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Nonlinear optical probes of conjugated polymers
Synthetic Metals, 4P-50 (1992) 21-35
21
Nonlinear optical probes of conjugated polymers* D. Neher**, W. E. Torruellas***, K. B. Rochford*, M. B. Marques**, R. Zanonittt, G. Assanto and G. I. Stegeman Center f o r Research in Electro-Optics and Lasers, University of Central Florida, 12424 Research Parkway, Orlando, FL 32826 (USA)
Abstract Nonlinear optical properties of conjugated polymers can be measured using various techniques, including third-harmonic generation, two-photon absorption, nonlinear grating coupling and interferometry. These methods will be compared with regard to their suitability for obtaining specific parameters. We illustrate the application of these techniques to the study of ~--conjugated polymeric systems, such as poly(4-BCMU), poly(3-decylthiophene) and 4-dialkylamino-4'-nitrostilbene (DANS) side-chain polymer, all of them regarded as candidates for the realization of all-optical switching devices, and outline relevance and limits of each technique.
1. I n t r o d u c t i o n Since the experimental work of Hermann and Ducuing on finite polyenes [1 ], there has been an increasing interest in investigating the third-order nonlinear susceptibility )((3) of ~--electron conjugated organic molecules. Using third-harmonic generation Sauteret et al. measured values of X(3) exceeding 10 -x° e.s.u, in polydiacetylene (PDA) crystals [2], and numerous later experiments have established the suitability of conjugated organic materials for the realization of ultrafast switching devices in an integrated-optical format. In addition to short response times and large third-order nonlinearities, many of these polymers, in fact, present physical and chemical properties which allow the fabrication of guiding (planar) structures where the optical excitation can be optimized and maintained at high levels over long propagation distances [3 ]. All-optical devices rely on an intensity-dependent index of refraction (or optical Kerr effect), usually expressed as *Invited paper. **Present address: Max-Planck-Institut ftir Polymerforschung, Ackermannweg 10, 6500 Mainz, Germany. ***Present address: Raytheon Research Division, 131 Spring Street, Lexington, MA 02173, USA. tpresent address: Dylor Corporation, RD5, P.O. Box D, Ligonier, PA 15658, USA. ttpresent address: Centro de Fisica da Universidade de Porto (INIC), 4000 Porto, Portugal. *ttPresent address: Center for Laser Research, Oklahoma State University, Stillwater, OK 74078, USA.
0379-6779/92/$5.00
© 1 9 9 2 - Elsevier Sequoia. All rights reserved
22 (1)
n=no +neI
where the nonlinear refractive index coefficient n2 is related to the susceptibility X(a)(- w; ~o, - ~o, to) by 3 n2 - 4no2eo c )((3)( _ to; to, - ~o, w)
(2)
A variation in the refractive index with intensity leads to a nonlinear phase shift experienced by the optical wave upon propagation, and it is on the size of the obtainable phase shift that all-optical switches are based [3]. However, various other nonlinear effects are usually associated with the Kerr dependence in eqn. (1), among them index saturation, two-photon absorption (TPA) and thermo-optic effect. For example, recent investigations demonstrated that TPA can limit all-optical switching [4]. It is therefore of particular importance to investigate all these properties when characterizing organic materials for all-optical switching applications, and to compare them with accepted theoretical models. Various techniques are available for the nonlinear characterization of third-order materials. Unfortunately, none of them is suited to provide a complete set of information on a given material and distinct aspects of the optical nonlinearity have to be probed with different techniques. In the following we will briefly review four of these techniques: third-harmonic generation (THG), two-photon absorption, nonlinear interferometry and nonlinear grating coupling. Finally, the results will be discussed with the aid of simple two- and four-level models which properly describe most v-electron conjugated systems.
