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SPECTROSCOPIC AND STIMULATED EMISSION PROPERTIES OF Er-DOPED CRYSTALS FOR

THREE-MICRON LASERS

V. Lupei

To cite this version:

V. Lupei. SPECTROSCOPIC AND STIMULATED EMISSION PROPERTIES OF Er-DOPED

CRYSTALS FOR THREE-MICRON LASERS. Journal de Physique IV Proceedings, EDP Sciences,

1991, 01 (C7), pp.C7-395-C7-402. �10.1051/jp4:19917102�. �jpa-00250750�

JOURNAL DE PHYSIQUE I V

Colloque C7, supplCment au Journal de Physique 111, Vol. 1, decembre 1991

SPECTROSCOPIC AND STIMULATED EMISSION PROPERTIES OF Er-DOPED CRYSTALS FOR THREE-MICRON LASERS

V. LWEI

Institute of Atomic Physics, 76900-Bucharest, Romania

A b s t r a c t

-

B a s e d o n s p e c t r o s c o p i c d a t a t h e v a r i o u s p r o c e s s e s e n e r g y t r a n s f e r s , e x c i t e d s t a t e a b s o r p t i o n ) t h a t i n f l u e n c e t h e : o p u l a t l o n d y n a m i c s o f t h e e x c i t e d l e v e l s i n c o n c e n t r a t e d ~ r 3 + d o p e d l a s e r c r y s t a l s a r e d i s c u s s e d a n d t h e i r r o l e i n e t e r r n i n -

i n g t h e p o p u l a t i o n i n v e r s i o n b e t w e e n t h e 4~ a n d t1 1 3 / 2 i n - v o l v e d i n t h r e e - m i c r o n l a s e r e m i s s i o n i s e s t i m a t e d b y s o l v i n g t h e l a s e r r a t e e q u a t i o n s f o r s t a t i o n a r y r e g i m e u n d e r s e l e c t i v e o r n o n - s e l e c t i v e p u m p i n g . T h e r o l e o f c o - d o p i n g t h e c r y s t a l s w i t h i o n s t h a t m o d i f y t h e m e c h a n i s m o f p o p u l a t i o n o f t h e i n i - t i a l l a s e r l e v e l ( s u c h as ~ r 3 ' ) o r o f i o n s t h a t d e - e x c i t e t h e t e r m i n a l l e v e l ( s u c h a s ~ d 3 + , ~ m 3 + o r H O ~ + ) i s a l s o d i s c u s s e d .

I t i s t h u s shown t h a t b y a p r o p e r c h o i c e o f t h e a c t i v e m e d i u m a n d b y c o r r e l a t i o n o f t h e s p e c t r o s c o p i c p r o p e r t i e s w i t h t h e pump c o n d i t i o n s a g o o d c o n t r o l o f t h e e m i s s i o n ( w a v e l e n g t h , r e - g i m e o f e m i s s i o n , e f f i c i e n c y a n d s o o n ) c o u l d b e o b t a i n e d .

I . I n t r o d u c t i o n

D e s p i t e of a l i f e t i m e of t h e l a s e r t e r m i n a l l e v e l much l o n g e r t h a n t h a t of t h e e m i t t i n g l e v e l , e f f i c i e n t room temperature three-micron l a s e r emission has been o b t a i n e d between t h e l e v e l s 4111/2 and 41~3/2 o f ~ r 3 + i n h i g h l y c o n c e n t r a t e d c r y s t a l s [ l ]

.

P r e l i m i n a r y s t u d i e s

[ 2

-

⁴¹ on t h e p o p u l a t i o n dynamics of e x c i t e d l e v e l s i n YAG:Er have shown t h a t t h i s i s determined by t h r e e energy t r a n s f e r p r o c e s s e s by c r o s s - r e l a x a t i o n i n s i d e t h e system of E r i o n s : ( i ) a p r o c e s s of r a t e W4, b i - i o n i c f o r low-and t h r e e - i o n i c f o r high-Er c o n c e n t r a t i o n s [ 5 ] , t h a t d e - a c t i v a t e s t h e l e v e l 4 ~ 3 / 2 l e a d i n g t o an e q u a l p o p u l a t i o n of l e - v e l s 4~11/2 and 4113/2 ; however a s m a l l p o p u l a t i o n between d e f i - n i t e p a i r s of c r y s t a l f i e l d components x i and y j of t h e s e l e v e l s may e x i s t and t h i s could be s u f f i c i e n t t o s t a r t t h e l a s e r emission; a pro- c e s s (wl) o f Up-conversion from l e v e l 4 ~ 1 3 C 2 : (4113/2 + 4115/2)

