Optical Nonlinearities and Photoinduced Solitons in Conjugated

8

Downloaded by NORTH CAROLINA STATE UNIV on May 9, 2015 | http://pubs.acs.org Publication Date: September 29, 1983 | doi: 10.1021/bk-1983-0233.ch008

Optical Nonlinearities and Photoinduced Solitons in Conjugated Polymer Crystals CHRISTOS FLYTZANIS Laboratoire Propre du Centre National de la Recherche Scientifique (CNRS), Ecole Polytechnique, Laboratoire d'Optique Quantique, 91128 Palaiseau, Cedex, France

The linear and nonlinear optical properties of the conjugated polymeric crystals are reviewed. It is shown that the dimensionality of the π - e l e c t r o n dis tribution and electron-phonon interaction drastically influence the order of magnitude and time response of these properties. The one-dimensional conjugated crystals show the strongest nonlinearities ; their response time is determined by the diffusion time of the i n t r i n s i c conjugation defects whose dynamics are described within the soliton picture. It is also shown that the electron-phonon interaction is operative in the polymerization process of the one-dimensional conjugated polymeric crystals ; a simple dynamical model for the polymerisation in po lydiacetylenes is presented that accounts for the existing observations. The p o t e n t i a l use and a p p l i c a t i o n s of very s o p h i s t i c a t e d non l i n e a r o p t i c a l processes i n o p t i c a l telecommunications and i n t e g r a ted o p t i c s have put requirements on the nonlinear o p t i c a l m a t e r i a l s which cannot a l l be met with the c u r r e n t l y used inorganic c r y s t a l s , i o n i c or semiconductors. The use of organic m a t e r i a l s and polymers i n p a r t i c u l a r became more imperative than ever. The i n t e r p l a y of high n o n l i n e a r i t y , appropriate form, s i z e and response time of the nonlinear o p t i c a l m a t e r i a l which i s very important i n these a p p l i cations can be more ingenuously optimized with the l a t t e r ones. Furthermore with a b e t t e r understanding of the topochemical r e a c t i o n s that govern the growth and d e p o s i t i o n of these m a t e r i a l s new far reaching a p p l i c a t i o n s may be conceived by combining chemical and o p t i c a l o p e r a t i o n s .

