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MULTIPHOTON ROTATIONAL SPECTROSCOPY OF THE NO MOLECULE : POLARIZATION EFFECTS IN THE FLUORESCENCE SPECTRUM COMPARED TO PHOTOIONIZATION, A WAY FOR
DETERMINING THE CHANNELS TOWARDS IONIZATION
C. Mainos, E. Boursey, H. Damany, Y. Le Duff, J. Subtil
To cite this version:
C. Mainos, E. Boursey, H. Damany, Y. Le Duff, J. Subtil. MULTIPHOTON ROTATIONAL SPEC- TROSCOPY OF THE NO MOLECULE : POLARIZATION EFFECTS IN THE FLUORESCENCE SPECTRUM COMPARED TO PHOTOIONIZATION, A WAY FOR DETERMINING THE CHAN- NELS TOWARDS IONIZATION. Journal de Physique Colloques, 1987, 48 (C7), pp.C7-643-C7-645.
�10.1051/jphyscol:19877155�. �jpa-00226977�
JOURNAL DE PHYSIQUE
Colloque C7, suppl6ment au n012, Tome 48, dgcembre 1987
MULTIPHOTON ROTATIONAL SPECTROSCOPY OF THE NO MOLECULE
:POLARIZATION EFFECTS IN THE FLUORESCENCE SPECTRUM COMPARED TO PHOTOIONIZATION, A WAY FOR DETERMINING THE CHANNELS TOWARDS IONIZATION
C. MAINOS, E. BOURSEY*, H. DAMANY*, Y.
LEDUFF and
J.L.SUBTIL*
CNRS, LIMHP, Universite Paris-Nord, F-93430 Villetaneuse, France
'CNRS,
UA-171,Equipe de Spectroscopie et Celphyra, 158 bis, Cours Fauriel, F-42023 Saint-Etienne Cedex, France
The development of high power narrowband t u n a b l e pulsed l a s e r s b r i n g s new inves- t i g a t i o n p o s s i b i l i t i e s i n t h e f i e l d of t h e o p t i c a l spectroscopy of atoms and molecu- l e s . Although molecular spectroscopy i s one of t h e r e s e a r c h f i e l d i n s c i e n c e having been e x t e n s i v e l y s t u d i e d a v a r i e t y of important a s p e c t s have been demonstrated very r e c e n t l y i n t h i s f i e l d 1 : 2 9 3 y 4 a s r a d i a t i o n sources have been improved. Here, we in- tend t o d i s c u s s p o l a r i z a t i o n e f f e c t s on t h e i n t e n s i t i e s of multiphoton e x c i t e d r o t a - t i o n a l l i n e s of simple mole'cules. Let us f i r s t r e c a l l t h e p r i n c i p l e s which govern t h e s e e f f e c t s
.
I n one-photon t r a n s i t i o n s t h e Born-Oppenheimer and Franck-Condon p r i n c i p l e s a l - low a complete t r e a t m e n t and s e p a r a t i o n of t h e dynamics i n t o r o t a t i o n a l and v i b r o n i c p a r t s s i n c e i n t h i s c a s e t h e r e i s only one p o s s i b l e v a l u e f o r t h e quantum number (k) of t h e t r a n s f e r e d a n g u l a r momentum k , t h i s i s k = 1 , whereas t h e a b s o r p t i o n of a photon w i l l change t h e t o ' t a l angular momentum by 0 o r 2 1 r e g a r d l e s s of t h e i n c i d e n t p o l a r i z a t i o n . The f a c t t h a t t h e r e i s o n l y one v a l u e f o r k w i l l permit one t o o b t a i n measurements on t h e r e l a t i v e r o t a t i o n a l l i n e i n t e n s i t i e s of one-photon t r a n s i t i o n s without s p e c i f y i n g t h e v i b r o n i c p a r t .
However, i n multiphoton t r a n s i t i o n s , t h e t r a n s f e r of a n g u l a r momentum from t h e l a s e r beam t o t h e molecule i s r e a l i z e d through a b s o r p t i o n of more than one photon.