+

+ ( 4 ~ 1 3 / 2 ⁺ 4 ~ 9 / 2 ) , followed by a very £as multiphonon r e l a x a t i o n on 4~11/2 t (ii) an up-conversion p r o c e s s (w2) from 4~11/2: ( 4 ~ 1 2 ⁺ 411512)

+

(4111/2 + 4117/2), followed by a r a p i d r e l a x a t i o n on fS{/2.Of t h e s e p r o c e s s e s w2 i s e s s e n t i a l f o r three-micron l a s e r emission s i n c e i t depopulates t h e t e r m i n a l l e v e l and re-pumps t h e e m i t t i n g le- v e l t h u s p r e c l u d i n g t h e s e l f - s a t u r a t i o n of t h e emission.

A p r a c t i c a l problem t h a t has t o b e answered t o i s : why t h e three-micron l a s e r emission of ~ r i s ~r e s t r i c t e d t o only a few + of t h e t r a n s i t i o n s observed i n t h e 4~11/2 ⁺ 4113/2 luminescence s p e c t r a ( f i g u r e 1 show6

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jp4:19917102

c 7 - 3 9 6 JOURNAL DE PHYSIQUE I V

t h e s e s p e c t r a f o r ~ r i n ~YAG + and Y S G G ) and what can be done i n o r d e r t o extend t h e l a s e r emission wavelength range.

F i g . 1 . L u m l n e s c e n s e s p e c t r a o f 4 ~ 1 1 2 + 4 ~ 1 p / 2 t r a n s i t i o n o f ~ r 3 + i n YAG ( a ) and YSGG ( b j .

Tab& 1 l i s t s t h e main luminescence l i n e s of t h i s spectrum f o r ~ ri n ~ + YAG and YSGG t o g e t h e r w i t h t h e i d e n t i f i c a t i o n of c r y s t a l f i e l d compo- n e n t s i n v o l v e d i n t r a n s i t i o n and w i t h a f i g u r e of m e r i t p t h a t w i l l be d e f i n e d l a t e r .

T a b l e 1 . T h e m a i n l i n e s i n t h e 4 1 1 1 1 2 + 4 ~ 1 3 / 2 l u m l n e s s e n c e s p e c t r u m o f ~ r 3 + i n Y A G a n d YSGG.

C r y s t a l L u m i n e s c e n c e l i n e s A s s i g n m e n t F i g u r e o f

cm- I _{~ m} X i ⁺ Y j m e r i t p

This p a p e r shows t h a t a good understanding of t h e three-micron l a s e r p r o c e s s e s i n c o n c e n t r a t e d E r systems could be o b t a i n e d by a n a l y s i n g t h e a n a l y t i c a l s o l u t i o n s t h a t can be o b t a i n e d by s o l v i n g the system of

l a s e r r a t e e q u a t i o n s f o r t h e s t a t i o n a r y e m i s s i o n regime, i m p o r t a n t f o r long-pulse o r cw Erbium l a s e r s .

2 . L a s e r r a t e e q u a t i o n s

The three-micron l a s e r p r o c e s s e s f o r E r 3+ can be d e s c r i b e d by t h e system of r a t e e q u a t i o n s 12, 3,