2. T h e o r e t i c a l
models
The macroscopic nonlinearity results from an orientational average of the microscopic hyperpolarizibflity. For the case of a one-dimensional 7relectron conjugation along the axis if, the general expression reads: X!3.~l(- w; ~o~, a~, to3)=f~ccT¢¢¢¢(- w; wl, ~o2, aJ3)f~c~j~c~J~¢~
(3)
In isotropic materials, the orientational average gives a factor of 1/5. Furthermore in eqn. (3) we assumed the local field tensor re, to be diagonal in the molecular frame. One approach to explaining T in conjugated polymers starts from calculations on finite-size conjugated model compounds like polyenes. These molecules belong to the centro-symmetric C2h group. Here the electronic states have either even parity (~Au states), or odd parity (~Bu states) and the ground state configuration is always SAg. Theoretical calculations, that used a Hamiltonian extended by electron--electron correlation effects [5-7], showed large transition dipole moments between I'A~ and llBu, the lowest lying one-photon allowed transition and from l'Bu and a higher lying two-
23
photon state m~Ag. With increasing length of the conjugated system, this two-photon state approaches the visible lZBu band [7]. Such a three-level model is in quantitative agreement with early calculations on 1D 7r-conjugated polymers using the simple noninteracting nearest-neighbor Htickel Hamiltonian [8, 9]. These calculations suggested that the strong interband transition to the edge of the conduction band and successive intraband transitions inside the conduction band are responsible for the large nonresonant nonlinearity in these polymers, which increases dramatically with the inverse of the sixth power of the gap energy EG. These relations seemed to be verified in various experiments [2, 10, 11]. Close to resonance, the 2lAg state located slightly below the visible 1 ~Bu state [12] m a y contribute to the interaction pathway, although the transition dipole m o m e n t with the 1 iBu state is considerably smaller than that between llBu and m~Au. In conclusion, a three- or four-level system (as shown in Fig. 1) may be sufficient to explain the low frequency dispersion of the nonlinear susceptibility in conjugated polymers. Different treatments of the semiclassical perturbation theory in a discrete level system have been published, namely, an averaging method [13] or a diagrammatic analysis [14]. Nevertheless, both procedures lead to similar expressions [15], in particular in the nonresonant regime, and contain the same dominant terms in the near-resonant case, i.e.: ) ( 3 ( - 0); 031, 0)2, 0)3)(X
e4 _- ~g~--/x_~,~,xjg_,______~x/~__~_g --5 h u ~ ' (0)- 0)~,g+ iFu,g)(~o~+ 0)1 - 0)g,g+ iFg,g)(0)l - ~%g+ iFug)
(4)
The sum extends over all excited states u=nIBu and g the even parity states, including the ground state itself. Note that all transitions from the ground level to lAg states are one-photon-forbidden. gl! ,A I 1.1
A
,A g ! tgu
3-
L
~
4-I
Fig. 1. Schematic diagram of the three- and four-level models, g denotes the ground state (l~Ag) of even parity, g' and ge, excited states with the same parity and u the lowest state with odd symmetry (11B~). The/x t e r m s are transition dipole moments. A and A' are respectively the energy difference between the I IB~ state and the lowest excited two-photon states 2JAg and the second excited two-photon state m~Ag.
24
3. N o n l i n e a r optical m e t h o d s 3.1. T h i r d - h a r m o n i c
generation
