Nonlinear Optical Properties of Organic and Polymeric Materials

2 Design and Characterization of Molecular and Polymeric Nonlinear Optical Materials: Successes and Pitfalls Downloaded by NORTH CAROLINA STATE UNIV on September 5, 2012 | http://pubs.acs.org Publication Date: September 29, 1983 | doi: 10.1021/bk-1983-0233.ch002

G E R A L D R. M E R E D I T H Xerox Corporation, Webster Research Center, Webster, NY 14580

Over the past decade it has been learned that organic materials containing appropriately constituted or substituted conjugation systems may exhibit highly enhanced electronic nonlinear o p t i c a l polarization responses (1-4). Since the microscopic second-order nonlinear hyperpolarizability tensor, β, i s orientationally averaged to zero in random media (except the nonuseful pseudoscalar component (5)), the realization that elements of β could be so s i g n i f i c a n t l y enhanced developed in large part as result of studies of e l e c t r i c f i e l d induced second harmonic (EFISH) generation in molecular l i q u i d s (1-2). In the EFISH technique characteristics of β are sampled as a weak molecular alignment i s induced by a s t a t i c e l e c t r i c field and the subsequent frequency doubling of laser l i g h t is observed. Correlation o f molecular charge transfer characteristics with β enhancement was shown and several highly nonlinear crystals were discovered based on t h i s knowledge (6-8). However, a major l i m i t a t i o n to achieving the enormous potential of molecular materials (e.g. crystals with χ ~10 esu (3) to be compared to χ ~10 -10 esu of common nonlinear optical media) has been the requirement to achieve appropriate alignment of microscopic units. This requirement i s to minimize orientational cancellation of the third rank polar β tensors whose contributions determine the macroscopic second-order electric dipole s u s c e p t i b i l i t y , χ . In nearly all cases, such alignments are achieved through packing forces in crystals with structures belonging to one of the noncentrosymmetric c r y s t a l classes. Unfortunately, details of these forces are currently too poorly understood to enable a molecular design approach for crystal structure and molecular alignment control. In the first part of this paper several novel approaches to the alignment problem of second-order nonlinearity will be presented. The molecular information which guided and motivated these efforts, and others described i n this symposium, derives from third-order nonlinear o p t i c a l experimentation (EFISH and others). In the second (2)

(2)

-9

-5

-7

(2)

0097-6156/83/0233-0027S08.50/0 © 1983 American Chemical Society

In Nonlinear Optical Properties of Organic and Polymeric Materials; Williams, D.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

NONLINEAR OPTICAL PROPERTIES

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h a l f o f t h i s paper i n a c c u r a c i e s , s u b t l e t i e s and p i t f a l l s o f these and o t h e r t h i r d - o r d e r experiments w i l l be discussed. Besides β, t h i r d - o r d e r e l e c t r o n i c nonlinear h y p e r p o l a r i z a b i l i t i e s , γ , are a l s o known to be enhanced i n c e r t a i n organics. Due to p r o p e r t i e s of polar f o u r t h rank c a r t e s i a n t e n s o r s , i n c o n t r a s t to the t h i r d rank (?) polar xK£LJ t e n s o r s , alignment i s a l e s s s i g n i f i c a n t f a c t o r i n o b t a i n i n g media d i s p l a y i n g h i g h l y enhanced χ ( 3 ) from molecules possessing l a r g e γ ( 4 ) . This, coupled with p r e d i c t i o n s o f recent molecular o r b i t a l c a l c u l a t i o n s o f y ( 9 _ ) , have l e d us t o develop accurate techniques to r e l i a b l y study these q u a n t i t i e s . These techniques and r e s u l t s w i l l a l s o be discussed. Methods and E v a l u a t i o n of Second-Order N o n l i n e a r i t y P r e s e r v i n g Alignments Θ

Downloaded by NORTH CAROLINA STATE UNIV on September 5, 2012 | http://pubs.acs.org Publication Date: September 29, 1983 | doi: 10.1021/bk-1983-0233.ch002

β

e

C r y s t a l s . A necessary c o n d i t i o n f o r to be nonvanishing i s that the medium have a noncentrosymmetric microscopic o r g a n i z a t i o n . The most common such s t r u c t u r e s are c r y s t a l s w i t h space groups from the noncentrosymmetric c l a s s e s . For molecular c r y s t a l s t o e x h i b i t n o n n e g l i g i b l e χ(^) both the molecular s t r u c t u r e and the u n i t c e l l s t r u c t u r e must meet t h i s c o n d i t i o n . The former c o n d i t i o n i s met by the u t i l i z a t i o n o f compounds s a t i s f y i n g c o n d i t i o n s which enhance β. Recognizing the d i f f i c u l t y of p r e d i c t i n g the nature of c r y s t a l u n i t c e l l s t r u c t u r e s , i f one i s i n t e r e s t e d simply i n i d e n t i f y i n g p o t e n t i a l new n o n l i n e a r media, as a lowest l e v e l s t r a t e g y one might survey large numbers o f c r y s t a l s of these compounds w i t h the hope o f f i n d i n g a few f a v o r a b l y a l i g n e d . A method which may be employed f o r t h i s e v a l u a t i o n ; as an a l t e r n a t i v e t o time consuming s i n g l e c r y s t a l c h a r a c t e r i z a t i o n , i s observation o f second harmonic generation (SHG) from c r y s t a l l i n e powders ( 1 0 - 1 1 ) . We have screened s e v e r a l hundred compounds by SHG powder methods, as have s e v e r a l other research groups. These methods represent a very complex o p t i c a l s i t u a t i o n i n which the observation of one i n t e n s i t y or a s e r i e s of i n t e n s i t i e s as f u n c t i o n of powder s i z e or doubling wavelength i s performed and as such a r e not q u a n t i t a t i v e , are s u b j e c t to a r t i f a c t s and must be approached w i t h a s p e c i f i c s e t of expectations for their interpretation. We recognize that there are a p p l i c a t i o n s i n two- and threedimensional waveguides ( 1 2 , 1 3 ) which do not have the same c r i t e r i a of phase-matching as i n simple c r y s t a l s or that one may j u s t as w e l l be i n t e r e s t e d i n screening these m a t e r i a l s f o r the r e l a t e d e l e c t r o o p t i c performance by the simple SHG powder method. ( I t has been shown f o r s e v e r a l organic m a t e r i a l s that although the e l e c t r o - o p t i c and SHG tensors are i n p r i n c i p l e unequal, due to d i s p e r s i o n and due t o the p o s s i b l e c o n t r i b u t i o n o f atomic and molecular d i s t o r t i o n s


2.

MEREDITH

Design and Characterization

29

i n the former, the predominance o f the e l e c t r o n i c c o n t r i b u t i o n s t o χ( ) i n these m a t e r i a l s causes these tensors t o be n e a r l y equal ( 1 4 - 1 6 ) . ) I t i s , t h e r e f o r e , worthwhile to know t h a t l i m i t a t i o n o f powder p a r t i c l e s i z e s t o l e s s than a t y p i c a l SHG coherence length a l l o w s more elements of the tensor to contribute s i g n i f i c a n t l y , and thus be sampled, i n the SHG t e s t than when l a r g e r p a r t i c l e s i z e s are used. (The coherence length i s the d i s t a n c e over which the n o n l i n e a r p o l a r i z a t i o n wave, Ρ Γ χ ( 2 ) · · Ε Ε , r e s p o n s i b l e f o r SHG a c q u i r e s a phase mismatch i n temporal o s c i l l a t i o n o f magnitude π r e l a t i v e t o t h a t o f the normally propagating l i g h t wave a t frequency 2ω because o f d i s p e r s i o n o f r e f r a c t i v e index and b i r e f r i n g e n c e ; effective interaction lengths caused by beam w a l k - o f f i n biréfringent c r y s t a l s o b v i o u s l y a r e not a p p r o p r i a t e i n powders ( H > l f i ) . ) Larger p a r t i c l e s i z e serves as a d i s c r i m i n a t o r f o r s i n g l e c r y s t a l phase-matching p r o p e r t i e s and the components o f so a s s o c i a t e d ( 1 0 , 1 1 ) . F u r t h e r , to a l l o w the s c r e e n i n g o f a wider range of m a t e r i a l s , such as dye compounds, we have undertaken t o monitor SHG appearing a t 954 nm i n response t o the i n t e n s e 1.91 μπι wavelength l i g h t produced by s t i m u l a t e d Raman c o n v e r s i o n o f the 1.064 μπι output of a Q-switched Nd3 /YAG l a s e r . Such low frequency l i g h t g i v e s a t e s t l e s s dependent on the i n f l u e n c e s o f e l e c t r o n i c resonance on r e f r a c t i v e index and n o n l i n e a r i t y d i s p e r s i o n than the more t y p i c a l 1064-»532 nm SHG t e s t s . In keeping w i t h these comments on g e n e r a l i t y and p a r t i c l e s i z e , i n our t e s t s , p a r t i c l e s have been t y p i c a l l y i n the approximate range 20 to 40 μπι. T h i s r e l a t i v e l y l a r g e s i z e s t i l l assures n o n d i s c r i m i n a t i o n by phase matching c h a r a c t e r i s t i c s due to s m a l l e r index d i s p e r s i o n and longer wavelength i n 1 . 9 1 - * 0 . 9 5 4 μπι SHG. 2