6 1

:

where u i s t h e l a s e r e m i s s i o n c r o s s - s e c t i o n , 4 t h e photon f l u x d e n s i - t y , p t h e t o t a l l o s s e s a t t h e wavelength o f e m i s s i o n , v t h e speed of

l i g h t i n t h e a c t i v e medium, t h e pump r a t e i n l e v e l i and a and 6 a r e t h e Boltzmann therma? p o p u l a t i o n c o e f f i c i e n t s of c r y s t a l f i e l d components xi ( 4 ~ 1 1 / 2 ) . and yi ( 4 ~ 1 3 / 2 ) in v o l v e d i n t h e l a s e r emission. N 1 t o N5 a r e t h e p o p u l a t i o n s of t h e l e v e l s 4 ~ 1 3 / 2 , 4~11(2, 4 ~ 9 [ 2 , 4 ~ 3 [ 2 and 4 ~ 9 / 2 r e s p e c t i v e l y , T1 t o T5 b e i n g t h e i r l i f e t i m e s . The exponent Ic of No i n e q u a t i o n s f o r N q , N g and N 1 t a k e s t h e v a l u e of 1 f o r two-ion p r o c e s s e s Wq and 2 f o r t h r e e - i o n p r o c e s s e s .

m i

For s t a t i o n a r y regime ( ?JE = 0 ,

$$

^{= 0 and} formedium o r h i g h E r concen- t r a t i o n s (W4N0>>1/T4) t h e system (1) g i v e s an e x a c t s o l u t i o n f o r popu- l a t i o n ~1 o f 4 1 ~ ~ 1 ~ :

w i t h = 1.

and

R1 = ⁺ R ~ 4

Below t h e l a s e r t h r e s h o l d ( $ % 0 )

JOURNAL DE PHYSIQUE IV

w i t h

Thus t h e d i f f e r e n c e of p o p u l a t i o n s of c r y s t a l f i e l d s u b l e v e l s of 4 and 4 ~ 1 3 / 2 below laser t h r e s h o l d i s : ^=w2

The parameter [ 7 1

i n ( 6 ) could be c o n s i d e r e d a s a f i g u r e of merit f o r a given t r a n s i - t i o n ; i t depends on t h e p a r t i c u l a r h o s t c r y s t a l ( v i a W 1 and W2) and on t h e p a r t i c u l a r l a s e r t r a n s i t i o n x i + y j ( v i a a and f3 ) ; i t a l s o depends on temperature. For a g i v e n temperature t h e t r a n s i t i o n s o r i g i - n a t i n g on t h e lower c r y s t a l f i e l d components of 4~11{2 and t e r m i n a t - i n g on t h e upper components of 4 ~ 1 3 / 2 w i l l have sma 1 f i g u r e s of me- r i t and v i c e v e r s a .

A p o s i t i v e p o p u l a t i o n d i f f e r e n c e AN (i. e. a p o p u l a t i o n i n v e r s i o n ) be- low l a s e r t h r e s h o l d i m p l i e s t h a t

a t l a s e r t h r e s h o l d t h i s c o n d i t i o n s becomes

For t h e s t a t i o n a r y regime t h e photon f l u x d e n s i t y above t h r e s h o l d i s given by

a p o s i t i v e f l u x d e n s i t y i m p l i e s a c o n d i t i o n f o r f i g u r e o f m e r i t p i d e n t i c a l t o ( 9 ) .

I f we d e f i n e a quantum e f f i c i e n c y as t h e r a t i o between t h e number of q u a n t a g e n e r a t e d i n t h e l a s e r c a v i t y and t h e number of pump q u a n t a , t h e upper l i m i t o f t h i s e f f i c i e n c y f o r very h i g h pumping i n l e v e l i i s

s i v e n bv

-

^q

-

-

R2+ ( R1+R2 ( 1-pC

' e i

- RPi

^,

t h u s we have

A l l t h e s e r e s u l t s show t h a t t h e c r o s s - r e l a x a t i o n p r o c e s s e s W can a s s u r e l a s e r e m i s s i o n between t h e l e v e l s 4111/2 and Erbium. The p r e s e n c e of e x c i t e d s t a t e a b s o r p t i o n (EsA)

t i o n from t h e e x c i t e d l e v e l 4 1 ~ ~ 1 2 can have a p o s i t i v e e f f e c t on t h e l a s e r e m i s s i o n , r e f l e c t e d by a p o s i t i v e t e r m [ ~ ~ + ( 2 - ~ 2 ) ~ 2 N ~ / P 1 i n t h e photon f l u x d e n s i t y , b e i n g t h e a b s o r p t i o n r a t e of pump r a d i a - t i o n o f wavelength l a r g e r t h a n 0.85 pm and Q2 t h a t c o r r e s p o n d i n g t o