0097-6156/83/0233-0167$06.00/0 © 1983 American Chemical Society

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


168

NONLINEAR OPTICAL PROPERTIES

T h e o r e t i c a l estimations and experimental i n v e s t i g a t i o n s r i r m l y e s t a b l i s h e d (J_) that large e l e c t r o n d e r e a l i z a t i o n i s a p e r e q u i s i t e for large values of the n o n l i n e a r o p t i c a l c o e f f i c i e n t s and t h i s can be met with the π - e l e c t r o n s i n conjugated molecules and p o l y mers where a l s o charge asymmetry can be adequately introduced i n order to o b t a i n non-centrosymmetric s t r u c t u r e s . Since the e l e c t r o nic d e n s i t y d i s t r i b u t i o n of these systems seems to be e a s i l y modi f i e d by t h e i r i n t e r a c t i o n with the molecular v i b r a t i o n s we a n t i c i pate that these m a t e r i a l s may possess l a r g e p i e z o e l e c t r i c , pyroel e c t r i c and photoacoustic c o e f f i c i e n t s . Conjugated polymer c r y s t a l s are expected to occupy a p r i v e leged p o s i t i o n i n d i v e r s e n o n l i n e a r o p t i c a l devices i f t h e i r topochemical growth i s adequately mastered and t h e i r i n t r i n s i c defects are p r o p e r l y c h a r a c t e r i z e d . Here we assess the main f a c t o r s and mechanisms that determine the magnitude and dynamics of the non l i n e a r o p t i c a l c o e f f i c i e n t s i n c r y s t a l l i n e conjugated systems and s t r e s s the key r o l e played by the d i m e n s i o n a l i t y of the e l e c t r o n d e r e a l i z a t i o n and the electron-phonon i n t e r a c t i o n . It i s shown that these f a c t o r s have t h e i r strongest impact i n one-dimensional conjugated systems but with c o n f l i c t i n g tendancies ; one-dimensio nal d e r e a l i z a t i o n enchances the nonlinear c o e f f i c i e n t s while e l e c tron-phonon i n t e r a c t i o n i n such systems introduces i n t r i n s i c c o n j u gation defects that may l i m i t t h e i r time response. The p o l y d i a c e t y l e n e c r y s t a l s (1-4) most s t r i k i n g l y c o r r o b o r a te these c o n j e c t u r e s . Along t h i s l i n e of thought i s a l s o shown that t h i s electron-phonon i n t e r a c t i o n i s i n t i m a t e l y interwoven with the p o l y m e r i s a t i o n process i n these m a t e r i a l s and plays a profound r o l e t h e r e . We make the conjecture that t h i s occurs through the mo t i o n of an unpaired e l e c t r o n i n a non-bonding p - o r b i t a l dressed with a bending mode and guided by a c l a s s i c a l i n t e r m o l e c u l a r mode. Such a polaron type d i f f u s i o n combined with the theory of non r a d i a t i v e t r a n s i t i o n s explains the e s s e n t i a l s of the s p e c t r a l c h a r a c t e r i s t i c s of the m a t e r i a l s as w e l l as t h e i r p o l y m e r i s a t i o n dy namics. Main s t r u c t u r a l and o p t i c a l p r o p e r t i e s of conjugated polymers Conjugated polymers are i n general c h a r a c t e r i z e d by h i g h l y a n i s o t r o p i c o p t i c a l , d i e l e c t r i c , conducting and mechanical p r o p e r t i e s ( 2 , 5 ) . This i s because the valence e l e c t r o n s , r e s p o n s i b l e for these p r o p e r t i e s , respond more e a s i l y to p e r t u r b a t i o n s along d i r e c t i o n s where the conjugation occurs than i n others ; t h e i r d e r e a l i z a t i o n i n the other d i r e c t i o n s i s hindered by saturated bonds which keep the conjugated systems with an i s o l a t o r type behavior i n d i r e c t i o n s across the conjugation d i r e c t i o n but semiconducting behavior along t h i s d i r e c t i o n . In the present review we s h a l l l i mit ourselves i n the semiconducting polymers. The c h a r a c t e r i s t i c valence four of the C-atom i s the o r i g i n of the enormous v a r i e t y of these systems. Purely s t e r i c and topo l o g i c a l c o n s i d e r a t i o n s i n d i c a t e that carbon conjugated polymeric s t r u c t u r e s can be e i t h e r one- or two- dimensional since the c o n j u -