2 ω

ω

ω

+

S t r a t e g i e s f o r d i s c o v e r i n g new organic n o n l i n e a r c r y s t a l l i n e m a t e r i a l s have been v a r i e d . As mentioned above, the most s t r a i g h t f o r w a r d i s a "shotgun" approach wherein many a v a i l a b l e m a t e r i a l s are t e s t e d . A f i r s t l e v e l s t r a t e g y which assures a t l e a s t that the compounds w i l l e x h i b i t noncentrosymmetric s t r u c t u r e s i s to t e s t c r y s t a l s o f e i t h e r enantiomorph o f c h i r a l compounds ( L > 1 £ ) . I t i s our b e l i e f t h a t t h i s i s a mathematically c o r r e c t concept, but the p h y s i c s o f t h i s s i t u a t i o n does not c o n t a i n s p e c i f i c i n t e r m o l e c u l a r f o r c e s which assure f a v o r a b l e alignment of the p o r t i o n o f the molecules which possess the enhanced n o n l i n e a r p o l a r i z a b i l i t y . In a second s t r a t e g y , employing some p h y s i c a l i n t u i t i o n i n t o packing f o r c e s , i t i s hypothesized that a c o r r e l a t i o n between the d i p o l a r and c o n j u g a t i o n c h a r a c t e r i s t i c s of n o n l i n e a r l y enhanced molecules and the common occurrence of a n t i p a r a l l e l alignments e x i s t s (§_). We have attempted to overcome the s t r u c t u r e determining i n f l u e n c e s o f these f a c t o r s u s i n g the general requirement o f dense molecular packing i n c r y s t a l s (20) but employing l e s s g e o m e t r i c a l l y simple molecules created by asymmetrical a d d i t i o n o f bulky s u b s t i t u e n t s . While we



30


have i d e n t i f i e d s e v e r a l m a t e r i a l s d i s p l a y i n g powder SHG comparable to the best reported organic compounds (6.-8), space l i m i t a t i o n s d i c t a t e that we d e t a i l r e s u l t s of a t h i r d s t r a t e g y . In t h i s s t r a t e g y some second component which i s intended to modify or a f f e c t the packing o f the n o n l i n e a r moiety occurs i n the c r y s t a l . Under t h i s l a s t s t r a t e g y we have studied molecular s a l t s chosen such t h a t the c a t i o n c a r r i e s β enhancing a t t r i b u t e s . An experimental advantage of t h i s approach i s t h a t by metathesis one can s t r a i g h f o r w a r d l y o b t a i n new compounds and c r y s t a l s w i t h v a r i e d anions, thus e l i m i n a t i n g the need f o r new s y n t h e s i s w i t h each compound m o d i f i c a t i o n one hopes w i l l a f f e c t c r y s t a l s t r u c t u r e and improve alignment. In molecular s a l t s we expect t h a t monopolar i n t e r a c t i o n s w i l l o v e r r i d e the d e l e t e r i o u s d i p o l a r e f f e c t s i n determining the alignments of β enhanced s p e c i e s . Examination o f s t r u c t u r e s of r e l a t e d c a t i o n i c dye s a l t s supports the v a l i d i t y o f t h i s i d e a . In the i o d i d e s a l t of the trans-4'-dimethylamino-N-methyl4 - s t i l b a z o l i u m i o n the c a t i o n s stack i n l a y e r s (as i n smectic l i q u i d c r y s t a l ) i n which they a r e t i l t e d r e l a t i v e t o the plane normal but stand p a r a l l e l i n a p o l a r sense ( 2 1 ) . T h i s s t r u c t u r e can be r a t i o n a l i z e d by the need f i r s t t o maximize the Madelung energy through the arrangement t h a t the p y r i d i n i u m r i n g s and i o d i d e ions be i n c l o s e p r o x i m i t y and second to maximize d i s p e r s i o n energy through p a r a l l e l side-by-side s t i l b a z o l i u m packing. U n f o r t u n a t e l y , f u r t h e r increase of Madelung energy r e s u l t s from arrangement o f an i n v e r t e d layer o f p a r a l l e l c a t i o n s accompanied by counter ions adjacent to the f i r s t , doubling the s i z e of the i o n i c r e g i o n but causing a centrosymmetric s t r u c t u r e . The p r i n c i p l e s o f maximizing coulombic and d i s p e r s i o n s t a b i l i z a t i o n energies can a l s o be us.ed t o p a r t i a l l y e x p l a i n the s t r u c t u r e o f the (+)-camphor-10-sulfonate s a l t of the trans-4'-hydroxy-N-methyl-4-stilbazolium ion ( 1 2 ) , which i s a protonated analogue of a simple merocyanine dye c l a s s e x h i b i t i n g the l a r g e s t reported values o f β (4,22). In t h i s s a l t l a y e r s o f d i s t i n c t type ( a l i p h a t i c - i o n i c - a r o m a t i c - i o n i c - a l i p h a t i c - e t c . ) e x i s t as can be seen i n Figure 1. The unfortunate n o n l i n e a r i t y c a n c e l l i n g pseudoa n t i p a r a l l e l o r i e n t a t i o n o f the c a t i o n s (as pseudo-inversion dimers) can be p a r t i a l l y a t t r i b u t e d i n t h i s case to the large s i z e of the anion (a volume packing argument) and t o the s t a b i l i z i n g i n f l u e n c e o f hydrogen bonding between the hydroxy 1 and s u l f o n a t e groups. To avoid the apparently adverse e f f e c t s o f hydrogen bonding with the l a s t c a t i o n mentioned we have concentrated on s a l t s of the dimethylamine c a t i o n . A l s o i n c o n s i d e r a t i o n o f the importance of an anion bulk packing f a c t o r we have t r i e d s e v e r a l s i z e and shape anions, f i n d i n g t h a t members of a c l a s s of c r y s t a l s i n v o l v i n g medium s m a l l , l a r g e l y pseudo-tetrahedral anions t y p i c a l l y e x h i b i t l a r g e powder SHG - up to an order of magnitude g r e a t e r than the best



Figure 1. Crystal structure of trans-4'-hydroxy-N-methyl-4-stilbazolium (+)-camphor10-sulfonate.



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organics i n the l i t e r a t u r e . Table I contains data f o r some s a l t s t o be compared t o three known m a t e r i a l s , MNA having the l a r g e s t reported χ(^) among organic c r y s t a l s ( 6 ) . R e s u l t s f o r the two s a l t s discussed i n the l a s t paragraph are c o n s i s t e n t with t h e i r s t r u c t u r e s . The s e n s i t i v i t y o f the s t r u c t u r e o f the txans-4'-dimethylamino-N-methyl-4s t i l b a z o l i u m i o d i d e s a l t t o the monopolar i n t e r a c t i o n s i s evidenced by the s u b s t a n t i a l SHG value observed i n the t rans-4'-dimethylamino-Ne t h y l - 4 - s t i l b a z o l i u m i o d i d e s a l t ; t h e replacement o f a methyl group on the charged p y r i d i n i u m r i n g by an e t h y l group apparently reduces Madelung energy and d e s t a b i l i z e s t h e centrosymmetric s t r u c t u r e r e l a t i v e t o some other which i s noncentrosymmetric. Table I . R e l a t i v e SHG Powder I n t e n s i t i e s . Crystal

Harmonic I n t e n s i t y

α-quartz m e t a n i t r o a n i l i n e (mNA) 2 - m e t h y l - 4 - n i t r o a n i l i n e (MNA) trans-4'-hydroxy-N-methyl-4-stilbazolium (+) -camphor-10-sufonate trans-4'-dimethylamino-N-ethyl-4-stilbazolium iodide tr^ns-4'-dimethylamino-N-methyl-4-stilbazolium X X" = I" I0 "

0.008 1 3 0.007 0.7 0 0.01

3

N0 " cinnamate ClOij-

0.5 1.5 5

3

BF4"

10

ReOn'

18

CH3SO4"

30

X-ray s t r u c t u r a l a n a l y s i s o f the m e t h y l s u l f a t e compound i n d i c a t e s the orthorhombic c r y s t a l u n i t c e l l contains two t r a n s l a t i o n a l l y i n e q u i v a l e n t c a t i o n s p o s i t i o n e d on mirror planes and t i l t e d a t 34° r e l a t i v e t o the two-fold screw (c) a x i s ( 2 3 ) . This i s a compromise orientation f o r simultaneously, rather than i n d i v i d u a l l y , maximizing X ^ and X^/>{bb } polar s t r u c t u r e . This s t r u c t u r e i s t h e r e f o r e c o n s i s t e n t with the extremely l a r g e SHG i n t e n s i t y reported i n Table 1 w h i l e , a l s o c o n s i s t e n t l y , p r e l i m i n a r y x-ray data show the perrhenate and t e t r a f l u o r o b o r a t e s a l t s t o be i s o s t r u c t u r a l (£L3). D e t a i l s o f the packing c o n s i d e r a t i o n s i n t h i s c l a s s have n o t yet been analyzed. Attempts t o i n

c

c

c

t

n

i

s

C



2.

