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ROLE OF STIMULATED EMISSION UPON THE
KINETICS OF THE VIBRATIONAL POPULATIONS
OF 13Cl8O DILUTED IN Ar MATRIX
J. Zondy, J. Harbec, J. Galaup, R. Charneau, H. Dubost
To cite this version:
J O U R N A L DE PHYSIQUE
Colloque C7, suppl6ment au nOIO, Tome 46, octobre 1985 page C7-305
ROLE OF STIMULATED EMISSION UPON THE KINETICS OF THE VIBRATIONAL
POPULATIONS OF 13cL80 DILUTED IN Ar MATRIX
J.J. Zondy, J.Y. ~ a r b e c * , J.P. Galaup, R. Charneau and H. Dubost
++
Laboratoire de Photophysique MoZ&cuZaire du C.N.R.S.
,
Bztirnent
213,Universite' de Paris-Sud,
91405Orsay Cedex, France
Resume
-
Lorsque l ' o n pompe optiquement 13c1'0 en m a t r i c e d'argon basse temperature p a r l a t r a n s i t i o n harmonique v = O + v = 2 au moyen d'un l a s e ra c e n t r e s colores, on observe des molecules t r e s fortement e x c i t e e s v i b r a - t i o n n e l l e m e n t j u s q u ' a v
=
30. L ' a n a l y s e de La f l u o r e s c e n c e I R r e s o l u e en temps r a i e par r a i e a permis d ' e t u d i e r La c i n e t i q u e des p o p u l a t i o n s v i b r a - t i o n n e l l e s . Des s i m u l a t i o n s numeriquesa
p a r t i r d ' e q u a t i o n s d ' e v o l u t i o n phe- nom6noloqiques o n t e t e r e a l i s e e s pour r e p r o d u i r e l e comportement experimental. ELLes conduisenta
La c e r t i t u d e que Les t r a n s f e r t s V-V ne peuvent eux s e u l s e x p l i q u e r n i L ' e x c i t a t i o n de niveaux v i b r a t i o n n e l s aussi eleves, n i l e s temps d ' e v o l u t i o n c a r a c t e r i s t i q u e s de l a c i n e t i q u e observee. Des s i m u l a t i o n s s a t i s - f a i s a n t e s ne peuvent t t r e obtenues que s i l ' o n suppose que Le n i v e a u v = 2 r e l a x e vers v = 1 p a r emission stirnulee. Les d i f f e r e n t e s c o n t r i b u t i o n s des processus dynamiques rnis en cause-
emission stirnulee, t r a n s f e r t s V-V e t d e s e x c i t a t i o n r a d i a t i v e-
sont d i s c u t e e s en d e t a i l .A b s t r a c t
-
I R overtone pumping o f t h e v =0
+ v=
2 v i b r a t i o n a l t r a n s i t i o n o f " ~ ' " 0 d i l u t e d i n A r m a t r i x a t low temperature by a modulated CW KC1:Li c o l o r - c e n t e r Laser has Led t o the p r o d u c t i o n o f h i g h l y e x c i t e d v i b r a t i o n a l s t a t e s up t o v = 30. Time and frequency r e s o l v e d a n a l y s i s o f t h e I R f l u o r e s - cence has a l l o w e d t o study the k i n e t i c s o f CO v i b r a t i o n a l p o p u l a t i o n s . Nume- r i c a t s i m u l a t i o n s of t h e v i b r a t i o n a l k i n e t i c s based upon phenomenologi c a t r a t e equations have been c a r r i e d o u t t o reproduce t h e e x p e r i m e n t a l r e s u l t s . Undoubtfully, t h e y demonstrate t h a t V-V t r a n s f e r cannot e x p l a i n by i t s e l f n e i t h e r t h e pumping o f such h i g h l e v e l s n o r t h e v a r i o u s t i m e constants o f t h e e v o l u t i o n o f t h e k i n e t i c s . S a t i s f a c t o r y s i m u l a t i o n s a r e achieved f o r Low temperature o n l y i f allowance i s made f o r s t a t e v=
2 t o r e l a x t o s t a t e v = 1 throuqh s t i m u l a t e d emission. The v a r i o u s c o n t r i b u t i o n s o f t h e dyna- mica1 processes i n v o l v e d i n t h e k i n e t i c s-
s t i m u l a t e d emission, V-V t r a n s f e r and r a d i a t i v e decay-