T h i r d - h a r m o n i c g e n e r a t i o n (THG) is widely u s e d to d e t e r m i n e the nonlinear optical susceptibility X(3)(- 3w; co, w, to) of materials b o t h in the solid p h a s e and in solution. THG is insensitive to the t h e r m o - o p t i c effect and, far f r o m r e s o n a n c e s , the value o f X(a)( - 3w; w, oJ, w) can be u s e d to estimate n2, b u t an a c c u r a t e e x t r a p o l a t i o n is v e r y difficult w i t h o u t p r e c i s e i n f o r m a t i o n on all the r e s o n a n t levels in the molecule. The relative simplicity o f this m e t h o d o p e n s the w a y for wide-range tunability of the f u n d a m e n t a l w a v e l e n g t h in o r d e r to d e t e r m i n e the spectral dispersion o f X(3)( - 3w; w, w, ~o). Tunable THG n e a r the e l e c t r o n i c r e s o n a n c e s of the material e n a b l e s o n e to scan t h e electronic levels that p r e s u m a b l y d o m i n a t e the n o n l i n e a r p r o p e r t i e s . In b o t h theoretical m o d e l s outlined a b o v e [13, 14], the n e a r - r e s o n a n t X(3)(-3w; w, w, ~o) f r e q u e n c y d e p e n d e n c e is d o m i n a t e d by only o n e term, i.e., in the fourlevel model: X(3)( - 3oJ; o~, oJ, o~)= 6Ne4
~-~ f
3~
~ 3 ]P~gl2[~ug'lz I f ]' ~g, (3eo-eOug+i/'ug)(2W-Wg,g~-iFg,g)(W-O~g+iFug)
(5)
The s u m m a t i o n e x t e n d s o v e r the g r o u n d state g and the d o m i n a n t e x c i t e d t w o - p h o t o n states and u is the d o m i n a n t o n e - p h o t o n level. While the transition dipole m o m e n t s Pug, f r e q u e n c i e s O~ugand b a n d w i d t h Fug are directly accessible via linear absorption, values for ~ug,, Wg,g and /'g,g can be d e d u c e d b y a fit of the e x p e r i m e n t a l data for X¢3)(-3w; w, w, w). W e included a f r e q u e n c y d e g e n e r a c y f a c t o r of six in eqn. (5) that a p p e a r s w h e n the 48 different t e r m s for T(-oJ4; w3, we, ~o,) c o n v e r t into eight different t e r m s with d e g e n e r a c y six for T ( - 3 w ; w, oJ, o~). This f a c t o r was s u g g e s t e d r e c e n t l y b y Shen [16], although we n e v e r f o u n d it to be u s e d in the data evaluation in c o m m o n literature and it m a y be c a n c e l e d out b y an a v e r a g i n g f a c t o r of 1/3! [15]. In the c u r r e n t setup [17l all THG m e a s u r e m e n t s w e r e p e r f o r m e d in t r a n s m i s s i o n on thin p o l y m e r films spun or cast o n t o f u s e d silica substrates. A Q-switched Nd:YAG laser, g e n e r a t i n g 10 ns pulses at 10 Hz, was f r e q u e n c y doubled to p u m p a dye laser. D o w n - c o n v e r s i o n of the dye laser light in LiIO3 c o v e r e d the 1 . 4 5 - 1 . 7 3 ~ m wavelength region. W a v e l e n g t h s b e t w e e n 1.22 and 1.45 ~ m w e r e o b t a i n e d by Raman shifting the dye laser s o u r c e in a 1 m long He cell. With the same Raman cell we c o n v e r t e d the f u n d a m e n t a l and the s e c o n d h a r m o n i c of the Nd:YAG to 1906, 956, 1367 and 1567 nm. Pulses o f energies ranging b e t w e e n 25 and 2 5 0 p J w e r e f o c u s e d with a lens ( f = 20 cm) o n t o the sample, m o u n t e d on a c o m p u t e r - c o n t r o l l e d r o t a t i o n stage inside a 200 m T o r r v a c u u m cell. The h a r m o n i c light g e n e r a t e d t h r o u g h the sample was d e t e c t e d and r e c o r d e d as a function of the i n c i d e n c e angle. Both the m a g n i t u d e and p h a s e o f X(3)( - 3w; to, w, w) c o u l d be e x t r a c t e d by r e p e a t i n g the e x p e r i m e n t s at the same location on the s u b s t r a t e b u t a f t e r c o m p l e t e removal o f the film. An e x a c t d e t e r m i n a t i o n o f the p h a s e r e q u i r e s
25 that the signal p r o d u c e d by the film is c o m p a r a b l e in m a g n i t u d e to that o f the substrate. With X(3) o f c o n j u g a t e d organic systems typically t h r e e o r d e r s o f m a g n i t u d e larger t h a n t h a t o f fused silica, this is equivalent to a thickness o f the p o l y m e r i c film less t h a n 100 nm. The data w e r e finally fitted using the Simplex m e t h o d and the e x p r e s s i o n derived by Kajzar et al. [18]. Note that, since the thickness o f the films usually did not e x c e e d 100 nm, the p r e c i s e value o f the refractive i n d e x o f the c o n j u g a t e d p o l y m e r at the f u n d a m e n t a l and h a r m o n i c f r e q u e n c i e s has a negligible influence on the c a l c u l a t e d p h a s e and m a g n i t u d e o f X(3)(-3~o; o~, ~o, ~o).