MEREDITH

33


grow l a r g e s i n g l e crystals t o be used for tensor c h a r a c t e r i z a t i o n are i n progress. While an o r i e n t e d molecule a n a l y s i s i s not completely r i g o r o u s due to c o m p l e x i t i e s o f the l o c a l f i e l d e f f e c t s , one would expect t o be approximately c o r r e c t i n p r e d i c t i n g the p r o p e r t i e s o f through such an e x e r c i s e . Unfortunately the c h a r a c t e r i s t i c s o f β i n the t rans-4'-dimethylaminoN-methyl-4-stilbazolium i o n cannot be determined by the EFISH technique due t o the i n a b i l i t y o f i o n i c s o l u t i o n s t o support e a s i l y characterized s t a t i c e l e c t r i c f i e l d s . However, by a method o f a n a l y s i s o f o p t i c a l t h i r d harmonic generation (THG) i n s o l u t i o n s u t i l i z i n g cascading o f molecular second-order n o n l i n e a r responses, we have r e c e n t l y i n f e r r e d that the second-order n o n l i n e a r i t y o f t h i s c a t i o n i s n e a r l y equal t o that o f 4-dimethylamino-4'-nitrostilbene (DANS). DANS has been c h a r a c t e r i z e d by EFISH t o be an order o f magnitude more n o n l i n e a r than the b e s t s i n g l e r i n g species such as pn i t r o a n i l i n e (pNA) and MNA (2 ,£). In the o r i e n t a t i o n o f the m e t h y l s u l f a t e s a l t , i f one reasonably assumes the c a t i o n s secondorder response t o occur predominantly i n the β tensor element (z 1

ζ ζ ζ

being the c a t i o n l o n g a x i s ) , trigonometry p r e d i c t s that ~55% and ~10% o f the maximum a t t a i n a b l e m OV X ^ p { i j j } ^ other s t r u c t u r e o c c u r . I t i s t h e r e f o r e expected that the l a r g e r elements o f the tensor o f these s a l t s w i l l prove t o be i n

h i s

o r

a n v

s u b s t a n t i a l l y g r e a t e r than those achieved i n c r y s t a l s of pNA and MNA r e l a t e d molecules except i n p a r t i c u l a r resonance enhancement frequency regimes. Q u a s i c r y s t a l s . As d e s c r i b e d i n an e a r l i e r paper o f t h i s symposium there is an interesting photochemically initiated noncentrosymmetric o r d e r i n g o f d i p o l a r s p e c i e s d e r i v e d from s o l u t i o n s of c e r t a i n s p i r o p y r a n compounds d i s s o l v e d i n a l i p h a t i c s o l v e n t s (24). T h i s o r d e r i n g i s d r i v e n by sudden, d r a s t i c change o f s o l u t e c h a r a c t e r . S i n c e the photochemically m o d i f i e d s p i r o p y r a n has a merocyanine form which i s expected to d i s p l a y second-order n o n l i n e a r i t y , the net e f f e c t o f the spontaneous o r d e r i n g i s a l s o expected to c r e a t e a nonvanishing macroscopic second-order nonlinearity. The process of alignment i s understood t o proceed through the f o l l o w i n g sequence: the i n i t i a l photoprocess c r e a t e s at l e a s t two s p e c i e s c o n t a i n i n g d i f f e r i n g numbers o f merocyanine and spiropyran molecules. Stacked aggregates o f one e n t i t y form and coalesce i n t o m i c r o c r y s t a l l i t e s w i t h diameters approximately 40 nm. These are covered w i t h amorphous m a t e r i a l d e r i v i n g from another i n i t i a l s p e c i e s , forming g l o b u l e s which appear i n d i s c r e t e s i z e s indexed by g e n e r a t i o n number ( t h e r e being a time sequence f o r t h e i r c r e a t i o n governed by the changing r a t i o of c o n c e n t r a t i o n s o f the globule forming s p e c i e s remaining i n s o l u t i o n ) . I f formed i n an



34


e l e c t r i c f i e l d , g l o b u l e s fuse i n a s t r i n g - o f - b e a d s morphology. This process i s a t t r i b u t e d to e n e r g e t i c l i m i t a t i o n s on globule contact approach paths f o r h i g h l y d i p o l a r p a r t i c l e s a l i g n e d by the f i e l d . We have used SHG to c o n f i r m and probe these s t r u c t u r e s . Q u a n t i t a t i v e c h a r a c t e r i z a t i o n i s complicated s i n c e the g l o b u l e s o f a sample have c o r r e l a t e d but not p e r f e c t p o s i t i o n i n g and they are smaller but not s u b s t a n t i a l l y s m a l l e r than the wavelengths o f l i g h t employed. Thus determination o f f a r - f i e l d harmonic r a d i a t i o n patterns based on SHG response t o a l a s e r beam i s not s t r a i g h t f o r w a r d . We have found though that v a r i o u s schemes o f index matching and EFISH type experiments a l l o w us t o observe SHG, comment on i t s o r i g i n , to observe m o d i f i c a t i o n s o f s t r u c t u r e i n a s t a t i c f i e l d and to f o l l o w dynamics of g l o b u l e m o d i f i c a t i o n (2_ϋ,2£). The reader i s r e f e r r e d t o the accompanying paper on t h i s t o p i c . M o l e c u l a r l v Doped L i q u i d C r y s t a l l i n e Polymer. Regarding the infrequent occurrence o f c r y s t a l s o f h i g h l y nonlinear molecules showing s u b s t a n t i a l alignment, as monitored by SHG, one might a t t r i b u t e t h i s t o a n t i p a r a l l e l , d i m e r - l i k e alignment favored by more symmetric or simple molecular shapes, enhancement of d i s p e r s i o n f o r c e s and m i n i m i z a t i o n o f d i p o l e - d i p o l e i n t e r a c t i o n energies (§_). While l a r g e permanent d i p o l e moments appear t o be a hinderance to appropriate alignment i n c r y s t a l s , they a l l o w that s u b s t a n t i a l macroscopic n o n l i n e a r i t y may be achieved when the more h i g h l y n o n l i n e a r s p e c i e s are a l i g n e d i n f l u i d media by a l a r g e s t a t i c e l e c t r i c f i e l d . I f a l i q u i d c r y s t a l solvent i n which the n o n l i n e a r molecule e x h i b i t s a l a r g e alignment c o r r e l a t i o n i s employed, the alignment p o r t i o n o f the r e s u l t a n t s u s c e p t i b i l i t y may be enhanced by up to a f a c t o r o f f i v e over that i n i s o t r o p i c s o l v e n t s . A l t e r n a t i v e l y , by an appropriate sequence of temperature and f i e l d treatment, the alignment may be induced i n a low v i s c o s i t y s t a t e and become permanent i n a higher v i s c o s i t y s t a t e o f a polymer ( 2 1 ) , thus producing a m a t e r i a l w i t h nonvanishing . Such an alignment i s , of course, unstable and would g r a d u a l l y disappear i f not f o r the p o s s i b i l i t y o f s t r a i n and i m p u r i t y charge compensation o f the p o l a r i z a t i o n d e n s i t y f i e l d . By combining the l i q u i d c r y s t a l l i n e and polymeric a t t r i b u t e s both gains a r e achieved, but an a d d i t i o n a l advantage i s obtained. The high cooperative l i g h t s c a t t e r i n g and a t t e n u a t i o n c o e f f i c i e n t which i s a tremendous disadvantage f o r the a p p l i c a t i o n o f t y p i c a l l i q u i d c r y s t a l s i n n o n l i n e a r o p t i c a l devices i s reduced by the l a r g e increase i n i n t e r n a l v i s c o s i t y . A s u i t a b l e m a t e r i a l has been 'described i n an e a r l i e r paper o f t h i s symposium. DANS (4-dimethylamino-M'-nitrostilbene), which has one o f the l a r g e s t β s known and which d i s p l a y s a large S ^ ) order parameter i n that m a t e r i a l , was used a t 2% dopant c o n c e n t r a t i o n . SHG was used to c h a r a c t e r i z e t h i s m a t e r i a l ( 2 £ ) and the reader i s r e f e r r e d t o the paper i n t h i s volume d e s c r i b i n g the f i n d i n g s . 1


2.