are discussed i n d e t a i l s .EXPERIMENTAL
Overtone pumping i n t h e 2.46 pm s p e c t r a l r e g i o n o f
'
3 ~'0 m01ecuLe~ embedded i n A r ' o r N2 LOW temperature m a t r i c e s a t a d i l u t i o n r a t i o r a n g i n g from 0.2 % t o 1 % hasLed t o t h e o b s e r v a t i o n o f an i n t e n s e f l u o r e s c e n c e emission ( d e s p i t e the weakness o f t h e pump power % 4 mW) and t h a t o f t h e o s c i l l a t o r s t r e n g t h o f t h e overtone t r a n s i - t i o n . Fluorescence s p e c t r a o f t h e Av
=
1, 2, 3 emission sequences r e v e a l t h e pre- sence o f h i g h l y e x c i t e d molecular s t a t e s (up t o v = 30). I n N2 matrix, under some c r i t i c a l c o n d i t i o n s on b o t h t h e f o c u s s i n g o f t h e Laser beam and t h e temperature, t h e fluorescence L i g h t e m i t t e d on the v=
2 + v = 1 t r a n s i t i o n e x h i b i t s a s t r o n g random s p i k y behaviour which i s a t t r i b u t e d t o s t i m u l a t e d emission ( l a 2 ) . I n A r m a t r i x thoughs u c h a phenomenon i s n o t observed t h e energy i s d i s t r i b u t e d among v e r y h i g h s t a t e s i n the v i b r a t i o n a l ladder. Figure 1 shows a t y p i c a l r e c o r d i n g o f t h e k i n e t i c s . For the sake o f c l a r i t y , p o p u l a t i o n s o f s t a t e s v >9 a r e n o t p l o t t e d b u t t h e f l u o r e s - cence emission coming from l e v e l s up t o v
=
20 has been recorded w i t h a r a t h e r few numbers o f shots. No f l u o r e s c e n c e i s d e t e c t e d on t h e fundamental t r a n s i t i o n because o f photon t r a p p i n g . The sample c o n s i s t s o f a f i l m o f t h i c k n e s s v a r y i n g +present address : Ddpartement de Physique, U n i v e r s i t d de Montrbal, case p o s t a l e 6128, succursale "A" MontrBal, Quebec, Canada H3C 357+ + ~ a b o r a t o i r e associ6
B
l r U n i v e r s i t 6 de Paris-SudC7-306
JOURNAL DE PHYSIQUE
Fig. 1
Time-resolved fluorescence i n t e n s i t i e s o f a few Lines (Av = 1) o f Ar:CO
=
500 a t T=
2.7 K, r e c o r d e d w i t h a m u l t i c h a n n e l averager f o r d i f f e r e n t r e l a t i v e a m p l i f i - c a t i o n s and number o f shots.from 0.2 t o 1 mm d e p o s i t e d o n t o a gold-coated copper s u b s t r a t e h e l d a t l i q u i d h e l i u m temperatures.
11. BRIEF REVIEW OF VIBRATIONAL ENERGY TRANSFER MECHANISMS
I t i s w e l l known t h a t t h e decay o f CO i n rare-gas m a t r i c e s i s p u r e l y r a d i a t i v e
( 3 ) and t h a t t h e k i n e t i c s can be modelized by a s e t o f macroscopic r a t e equations
("') based on t h e "hopping" model f o r t h e f a s t m i g r a t i o n o f a v
=
1 e x c i t a t i o n which moves accross t h e c r y s t a l from one s i t e t o another a c c o r d i n g t o t h e reso- nant exchange :CO(v=O)
+
Co(v=l)- CO(v=l)+
Co(v=o) (1)u n t i l i t meets another v >, 1 e x c i t a t i o n , i n which case exothermic f u s i o n process : ,v+v+l
CO(v=l)
+
C O ( V > I) CO(v=O)+
CO(v+l) + A€ (2a)occurs. AE = v x 2 4 cm-I i s t h e l 3 2 ' 0 a n h a r m o n i c i t y energy mismatch which i s d i s s i p a t e d as l a t t i c e phonons. T h i s process which i s r e s p o n s i b l e f o r t h e pumping o f h i g h l e - v e l s i s o f course counterbalanced by t h e r e v e r s e c r o s s - r e l a x a t i o n process :
Kv+l+v
CO(v+l)
+
CO(v=O)+
AE(
CO(v)+
CO(v=l)F
(2b).