For t h e n-order d i p o l e p r o c e s s , t h e change i n t o t a l a n g u l a r momentum must be
5
n s i n c e t h e a b s o r p t i o n of each photon can a l t e r t h e angular momentum by 0 o r2
1. Ins- t e a d t h e one-photon t r a n s i t i o n s , now t h e quantum number (k) f o r t h e t r a n s f e r e d angu- l a r momentum cantakemore than one value, each v a l u e f o r t h e quantum number (k) w i l l cou- p l e t h e r o t a t i o n a l and v i b r o n i c p a r t . Therefore, s i n c e t h e i n t e n s i t y of a r o t a t i o n a l l i n e i n a multiphoton t r a n s i t i o n g e n e r a l l y may have one c o n t r i b u t i o n from each quan- tum number (k) and t h e corresponding v i b r o n i c p a r t s a r e d i f f e r e n t , we a r e n o t a b l e t o s e p a r a t e t h e r o t a t i o n a l l i n e s t r e n g t h i n t o a r o t a t i o n a l and a v i b r o n i c p a r t .Consequently, i n a multiphoton t r a n s i t i o n , t h e r e i s a number of unknown v i b r o n i c c o n s t a n t s which i s equal t o t h e p o s s i b l e v a l u e s f o r t h e quantum number ( k ) . To each v a l u e of k , we have a k-term which may c o n t r i b u t e t o t h e i n t e n s i t y of a r o t a t i o n a l l i n e . The change i n t h e t o t a l a n g u l a r momentum can be 0 , 5 1 , ? 2,
. . . ,
2 k whereas t h e c o n t r i b u t i o n of t h e k-term t o a r o t a t i o n a l l i n e must s a t i s f y s e l e c t i o n r u l e s which a s s u r e t h e a n g u l a r momentum c o n s e r v a t i o n of multiphoton p r o c e s s .Although t h e multiphoton r o t a t i o n a l lLne f a c t o r s a r e e x p l i c i t y known, t h e vibro- n i c c o n s t a n t s a r e n o t , t h i s renders incomplete t h e e x p r e s s i o n f o r t h e t o t a l r o t a t i o - n a l l i n e s t r e n g t h and t h u s one i s unable t o compare r o t a t i o n a l l i n e i n t e n s i t i e s pre- d i c t e d by t h e o r y with t h o s e o b t a i n e d by t h e experiment. Our work i n t e n d s t o f i l l t h i s gap.
T h e o r e t i c a l :
According t o our c a l c u l a t i o n s 5, l e t us b r i e f l y r e c a l l t h a t t h e r o t a t i o n a l l i n e s t r e n g t h (RLS) i n t h e e l e c t r i c d i p o l e approximation of a n-photon t r a n s i t i o n between an i n i t i a l s t a t e g and a f i n a l s t a t e f , w i l l l e a d t o a decomposition of t h e r o t a t i o - n a l s t r u c t u r e i n t o a sum of c o n t r i b u t i o n s
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19877155
JOURNAL
DE
PHYSIQUE(n)
S ( n , ~ ) = IBk,np (n) (n>
C
2k+
1 'k, (Jg ~ f ) ITk,AAl'
f g k
(n) i s a c o n s t a n t which depends on t h e p o l a r i z a t i o n and t h e number of absorbed :kb?gns and g i v e s t h e r e l a t i v e weighting of t h e c o n t r i b u t i o n of the k-term. p=Ostands f o r l i n e a r l y p o l a r i z e d photons w h i l e p =
2
1 hold f o r c i r c u l a r l y p o l a r i z e d photons, the s e n s e of t h e p o l a r i z a t i o n i n t h e c i r c u l a r c a s e has no any e f f e c t on t h i s cons- t a n t . The p o l a r i z a t i o n v e c t o r e i s d e f i n e d i n t h e space f i x e d frame (SFF) and we suppose t h a t a l l t h e absorbed pgotons have t h e same energy and p o l a r i z a t i o n s t a t e .(Jg -t J ~ ) i s t h e r o t a t i o n a l l i n e f a c t o r which c o n t a i n s t h e r o t a t i o n a l dependen- c e of t h e (RLS) and t h e coupling c a s e of t h e i n i t i a l and f i n a l s t a t e s . E x p l i c i t forms f o r t h e r o t a t i o n a l l i n e f a c t o r s a f any s p i n - m u l t i p l i c i t y have been p r e s e n t e d i n pre- v i o u s works, they hold f o r t r a n s i t i o n s between two s t a t e s which both belong t o Hund's case ( a ) o r case ( b ) , a s w e l l a s , f o r t r a n s i t i o n s between a s t a t e with a case