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35


C h a r a c t e r i z a t i o n s bv Third-Order N o n l i n e a r O p t i c a l Experimentation Except through the study o f l i n e a r and 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 o f molecular c r y s t a l s , methods t o determine the nature o f β r e q u i r e e v a l u a t i o n o f a p p r o p r i a t e χ^3) c h a r a c t e r i s t i c s o f molecular ensembles i n conjunction w i t h some type o f modeling o f the manner i n which molecular n o n l i n e a r i t y c o n t r i b u t e s t o the bulk s u s c e p t i b i l i t y . We have considered the two aspects o f t h i s task and have found t h a t due t o the complexity o f the c o n s i d e r a t i o n s there a r e many p i t f a l l s . I n t h i s second p a r t o f the paper d i s c u s s i o n s a r e presented which d e a l w i t h l i g h t propagation e f f e c t s a f f e c t i n g χ(3) d e t e r m i n a t i o n s , which w i l l show, among other t h i n g s , the n e c e s s i t y for newly developed techniques t o measure χ ^ ) by o p t i c a l t h i r d harmonic g e n e r a t i o n (THG). Subsequently comments about molecular i n t e r p r e t a t i o n s o f χ(3) a r e made. N o n i n t u i t i v e L i g h t Propagation E f f e c t s In T h i r d - O r d e r Experiments. One o f the f i r s t t a s k s f o r a chemist d e s i r i n g t o q u a n t i f y second- and third-order o p t i c a l nonlinear p o l a r i z a b i l i t y i s t o g a i n an a p p r e c i a t i o n o f the q u a n t i t a t i v e m a n i f e s t a t i o n s o f macroscopic o p t i c a l n o n l i n e a r i t y . As w i l l be shown t h i s has been a problem as w e l l f o r e s t a b l i s h e d workers i n the f i e l d . We w i l l present p i c t u r e s which h o p e f u l l y w i l l make these s i t u a t i o n s more p h y s i c a l l y o b v i o u s . Two s t r a i g h t f o r w a r d 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 phenomena which a r e used t o c h a r a c t e r i z e β and γ are EFISH (L,2,4) and THG (3.) (or t h e i r m u l t i c o l o r analogues ( 2 < £ ) ) . Using c l a s s i c a l physics d e s c r i p t i o n s , as source o f these phenomena there e x i s t n o n l i n e a r p o l a r i z a t i o n waves o s c i l l a t i n g a t frequencies 2ω or 3ω (3.Q), 2 (

P °(r,t) = E

3 c o

(r,t) =

3χ ( 3 ) X

( 3 )

ω

ω

0

(η)···Ε (ιι^)Ε (Γΐ^)Ε (Γΐ^) w

w

w

( r ) — E (t,t)E (L,t)E (n,t)

induced by components o f the t o t a l e l e c t r i c f i e l d which a r e u s u a l l y n e a r l y monochromatic, l i n e a r l y p o l a r i z e d · t r a v e l l i n g waves having some s l o w l y time v a r y i n g amplitudes (the sources being pulsed high voltage a c r o s s e l e c t r p d e s and/or h i g h peak power pulsed l a s e r s ) . S p a t i a l v a r i a t i o n s o f Ε and Ρ w i l l e x i s t between the d i f f e r e n t media and a c r o s s the p r o f i l e o f l a s e r beams used i n r e a l experiments. I t i s not easy i n general t o p r e d i c t the form, magnitude or dependencies o f the total harmonic waves "broadcast" from the o s c i l l a t i n g polarization densities resulting from focused laser beams propagating through d i f f e r e n t m a t e r i a l s and p o s s i b l y through the f r i n g i n g f i e l d s o f the e l e c t r o d e s used t o e s t a b l i s h the zero frequency e l e c t r i c f i e l d f o r EFISH. Some s u r p r i s i n g propagation phenomena a r e : 1) EFISH i s observed from gases placed between charged c a p a c i t o r p l a t e s y e t none i s seen from l i q u i d s unless two d i s s i m i l a r



36


m a t e r i a l s (e.g. l i q u i d and a glass p l a t e ) form an o p t i c a l i n t e r f a c e , and the r e s u l t i n g s i g n a l depends on the d i f f e r e n c e s i n response o f the two m a t e r i a l s a t the i n t e r f a c e ; 2 ) t r u e THG i s not observed from normally d i s p e r s i v e m a t e r i a l when a gaussian l a s e r beam i s focused through i t , but here a l s o THG i s observable i f an i n t e r f a c e i s created, the magnitude again depending on the d i f f e r e n c e o f nonlinear responses o f the two m a t e r i a l s at t h a t i n t e r f a c e ; and 3) SHG by a focused gaussian beam i n a f i n i t e noncentrosymmetric c r y s t a l i s sometimes maximum when the minimum beam waist f a l l s a t a c r y s t a l face. Two p i c t o r i a l models are u s e f u l i n understanding or d e s c r i b i n g these and other r e l a t e d phenomena: c o n s i d e r a t i o n s o f the coherent f i e l d from amplitude and phase modulated d i p o l e a r r a y s , and v i b r a t i o n diagrams. These problems of macroscopic m a n i f e s t a t i o n o f the n o n l i n e a r i t y hinge on aspects o f energy t r a n s f e r through the nonlinear p o l a r i z a t i o n waves among the normal ( l i n e a r ) electromagnetic waves of the media. U s u a l l y i n c h a r a c t e r i z a t i o n experiments conversions are n e g l i g i b l y small so t h a t nonlinear m o d i f i c a t i o n o f the l a s e r f i e l d s may be neglected and one may concentrate on v a r i a t i o n o f the harmonic f i e l d . The l o c a l r e l a t i o n s h i p between the o s c i l l a t i n g nonlinear p o l a r i z a t i o n d e n s i t y and the l i n e a r o s c i l l a t i n g e l e c t r i c f i e l d determine the r e s u l t . As i n l i n e a r o p t i c s (3_1) where the i n phase component o f p o l a r i z a t i o n density i s associated with r e t a r d a t i o n ( r e f r a c t i v e index) and the out-of-phase component with a t t e n u a t i o n (absorption c o e f f i c i e n t ) o r gain ( a s s o c i a t e d with a n phase a l t e r a t i o n o f Ρ r e l a t i v e to the l o s s case, as i n l a s e r s or o p t i c a l a m p l i f i e r s ) , the v a r i a t i o n o f phase o f Ρ r e l a t i v e t o that of Ε governs whether the harmonic wave i s a m p l i f i e d or diminished i n amplitude (and whether a change o f phase o c c u r s ) . I t i s l a r g e l y the e f f e c t s o f v a r i a t i o n o f the phase-mismatch between these waves, i n t e g r a t e d along the o p t i c a l path, which i s important i n determining the magnitude o f detected harmonic l i g h t . As w i l l be done below, i t i s p r e f e r a b l e i n attempting to d e s c r i b e the i n t e g r a t e d e f f e c t to f a c t o r out the r a p i d s p a t i a l v a r i a t i o n o f the phase o f the l i n e a r electromagnetic wave and p i c t u r e only t h i s r e l a t i v e phase v a r i a t i o n along the l i g h t r a y s . While wavelengths o f l i g h t are on the s c a l e o f microns, d i s t a n c e s along which these v a r i a t i o n s occur vary from a few microns to meters. η

η

ω

ω

Dipole Array Model. In Figure 2 s e v e r a l i l l u s t r a t i v e cases are depicted. The magnitude o f the component o f d i s c r e t e d i p o l e s (Ρ_ i n t e g r a t e d over some small volume) o s c i l l a t i n g out-of-phase with Ε . along one ray i s d e p i c t e d . ( D e t a i l s o f transverse s t r u c t u r e are ignored, i t being assumed that s u f f i c i e n t breadth e x i s t ; that d i f f r a c t i o n o f the r e s u l t a n t e l e c t r i c wave i s n e g l i g i b l e . ) The

ηω

η ω


2.