8. F L Y T Z A N I S

169

Conjugated Polymer Crystals

g a t i o n a r i s e s from the e l e c t r o n s i n p - o r b i t a l s which do not p a r t i c i p a t e i n s p - h y b r i d i z a t i o n to form the skeleton of the saturated bonds. Indeed conjugation cannot be present i f the four e l e c t r o n s are involved i n four d i f f e r e n t bonding d i r e c t i o n s l i k e i n the d i a mond s t r u c t u r e . Besides carbon, n i t r o g e n or s u l f u r can a l s o be used as b u i l d i n g blocks of conjugated polymers but such m a t e r i a l s are not yet f u l l y c h a r a c t e r i z e d and w i l l not be e x p l i c i t l y d i s c u s s e d . The d i f f e r e n t expressions f o r the nonlinear c o e f f c i e n t derived be low are however so parametrized that they may be used for other than carbon polymers as w e l l . Two-dimensional conjugated systems are thus expected to be formed by benzene type hexagonal r i n g s so arranged to form plans and the π - e l e c t r o n s are d e l o c a l i z e d there with only s l i g h t a n i sotropy ; these plans are w e l l separated from each other so that the o p t i c a l p r o p e r t i e s of these systems are q u i t e d i f f e r e n t accross and p a r a l l e l to the p l a n s . T o p o l o g i c a l l y we may d i s t i n g u i s h ( F i g u re 1) two s t r u c t u r e s the A and B, the l a t e r being non centrosymmet r i c ; the l i m i t i n g case of the A - s t r u c t u r e i s the graphite (C) p r o f a b l y the only s t a b l e c o n f i g u r a t i o n . The r e f r a c t i v e i n d i c e s and o p t i c a l gaps of graphite p a r a l l e l and perpendicular to the plans are (6) n = 2.73, E , , - 0.0-0.1 eV and η^= 1.53, E ^ - 6 eV r e s p e c t i v e l y ; i t s d e n s i t y p-1.7g/cm3. There are no measurements of n o n l i n e a r coefficients yet. One dimensional conjugated carbon polymers can occur i n many c o n f i g u r a t i o n s as depicted i n F i g u r e 2 where a l s o we included some chains with n i t r o g e n and s u l f u r f o r l a t e r r e f e r e n c e . A l s o included there are i n o r g a n i c one dimensional semiconductors, l i k e SbSI and SbSBr f o r l a t e r comparison. Besides the depicted one-dimensional systems, others l i k e TCNQ- and K C P - s a l t s could be included here as w e l l but rough measurements of t h e i r n o n l i n e a r c o e f f i c i e n t s gave d e c e p t i v e l y small values which combined with t h e i r i l l - c h a r a c t e r i s a t i o n make them poor candidates f o r n o n l i n e a r o p t i c a l d e v i c e s . P o l y d i a c e t y l e n e s (2) come c l o s e s t to the model one-dimensional organic semiconductor and can be r e a d i l y obtained i n form of l a r g e , n e a r l y d e f e c t - f r e e s i n g l e c r y s t a l s so that a large number of expe riments and measurements have been c a r r i e d out on these m a t e r i a l s . T h e i r s t r u c t u r e i s shown i n F i g u r e 3 where a l s o some t y p i c a l s i d e groups R are i n d i c a t e d . On t a b l e I we summarize some measured v a M

Table I . O p t i c a l p r o p e r t i e s of p o l y d i a c e t y l e n e Compound L i g t h O p t i c a l Density R e f a c t i v e (R) polar gap (gr/cm^) index Eoicm" ) η

1

2

10 χ^ (esu)

1

PTS TCDU

II

15800

II

17900

JL

1.46

1.86 1.58 1.80 1.65

160 50 >1700 6 60 100 2300 1 2

36

of some organic compounds

10 3(esu) 42 21 10 3

3

36

10 y(esu) 10 10 13 5 3

2

ref. 14 14 15 16 17

values of i n o r g a n i c m a t e r i a l s and i n t a b l e I and I I I those of orga n i c ones. To make the comparison e a s i e r we have a l s o i n s e r t e d the corresponding values of the macroscopic p o l a r i s a b i l i t i e s a^ ^ f o r mally defined by x ( ) = a ' V v where ν i s the^value of the repeat un i t i n the c r y s t a l (unit c e l l ) ; we put 3=ot and γΞοΛ Let us evaluate the order of magnitude of these c o e f f i c i e n t s . In p e r i o d i c systems the e l e c t r o n i c s t a t e s are d i s t r i b u t e d i n Bloch type bands (18,19). For the d e s c r i p t i o n of the o p t i c a l p r o p e r t i e s i n the transparency r e g i o n of an organic semiconductor to which conjugated polymer c r y s t a l s can be a s s i m i l a t e d we may l i m i t ourselves to two bands, the highest valence (v) and the lowest con d u c t i o n (c) bands. Using the Genkin-Mednis (20,12) approach, one can d e r i v e the expressions of the n o n l i n e a r s u s c e p t i b i l i t i e s as i n t e g r a l s of c e r t a i n combinations of i n t e r - and intraband terms over the whole B r i l l o u i n Zone (or e v e n t u a l l y the extended Jones Zone (18,19)). Thus f o r the xx-components of the l i n e a r and t h i r d order s u s c e p t i b i l i t i e s of a centrosymmetric semiconducting c r y s t a l one has (4,21,22) n

n

n



174

X

0

)

