e r e n t i f the neighbour ion is excited or n o t . Consequently the two

suc-cessive t r a n s i t i o n s (at v'i and V2) must occur at d i f f e r e n t frequencies (v2 / v i )

even i f the energy levels of a and b are the same. This frequency d i f f e r e n c e ,

e = V2 - v i , w i l l be an important experimental parameter.

*work partly supported by D.R.E.T. supported by C.N. Pq (Brazil)

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C7-556 JOURNAL

DE

PHYSIQUE

In a real crystal the t r a n s i t i o n s are inhomogeneously broadened. The physical o r i -

gins of t h i s broadening a r e numerous

:

microscopic internal s t r a i n s , random e l e c t r i c

f i e l d and f i e l d gradients induced by charged defects, e t c . . . In r e f . 3 we have de-

velopped some q u a l i t a t i v e arguments t o show t h a t the imperfections could have l e s s

e f f e c t s on the q u a n t i t i e s

E

than on the ion t r a n s i t i o n frequencies. In other words

the inhomogeneous d i s t r i b u t i o n of the two successive t r a n s i t i o n s needed f o r a double

excitation of a p a i r can be strongly correlated, i f some conditions a r e

w t .

Now we can examine the spectroscopic consequences of t h i s c o r r e l a t i o n . Since only

one c

. W .

monochromatic l a s e r was used f o r the experiments reported in Section 111,

we s h a l l consider only the case of successive absorption of two photons of equal

frequencies. For a given pair we assume t h a t each of the two successive t r a n s i t i o n s

can be described by an homogeneous l i n e

of

Lorentzian shape,

LA^^

(v

-

v1) and

LAv2

(v

-

v2) of width

AV

and Av2. The population of the singly and doubly excited

staces of a given class o!' pairs characterized by the s e t ( v l , v2, Avl,

AV )

a r e

proportional t o

LA,

( v

-

v l ) and LA,

(v

-

v l )

.

LAv

( v

-

v2) respectivefy, where

v i s the l a e r freq?iency. For the abod'e classe of pai$s, v1 and v2 are random varia-

bles. Let

b o ?

/v1

-

Q

be a d i s t r i b u t i o n function of v l , centered a t Q1 of width

01. I t i s possib e t o t d e into account the correlation between v1 and v2 i f we

suppose t h a t f o r each value of v1 we have the same d i s t r i b u t i o n of v2 centered a t

v1

+

E .

In order t o s-implify the following cal'culation we represent t h i s distribu-

tion by a Lorentzian Lc Iv2

-

(v1

+

E )

I

.

The width c of t h i s d i s t r i b u t i o n i s a

c h a r a c t e r i s t i c parameter of the correlation. I t i s then easy t o calculate the s i n -

gly and doubly excited s t a t e population

=Sdvl LAvl ( V

-

v l ) % o l (v1

-

"1)

From which i t i s easy t o compute the areas

( A 1

and A2) and barycenters (K1 and 142)

of the l i n e s . For the single excitation l i n e

A1

and

don'tdepend on the homoge-

neous widths of the t r a n s i t i o n s . On the contrary, f o r the doubly excited l i n e (L2)

we have

which i s a new r e s u l t

:

the area and barycenter of the L2 l i n e depend .on the homo-

geneous widths of the two t r a n s i t i o n s and on the correlation between the inhomoge-

neous d i s t r i b u t i o n , but d o n ' t on the inhomogeneous d i s t r i b u t i o n of each t r a n s i t i o n

I11

-

EXPERINENTAL RESULTS

The

N ~ ~ + : L ~ Y F ~

energy levels of i n t e r e s t are shown in figure 1. We focus our atten-

tion on the 4 ~ 9 1 2 ( 0 )

-t

4 ~ ~ 1 2

( 0 )

t r a n s i t i o n in absorption. Dueto a f a s t mu1 tipho-

non relaxation the population of

( 0 ) i s quickly established. I t s well known

near i n f r a r d fluorescence w i l l serve as a probe of t h e

4 ~

( 0 )

~

population. For

/ ~

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F i g . 1

-

Energy l e v e l s o f N ~ ~ + : L ~ Y F ~ .

F i g . 2

-

U.V. and I.R. e x c i t a t i o n spectra o f t h e s a t e l l i t e l i n e B obtained w i t h t h e s i n g l e mode C.W. dye l a s e r . I n t h e r i g h t p a r t o f t h e f i g u r e , t h e 5 o t t e d l i n e repre- sents t h e f i t t i n g o f t h e lineshape a t 40 K, as explained i n Section I V .

As i t i s c l e a r l y shown i n f i g u r e 2, a t low temperature t h e narrow U.V. and I . R . e x c i t a t i o n l i n e s have n e a r l y t h e same shapes and l i n e w i d t h s , b u t t h e r e i s a small frequency d i f f e r e n c e between t h e i r maximum which i s A!? = (0.28 5 0.02) 6Hz. I n the range o f i n t e r m e d i a t e temperatures, where t h e l i n e w i d t h s and lineshapes are n o t much a f f e c t e d , t h i s frequency d i f f e r e n c e i s e a s i l y measured and remains constant.