MEREDITH

37

question of r e s u l t a n t energy t r a n s f e r i s the same a t o p t i c a l o r r a d i o f r e q u e n c i e s , t h e l a t t e r being more i n t u i t i v e . In F i g u r e 2a r o s c i l l a t i n g d i p o l e s (antennae) broadcast "in-phase w i t h one another". The downstream f i e l d i s r ( e p ) where e i s the f i e l d o f one d i p o l e element ( r e a l l y one t r a n s v e r s e plane o f d i p o l e s ) d i v i d e d by i t s amplitude p. Since i n t e n s i t y i s p r o p o r t i o n a l to the square o f e l e c t r i c f i e l d , I o c ( r p ) . This i l l u s t r a t e s t h a t i n phase-matched i n t e r a c t i o n s i n t e n s i t y v a r i e s as t h e i n t e r a c t i o n l e n g t h times ω η 2 s u s c e p t i b i l i t y times ( ι ) / t o t a l q u a n t i t y squared. R e l a t i n g the discrete model to continuous media this is Ι α( ρ) (χ(/ (Ε ) ) ο:(/ ) (ι ) . i n the r e g i o n o f t h e d i p o l e s v a r i a t i o n o f t h e harmonic f i e l d i s simple. S i n c e the phase i s depicted r e l a t i v e t o a forward t r a v e l l i n g wave, the e l e c t r i c f i e l d v a r i a t i o n i n t h a t region depends on d e t a i l s of a backward t r a v e l l i n g wave. The corresponding p i c t u r e o f out-of-phase d i p o l e s f o r the backward wave would vary s i n u s o i d a l l y , but with wavelength h a l f that of t h e l i n e a r electromagnetic wave - a s i t u a t i o n incapable o f broadcasting more than a n e g l i g i b l e f i e l d a t o p t i c a l f r e q u e n c i e s where the wavelength i s very short compared to a r r a y (sample) s i z e . Therefore Ε grows l i n e a r l y as the d i p o l e array i s t r a v e r s e d i n the forward d i r e c t i o n . The l a t t e r c o n c l u s i o n i s n o t n e c e s s a r i l y so a t r a d i o wavelengths (or f o r the case o f a few stacks o f q u a s i c r y s t a l s a t o p t i c a l frequencies). n < 0


n a )

2

η ω

ω

Γ

n

w

2

η

2

2

ω

η

χ

χ

η ω

η ω

F i g u r e 2b d e p i c t s a case where Ρ possesses a l i n e a r l y i n c r e a s i n g phase d e v i a t i o n r e l a t i v e t o the l i n e a r forward t r a v e l l i n g Ε wave, as occurs f o r harmonic generation when r e f r a c t i v e i n d i c e s of fundamental and harmonic waves a r e not equal. Downward p o i n t i n g Ρ i n d i c a t e phase r e l a t i o n s h i p s which e x t r a c t energy from the Ε _ wave. C o n s i d e r a t i o n o f "broadcasting" i n t h i s s i t u a t i o n shows that Ε grows and s h r i n k s p e r i o d i c a l l y w i t h the p e r i o d o f t h e phasemismatch as f u n c t i o n o f ζ i n the r e g i o n o f t h e d i p o l e s . This approximately d e p i c t s t h e behavior o f non-phase-matched harmonic generation as f u n c t i o n o f p o s i t i o n , ζ (or c r y s t a l t h i c k n e s s ) . Also an important p o i n t which can be v e r i f i e d with a l i t t l e thought i s that the amplitude o f the s i n u s o i d a l s p a t i a l v a r i a t i o n o f Ε is p r o p o r t i o n a l to p/ , the magnitude o f the d i p o l e s times the e f f e c t i v e broadcasting d i s t a n c e before phase r e v e r s a l . One can r e a d i l y see through these p i c t u r e s t h e o r i g i n o f the standard relation η ω

η ω

ηω

η ω

η

ω

Q

Ι α ( /c ) ( i ) s i n U z / 2 /cJ , where Lc i s t h e coherence length ( d i s t a n c e for a c c r u a l of a m phase mismatch). The f o l l o w i n g cases a r e somewhat more s u b t l e . Figure 2c d e p i c t s a s l o w l y varying amplitude Ρ w i t h a very s l o w l y v a r y i n g phaseΠ ω

2

w

n

2

χ

η ω




Figure 2. Dipole array pictures ofsome situations in nonlinear optical harmonic generation. (See text for further discussion.)


2.

MEREDITH

mismatch. This corresponds to EFISH i n gases where the s p a t i a l extent o f the t y p i c a l electrode f i e l d i s smaller than the coherence length f o r SHG (consider / =7το/2ω{η -η2 }). A s u b s t a n t i a l EFISH s i g n a l may r e s u l t s i n c e l i t t l e phase d e v i a t i o n e x i s t s . In c o n t r a s t Figure 2d d e p i c t s a s i m i l a r s i t u a t i o n , but i n which a much more r a p i d l y v a r y i n g phase-mismatch appears. This might correspond t o EFISH i n condensed phase i f hundreds r a t h e r than ~10 c y c l e s o f phasemismatch occured i n the electrode r e g i o n . Absolute d i s p e r s i o n o f r e f r a c t i v e i n d i c e s being s u b s t a n t i a l l y greater i n condensed phases than i n gases causes correspondingly shorter l . A totally different p i c t u r e r e s u l t s : an i n s i g n i f i c a n t harmonic f i e l d w i l l be "broadcast" to the l a r g e ζ r e g i o n , but n o n n e g l i g i b l e Ε w i l l appear i n the region o f large E° between the e l e c t r o d e s . The amplitude there i s p r o p o r t i o n a l to / ρ α / χ ( Ε ) Ε ° ( ζ ) α : / ι Ε ( ζ ) / η where E°(z) i s the 0


39


ω

ω

Q

2 ω

ω

ο

ο

2

ω

0

οχ

ω

ω

ω

2

amplitude o f the s t a t i c f i e l d at ζ and where the r e l a t i o n Ι 4Q). This has important i m p l i c a t i o n s i n r e l a t i o n to s t u d i e s o f s o l u t i o n s o f molecules i n d i f f e r i n g s o l v e n t s . There i s another propagation r e l a t e d e f f e c t which has caused technique e r r o r i n the past, but i s not r e a d i l y analyzed by the above models because i t i n v o l v e s the n o n l i n e a r g e n e r a t i o n o f s e v e r a l frequencies simultaneously. As example c o n s i d e r that i n noncentrosymmetric s o l i d s i t i s u s u a l l y the case t h a t second-order allowed SHG o c c u r s simultaneously w i t h d i r e c t t h i r d - o r d e r THG (22)41). The a d d i t i o n a l allowed second-order frequency mixing, 2 ω + ω - * 2 ω , c a l l e d cascading (when o c c u r r i n g not due t o the p r o v i s i o n o f both summing frequencies by the e x p e r i m e n t a l i s t ) , causes i n t e r f e r e n c e s i n χ(3) determinations. This e f f e c t , i n a d d i t i o n to the n e g l e c t o f atmospheric e f f e c t s , i n v a l i d a t e s the o r i g i n a l aq u a r t z experiment (42) which was subsequently used f o r THG χ^3) calibrations (4)! Recognition o f t h i s e f f e c t i s p a r t i c u l a r l y important s i n c e a p o r t i o n of the cascading, when allowed by


2.


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47

;

nonvanishing χ ^ tensor elements, always generates a component o f n o n l i n e a r p o l a r i z a t i o n w i t h i d e n t i c a l frequency a n d wave v e c t o r as the d i r e c t t h i r d - o r d e r process under study. The magnitude o f the cascaded c o n t r i b u t i o n may be a r b i t r a r i l y l a r g e , depending on d e t a i l s °f d the experimental c o n f i g u r a t i o n . Because o f the r e l a t i v e complexity o f the formalism the reader i s r e f e r r e d t o other works f o r f u l l e r e x p o s i t i o n o f these e f f e c t s (13,ίϋ,ίΒ) · A s i g n i f i c a n t problem i n a b s o l u t e s u s c e p t i b i l i t y measurements i s that o f modal i n t e r f e r e n c e s when non-single-mode l a s e r s a r e used t o e s t a b l i s h n o n l i n e a r p o l a r i z a t i o n d e n s i t i e s ( 3 L Z ) . Frequently the problens o f multimodal l a s e r s f o r s u s c e p t i b i l i t y determinations are bypassed through the use of r e l a t i v e measurements f o r which i d e n t i c a l behaviors occur. Alternatively, an i n t e r n a l microscopic i n t e r f e r e n c e i s employed, such as the use of Raman i n t e r f e r e n c e s i n χ^ characterization by CARS o r RIKES, although those c o n s i d e r a t i o n s are not n e c e s s a r i l y s i m p l e or unambiguous (44-46). A case we have seen which i s a p p a r e n t l y s i g n i f i c a n t l y a f f e c t e d by multimodal sources i s cascading i n THG. I n i t i a l l y i t was b e l i e v e d t h a t the multimode a s s o c i a t e d ambiguity which a r i s e s when the f i n a l e l e c t r i c f i e l d s are added and squared t o determine i n t e n s i t y would be unimportant. Here the p u r e l y bound wave" cascaded c o n t r i b u t i o n s are created and summed i n a s i m i l a r manner t o the d i r e c t THG response and the "intermediate f r e e wave" c o n t r i b u t i o n to Ρ ^ i s e s t a b l i s h e d over a d i s t a n c e short compared t o the s p e c t r a l l y determined coherence l e n g t h . However, comparison o f n o n l i n e a r i t i e s o f various m a t e r i a l s determined r e l a t i v e l y by t o t a l l y t h i r d - o r d e r THG experimentation t o values e s t a b l i s h e d by other methods suggests t h e r e i s a technique e r r o r i n n e g l e c t i n g multimode e f f e c t s i n cascading which are important f o r the c a l i b r a t i o n o f a standard r e l a t i v e to cascaded X parameters (33,35,41).