( a ) coupling and a s t a t e with case (b) coupling. Generally, t h e molecular s t a t e s may
have any coupling i n t e r m e d i a t e between (a) and ( b ) . q
The v i b r o n i c dependence of t h e (RLS) i s contained i n t h e q u a n t i t y ITk (n)
A n l
which i s coupled w i t h t h e r o t a t i o n a l l i n e f a c t o r and t h e p o l a r i z a t i o n c y s t a n t (6)
through t h e quantum number (k) of t h e absorbed photon angular momentum k , t h e above q u a n t i t i e s v a n i s h when k < A A l o r k < Inpl. Angular momentum c o n s e r v a t i o n arguments show t h a t t h e p o s s i b l e v a l u e s of t h e quantum number (k) a r e n , n
-
2, n - 4...,
1
L\A) i f n -Ian1
i s even o r ,I A A ]
+ 1 i f n - i s odd. The q u a n t i t y ~ (i n c l u - ~ j des summation over s e t s defined by t h e couple ( ~ , A A ) and each c h a r a c t e r i z e s a p r e c i s e multiphoton pathway which can be t r a c e d w i t h i n t h e molecule following symmetry consi- d e r a t i o n s and s e l e c t i o n r u l e s . The presence of r e a l molecules s t a t e s p l a y s t h e r o l e of v i r t u a l i n t e r m e d i a t e s t a t e s i n t h e o v e r a l l multiphoton p r o c e s s 6. We i n t e n d t o p r e s e n t now some p r e l i m i n a r y r e s u l t s which conform t h e v a l i d i t y of our t h e o r e t i c a l a s s .Experimental : t h e two photon spectrum of NO
B r i e f l y , t h e t h i r d harmonic o u t p u t of a Quantel NdYag l a s e r i s s e n t i n a gra- zing i n c i d e n c e d e s i g n dye l a s e r w i t h a m p l i f i e r s t a g e . P o l a r i z a t i o n of l i g h t i s achie- ved by an i n t r a c a v i t y g l a n p o l a r i z e r . The o u t p u t of t h e a m p l i f i e r s t a g e t r a v e l s
through a g l a n a n a l y s e r followed by a F r e s n e l rhomb hence producing e i t h e r l i n e a r l y a c i r c u l a r l y p o l a r i z e d photons. The beam i s focused i n t o a f l u o r e s c e n c e (TPEF) o r i o n i z a t i o n (MPI) c e l l . Fluorescence l i g h t i s viewed a t 90' by t h e p h o t o m u l t i p l i e r through a H-20 F14.2 Jobin-Yvon monochromator. Both TPEF o r MPI s i g n a l and t h e i n c i - dent l a s e r power a r e d i g i t i z e d with a PAR Boxcar i n t e g r a t o r o r a K e i t h l e y e l e c t r o - meter and passed t o a P1600 Logabax computer f o r s t o r a g e and p r o c e s s i n g .
R e s u l t s : Two photon r o t a t i o n a l l i n e s t r u c t u r e f o r t h e A 2 ~ ' ( ~ ' = 0 )
-
X 211(v"=~) gamma band of n i t r i c oxide.I n such a c a s e , t h i s i s t h e f i r s t molecular e x c i t e d s t a t e hence t h e r e a r e no resonant i n t e r m e d i a t e e x c i t e d s t a t e . Then, t h e RLS w i l l be p r o p o r t i o n a l t o t h e
'2
Ah term of our t h e o r e t i c a l e x p r e s s i o n m u l t i p l i e d by t h e Boltzman f a c t o r . F i g . l a anh o e x h i b i t t h e p r e d i c t e d and experimental two photon e x c i t a t i o n s p e c t r a i n t h e NOY(0,O) 012 branch. The s y n t h e t i c i n t e n s i t i e s have been deduced from t h e w e l l known molecular c o n s t a n t s of both s t a t e s 7.F i g . l c e x h i b i t s t h e corresponding multiphoton spectrum
Another i n t e r e s t i n g a s p e c t l i e s i n ~ o l a r i z a t i o n e f f e c t s . From our t h e o r e t i c a l e x p r e s s i o n of t h e RLS, one can deduce t h e r a t i o of t h e i n t e n s i t y of a r o t a t i o n a l l i n e w i t h l i n e a r l y p o l a r i z e d l i g h t o v e r t h e i n t e n s i t y of t h e same l i n e o b t a i n e d from c i r c u l a r l y p o l a r i z e d l i g h t . From t h i s , i t r e s u l t s t h a t
We checked t h i s r a t i o e x p e r i m e n t a l l y f o r t h e two photon e x c i t e d Y band NO w i t h a good agreement of 1.4 w i t h r e s p e c t t o t h e t h e o r e t i c a l v a l u e o f 1.5.
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