I n the range o f h i g h temperatures one can see, t h a t t h e U.V. and

I.R.

e x c i t a t i o n spectra have n o t t h e salre lineshapes and l i n e w i d t h s . The I . R . l i n e can be f i t t e d by a Lorentzian f u n c t i o n w h i l e t h e U.V. lineshape i s , i n f i r s t approximation, the square o f t h e I.R. l i n e . The frequency d i f f e r e n c e between t h e i r maximum i s more d i f f i c u l t t o observe. However t h e barycenter o f each l i n e can be e a s i l y c o ~ p u t e d a f t e r s u b s t r a c t i o n o f t h e m i n l i n e wings and we deduce t h e same value as b e f o r e f o r the At4 q u a n t i t y

.

T e m p e r a t u r e ( K ) F i n a l l y we may note a s t r o n g v a r i a t i o n o f t h e U.V. e x c i t a t i o n l i n e area shown i n f i g u r e 3.

F i g . 3

-

Temperature dependence o f U.V. and

I

.R. e x c i t a t i o n l i n e area.

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JOURNAL D E PHYSIQUE

I V

-

DISCUSSION

The e v o l u t i o n o f t h e e x c i t a t i o n s p e c t r a o f t h e up conversion i s complex, b u t i s e x p l a i n a b l e i n t h e frame o f o u r thecsretical model.

-

A t low temperatures, t h e main f e a t u r e s o f t h e U.V. and I .R. e x c i t a t i o n spectra,

i .e. t h e i r i d e n t i c a l lineshapes and a frequency d i f f e r e n c e between t h e i r maximum

(AN

=

0.3 GHz), a r e w e l l accounted f o r by expression (11) i f t h e inhomogeneous d i s t r i b u t i o n i s dominating over both the homogeneous c o n t r i b u t i o n , E and c. This i s

the f i r s t i n d i c a t i o n o f a c o r r e l a t i o n between the inhomogeneous d i s t r i b u t i o n o f t h e two successive t r a n s i t i o n s

.

-

For h i g h temperatures on t h e c o n t r a r y t h e homoge eous broad n i n g becomes t h e domi- nant term. The I.R. and U.V. l i n e s , r e s p e c t i v e l y

Q l ( v )

and

$p(v)

i n the t h e o r e t i - c a l s e c t i o n , have n o t t h e same shape b u t t h e y are w e l l accounted f o r by expression

I 1 i f

Avl

=

Av2

+

c and E <<

Avl.

These c o n d i t i o n s combined w i t h t h e t h e o r e t i c a l

expression o f AM i m p l y AM =

~ / 2

and consequently E = 0.56 GHz.

The f a c t t h a t t h e AFi value remains c o n s t a n t i n t h e whole temperature leads us t o conclude t h a t t h e c o n d i t i o n

Avl

-

Avp

+

c i s always v a l i d even f o r t h e s m a l l e s t homogeneous widths

Avl

(0) and

Avp

( 0 ) obtained a t 4 K. This means t h a t we are i n the s t r o n g c o r r e l a t i o n case : c <

Avl

( 0 ) .

The U.V. l i n e area dependence on t h e , temperature

Ap

(T) shown i n f i g u r e 3 can be accounted f o r by t h e t h e o r e t i c a l area dependence on t h e homogeneous widths (expres- s i o n 111) because t h e y have q u a t i t a t i v e l y t h e same shape. This i n d i c a t e s t h a t t h e homogeneous l i n e w i d t h s dependence on the temperature :

Avl

(T)

+

AV (T) i s a mono- tonous f u n c t i o n which increases as t h e temperature. I t i s p o s s i b l e 20 deduce t h e temperature dependence o f

Avl

+

Avp

+

c by t h e computation o f

Avl

(T)

+

Avp

(T) + c =

g-l ] A 2 (T)

I

f o r each experimental value o f t h e area measured a t a given temperature. The r e s u l t s are r e p o r t e d i n f i g u r e 4. We may n o t e a s t r o n g v a r i a t i o n o f

Avl

+

Avp

+

c except f o r t h e very low temperature domain where

Avl

+

Avp

+

c takes the c o n s t a n t value

Avl

( 0 )

+

Avp

( 0 )

+

c

=

8

+

2 MHz. This l a s t r e s u l t combined w i t h the

Avl

=

Av2

+

C c o n d i t i o n s leads us t o conclude t h a t

Avl

( 0 )

=

4

+

1 YHz.

F i g . 4

-

T o m ~ r r a t u r o

[K)

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A t t h i s stage i t would be i n t e r e s t i n g t o compare these l i n e w i d t h values t o those which c o u l d be obtained i n a more c l a s s i c a l manner. A t very low temperatures the main c o n t r i b u t i o n t o the homogeneous l i n e w i d t h s o f t h e two t r a n s i t i o n s i s c e r t a i n - l y t h e f a s t multiphonon r e l a x a t i o n from t h e 4 ~ ( 0 ) s t a t e . The l i n e w i d t h AV ~ / ~ = 1/m

deduce from o u r l i f e t i m e e s t i m a t i o n i s 10 ? 7

FHz.

I n s p i t e o f i t s low accuracy, t h i s r e s u l t i s c o n s i s t e n t w i t h A v l ( 0 )

-

4 KHz.

REFERENCES

/l/ Flach, R., Hamilton, D.S., Selzer, P.M. and Yen, W .V., Phys. Eev.

B

(1977) 1248.