a n

Tf

ω

( 2 )

Other l e s s d e f i n i t e y e t important e f f e c t s such as p r o f i l e changes due t o n o n l i n e a r r e f r a c t i v e index a l t e r a t i o n i n s p a t i a l l y nonuniform high power beams must be c a r e f u l l y considered. As example, the use o f n o n i d e n t i c a l l i q u i d s and o p t i c a l paths p r i o r t o and i n , say, EFISH c e l l s and the u s u a l quartz c a l i b r a t i o n c e l l s could cause p o t e n t i a l l y i n a c c u r a t e χ^3) d e t e r m i n a t i o n s . Obviously these types o f c o n s i d e r a t i o n s are important when p r e c i s e experimentation t o t e s t f i n e models o f molecular behavior are intended, but have not stood as o b s t a c l e t o uncovering t h e important general t r e n d s i n molecular n o n l i n e a r i t y enhancement. New THG Methods For Molecular L i q u i d C h a r a c t e r i z a t i o n . An area which i s e s s e n t i a l f o r understanding g e n e r a l t h i r d - o r d e r n o n l i n e a r p o l a r i z a b i l i t y i s c h a r a c t e r i z a t i o n o f the p u r e l y e l e c t r o n i c c o n t r i b u t i o n s (48). S e v e r a l methods have been employed f o r t h i s

American Chemical Society Library 1155 16th St. N. W. In Nonlinear Optical Properties of Organic and Polymeric Materials; Williams, D.; Washington, D. C. 20031 ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

48


purpose on r e l a t i v e l y simple s p e c i e s , but a more general survey o f more complex compounds has not been p o s s i b l e due t o the l a c k o f a method o f s u f f i c i e n t r e l i a b i l i t y and s i m p l i c i t y (4JjS). Besides academic c u r i o s i t y t h i s area should be of some i n t e r e s t s i n c e there have been p r e d i c t i o n s o f very large enhancements o f e] nic thirdorder h y p e r p o l a r i z a b i l i t y , y , (9.) which could prov .lird-order s u s c e p t i b i l t i e s capable o f matching t y p i c a l second-oraer responses at achievable e l e c t r i c f i e l d strengths. S i n c e c o n s t r a i n t s on alignment o f molecules to achieve s u b s t a n t i a l a r e very f o r g i v i n g r e l a t i v e t o the s i t u a t i o n o f d e s c r i b e d i n the f i r s t part o f t h i s paper, there i s s t r o n g t e c h n o l o g i c a l m o t i v a t i o n f o r work i n t h i s area. Another reason f o r i n t e r e s t i n t h i s p o s s i b i l i t y i s t h a t ( n o n e x c i t a t i o n a l ) e l e c t r o n i c responses a r e extremely f a s t u n l i k e d i f f u s i o n , r o t a t i o n , or thermal c o n t r i b u t i o n s which dominate X i n most strong K e r r , nonlinear r e f r a c t i o n , e t c . media. For use i n extremely high bandwidth a p p l i c a t i o n s , such as t o t a l l y o p t i c a l p r o c e s s i n g , predominantly e l e c t r o n i c responding media are needed (4a). We have developed techniques f o r c o r r e c t l y (at l e a s t i n r e l a t i o n t o the i s s u e s r a i s e d i n the l a s t s e c t i o n ) measuring χ(3) i l i q u i d s by o p t i c a l t h i r d harmonic generation (15,5Q). The of THG i s most s t r a i g h t f o r w a r d c o n c e p t u a l l y , s u f f e r i n g from the l e a s t complex d i s p e r s i o n and resonance c o n t r i b u t i o n s i n the set o f p o s s i b l e t h i r d - o r d e r s u s c e p t i b i l i t i e s (25,48) · Because o f the occurrence o f only p o s i t i v e (summation o f ) f r e q u e n c i e s , i t may g e n e r a l l y be assumed to be a measure of e l e c t r o n i c n o n l i n e a r i t y alone. Furthermore, w i t h the use o f a s u f f i c i e n t l y long wavelength fundamental, e l e c t r o n i c d i s p e r s i o n enhancement can be minimized. T h i s allows a more s t r a i g h t f o r w a r d approach to the i n t e r p r e t a t i o n of relative n o n l i n e a r i t i e s , being l e s s dependent on s p e c i f i c p r o p e r t i e s o f the lowest few e l e c t r o n i c e x c i t a t i o n l e v e l s . In two THG methods f o r c h a r a c t e r i z a t i o n o f l i q u i d s t h a t we've devised, the i n t e r f e r e n c e s of a i r are e l i m i n a t e d by working i n vacuum. Because weak focusing i s employed (~1 m i n our apparatus) the beam p r o f i l e near focus can be considered n e a r l y constant. The vacuum c e l l , o f course, i s a l s o r e q u i r e d to be l o n g enough t o a v o i d s i g n i f i c a n t generation of ? } a t i t s windows. The obvious g e n e r a l i z a t i o n of the wedge method i s that the l i q u i d chamber o f the c e l l being placed i n the apparatus be wedged. U n f o r t u n a t e l y , s i n c e the windows o f the c e l l a l s o generate nonzero Ρ_3 and s i n c e t h e i r phased c o n t r i b u t i o n s t o the t o t a l Ε.^ must be known, there i s l i t t l e choice but t o make them wedges as w e l l ( c o n s i d e r i n g the p r i o r d i s c u s s i o n o f the c r i t i c a l nature o f ψ i n condensed phase m a t e r i a l s ) . We have t h e r e f o r e constructed such a c e l l i n which two wedged windows


e

w /

n

ω

ω

ω


2.

MEREDITH

49


of fused s i l i c a ( f . s . ) d e f i n e a wedged l i q u i d chamber. The shape o f THG f r i n g e s generated when the c e l l i s placed i n vacuum and t r a n s l a t e d t r a n s v e r s e t o the o p t i c a l path i s complex but may be analyzed to e x t r a c t ( x ^ n q . / x ^ f . ) · f a c t , t h i s a n a l y s i s of shape (not magnitude o f s i g n a l r e l a t i v e t o a secondary standard as i n EFISH) i s overdetermined and two independent e v a l u a t i o n s are p o s s i b l e from the same data, g i v i n g an i n d i c a t i o n o f r e l i a b i l i t y . This a n a l y s i s i s d e t a i l e d and the reader i s r e f e r e d elsewhere f o r fuller exposition (35). A second method was devised t o s i m p l i f y the complexity and laboriousness o f the g e n e r a l three-wedge method (5fi). Here the c e l l i s constructed w i t h a long l i q u i d chamber. I f the l i q u i d absorbs the l a s e r weakly but n e a r l y completely, Ρ ^ ^ 0 a t the back window with significant simplification resulting. Since n e a r l y a l l organic l i q u i d s have some weakly allowed h i g h v i b r a t i o n a l s t a t e t r a n s i t i o n s around 1.91 /im, t h i s s i t u a t i o n can u s u a l l y be achieved w i t h "-6 cm long l i q u i d chamber f o r the 1.91 /im-^636 nm THG which we have s t u d i e d . Disregarding f o c u s i n g , v i b r a t i o n diagrams d e s c r i b i n g THG i n the absorbing l i q u i d s are s p i r a l s . F i g u r e 6 shows the r e s u l t o f s p l i c i n g a s p i r a l onto the c i r c l e o f the f r o n t window wedge. Here again the dashed curve represents the s e t of a l l p o s s i b l e p o i n t s due to the a r b i t r a r y value o f ψ a p p r o p r i a t e t o the f r o n t window t h i c k n e s s . Simple i n t e n s i t y f r i n g e s are p r e d i c t e d w i t h p e r i o d o f the window wedge, but w i t h nonunity c o n t r a s t r a t i o . S i m i l a r diagrams have been analyzed and i t was found t h a t e v a l u a t i o n both of the magnitude and o f the c o n t r a s t r a t i o o f THG f r i n g e p a t t e r n s from such a l i q u i d f i l l e d c e l l r e l a t i v e t o a simple g l a s s wedge a l l o w s two independent determinations o f the r a t i o o f l i q u i d and window χ(3) » . One might be somewhat concerned t h a t the d e p o s i t i o n o f the e n t i r e energy o f the l a s e r pulse i n t o the l i q u i d d u r i n g the short 20 nanosecond pulse d u r a t i o n might cause an unacceptable temperature r i s e and d e n s i t y v a r i a t i o n . However, s i n c e the method r e l i e s on the establishment of a liquid c o n t r i b u t i o n to Ε? which i s p r o p o r t i o n a l to __χ(1)^]? k i y d e n s i t y dependent q u a n t i t y χ (3)/[ χ (1) I n