l
This process tends t o be predominant f o r t h e Lowest Levels as t h e temperature i s r a i s e d f o r t h e r a t i o of the two r a t e s obeys t h e p r i n c i p l e o f d e t a i l e d b a l a n c i n g :
I 1 1
-
MASTER RATE EQUATIONSi n t h e f o l l o w i n g convenient form :
Stimulated
Pump Spontaneous emission emission Transfer terms
No = -k0zNo + k2,,N2 + A l ~ N 1 + A20N2
+g
K G t 1 NINy-
Kg;-' NONv L a 2 - A N + A N + AS1N3 N1 = 1 0 1 2 1 2 + k 2 1 ( ~ 2 - ~ l ) . ~ 2 1 + Z ( K ~ ; NON2-
KZ
N12)-g2
K G t 1 NINv N2 x ~-
~L N~ ~~ - ( A ~ ~ + A ~ ~ ) N ~ N ~ A ~+ ~ N ~-
L ~ ~ ( N ~ - N ~ ) . ~ ~ ~ +KG -
KZ
N ~-
N ~ N ~ N ~ N" = -(~",rl+~","-2'NY + A"*l,"N"*l A"+2,~N"t2+ KV-l*' 1 4 NINy-l
-
K Z 1 NINy + NoNv*l-
Kg:' NoNIcv m
=
'
~ A ~ 1 " 2 + k 2 1 2 (N -N 1 > .iZ1-
k ii**w i t h t h e i n i t i a l c o n d i t i o n s No
=
1 ; Nv+O=
=
0 a t t=
0 andI
X = 0 f o r system f r e e o f-
X = l f o r system coupled kzl = k = 0 s t i m u l a t e d emission'
kZl = 0.5 lol's-' w i t h s t i m u l a t e d emis-k = l o 1 l s - l s i o n . Parameters
i) k02
=
u02!lL where 0 0 2 i s t h e a b s o r p t i o n c r o s s - s e c t i o n andg L
t h e number o fphotons o f t h e Laser p e r u n i t t i m e and u n i t surface. For an average f o c u s s i n g area o f 0.01 mm2 and a 0 2 = 1 0 - ~ ~ c m ~ , we have k 0 2
=
60 S-I i f t h e l a s e r o u t p u t power i s4 mW.
ii) k Z 1 i s t h e r a t e o f s t i m u l a t e d emission and depends on t h e molecular p r o p e r t i e s . T y p i c a l l y one has
loi3
< k Z 1 <loi2
( s - l ) .iii) k i s t h e l o s s r a t e of t h e photon d e n s i t y g21 which remains c o n f i n e d i n s i d e t h e medium d u r i n g an average t i m e ne/c
=
k - l where e i s t h e t h i c k n e s s o f t h e sample o f index n and c t h e speed o f l i g h t .v, Av,v-l/ Av,v-2 a r e t h e p r o b a b i l i t i e s o f Av = 1 and Av = 2 r a d i a t i v e decays.
V) t h e t r a n s f e r r a t e s which have been used t o o b t a i n t h e f i t s i n Fig. 3 cor- responding t o t h e e x p e r i m e n t a l k i n e t i c s o f Fig. 2 a r e L i s t e d i n Table 1. They a r e i n good agreement w i t h t h e values e x t r a p o l a t e d from p r e v i o u s measurements C 5 ) .
JOURNAL
DE
PHYSIQUEFig. 2
Experimental k i n e t i c s o f Av
=
1 sequence o f A r : CO = 100 and T=
4.7 K. The popu- l a t i o n s a r e o b t a i n e d from fluorescence i n t e n s i t i e s through t h e r e l a t i o n : NV/N2 ='
12*1). (A2+1 Av+v-l) ' The 1 + 0 f l u o r e s c e n c e l i n e i s n o t observed because o f photon t r a p p i n g . Fig. 3Simulated k i n e t i c s u s i n g r a t e equations (equ. 3) r e s t r i c t e d t o v
=
9 and t r a n s f e r r s t e s o f t a b l e 1.a) w i t h o u t s t i m u l a t e d emission
b) w i t h s t i m u l a t e d emission on 2 + l and 3 + 2
I n b o t h cases, t h e f r a c t i o n o f pumped molecules i s Q, 18 % . I n Fig.3a most o f t h i s
0
amount i s t r a p p e d among v = 1 t o v = 9 ( N = 18 %), w h i l e i n Fig. 3b
9 v = l
x
Nv = 3 %, t h a t i s t h e remaining I 5 % have escaped toward v > 9 owing t o t h e v=lI V
-
DISCUSSIONF i g . 3a shows t h e r e s u l t o f t h e c a l c u l a t e d k i n e t i c s r e s t r i c t e d t o v = 9 o f
A r : C O
=
100 a t T =4.7
K w i t h o u t s t i m u l a t e d emission w h i l e i n Fig. 3b, s t i m u l a t e d emissions on t h e 2 + l and 3 + 2 t r a n s i t i o n s have been i n t r o d u c e d . The p o p u l a t i o n i n v e r s i o n s e s t a b l i s h on a Longer t i m e s c a l e i n Fig. 3a. I n b o t h cases, 18 % o f t h e molecules o f t h e ground s t a t e have been pumped a t t h e end o f t h e e x c i t a t i o n pulse. Besides t h e f a c t t h a t p o p u l a t i o n i n v e r s i o n s cease beyond v=