3.2. Two-photon absorption M e a s u r e m e n t s of the dispersion of the t w o - p h o t o n coefficient fl w e r e p e r f o r m e d using the t u n a b l e ns-laser s o u r c e d e s c r i b e d a b o v e [ 19]. W e r e c o r d e d directly the t r a n s m i s s i o n T t h r o u g h a thick p o l y m e r i c s a m p l e as a f u n c t i o n o f the input p o w e r I and fitted the e x p e r i m e n t a l data to the e x p r e s s i o n [20]: T(/) -
To l + [3IL
(6)
A half-wave plate b e t w e e n two c r o s s e d polarizers was u s e d in o r d e r to v a r y the input intensity.
3.3. N o n l i n e a r i n t e r f e r o m e t r y An intensity-driven c h a n g e in the refractive index is always related to a c o r r e s p o n d i n g n o n l i n e a r p h a s e shift after a finite p r o p a g a t i o n length: A~b(/) = ko 1An(~)
(7)
with An(/) =n2I
(8)
for a Kerr-type nonlinearity. T h e i n t e r f e r o m e t r i c d e t e r m i n a t i o n of such a p h a s e c h a n g e can be a c c o m p l i s h e d with high a c c u r a c y and readily related to the n o n l i n e a r coefficient he, p r o v i d e d that electronic and t h e r m a l effects can be s e p a r a t e d . F u r t h e r m o r e , t w o - p h o t o n a b s o r p t i o n can be m o n i t o r e d s e p a r a t e l y b y m e a s u r i n g the t r a n s m i s s i o n t h r o u g h the s a m p l e as a f u n c t i o n o f input power. T h e r m a l p r o b l e m s are r e d u c e d or eliminated b y using s h o r t p u l s e s s e p a r a t e d in time b y m o r e t h a n the thermal r e l a x a t i o n constant. The i n d e x s a t u r a t i o n can b e e v a l u a t e d and t a k e n into a c c o u n t in the data analysis. In o u r e x p e r i m e n t s a c h a n n e l w a v e g u i d e o f a n o n l i n e a r material was p l a c e d in one a r m of a M a c h - Z e h n d e r i n t e r f e r o m e t e r [21 ]. As a high p o w e r s o u r c e we u s e d a m o d e - l o c k e d Nd:YAG laser that p r o v i d e d 60 p s pulses at 1.319 t~m at 76 MHz. The i n t e r f e r e n c e fringes, f o r m e d after the two interf e r o m e t e r a r m s w e r e c o m b i n e d , w e r e e x p a n d e d and a small fraction was d e t e c t e d by a 3 0 0 /zm e InGaAs p h o t o d i o d e . A 4 Hz periodic m o d u l a t i o n o f t h e optical p a t h length in one a r m of the i n t e r f e r o m e t e r i n d u c e d a sinusoidal m o d u l a t i o n o f the fringe pattern, that in t u r n c a u s e d an oscillation o f the signal at the p h o t o d i o d e . An e l e c t r o - o p t i c pulse e x t r a c t i o n s y s t e m was u s e d
26
to provide single pulses at 1 kHz for thermal measurements. In both arrangements, the peak intensity reached 200 MW/cm2 in the waveguide.
3.4 Nonlinear grating coupling The geometry of a grating coupler is shown in Fig. 2. A periodic perturbation in the plane of the waveguide provides the appropriate m o m e n t u m along the propagation direction to match the wavevector kx = k0 sin 0 of an incident beam to fl of the confined guided wave throughout the coupling region. In a waveguide with a nonlinear index this condition is altered during the coupling process and along the coupling region, due to the dependence of the guided-wave wavevector on the index of the film forming the guide itself. In a grating coupler realized in a nonlinear waveguide, therefore, the coupling efficiency and the angle for optimum excitation become powerdependent, and such effects can be related to the magnitude and sign of n2. The role of thermal effects can be inferred by the pulse shape in time after the coupler and by analyzing the coupler operation when employing pulses of different duration. TPA mainly affects throughput measurements, i.e., measurements of the guided light after a finite propagation length. The pertinent equations from coupled-mode theory have been analyzed in detail elsewhere [22-24]. In our setup [25], we employed 30 ps pulses from a flashlamp pumped, pulsed actively/passively mode-locked Nd:YAG laser operating at 1064 um at a 10 Hz repetition rate. Our samples had two grating couplers for input and output of a guided-wave field, and during the experiments we monitored both the light transmitted through the input grating and the light out-coupled at the second grating after propagation (typically 1 cm) Z
f z/ n c
ns x~
Fig. 2. Layout o f the nonlinear grating c o u p l i n g geometry. The n o n l i n e a r m e d i u m of t h i c k n e s s h and linear refractive index nf is coated o n t o a s u b s t r a t e having refractive index ns. A grating s t r u c t u r e o f periodicity A is etched into the s u r f a c e of the s u b s t r a t e . The incident b e a m is characterized by the intensity I, the s p o t size w o and w a v e v e c t o r k0, w h e r e a s fl" d e n o t e s the p r o p a g a t i o n c o n s t a n t of the confined waveguide m o d e m . In o u r e x p e r i m e n t s we u s e d a grating periodicity of 0.6 ]zm and a s p o t size of 3.5 ram.