X s m a l l e r t h a n 0,85 pm. However t h e e f f e c t of ESA depends on t h e r a t i o N 1 / N o t h a t i s u s u a l l y f a i r l y s m a l l ; t h u s ESA i s n o t a l e a d i n g mecha

-

nism f o r three-micron Erbium l a s e r i n p r e s e n c e of c r o s s - r e l a x a t i o n W 1 . The e x p r e s s i o n given above f o r t h e p o p u l a t i o n s and photon f l u x d e n s i t y

l e a d t o i m p o r t a n t c o n c l u s i o n s on t h e r o l e of t h e ^various p a r a m e t e r s o f

t h e system i n d e t e r m i n i n g t h e performances of t h e three-micron l a s e r s : ( i ) The f i g u r e of m e r i t p g i v e n by ( 7 ) p l a y s a c r u c i a l r o l e i n d e t e r - mining a p o s i t i v e p o p u l a t i o n d i f f e r e n c e A N , a p o s i t i v e photon f l u x

d e n s i t y $ and a p o s i t i v e quantum e f f i c i e n c y f o r a given l a s e r t r a n s i - t i o n . I t i s t h u s s h w n t h a t even i n o p t i m a l pump c o n d i t i o n s , o n l y t r a n - s i t i o n s w i t h A 5 2.8 um could g i v e s t a t i o n a r y laser emission i n c a s e of YAG:Er. It a l s o shows t h a t f o r t h i s c r y s t a l s t a t i o n a r y e m i s s i o n can be o b t a i n e d f o r pump i n any of t h e l e v e l s c o n s i d e r e d above, even i n t h e t e r m i n a l l e v e l 4 ~ 1 3 2.

~t t h e same time, from the main luminescent 4 1 ~ ~ 1 2 + 4113/2 E r l i n e s i n YSGG l i s t e d i n T a b l e 1 o n l y t h e t r a n s i t i o n a t 2.794 pm gould g i v e l a s e r e m i s s i o n and o n l y f o r pump i n l e v e l s I s 3 / 2 . 4 ~ 9 { 2

,

I 9 / 2 and 411k/2

,

b u t n o t i n t h e t e r m i n a l l e v e l 4 1 ~ ~ 1 ~ ; even s o he quantum e f - f i c l e n c y i s much l a w e r t h a n i n c a s e of E r

+

i n YAG.

(ii) The l i f e t i m e T2 of 4111/2 s h o u l d b e as l a r g e as p o s s i b l e i n or- d e r t o reduce t h e l a s e r t h r e s h o l d .

(iii) The e f f e c t o f l i f e t i m e T I depends on t h e v a l u e of f i g u r e o f me- r i t p :

-

f o r t r a n s i t i o n s w i t h p < 1 t h e l a s t term i n ( 1 0 ) i s n e g a t i v e and reduces t h e v a l u e of photon f l u x d e n s i t y ; i n t h i s c a s e a l a r g e v a l u e o f TI i s d e s i r a b l e and any a t t e m p t t o reduce T I by co-doping w i t h i o n s such as Nd3+, H O ~ + o r ~ m 3 + would reduce t h e laser performances.

T h i s e x p l a i n s t h e n e g a t i v e e f f e c t o f t h e s e i o n s on t h e 2.938 pm e m i s - s i o n of ~ r 3 + i n YAG (p = 0.426).

-

f o r p > 1 t h e l a s t t e r m i n ( 1 0 ) i s p o s i t i v e and a s h o r t e r TI would i n c r e a s e i t s c o n t r i b u t i o n t o t h e f l u x d e n s i t y : f o r very s m a l l v a l u e s o f T I t h i s term c o u l d become c o m p e t i t i v e o r even dominant i n t h e pho- t o n f l u x d e n s i t y . Thus co-doping w i t h i o n s t h a t reduce d r a s t i c a l l y T I would make p o s s i b l e l a s e r t r a n s i t i o n s w i t h p > ¹ even i n c r y s t a l s where

C 7 - 4 0 0 JOURNAL DE PHYSIQUE IV

normally ( w h i t o u t co-dopin t h e s e t r a n s i t i o n s a r e n o t observed. Co-dqp- i n g w i t h Pld3+, H O ~ + o r Tm3? c o u l d t h u s e x t e n d t h e wavelength c a p a b i l i - t i e s of ~ r l a s e r s , even i f i n some c a s e s t h e e f f i c i e n c y o f t h e o r i g i - ~ + n a l p < 1 t r a n s i t i o n s i n t h e s e c r y s t a l s i s lowered because o f t h i s co- doping.