XX

=

$i

[

M

j

Ω R

7

vc

4

χ

(3) 8e = —χ— xxxx

ω cv

S dk cv as as cv vc 8k 8k

(2) Ω

S S S dk vc cv vc cv

where the band energy d i f f e r e n c e ^ = e - e , Ω i s the t r a n s i t i o n d i p o l e moment matrix element between the two bands, δ Ω /ω and ε are the band energies. It i s important to n o t i c e that the linear susceptibility only a r i s e s from interband t r a n s i t i o n s , while χ ^ ) a r i s e s from the competition of interband and intraband terms and t h i s i s true f o r a l l n o n l i n e a r s u s c e p t i b i l i t i e s ; f o r very d e l o c a l i z e d systems (namely strong overlap of wave functions) the q u a n t i t i e s ω and Ω ^ . vary s t r o n g l y with k over the B r i l l o u i n Zone and the intraband term becomes the dominant one (4). From the physicochemical p o i n t of view, the p r e v a i l i n g one i n the present review, the question i s how these c o e f f i c i e n t s r e l a t e to the c h a r a c t e r i s t i c s of the c o n s t i t u a n t molecules and how t h i s information can be extracted from ( 2 , 3 ) . The answer r e l i e s on the f a c t that the e s s e n t i a l c o n t r i b u t i o n s to these i n t e g r a l s come from only few nonoverlapping c r i t i c a l regions i n the j o i n t d e n s i t y of states (18,19) ; these are p o i n t s , l i n e s and surfaces depending on the s p a t i a l extension of the conjugated e l e c t r o n d i s t r i b u t i o n . They are defined by the c o n d i t i o n c v

c

v

Γ ( :

Ν Ο

α


(3)

>

=

ν α

ν ( :

ν

ο ν

v> =0 k cv

(4) '

This d i r e c t l y e s t a b l i s h e s a r e l a t i o n between the o p t i c a l s u s c e p t i b i l i t i e s χ( ' and the topology and d i m e n s i o n a l i t y of the j o i n t s den s i t y of states ; more importantly i t allows one to express χ^ in terms of the values that Ω and ω take at these c r i t i c a l r e g i o n s ; the l a t t e r being expressed i n terms of the c h a r a c t e r i s t i c s of the e l e c t r o n d i s t r i b u t i o n ( h e t e r o a t o m i c i t y , bond a l t e r n a t i o n and supera l t e r n a t i o n , chain p a i r i n g , electron correlation) this functional dependence allows one to g l o b a l l y assess the impact of these f e a t u res on the n o n l i n e a r s u s c e p t i b i l i t i e s . One-dimensional c r y s t a l s . In one-dimensional systems (ID) the problem i s amenable to an a n a l y t i c a l s o l u t i o n and allows one to gain some i n s i g h t to t h i s approach. We i l l u s t r a t e t h i s p o i n t w i t h the simple bond a l t e r n a t e d i n f i n i t e carbon c h a i n (polyene) and adopt the Huckel approximation. Such a c h a i n i s then c h a r a c t e r i z e d (23) by two resonance energies 3 i and 32 that a l t e r n a t e along the c h a i n . We assume complete s e p a r a t i o n between σ - and π - e l e c t r o n s and we concentrate our a t t e n t i o n only on the π - e l e c t r o n c o n t r i b u t i o n . The e l e c t r o n states i n such a c h a i n can be obtained a n a l y t i c a l l y and one has (see 2 1 , 22_ .) η ω = 2 3 2 ζ θ , eiï =iea(1-v )/4ζ§ where C Q = ( l + v + 2 v c o s k a ) j =ρ /ρ i n s e r t i n g t h i s expression of u ) i n (4) we see that the j o i n t d e n s i t y of s t a t e s becomes i n f i n i t e at the edge of the B . Z . , ka=n ( c r i t i c a l p o i n t ) , where a l s o the matrix element Ω ^ 3 ) a t t a i n s i t s maximum value (see Figure 5) η

0 Ν

ο ν

2

ο ν

Cv

2

a n (

ν

1

2 #

c v

Ο Γ


8.

