Chapter 14
Nonlinear Optics: Organic and Polymeric Systems A. F. Garito, Y. M. Cai, H. T. Man, and O. Zamani-Khamiri
Downloaded by CORNELL UNIV on June 3, 2017 | http://pubs.acs.org Publication Date: March 26, 1987 | doi: 10.1021/bk-1987-0337.ch014
Department of Physics and Laboratory for Research on the Structure of Matter, University of Pennsylvania, Philadelphia, PA 19104-6396
Organic and polymer structures exhibit unusually large, ultrafast second and third order nonlinear optical properties that are important to the fields of nonlinear optics and o p t i c a l device technologies. These important properties have been demonstrated in a large number of structures, phases and states. Experimental and t h e o r e t i c a l studies of such systems have achieved sig nificant advances in the understanding of these macroscopic n o n l i n e a r o p t i c a l responses based on theoretically calculated microscopic e l e c t r o n i c mechanisms. One recent example of the electronic origin of second order nonlinear optical processes in conjugated l i n e a r chain structures i s reviewed.
Organic and p o l y m e r s t r u c t u r e s e x h i b i t u n u s u a l l y large, u l t r a f a s t second and t h i r d o r d e r n o n l i n e a r o p t i c a l p r o p e r t i e s t h a t a r e i m p o r t a n t t o the f i e l d s o f n o n l i n e a r o p t i c s and optical device technologies. These important p r o p e r t i e s have been d e m o n s t r a t e d i n a l a r g e number o f structures, phases, and s t a t e s t h a t , as p r e v i o u s l y r e v i e w e d (1-9), i n c l u d e o r g a n i c c r y s t a l s and f i l m s , c o n j u gated polymers, monomolecular f i l m s , l i q u i d crystals, l i q u i d c r y s t a l p o l y m e r s , and more r e c e n t l y , h i g h p e r f o r m ance o r d e r e d p o l y m e r s ( 10,11), and p o l y m e r g l a s s e s (12). F o r t h e s e c l a s s e s o f c o n j u g a t e d m o l e c u l a r and p o l y m e r s t r u c t u r e s , the p r i n c i p a l p r o p e r t y i s that t h e i r nonreson a n t , n o n l i n e a r o p t i c a l r e s p o n s e s a r e d o m i n a t e d by u l t r a f a s t , v i r t u a l e x c i t a t i o n s o f the π-electron s t a t e s . This was d i r e c t l y d e m o n s t r a t e d by MNA ( 2 - m e t h y 1 - 4 - n i t r o a n i l i n e ) s i n g l e c r y s t a l measurements o f m a c r o s c o p i c second order s u s c e p t i b i l i t i e s a t de (JJ3.) and o p t i c a l f r e q u e n c i e s ( 1 315) and combined second h a r m o n i c measurements and t h e o 0097-6156/87/0337-0177$06.00/0 © 1987 American Chemical Society
Sandman; Crystallographically Ordered Polymers ACS Symposium Series; American Chemical Society: Washington, DC, 1987.
178
CRYSTALLOGRAPHICALLY ORDERED POLYMERS
r e t i c a l c a l c u l a t i o n s o f t h e frequency dependent m o l e c u l a r second o r d e r s u s c e p t i b i l i t y (3,16,17). Similar results are being obtained f o r t h i r d order p r o p e r t i e s o f l i q u i d c r y s t a l monomers and p o l y m e r s (18-22), and s i n g l e crystal polymers (23-24). Importantly, π-electron excitations a r e i n t r i n s i c a l l y u l t r a f a s t o f o r d e r 1 0 " ^ s e c o n d s (1 f s ) (25) w h e r e a s o t h e r p o t e n t i a l e x c i t a t i o n modes s u c h as phonons, o r i o nmotions, involve slower nuclear dis placements a n d v i b r a t i o n s o f o r d e r 10 seconds (ips). C u r r e n t l y , t h e π-electron e x c i t a t i o n s a r e v i e w e d as o c c u r r i n g on i n d i v i d u a l m o l e c u l a r , o r p o l y m e r c h a i n , s i t e s and p r o v i d i n g m a c r o s c o p i c sources of nonlinear o p t i c a l response through the corresponding o n - s i t e microscopic nonlinear optical susceptibility. Thus, i n a r i g i d /lat tice approximation, the macroscopic second order ' ( ω^·ω ,ω ) and t h i r d o r d e r X ^ ' ( - ; , ω , ω ^ ) responses a r e e x p r e s s e d by t h e e q u a t i o n s
Downloaded by CORNELL UNIV on June 3, 2017 | http://pubs.acs.org Publication Date: March 26, 1987 | doi: 10.1021/bk-1987-0337.ch014
1
2
Χ
(
2
2
)
ω
ί^- 3 6
i
l
;
ω
ω
=
1' 2) 1
ω
N
1
( ^
and X
( 3 )
=
Ν < Η
ijkl(-^i° 1 ω ι ω ω ωι, J ' n k ' o l v V i ' 2
f
,
f
Η
χπι·*όΛο· 1ρ· .
3
,
f
ω
V
ω
ό·κ·ΐ·(- 4'1
ω >
ω
2' 3
)
>
(2) where Ν i s t h e number o f m o l e c u l a r , o r polymer, sites per unit volume, ^i'j'k' * ^i'j'k'l' ^ P "tive m i c r o s c o p i c secon^, and t h i r d order n o n l i n e a r o p t i c a l sus ceptibilities, f local field tensors, R the rotation matrix transforming themolecular frame t o t h e l a b o r a t o r y frame, t h e b r a c k e t a n a v e r a g e o v e r t h e o r i e n t a t i o n a l d i s t r i b u t i o n , and t h e unprimed (primed) coordinates d e s i g n a t e t h e l a b o r a t o r y ( m o l e c u l a r ) f i x e d axes. Thus, unlike inorganic semiconductors and d i e l e c t r i c insula tors, the fundamental problem of understanding the o r i g i n of the l a r g e macroscopic responses Χ ±^ * X i j k l °^ c o n j u g a t e d π-electron o r g a n i c a n d p o l y m e r s t r u c t u r e s r e duces t o e x p e r i m e n t a l and t h e o r e t i c a l s t u d i e s o f t h e c o r r e s p o n d i n g m i c r o s c o p i c s u s c e p t i b i l i t i e s S^-j^ and Ύ ^ ^ ι o f s i n g l e m o l e c u l a r , o r p o l y m e r c h a i n , u n i t s , and t h e o r i e n t a t i o n a l d i s t r i b u t i o n f u n c t i o n s o f a s s e m b l i e s o f such u n i t s c o m p r i s i n g t h e n o n l i n e a r o p t i c a l medium. The ττ-electron s t a t e s a r e t r u e m a n y - b o d y states b e c a u s e e l e c t r o n c o r r e l a t i o n s due t o n a t u r a l r e p u l s i v e Coulomb interactions tend to localize the otherwise delocalized electrons. E l e c t r o n c o r r e l a t i o n s p l a y an i m p o r t a n t r o l e i n t h e n o n l i n e a r o p t i c a l responses o f con j u g a t e d o r g a n i c s t r u c t u r e s (1-3,16,17,26), and t h e i r des cription of 3 j and " Y j i k l markedly from inde pendent p a r t i c l e models. i n calculating the sign, magnia n