( i v ) A s m a l l W2 r a t e i s d e s i r a b l e ( v ) ^A l a r g e W l r a t e i s b e n e f i c i a l .

T h i s a n a l y s i s shows t h a t t h e s p e c t r o s c o p i c p a r a m e t e r s t h a t determine t h e wavelength range and t h e e f f i c i e n c y of three-micron l a s e r e m i s s i o n o f

~ r l a s e r a r e t h e c r o s s - r e l a x a t i o n r a t e s ~ + W 1 , W2 and W q , t h e l i f e t i m e s T 1 and T2, t h e Boltzmann p o p u l a t i o n c o e f f i c i e n t s a and b , t h e e m i s s i o n c r o s s - s e c t i o n o and t h e l o s s e s p ; a t t h e same t i m e it shows t h a t t h e l a s e r e m i s s i o n c h a r a c t e r i s t i c s c o u l d be changed by a c t i n g on t h e s e s p e c t r o s c o p i c p a r a m e t e r s .

I n t h i s r e s p e c t

,

t h i s a n a l y s i s shows t h a t t h e system Er:YSGG, d e s p i t e of a much l a r g e r v a l u e of T2 [ 71 as compared w i t h Er:YAG ( 1 . 4 msec ver- s u s 88 p s e c ) , i s e x p e c t e d t o have much worse l a s e r p a r a m e t e r s t h a n Er:

YAG b e c a u s e t h e t r a n s i t i o n s w i t h l a r g e e m i s s i o n c r o s s - s e c t i o n have l a r g e f i g u r e s of merit p. I n t h i s c a s e a p o s s i b i l i t y t o overcome t h e s i t u a t i o n would be t h e m o d i f i c a t i o n o f t h e mechanism o f p o p u l a t i o n o f l e v e l s 4111(2 and 4113/2 i n a way t h a t would r e l a x t h e c o n d i t i o n s imposed on h e f i g u r e of merit p i n o r d e r t o have p o s i t i v e pump term i n t h e e x p r e s s i o n of photon f l u x . A o s s i b l e s o l u t i o n i n t h i s ^respect i s the co-doping of c r y s t a l s w i t h C r 3 + ; t h i s i o n a b s o r b s very e f f e c t i v e l y the pump r a d i a t i o n due t o two i n t e n s e and broad t r a n s i t i o n s from t h e ground s t a t e 4 ~ 2 t o t h e l e v e l s 4 ~ ~ and 4 ~ ~ r 3 + ~ . e n t e r s i n t h e YSGG

l a t t i c e a s a s u b s t i t u t i o n a l i o n i n t h e l a r g e o c t a h e d r a l s i t e of S C ~ + : t h e c r y s t a l f i e l d e f f e c t s a r e f a i r l y weak and t h e l e v e l 2 ~ l i e s o n l y about 200 cm-1 below 4 ~ ~ s o t h a t t h e s e two l e v e l s a r e t h e r m a l i z e d a t room t e m p e r a t r e and a very e f f e c t i v e (n

*

1) e n e r g y t r a n s f e r from

cr3+

t o t h e h g / 2 l e v e l of

er3'

t a k e s p l a c e ; t h u s

cr3+

c o n t r i b u t e s t o a b e t e r utilization o f t h e pump r a d i a t i o n f o r p o p u l a t i o n of t h e e m i t t i n g l e v e l 4~11/2 of ~ r 3 + . A t t h e same t i m e

,

an e f f e c t i v e t r a n s - f e r from 4 s 3 l 2 E r t o 4 ~ 2 C r c o u l d t a k e p l a c e . The c h a i n o f t r a n s f e r 4s3/2 ⁺ 4 ~ 2 ~ r ⁺ 4 1 ~ / 2 E r