6 i n t h e case o f Fig. 3a, a l l t h e e x c i t e d molecules a r e d i s t r i b u t e d among t h e f i r s t n i n e Levels9 9
(
C
Nv = 18 %) whereas C N = 3 % i n t h e case o f Fig. 2b. I n t h i s Last case t h ev = l v = l
remaining 15 % o f e x c i t e d molecules have escaped t o s t a t e s v > 9 because t h e system
(3) must be Let open v i a t h e term K:',:; N1N9 i n t h e Ng e q u a t i o n t o prevent a c c u m u l s t i o n o f t h e upward f l o w i n Level v
=
9. These remarks suggest t h a t t h e main process which feeds s t a t e v = 1 i n Fig. 3a (i.e. c r o s s - r e l a x a t i o n o f N2 according t o p r o - cess 2b) i s slower t h a t t h a t o f Fig. 3b ( s t i m u l a t e d emission). E x p e r i m e n t a l l y (Fig. 2 ) when t h e pump i s on, t h e t i m e e v o l u t i o n s o f Ng t o Ng a r e c l o s e l y t i e d t o t h a t o f Np.
T h i s i s most L i k e l y reproduced i n t h e s i m u l a t i o n of Fig. 3b where Np reaches very e a r l y a steady s t a t e regime r e s u l t i n g from an e q u i l i b r i u m between pump flow, s t i m u l a t e d f l o w towards v = 1 and c r o s s - r e l a x a t i o n . N1 i s t h e n maintained a t a non n e g l i g i b l e value, enhancing t h e energy t r a n s f e r t o t h e upper s t a t e s . The bumps a f t e r t h e end o f t h e p u l s e can be a t t r i b u t e d t o t h e cascade o f r a d i a t i v e decays o f p o p u l a t i o n s i n s i t u a t i o n o f i n v e r s i o n . To a v o i d such a bump on Ng which i s i n a s i t u a t i o n o f i n v e r s i o n w i t h respect t o Nb,
we must i n t r o d u c e i n t h e pre- v i o u s s e t o f equations another s t i m u l a t e d emission process between l e v e l s v = 3and v
=
2 by adding s i m i l a r corresponding terms as i n e q u a t i o n (3) and i n t r o d u c i n g t h e corresponding photon d e n s i t y 3 3 2 . Indeed, t h e r a d i a t i v e downward f l o w a t the end o f t h e p u l s e c o n f r o n t s v = 2 and v=
3 t o a s t r o n g s i t u a t i o n o f inversion, s i n c e N2 i s p r a c t i c a l l y emDty then. S t i m u l a t e d emission on t h e v=
3 + v=
2 t r a n - s i t i o n may then depopulate a p p r e c i a b l y s t a t e v=
3 i n t h e b e n e f i t o f s t a t e v=
2, b u t t h e L a t t e r beeing i n t u r n coupled t o s t a t e v=
1, t h e downward f l o w a r r i v e s very r a p i d l y a t s t a t e v = 1 where processes 2(a,b) s t a r t again. T h i s auto feed-
back p a r t l y e x p l a i n t h e a b n o r m a l l y Long 40 ms l i f e t i m e o f t h e fluorescence
I
N
v
A
2
from l e v e l s v > 4 which i s 10 times Lon ger t h a n t h e i r n a t u r a l L i f e t i m e . Ano- t h e r f a c t o r r e s p o n s i b l e f o r t h i s long
Fig. 4
.l-
73
3
Simulated k i n e t i c s a t 2.7 K u s i n g the same parameters as i n Fig. 3a b u t w i - t h o u t t a k i n g i n t o account any s t i m u l a - t e d emission. Most o f t h e pumped mole- cules a r e t r a p p e d on v
=
2 because t h e c r o s s - r e l a x a t i o n o f t h e v = 2 e x c i t a - t i o n i s frozen.0.
L i f e t i m e comes from t h e r a d i a t i v e f l o w due t o Levels v > 9 which were n o t t a - ken i n t o account i n t h e s i m u l a t i o n . The s l i g h t h o l l o w shape on N8 i s imputed t o t h a t .