27 as a function of input power. The two output signals are affected to different extents by dispersive (n2) and absorptive (TPA) nonlinearities [24].
4. M a t e r i a l s
All polymeric materials that we addressed in our experiments are soluble, thus allowing the fabrication of amorphous, good quality films by spin-coating or casting. Unlike other polydiacetylenes (PDA) that can be grown only in crystalline form, poly(4-BCMU) is soluble in common organic solvents, allowing the fabrication of low-loss waveguide structures [26, 27]. Optical and electrical probes applied to PDA include photoconductivity [28], THG [29, 30], threewave mixing [31], transient absorption [32, 33], electro-absorption [30] and DFWM [34]. These investigations showed the excitonic nature of the main absorption peak. Two-photon levels slightly below and between 4000 to 9000 c m - i above this peak have been located in different experiments. Nevertheless none of these experiments found both 1A~ states simultaneously. Poly(3-alkylthiophene)s are soluble forms of the insoluble polythiophene. The pronounced thermochroism in solution can be interpreted due to confomml defects along the backbone [35], created by twists between neighboring thiophene units. These may also explain the broad inhomogeneous absorption band. Various THG measurements on this class of materials showed contradictory results [36-39] and no clear evidence for the dominant two-photon level could be found. DFWM measurements [40-43] showed sub-picosecond time response and spectral behavior, that could be explained by an inhomogeneously broadened absorption line. Side-chain polymers containing 4-dialkylamino-4'-nitrostilbene (DANS) as the active moiety were initially developed for electro-optic applications [44]. Nevertheless the strong absorption in the visible peaking around 430 nm should initiate strong third-order nonlinearities. Because of the broken symmetry, no hidden two-photon levels should exist and the two-photon spectrum is expected to follow the shape of the linear absorption peak.
5. R e s u l t s a n d d i s c u s s i o n
5.1. P oly (4-BCMU) a n d poly (3-alkylthiophene) The experimental results of the magnitude and phase of X(3)(-3w; (o, w, o~) of poly(4-BCMU) relative to fused silica are shown in Fig. 3. The magnitude shows a broad maximum around 1500 nm that is due to the three-photon resonance with the excitonic absorption. No pronounced feature that can be associated with a two-photon resonance is visible. The interaction with the two-photon state is strongly reflected in the phase of X(3)(-3w~ co, oJ, w). While a simple two-level model including only the ground state and the l lBu state predicts a negative nonresonant X(a), the measured values
28
50001 4-LEVEL3-AL=EVEL ;000 .
.
.
.
.
.
.
.
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3000 > 0
2000
C12 1000-
(a)
o 4OO
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(D -C}
...... 3-LEVEL (A:-3OOOcrn-') - - - 3-LEVEL (A'=+4500cm-') ............. ~ 4--LEVEL (A=-3OOOcmU-1, -- . 5':+4500cm-') 300
'.,
i
,,
200 0 (,3 E]
~O_
I O0
900
(b)
1100
WAVELENGTH (nm) 1300
1500
1700
1900
Fig. 3. E x p e r i m e n t a l l y m e a s u r e d magnitude (a) and p h a s e (b) o f X ( m ( - 3w; ~, a~, eo) relative to fused silica as a function of fundamental w a v e l e n g t h for a 3 0 n m t h i c k film o f poly(4BCMU). The solid and broken lines r e p r e s e n t theoretical fits to t h e three- and four-level m o d e l s s h o w n in Fig. 1 [17].
