HAL Id: jpa-00221850
https://hal.archives-ouvertes.fr/jpa-00221850
Submitted on 1 Jan 1982
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
FLOQUET THEORY AND QUASI-ENERGY METHODS FOR INTENSE FIELD MOLECULAR MULTIPHOTON EXCITATION AND DISSOCIATION
Shih-I Chu
To cite this version:
Shih-I Chu. FLOQUET THEORY AND QUASI-ENERGY METHODS FOR INTENSE FIELD MOLECULAR MULTIPHOTON EXCITATION AND DISSOCIATION. Journal de Physique Collo- ques, 1982, 43 (C2), pp.C2-449-C2-450. �10.1051/jphyscol:1982238�. �jpa-00221850�
JOURNAL DE PHYSIQUE
CoZZoque C2, suppZ6ment au n o l l , Tome 43, novemhre 1982 page C2-449
FLOQUET THEORY A N D QUASI-ENERGY METHODS FOR INTENSE FIELD MOLECULAR MULTIPHOTON EXCITATION AND DISSOCIATION
Shih-I Chu
Department of Chemistry, U n i v e r s i t y of Kansas, Lawrence, Kansas 66045, U.S.A.
A b s t r a c t
(1) A n o n - p e r t u r b a t i v e q u a s i - v i b r a t i o n - r o t a t i o n a l e n e r g y method h a s been developed f o r t h e t r e a t m e n t of t h e quantum dynamics of n o n - l i n e a r high-order m u l t i - photon e x c i t a t i o n of m o l e c u l e s i n t h e p r e s e n c e of i n t e n s e laser and s t a t i c e l e c t r i c f i e l d s . ' The F l o q u e t t h e o r y i s a p p l i e d t o t h e s i n g l e and m u l t i p h o t o n e x c i t a t i o n s of t h e HF molecule. Non-linear e f f e c t s s u c h a s power b r o a d e n i n g , dynamics S t a r k s h i f t , Autler-Townes m u l t i p l e t s p l i t t i n g , h o l e b u r n i n g and S-hump b e h a v i o r s , e t c , , a r e observed and d i s c u s s e d i n t e r m s of quasi-energy diagrams. Many o f t h e s a l i e n t f e a t u r e s i n t h e s p e c t r a l l i n e s h a p e s may b e q u a l i t a t i v e l y u n d e r s t o o d i n t e r m s of a n a n a l y t i c a l t h r e e - l e v e l model. The a d d i t i o n of a d c e l e c t r i c f i e l d removes t h e r e s t r i c t i o n of t h e r o t a t i o n a l a i p o l e s e l e c t i o n r u l e and c a u s e s s i g n i f i c a n t i n t e r - n i x i n g of t h e b a r e m o l e c u l a r v i b r a t o r s t a t e s . Due t o t h e g r e a t e r number of s t r o n g l y coupled n e a r b y s t a t e s i n t h e d c f i e l d , n o n - l i n e a r e f f e c t s such a s t h o s e mentioned above a p p e a r a t a much lower a c f i e l d s t r e n g t h t h a n t h e y would i n t h e a b s e n c e of t h e d c f i e l d . The i n t r o d u c t i o n of a n e x t e r n a l dc f i e l d t h e r e f o r e s t r o n g l y enhances t h e m u l t i p h o t o n e x c i t a t i o n p r o b a b i l i t i e s and r e s u l t s i n a much r i c h e r spectrum.
(2) A p r a c t i c a l and n o n p e r t u r b a t i v e complex q u a s i - v i b r a t i o n a l e n e r g y method i s developed2 f o r s t u d y i n g m o l e c u l a r p h o t o d i s s o c i a t i o n p r o c e s s e s i n t h e p r e s e n c e of (weak o r i n t e n s e ) e l e c t r o m a g n e t i c f i e l d s , u s i n g o n l y s q u a r e - i n t e g r a b l e (L 2 ) func-
t i o n s . By means of t h e complex c o o r d i n a t e t r a n s f o r m a t i o n and L~ d i s c r e t i z a t i o n of t h e v i b r a t i o n a l c o n t i n u a , t h e complex q u a s i v i b r a t i o n a l e n e r g i e s (QVE) of t h e F l o q u e t Hamiltonian c a n b e d e t e r m i n e d by s t a n d a r d non-Hermitian e i g e n v a l u e a n a l y s i s . The r e a l p a r t s of t h e QVE's p r o v i d e t h e a c S t a r k - s h i f t e d v i b r o n i c e n e r g i e s , whereas t h e imaginary p a r t s a r e r e l a t e d t o t h e p h o t o d i s s o c i a t i o n t r a n s i t i o n r a t e s . The t h e o r y h a s been a p p l i e d t o t h e d i r e c t p h o t o d i s s o c i a ~ i o n of ~ ~ + ( l s o -2po ) i n b o t h weak and
g u +
s t r o n g f i e l d s . 2 E x t e n s i o n of t h e method t o m u l t i p h o t o n d i s s o c i a t i o n of H2 , HF and
SO i s i n p r o g r e s s , 2
T h i s r e s e a r c h i s s u p p o r t e d i n p a r t by t h e United S t a t e s Department of Energy, D i v i s i o n of Chemical S c i e n c e s , under c o n t r a c t NO. DE-AC02-80ER10748, and by t h e A l f r e d P. Sloan Fellowship. Acknowledgment i s a l s o made t o t h e Donors of t h e Petroleum Research Fund, a d m i n i s t e r e d by t h e American Chemical S o c i e t y , f o r p a r t i a l s u p p o r t of t h i s work.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982238
JOURNAL DE PHYSIQUE
References
1. Chu, S. I., Tietz, J. V., and Datta, K. K., "Quantum Dynamics of Molecular Multiphoton Excitation in Intense Laser and Static Electric Fields - Floquet Theory, Quasi-Energy Spectra and Application to the HF Molecule," J. Chem.
Phys. (to be published).
2. Chu, S. I., J. Chem. Phys. 2 (1981) 2215.