e S

ω

s

ω

a

m

u

c

h

m

o

r

e

w e a

(O) ν

than χ , the impact o f t h a t e f f e c t i s reduced. Since only r a t i o s o f l i q u i d t o window s u s c e p t i b i l i t i e s were determined by these methods we have determined the r a t i o s o f χ(3) i n f.s., BK-7 and α-quartz (41) and have performed a cascading experiment to determine α-quartz χ^3) r e l a t i v e t o i t s (3.3)· More d e t a i l e d a n a l y s i s o f methods and r e s u l t s are a v a i l a b l e i n the papers c i t e d . (0) F u r t h e r c o n s i d e r a t i o n s o f the g o a l to measure xKDJ and avoid i n t e r f e r e n c e s has l e a d us t o a more s t r a i g h t f o r w a r d scheme than the




50

v|/=2n7T

ψ

= ( 2 η + Ι)7Γ

Figure 6. Vibration diagram depicting optical third harmonic generation when an absorbing liquid follows a thin solid. (See text for further discussion.)


2.

51


MEREDITH

ο

;


two d e s c r i b e d above. Given that the THG χ has been measured f o r a number o f l i q u i d s , a method which r e l i e s on r e l a t i v e i n t e n s i t i e s o f THG might be used. We have devised an arrangement i n which t o achieve an accuracy o f a few percent one needn't measure coherence l e n g t h s , j u s t t h e r e l a t i v e i n t e n s i t i e s coupled with a r e f r a c t i v e index measurement. C u r r e n t l y we are attempting r e a l i z a t i o n o f t h i s method. I t i s a n t i c i p a t e d t h a t t h i s same concept can be a p p l i e d t o the determination o f EFISH n o n l i n e a r i t i e s . Molecular I n t e r p r e t a t i o n o f Third-Order S u s c e p t i b i l i t i e s . As s t a t e d i n the i n t r o d u c t i o n , development o f new organic n o n l i n e a r o p t i c a l media has r e l i e d on knowledge of molecular n o n l i n e a r p o l a r i z a b i l i t y . Experimentally, though, i t i s p r o p e r t i e s o f which are determined. Molecular p r o p e r t i e s must be e x t r a c t e d by a p p l i c a t i o n o f some model f o r t h e i r c o l l e c t i v e behavior i n e s t a b l i s h i n g χ ^ ) (g 1). D e s c r i p t i o n o f χ(3) i n molecular l i q u i d s i s a many-body problem, i m p l y i n g that most molecular i n t e r p r e t a t i o n s a r e fundamentally i n a c c u r a t e (4£). An example o f such an approximation i s that f o r THG and EFISH the molecules a r e g e n e r a l l y considered independent except through t h e i r mutual p o l a r i z i n g a c t i o n . Even i n t h i s case one must somehow s e l f - c o n s i s t e n t l y describe the l i n e a r and n o n l i n e a r p o l a r i z a t i o n s and microscopic f i e l d s experienced by each molecule o f a s t a t i s t i c a l ensemble. I n the d i p o l e approximation t h i s task can be achieved f o r m a l l y (5U,5_1): χ

( 3 )

χ

( 3 )

1

λ

Τ

λ

λ

λ

λ

= V' Σ ( Ν ) · ^ · · · Ν Ν Ν + χ

( 3 )

λ

' =V

1

λ

Τ

λ

λ

'

λ

Τ

Σ (& ) ·β ··Η Σ (Ε ^) ·Σ^·^·^ λ

μ

where i s a tensor which f u n c t i o n a l l y r e l a t e s t h e macroscopic and l o c a l e l e c t r i c f i e l d s a t molecule λ, and and are t e n s o r s o f the formalism which are a s s o c i a t e d w i t h f i e l d s a t molecule λ due t o p o l a r i z a t i o n o f molecule μ. To be u s e f u l the r e s u l t s must be averaged over p o s s i b l e c o n f i g u r a t i o n s o f the l i q u i d . The a v e r a g i n g processes i n v o l v e many unknown f a c t o r s . For the moment d i s r e g a r d i n g χ , one i s faced w i t h the t a s k o f ν

λ Τ λ Α

> /

Α λ λ Α

averaging Σ^(Ν ) ·χ ···ϋ îl îi . Steps which are necessary to proceed from t h i s term t o the commonly employed models employing averaged linear l o c a l f i e l d factors are: 1) T e n s o r i a l c o r r e l a t i o n s among χ \ and t h e p o l a r i z a b i l i t y o f the surrounding molecular ensemble which determine the details of a r e neglected; i s averaged independently of the other f a c t o r s .


52


2)

The t e n s o r i a l product o f l o c a l f i e l d tensors i s not averaged, but replaced by an a r i t h m e t i c product of the average magnitude of four l o c a l f i e l d f a c t o r s . 3) C o r r e l a t i o n s between molecular o r i e n t a t i o n s , that i s , between terms w i t h d i f f e r e n t λ, are disregarded (except i n EFISH where the d i p o l e c o r r e l a t i o n f a c t o r g i s employed i n the / ι · £ term (40) - a p r a c t i c e which assumes the t e n s o r i a l behavior o f the vector components of β_ t o show the same i n t e r m o l e c u l a r c o r r e l a t i o n s as the permanent d i p o l e ) ; s i n g l e terms f o r each molecular type are adopted. 4) Frequently c o r r e l a t i o n s o f l o c a l f i e l d amplitude and molecular type are ignored and a s i n g l e f a m i l y o f s o l u t i o n l o c a l f i e l d f a c t o r s i s adopted. The two common l o c a l f i e l d models which are employed are the Debye-Lorentz and the Onsager models ( 1 , 4 0 , 5 2 ) . Both replace the molecular s o l v e n t surroundings by a continuum w i t h a c a v i t y i n which the λ molecule r e s i d e s . Assuming a s p h e r i c a l c a v i t y shape does not make the l o c a l f i e l d p a r a l l e l to the macroscopic f i e l d due to the a n i s o t r o p i c p o l a r i z a b i l i t y (and o r i e n t a t i o n o f the permanent d i p o l e ) . At o p t i c a l frequencies ( d e t a i l s of the z e r o frequency l o c a l f i e l d s are beyond the scope of our i n v e s t i g a t i o n s ) a s c a l a r averaged e f f e c t i v e p o l a r i z a b i l i t y i s assumed, e s t a b l i s h i n g the p a r a l l e l n e s s . In the Debye-Lorentz model one assumes the l o c a l f i e l d s to be i d e n t i c a l f o r a l l molecules. The Onsager model a l l o w s t h i s average e f f e c t i v e p o l a r i z a b i l i t y and the c a v i t y s i z e to be d i f f e r e n t f o r each molecular type. Simple estimations w i t h parameters f o r a d i l u t e s o l u t i o n of d i s s i m i l a r molecules show that the product of s o l u t e o p t i c a l l o c a l f i e l d f a c t o r s (four f o r THG and t h r e e f o r EFISH) which m u l t i p l y γ i n t h i s model of xKDJ can d i f f e r by tens o f percent between the two models. This means that s o l u t e y s determined from » are subject to a t l e a s t t h i s magnitude u n c e r t a i n t y from the o p t i c a l l o c a l f i e l d s ! (This c o n t r a d i c t s the c o n c l u s i o n of Singer and G a r i t o (4_0), due to an unfortunate, simple a l g e b r a i c e r r o r i n the d e r i v a t i o n of t h e i r expressions c o n t r a s t i n g the two o p t i c a l l o c a l f i e l d models.) Because of the importance of choosing the b e t t e r model we have i n v e s t i g a t e d the behavior o f THG χ ^ ) over the ranges of m i s c i b i l i t y of s e v e r a l l i q u i d mixtures (53). These studies a l s o were intended to i n v e s t i g a t e the s e v e r i t y of the approximations 1)-4) above. However, although one might expect the high power of the l o c a l f i e l d f a c t o r s to cause t h i s to be a good t e s t , the s m a l l c o n t r i b u t i o n s to o f the h i g h l y d e v i a t i n g species a t low concentrations and the p l a y - o f f of the one increased c o n t r i b u t i o n and the one decreased c o n t r i b u t i o n i n the Onsager model i n the intermediate concentration region allowed both models to f i t our data comparably w e l l . We have seen by these


ν

f

s


2.