c o n v e r t to a p h a s e c l o s e to 0 °, e m p h a s i z i n g an e x c i t a t i o n p a t h w a y that i n c l u d e s higher l o c a t e d t w o - p h o t o n levels as the i n t e r m e d i a t e state [45]. This results s h o u l d be c o m p a r e d to t h e d i s p e r s i o n o f t h e TPA coefficient fl that is s h o w n in Fig. 4. Both the THG and TPA results w e r e fitted by applying the m e t h o d o f averaging by Orr and Ward [ 13 ] for a three- and four-level m o d e l , respectively. A m a g n i t u d e o f 3.11 x 10 -14 e.s.u. [46] and a p h a s e o f 0 ° w a s a s s u m e d for )((3)(_ 3(o; ~o, co, w) in f u s e d silica. The transition-dipole m o m e n t ~ug w a s
29 6000
5000
40OO (..9
E o
5000
2000
1000
0 700
900
1100
1500
WAVELENGTH (nm)
1500
Fig. 4. Two-photon absorption spectrum for a 70 /~m thick sample of poly(4-BCMU). The solid line shows the predictions of the four-level model [17]. TABLE 1 Fitting parameters used in the four-level fit for both THG and TPA data. The values for Am,x, Fug and p~g were calculated from the linear absorption data. The linewidth (Fg,g= Fg-g),transition dipole moments (~ug', P*u~')and energy differences (zi, A') were obtained from the least-square fits to the experimental data
(nm) Po~(4-BCMU) THG 545 TPA 545
(cm - 1)
(cm - 1)
(cm - l)
(cm- 1)
(debye)
(debye)
(debye)
4000 4000
1550 1550
-3000 -2000
4500 4500
13 13
12.5 7.5
17.5 17.5
3000
- 500
5000
17
6.0
11.5
Po~(3-decylthiophene) THG 510 3000
calculated by integrating the visible absorption line (assuming local field c o n t r i b u t i o n s t o b e n e g l i g i b l e ) . In t h e c a l c u l a t i o n s p u b l i s h e d o r i g i n a l l y [ 1 7 , 19] t h e p r o d u c t o f t h e l o c a l f i e l d f a c t o r s in e q n . ( 5 ) w a s s e t e q u a l t o s i x a n d n o f r e q u e n c y d e g e n e r a c y f a c t o r w a s i n c l u d e d ( t h i s is e q u i v a l e n t t o s e t t i n g the local field factor equal to one and using the frequency degeneracy factor o f s i x ) . T h e f i t t e d p a r a m e t e r s f o r /Zug,, /~u~, A a n d A' a r e s u m m a r i z e d in T a b l e 1. T h e g o o d a g r e e m e n t b e t w e e n t h e p a r a m e t e r s e v a l u a t e d f r o m b o t h m e a s u r i n g t e c h n i q u e s is r e m a r k a b l e . T h e f i t t e d v a l u e s f o r tzug, a n d /.Lug- a l s o d e m o n s t r a t e t h e d o m i n a n c e o f t h e n o n l i n e a r i t y b y t h e h i g h e r l y i n g m~Ag state as predicted by theory. A s i m i l a r l e v e l s t r u c t u r e c a n b e e x t r a c t e d f r o m t h e d i s p e r s i o n of)((3)( _ 3o~; co, ~o, oJ) o f p o l y ( 3 - d e c y l t h i o p h e n e ) t h a t is p l o t t e d in F i g . 5 t o g e t h e r w i t h
30 600
2000-
===== ~--
> o_
{3
1500
Experimenfal
- -
4-level
fit
- - ........
3-level 3-level
fit fit
v
DATA A=-1500cm-1 A=+7OOOcm-1
500 X
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• • • • • Experimenfo] ........ 3-level flf --3-level fit - 4-level
DATA A=+7OOOcrn-1 A=-1500cm-1
400
W U3 1000
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200 500 -
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WAVELENGTH (nm)
0 ,. 700
j,,
1900
(b)
.
.
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.
.
,
.
.
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.