,

c h a r a c t e r i z e d by a g l o b a l r a t e W q com- p e t e s w i t h t h e c r o s s - r e l a x a t i o n p r o c e s s W q i n d e - e x c i t a t i o n of 4 ~ 3 / 2 . However, by d i f f e r e n c e from W q t h e r o c e s s W q l e a d s o n l y t o t h e popu- l a t i o n o f t h e i n i t i a l l a s e r l e v e l

5Il1i2

(and n o t of b o t h 4111i2 and 4 I l 3 I 2 a s i n c a s e o f Wq) t h u s improving t h e b u i l d i n g o f a popu a t i o n i n v e r s i o n between t h e s e two l a s e r l e v e l s .

The r e l a t i v e c o n t r i b u t i o n of t h e two p r o c e s s e s ( W q and W 4 ) i n de-exci- t a t i o n o f 4s3/2 can b e e x p r e s s e d by a p a r a m e t e r

161

:

W 4 ' N o r

-

¹

f = W4 N o

= [ I +

I

(13)

W4No + W;No4 W4 *o

t h a t ranges between 0 (when o n l y W; i s a c t i v e ) t o 1 (when WIN,, i s e q u a l t o z e r o )

.

The system o f r a t e e q u a t i o n s f o r t h i s c a s e candot b e s o l v e d a n a l y t i c a l l y below-threshold; however, a t t h r e s h o l d a n a l y t i c a l e x p r e s s i o n f o r N1 and N2 s i m i l a r t o ( 2 ) and ( 4 ) c o u l d be o b t a i n e d b u t w i t h t h e p a r a m e t e r s p

,

^c

,

^{v and y} dependent on f . A t t h e same t i m e t h e e x p r e s s i o n f o r t h e f l u x d e n s i t y i s m o d i f i e d t o :

where t h e pump r a t e R t N o t a k e s i n t o account t h a t t h e pumping i s p e r f o r - med i n t h e s t r o n g a b s o r p t i o n bands of ~ r 3 +

The c o n d i t i o n imposed on t h e f i g u r e o f m e r i t p i n o r d e r t o have t h e f i r s t term ( t h e pump term) i n ( 1 4 ) p o s i t i v e i s now

2 2

P

2f

(15

S i n c e f i s s u b u n i t a r y and can t a k e q u i t e low v a l u e s when t h e r a t i o W'Ncr _WA N, i s l a r g e t h e c o n d i t i o n (15) i s much r e l a x e d and l a s e r t r a n s i -

t i o n g w i t h l a r g e r p v a l u e s t h a n f o r systems doped o n l y w i t h a r e now p o s s i b l e ; i n c a s e when t h e s e t r a n s i t i o n s have p

>

1, t h e l a s t term i n ( 1 4 ) i s p o s i t i v e to.0, c o n t r i b u t i n g t o t h e photon f l u x . Thus

cr3+

n o t o n l y i n c r e a s e s t h e e f f i c i e n c y o f u t i l i z a t i o n of pump b u t , by i t s e f - f e c t of s h o r t - c i r c u i t i n g t h e c r o s s - r e l a x a t i o n p r o c e s s W q it improves t h e p o p u l a t i o n i n v e r s i o n and i n c r e a s e s t h e c o n t r i b u t i o n o f t h e p o s i t i v e terms i n t h e photon f l u x t h u s l e a d i n g t o the r e d u c t i o n of t h e l a s e r e m i s s i o n t h r e s h o l d and t o t h e i n c r e a s e o f e m i s s i o n e f f i c i e n c y ; i t a l s o c o n t r i b u t e s t o t h e e x t e n s i o n 'of t h e wavelength range o f e m i s s i o n . Other p o s s i b l e Er-Cr c r o s s - e l a x a t i o n p r o c e s s e s as, f o r i n s t a n c e

( 4 ~ 1 3 / 2 + 4115/2)

+

^{( 4 + ~'T1) ~} c o u l d improve t h e l a s e r performances o f t h e co-doped c r y s t a l s . The e f f e c t of cc-doping E r : YSGG w i t h C r was t h e improvement of t h e long-pulse 2.794 pm e m i s s i o n and t h e o b s e r v a

-

t i o n of t h e cw e m i s s i o n a t 2.702, a laser t r a n s i t i o n w i t h p = 1.917, t h a t cannot be o b t a i n e d i n absence of Chromium.