FLYTZANIS


175

I n ( k a - i r ) I =a | S 3 | / | β - β | E L ( o p t i c a l d e l o c a l i z a t i o n length) and the energy d i f f e r e n c e η ω be comes smallest li(o (ka=7r)=2 | β 2 - 3 ι | =E ( o p t i c a l gap). The c o i n c i d e n ce of these three features at a s i n g l e p o i n t i s an e s s e n t i a l cha r a c t e r i s t i c of the ID systems and i s the o r i g i n of the enhancement of the π - e l e c t r o n c o n t r i b u t i o n over the σ - e l e c t r o n s i n χ ^ ^ . I n deed one f i n d s (4,22) that f o r strong d é l o c a l i s a t i o n , N jE4Ld/a> 1, the intraband term i n (4) i s the dominant one and c v

i +

2

2

d

χ

ο ν

cv

0


η

(

,0).

0

)

Χ

(3)_

(5)

2

- X N 3π σ d iN

16

45π

λ

σ

(6)

d

Figure 5. Energy bands (—), dipole transi and i n general tion moment (-·-), and density of states (—) for bond alternated chain. (2n-l) 4n-2 (2n-l) σ d

(7)

χ

»

where N = | 3 i + 3 | / | 3 i - 3 | and χ^ i s the expression of the s u s c e p t i b i l i t y f o r a chain of saturated bonds ( σ - e l e c t r o n s ) . It has been shown (4,22) that the above f u n c t i o n a l dependence of the odd order s u s c e p t i b i l i t i e s on the d e l o c a l i z a t i o n parameter N i s very general and c h a r a c t e r i s t i c of a l l ID systems (with or without center of i n v e r s i o n , chain p a i r i n g or el e c t r o n c o r r e l a t i o n ) . Since can a t t a i n high values f o r conjuga ted polymers the much higher dependence of the n o n l i n e a r s u s c e p t i b i l i t i e s on N than the q u a d r a t i c one found f o r χ ^ Ο j u s t i f i e s the neglect of the s i d e group c o n t r i b u t i o n to x ^ ^ while t h i s i s not . ° ( \\ xxxx, n e c e s s a r i l y the case f o r x ^ ' ; there the c o n t r i b u t i o n s of the σ d

2

2

d

d

3

1

/j j

XX

.

κ

and π - e l e c t r o n s to χ ' a r e round to be of the same order of magni tude. Thus the n o n l i n e a r s u s c e p t i b i l i t i e s can be e f f e c t i v e l y used to measure the conjugated e l e c t r o n d e l o c a l i z a t i o n . L o c a l f i e l d c o r r e c t i o n s can a l s o be taken i n t o account ( 2 1 , 2 2 ) . Expressions (5-7) can 4n-2 a l s o be cast i n the form (2n-l) (2n-l) A

X

^ Χ

(8)

σ

which contains d i r e c t l y a c c e s s i b l e experimental values ( E i s the Fermi l e v e l and Eg i s the o p t i c a l energy gap) and a l s o allows d i r e c t comparison with i n o r g a n i c semiconductors SbSI and SbSBr which can have high values of n o n l i n e a r i t i e s as w e l l s i n c e E-p/E >>1 there; u n f o r t u n a t e l y the c r y s t a l growth for these m a t e r i a l s i s at presen t l y an insurmontable problem (24). F


176


The s i t u a t i o n i s d r a s t i c a l l y d i f f e r e n t with the second order s u s c e p t i b i l i t y which i s non-vanishing only i n m a t e r i a l s without i n v e r s i o n symmetry. Its expression i s ( 2 2 ) rn\ 3r r ιr 3S 8S u

(2)=4i

g S (Ω -Ω ) - I s - £ 3 ϋ - - 2 £ s


x

dk

(9)