4
5
6
I But t h e s p e c t a c u l a r evidence t h a t s t i - mulated emission p l a y s a fundamental r o l e i n t h e pumping o f h i g h Levels i sC7-310
JOURNAL DE PHYSIQUE
p r o v i d e d by t h e k i n e t i c s a t T = 2.7 K. While t h e s i m u l a t e d k i n e t i c s remains prac- t i c a l l y unchanged i f s t i m u l a t e d emission i s considered except f o r t h e appearance o f a l o n g e r t a i l f o r Np a t t h e end o f t h e pulse, Fig. 4 shows t h a t when s t i m u l a t e d emission i s neglected, a l l t h e energy i s t r a p p e d on s t a t e v
=
2 because endother- mic process (2b) becomes no more e f f i c i e n t f o r t h e d e p o p u l a t i o n o f t h a t s t a t e . No i n - v e r s i o n i s then reached, and t h e t i m e e v o l u t i o n smoothens, which i s i n c o n t r a d i c - t i o n w i t h t h e e x p e r i m e n t a l k i n e t i c s a t 2.7 K (see f o r i n s t a n c e Fig. 1 ) .Temperature and pum energy d e n s i t t h r e s h o l d s f o r t h e e f f i c i e n c y o f s t i m u l a t e d emission have a l s o geen evidenced gy t h e s i m u l a t i o n s . No more d i f f e r e n c e s u b s i s t s between t h e k i n e t i c s undergoing o r n o t s t i m u l a t e d emission above T
=
7 K, o r when t h e pump energy d e n s i t y i s reduced below 30 s-'. Such a behaviour i s s i m i l a r t o t h a t observed f o r t h e s p i k i n g emission i n N2:CO.V
-
CONCLUSIONAssuming Manz's t h e o r y o f v i b r a t i o n a l energy t r a n s f e r and t h e p r i n c i p l e o f d e t a i - l e d b a l a n c i n g f o r t h e c r o s s - r e l a x a t i o n o f t h e v
=
2 s t a t e t o a p p l y t o o u r system, t h e r o l e o f s t i m u l a t e d emission as a major channel f o r t h e d e p o p u l a t i o n o f s t a t e v = 2 i s predominant i n t h e pumping o f h i g h v i b r a t i o n a l l e v e l s a t Low temperature ( T ~ 2 . 7 K ) . A t T = 4.7 K t h e r o l e o f c r o s s - r e l a x a t i o n i s non n e g l i g i b l e b u t stimu- l a t e d emission s t i 11 remains a c t i v e . I f temperature i s r a i s e d furthermore, stimu- l a t e d emission i s quenched because t h e c r o s s - r e l a x a t i o n d e s t r o y s t h e p o p u l a t i o n i n v e r s i o n between s t a t e s v=
2 and v = 1 . Endothermic t r a n s f e r processes (2b) compete t h e n s t r o n g l y w i t h t h e up-the-ladder processes (2a) so t h a t t h e V-V pumping e f f i c i e n c y i s reduced. I n m a t r i x i s o l a t e d d i a t o m i c molecules r e l a x i n g m a i n l y r a d i a - t i v e l y , p o p u l a t i o n i n v e r s i o n s a r e e a s i l y o b t a i n a b l e . T h e r e f o r e these systems have a g r e a t p o t e n t i a l i t y as s o l i d s t a t e l a s e r s . A c t u a l l y l a s e r a c t i o n has been observed i n s e v e r a l cases ( I ) .REFERENCES
( 1 ) J.P. Galaup, J.Y. Harbec, J . J . Zondy, R. Charneau and H. Dubost, p r e c e d i n g paper i n t h i s volume.
( 2 ) J.P. Galaup, J.Y. Harbec, R. Charneau and H. Dubost, Chem. Phys. Lett., i n press.
( 3 ) H. Dubost, "Spectroscopy o f v i b r a t i o n a l and r o t a t i o n a l Levels o f d i a t o m i c molecules i n r a r e gas c r y s t a l s " i n I n e r t Gases : P o t e n t i a l s , dynamics and energy t r a n s f e r i n doped c r y s t a l s , S p r i n g e r s e r i e s i n Chemical Physics, v o l . 34, e d i t e d by M.L. K l e i n ( S p r i n g e r Verlag, B e r l i n 1984), p. 145-257. ('+) J. Manz, Chem. Phys. 24
,
(1977) 51 ; A. Blumen, J. Manz, V. Yakhot,chem. Phys.,