As e x p e c t e d from e q . ( 1 4 ) t h e e f f e c t of s h o r t e n i n g TI i n c a s e of C r co- doped c r y s t a l s i s s i m i l a r t o t h e c a s e of c r y s t a l s doped o n l y w i t h E r : it can e x t e n d t h e range of e m i s s i o n wavelength and, f o r t r a n s i t i o n s w i t h p > 1 i t reduced t h e t h r e s h o l d of e m i s s i o n , i n c r e a s e s t h e e f f i - c i e n c y and, due t o a (RrNo)1/2 dependence on pump v i a N1, c o u l d g i v e a n o n - l i n e a r dependence o f t h e o u t p u t power on pump. These e f f e c t s have been i n d e e d observed [ l o ] i n t h e 2.702 pm

cw

e m i s s i o n of ~ r 3 + i n C r , Er: YSGG by co-doping w i t h ~ o 3 + t h a t l e a d s t o s t r o n g r e d u c t i o n of l i f e t i m e T1.

The p o s s i b i l i t y t o o b t a i n a n a l y t i c a l e x p r e s s i o n s f o r p o p u l a t i o n s o f l a - ser l e v e l s and photon f l u x d e n s i t y i n c a s e of t h e s t a t i o n a r y regime of three-micron l a s e r e m i s s i o n i n Er-doped c r y s t a l s e n a b l e s an a n a l y s i s of t h e i n f l u e n c e o f t h e v a r i o u s s p e c t r o s c o p i c p a r a m e t e r s of t h e system and of t h e pump c o n d i t i o n s on t h i s e m i s s i o n . T h i s a n a l y s i s shows t h a t t h e three-micron l a s e r e m i s s i o n i n c o n c e n t r a t e d Er systems f o r which t h e l i f e t i m e of t h e t e r m i n a l l e v e l i s l a r g e r t h a n t h a t of t h e e m i t t i n g l e v e l i s e s s e n t i a l l y determined by t h e c r o s s - r e l a x a t i o n p r o c e s s e s Wl, W2 and Wq. I t a l s o shows t h a t t h e f i g u r e of merit p i s e s s e n t i a l i n d e t e r m i n i n g t h e p o s s i b i l i t i e s t o o b t a i n l a s e r e m i s s i o n on a given l u

-

minescence t r a n s i t i o n .

I t i s a l s o shown t h a t t h e wavelength r a n g e of e m i s s i o n i s determined by t h e c o n d i t i o n s imposed on t h e f i g u r e o f m e r i t p i n o r d e r t o o b t a i n e m i s s i o n ( p o s i t i v e p o p u l a t i o n i n v e r s i o n and p o s i t i v e photon f l u x ) and t h a t t h e s e c o n d i t i o n s could be m o d i f i e d by a c t i n g e i t h e r on t h e system

(co-doping w i t h i o n s t h a t modify t h e mechanism o f p o p u l a t i o n o f t h e i n i t i a l and t e r m i n a l l a s e r l e v e l s o r / a n d w i t h i o n s t h a t reduce t h e l i f e t i m e of t h e t e r m i n a l l e v e l f o r t r a n s i t i o n s w i t h p > 1) o r on t h e p a r a m e t e r s t h a t determine t h e f i g u r e of m e r i t p i t s e l f . Concerning t h e e f f e c t of co-doping w i t h Chromium, it i s now e v i d e n t t h a t i t n o t o n l y i n c r e a s e s t h e u t i l i z a t i o n of pump b u t a l s o , p r o v i d e s a p a t h f o r overcoming t h e e f f e c t of c r o s s - r e l a x a t i o n W 4 thus , l e a d i n g t o a more e f f i c i e n t population o f t h e i n i t i a l l a s e r l e v e l 4I 11/2,

JOURNAL DE PHYSIQUE IV

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