Here the interband and intraband terms can each have e i t h e r s i g n so that they may add or s u b s t r a c t . I t i s i n t r u c t i v e so study again the bond a l t e r n a t e d carbon chain i n the Huckel approximation ; i n order to be asymmetric h e t e r o - a t o m i c i t y must be present as w e l l which i s taken i n t o account by l e t t i n g the coulomb i n t e g r a l to take a l t e r n a t i v e l y the values cq and (*2 along the c h a i n . The expressions of Ω and ω are given i n ( 2 1 , 2 2 ) . C a r e f u l a n a l y s i s of (9) reveals that c o n t r i b u t i o n s to the integrand only come from regions where Ω i s complex ; i t vanishes whenever Ω becomes r e a l or pure ima ginary and t h i s i s p r e c i s e l y what happens at the edse of the B r i l l o u i n zone of an I D system. Thus i n contrast to χ^ ' does not take f u l l advantage of the i n f i n i t e d e n s i t y of states there and the h i g h l y d e l o c a l i z e d character of these states ; or o t h e r w i se s t a t e d , charge assymetry, (a p e r e q u i s i t e f o r non-vani shing χ ^ ) , being a l o c a l feature shows i t s f u l l impact at most over a u n i t c e l l and l a r g e r d e r e a l i z a t i o n i s i r r e l e v a n t . Expression ( 9 ) with the commonly used values of the Coulomb and resonance i n t e g r a l s , (04,012) and ( 3 i , 3 2 ) r e s p e c t i v e l y , shows that x ^ ) cannot exceed ( 2 2 ) the value of 1 0 " ? esu which i s an order of magnitude below that of GaAs and two orders of magnitude below the one expected f o r a merocyanine c r y s t a l ( 1 7 ) ; t h i s seems to be confirmed from recent measurements i n a s y m é t r i e p o l y d i a c e t y l e n e s ( 2 5 ) . Therefore any improvement of the values of χ^ ought to be sought i n the o p t i m i s a t i o n of the p o l a r i z a b i l i t y values of small molecules ( l i k e the me rocyanine) and t h e i r packing i n the c r y s t a l . In p a r t i c u l a r s i d e groups with l a r g e second order p o l a r i z a b i l i t y values a p p r o p r i a t e l y attached along a p p l y d i a c e t y l e n e chain may provide c r y s t a l s with l a r g e values of χ^ ' along d i r e c t i o n s other than the chain d i r e c t i o n ; the c r y s t a l growth of such m a t e r i a l s seems however d i f f i c u l t i f not hopeless ( 2 5 ; . The I D i n o r g a n i c semiconductors SbSI and SbSBr (see Figure 2 and Table II) seem a l s o to be favorable m a t e r i a l s with large values of χ ( ) ( 2 4 ) ; u n f o r t u n a t e l y here too the c r y s t a l growth seems at p r e s e n t l y an insurmontable problem. Quite i n t r i g u i n g i s a l s o the case of centrosymmetric homoatomic bond a l t e r n a t e d chains which get coupled i n t o p a i r s i n an asym metric c o n f i g u r a t i o n (A). For such a system χ ( ) can a t t a i n ( 2 2 ) values l a r g e r than those of the s i n g l e heteroatomic bond a l t e r n a t e d chain. Two- and three-dimensional c r y s t a l s . I n two-dimensional ( 2 D ) systems the c r i t i c a l regions are of two kinds : points at energy E Q at the edge of the B . Z . reminiscent of I D patterns i n the e l e c tron d i s t r i b u t i o n with a c o n t r i b u t i o n i n χ Ο and χ ( ' as given by ( 7 ) and l i n e s at energy Ej i n t r i n s i c to the 2 D system. The e f f e c t γ ο

α γ

α ν

γ ο

9

2

2

2


8.