MEREDITH

53



s t u d i e s , though, t h a t beyond t h i s u n c e r t a i n t y

x

KôJ

o f THG i s verv

w e l l behaved compared to the i n t r i c a c i e s a s s o c i a t e d w i t h EFISH χ ^ ' (40). I n f a c t , simple a n a l y s i s of the χ ^ ) values o f 21 neat l i q u i d s determined by t h e two THG techniques described above using these l o c a l f i e l d models (they a r e e q u i v a l e n t i n neat l i q u i d s ) shows remarkably simple apparent orientational averaged h y p e r p o l a r i z a b i l i t y behavior (15>5Q). Systematics i n d i c a t i n g v a l i d i t y o f bond a d d i t i v i t y are present. Even simple s i n g l e r i n g aromatics are seen t o be p r e d i c t a b l e t o ~105& by t h a t approach. The v a r i a t i o n of accompanying " e x a l t a t i o n s ' of n o n l i n e a r p o l a r i z a b i l i t y of those compounds d i s p l a y s two phenomena. F i r s t , strong p e r t u r b a t i o n of the r i n g p o t e n t i a l , a s i n p y r i d i n e or fluorobenzene, reduces the n o n l i n e a r i t y . Second, s u b s t i t u t i o n w i t h e l e c t r o n donors enhances n o n l i n e a r i t y while e l e c t r o n withdrawing groups d i m i n i s h i t . A n a l y s i s o f r e s u l t s i n a l a r g e r s e t o f compounds i s underway. A d i s a p p o i n t i n g r e s u l t which stood out i n the s e t was the f a i l u r e t o observe the extremely l a r g e magnitude o f γ p r e d i c t e d t o occur i n TCNQ, one o f the molecules c a l c u l a t e d (9_) t o have enhanced γ (54)· In t h i s case the s o l u b i l i t y o f TCNQ i n common s o l v e n t s was so low t h a t an a b s o l u t e value was not determined, but an upper l i m i t on the magnitude o f the o r i e n t a t i o n a l average o f γ was e s t a b l i s h e d t o be s i g n i f i c a n t l y below the e x p e c t a t i o n . Returning a g a i n to the r e l a t i o n s h i p between molecular and bulk p r o p e r t i e s , the χ ^ ' term above d i s p l a y s the important f a c t i n t h a t i n condensed phase media n o n l i n e a r i t i e s beyond second-order are not purely and d i r e c t l y r e l a t e d t o t h e corresponding molecular o r microscopic n o n l i n e a r i t y (50,51,55,56). This i s d i f f e r e n t than the cascading problem mentioned above i n which the o v e r a l l high-order response o f a m a t e r i a l i s r e l a t e d not o n l y to the corresponding h i g h order s u s c e p t i b i l i t y , but a l s o to s e q u e n t i a l n o n l i n e a r i n t e r a c t i o n s of lower-order i n v o l v i n g the establishment o f intermediate macroscopic e l e c t r i c f i e l d s . The suggestion here i s t h a t cascading of lower-order n o n l i n e a r i t y through l o c a l e l e c t r i c f i e l d s must be considered. The argument i s s t r a i g h t f o r w a r d . While the o v e r a l l i n a l i q u i d vanishes and w h i l e each o f the averaged l o c a l f i e l d s a t a molecule due t o t h e n o n l i n e a r response o f other molecules o f the l i q u i d vanishes, there i s a s p e c i f i c c o r r e l a t i o n i n the summations o f χ ^ ' which does not. The term w i t h ρ=λ d e s c r i b e s the e f f e c t where molecule λ responds v i a β, t h a t n o n l i n e a r p o l a r i z a t i o n p o l a r i z e s i t s surroundings, and the accompanying r e a c t i o n f i e l d a t molecule λ p a r t i c i p a t e s i n another second-order p o l a r i z a t i o n . This term does not average to z e r o because the β tensor of the same molecule e n t e r s twice i n the process d e s c r i p t i o n . D e t a i l s o f t h i s phenomena may be found i n r e c e n t l y published works (50,55,56). As was mentioned i n 1

β

β

Θ


54


the f i r s t part o f t h i s paper, t h i s a n a l y s i s o f THG i n s o l u t i o n s o f DANS and o f the tr^ns-4'-dimethylamino-N-methyl-4-stilbazolium ion i n terms o f χ ^ ' has allowed us to conclude that the s t i l b a z o l i u m i o n i s n e a r l y a s n o n l i n e a r as DANS i n second-order. (5_1) Obviously the corresponding EFISH measurement would have been d i f f i c u l t t o acomplish.


Conclusion We have b r i e f l y described s e v e r a l types o f m a t e r i a l s development r e s e a r c h intended t o generate e i t h e r new h i g h l y n o n l i n e a r o p t i c a l m a t e r i a l s or new n o n l i n e a r o p t i c a l m a t e r i a l s having n o v e l f a b r i c a t i o n p o t e n t i a l . T h i s work u t i l i z e d the i n h e r e n t v e r s a t i l i t y and s p e c i a l p r o p e r t i e s o f molecular m a t e r i a l s . These and other n o v e l approaches we are pursuing, and the s e v e r a l i n n o v a t i v e approaches d e s c r i b e d i n other papers o f t h i s volume a r e q u i t e d i f f e r e n t than t h e p r a c t i c e s of m a t e r i a l s r e s e a r c h i n i n o r g a n i c n o n l i n e a r media. While i t i s u n r e a l i s t i c t o expect o r g a n i c s t o d i s p l a c e the c u r r e n t l y used inorganic n o n l i n e a r o p t i c a l media, as t h i s f i e l d progresses i t i s a n t i c i p a t e d that a p p l i c a t i o n s employing s p e c i a l e n a b l i n g c h a r a c t e r i s t i c s of the organics w i l l m a t e r i a l i z e . Several aspects of third-order nonlinear optical experimentation and m a t e r i a l s c h a r a c t e r i z a t i o n a s s o c i a t e d w i t h the development o f organic n o n l i n e a r o p t i c a l media were d e s c r i b e d i n a l a r g e l y nonmathematical manner. P i c t o r i a l models were employed t o show the o r i g i n o f s e v e r a l important n o n i n t u i t i v e l y obvious aspects of propagation. This opportunity was taken t o p o i n t out s e v e r a l experimental p i t f a l l s and describe e r r o r s o f technique which have p r e v i o u s l y appeared i n the l i t e r a t u r e . These models and the aspects they made obvious were used t o devise new, more c o r r e c t methods f o r third-harmonic generation c h a r a c t e r i z a t i o n of the p u r e l y e l e c t r o n i c t h i r d - o r d e r n o n l i n e a r p o l a r i z a t i o n response of m a t e r i a l s . F i n a l l y a b r i e f d i s c u s s i o n was given o f l i m i t a t i o n s a s s o c i a t e d w i t h d e s c r i b i n g χ^3) i n l i q u i d s i n a molecular b a s i s or o f e x t r a c t i n g molecular parameters from an experimentally determined l i q u i d . Acknowledgments The author would l i k e t o acknowledge the c o l l a b o r a t i o n s o f Drs. David W i l l i a m s , Ronald Z i o l o and V a l e r i Krongauz ( v i s i t i n g s c i e n t i s t , Weizmann I n s t i t u t e o f Science, I s r a e l ) i n a d d i t i o n t o t h e c o n t r i b u t i o n s made by John VanDusen and Ronald Weagley, a l l employees at Xerox Webster Research Center. F i n a l l y the r o l e o f two students i n t h i s e f f o r t , Cheryl H a n z l i k (APS Summer I n t e r n , Univ. o f Rochester) and Bonnie Buchalter (Cooperative Education Employee, Manhattan College) i s acknowledged.


2. MEREDITH


55


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Nonlinear Optical Properties of Organic and Polymeric Materials

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