177


FLYTZANIS

of the l a t t e r i n the n o n l i n e a r s u s c e p t i b i l i t i e s i s to reduce the impact of the p o i n t E Q by borrowing and d i f f u s i n g i t s o s c i l l a t o r strength and d e n s i t y of states and r e p e l l i n g E Q to higher energies ( E I < E Q ) . The a n a l y t i c a l c a l c u l a t i o n of (3) even i n the Huckel ap proximation i s quite involved although the expressions of Ω and ω can be r e a d i l y derived ; t h e o r e t i c a l c a l c u l a t i o n s i n graphite confirm the above q u a l i t a t i v e c o n c l u s i o n g i v i n g values of v(3) l o wer by one or two order of magnitude than f o r ID systems. In gene r a l planar systems are r a t h e r unstable and t h e i r use as n o n l i n e a r o p t i c a l devices i s q u e s t i o n a b l e . Three-dimensional (3D) conjugated systems do not e x i s t but one can conceive 3D organic semiconductors comparable to the i n o r g a n i c ones (Ge, GaAs). There, besides c o n t r i b u t i o n s from p o i n t s E Q and l i n e s E j , χ^ ^ w i l l a l s o c o n t a i n c o n t r i b u t i o n s from c r i t i c a l s u r faces at energy Ε2· Since E 2 < E J < E Q the impact of E Q i s f u r t h e r r e d u ced. This i s s t r i n k i n g l y evidenced i n i n o r g a n i c semi-conductors where estimations of the d i f f e r e n t c o n t r i b u t i o n s have been made using (26) simple models f o r the j o i n t d e n s i t y of s t a t e s . It i s found that the main c o n t r i b u t i o n to v(3) comes from the 2D and ID c r i t i c a l regions of the B . Z . while the c o n t r i b u t i o n from the c r i t i c a l point E Q (zero dimensional) the s o - c a l l e d Penn-gap i s substan t i a l l y reduced as one proceeds to low gap semiconductors. This i s because the intraband terms are more important i n the lower energy c r i t i c a l regions than i n the higher ones ( Ω and ω vary more r a p i d l y over the B . Z . . On the other hand a semiconductor l i k e Ge, with one of the l a r g e s t values of v ( 3 ) . as w i l l be discussed below, b a r e l y equals that of a p o l y d i a c e t y l e n e . This i s p a r t i c u l a r y s t r i king when contrasted with the f a c t that the d e n s i t y of valence e l e c trons i n Ge i s by an order of magnitude higher than that of the π - e l e c t r o n i n a p o l y d i a c e t y l e n e . Furthermore the p o l y d i a c e t y l e n e s have a higher transparency, are o p t i c a l l y a n i s o t r o p i c and possess a lower index of r e f r a c t i o n than Ge. It i s unfortunate that there i s no measurement of χ (3) i n i n o r g a n i c ID semiconductors (24) l i k e SbSI and SbSBr since they would allow a b e t t e r comparison with the organic semiconductors. P o l y d i a c e t y l e n e c r y s t a l s . The enhancement of v(3) because of one-dimensional e l e c t r o n d e r e a l i z a t i o n i s s t r i k i n g l y corroborated i n the p o l y d i a c e t y l e n e c r y s t a l s . T h e i r s t r u c t u r e i s that of a super a l t e r n a t e d chain with four atoms per u n i t c e l l and the Huckel appro ximation y i e l d s four bands f o r the π - e l e c t r o n s , two valence and two conduction bands. When depicted i n the extended Jones zone, each p a i r can be viewed as a r i s i n g by a d i s c o n t i n u i t y at the middle of the B r i l l o u i n zone of the polyene c h a i n . The dominant c o n t r i b u t i o n to " ^ comes from the c r i t i c a l point at the edge of the exten ded Jones zone ( i n i t i a l l y at the center of the reduced B . Z . ) . The complete expressions are derived i n (4,22) and c a l c u l a t e d f o r d i f ferent p o l y d i a c e t y l e n e s . We reproduce the values of f o r TCDU and PTS i n table IV. The c a l c u l a t e d values are i n good agreement with the measured Que s (3). They are of the same order of magnitude as the values of Χ ξ ξ ξ ξ i n Ge and GaAs which are 10"* and 1 0 e s u , ο ν


ο ν

η

ο ν

ο

ν

- 1 1


178


Table IV. C a l c u l a t e d values of χ ( 3 ) i n time p o l y d i a c e t y l e n e s (Ref. 22) Compound (R) PTS


TCDU

Light polarization

II

Refract Index

JL

1 .92 1.72

II

1 .76

1

1.65

1 2

3

10 χ( ) (esu) 70

Optical Nonlinearities and Photoinduced Solitons in Conjugated

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