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1900
WAVELENGTH (nrn)
Fig. 5. Magnitude (a) and p h a s e (b) of ~ a ) ( _ 3w; co, ~, ~) for a 50 n m thick film of p o l y ( 3 d e c y l t h i o p h e n e ) relative to that of fused silica. Experimental data points and theoretical fits to the three- and four-level m o d e l s are s h o w n [15].
theoretical calculations using the three- and four-level models as described above. The shoulder around to= 1100 nm in the dispersion of )((3)(_ 3(o; (o, to, oJ) clearly indicates a two-photon resonance with a state below the 1 lBu state. The corresponding fit parameters are summarized in Table 1. Again the best agreement between theory and the experimental data points is only possible within the four-level model, although the dispersion is dominated by the interaction with the higher energy mlAg. The interferometric measurements on poly(4-BCMU) channel waveguides yielded an electronic contribution to n 2 ( e l e c t r o n i c ) = 5 × 1 0 - s cm2/MW, an estimated thermal contribution n2(thermal) = - 8 x 1 0 - ' 1 cm2/MW and a twophoton coefficient /it < 0 . 2 cm/GW. Note, in particular, the positive sign of the electronic contribution in correspondence to the results of the THG experiments. The nonlinear index coefficient n2 of around 5 × 1 0 - a cm~./MW (or 150 times n~. of fused silica) is distinctly lower than a nonresonant value of about 1000 times the nonlinear susceptibility of fused silica, predicted from the THG results at 1904 /zm. The low value for fl suggests that the actual linewidth of the low-lying two-photon state is smaller than that assumed for the four-level fit. Although the electronic contribution is considerably larger than the thermo-optic effect, the latter accumulates at high repetition frequencies due to its long relaxation time in t h e / z s timescale and therefore dominates the intensity-dependent phase shift if no pulse selection is used.
5.2. DANS side-chain p o l y m e r Figure 6 shows the magnitude and phase of )((a)(-3~o; w, w, w) as a function of the fundamental wavelength. Because of the broken symmetry, the dispersion can be explained within a simple two-level model [47].
31
2000 ....
no c a s c a d i n g cascading
1500
-~ lOOO
.k Of
500 -
i
(a)
0
500 1 "
---
400~
no
]-
cascading
cascading
d
300
'~
200
T
1°I° oi 800 .
(b)
.
I±~ .
.
1000
.
.
.
.
1200
.
.
.
.
1400
WAVELENGTH
.
.
.
1600
.
1800
2000 •
(nm)
Fig. 6. Magnitude (a) and p h a s e (b) o f X(a)(- 3to; to, to, to) a s a function of w a v e l e n g t h for a 75 n m thick film o f DANS s i d e - c h a i n p o l y m e r [51]. The solid line through the data p o i n t s is the theoretical fit explained further in the text.
Furthermore, the large second-order nonlinearity requires the inclusion of the local cascading effect [48]: 1 X(s)(-3to; to, w, to)= -~ Nf3'~fof'~f'~[,),(-3w; w, to, to) + 2 f l ( - 3 w ; 2w, to)cfl(-2to; w, w)]
(9)
32 6e 4
y ( - 3 t o ; to, oJ, to)= - ~
[ - / z ~ g D , l + P~ngA~ng 2 2 D 111 ]
2e3 2 fl(-2o~; to, w)= -~-/.£ngA/.tngD21 e3
(10)
2
fl(-3~o; 2o~, ~o)= ~ t~ngAtL.gD22 where N is the n um ber density of molecules, tLng is the transition dipole m o m e n t between the ground and first excited state, At~,g is the difference between the excited state and ground state dipole moments, often called mesomeric m o m e n t and the D terms are resonant denominators that have been calculated using the diagrammatic model [14]. We included a factor of six in the expression for T and two for f l ( - 2 t o ; to, to) as frequency degeneracy factors, f is the local field factor according to the Lorentz-Lorenz model: f~=
[n(to)l 2 + 2 3
(11)
and c the local field cascading factor [48]: 87r ([n(2~0)] 2 - 1)([n(2o012 + 2) c - -~ N 3[n(2~o)12
(12)
Because of the strong d e p e n d e n c e of these factors on the refractive index n at 2~o, we calculated the refractive index dispersion from a Kramers-Kronig analysis of the absorption spectrum. For the fit of the nonlinear data we assumed a num ber density of 1 × 1021 cm -2. The width (Fng=6000 cm -1) and position (Am~=450 nm) of the excited state were calculated from the absorption spectrum after correcting for dispersion effects. The value for the mesomeric m om ent was set to 18 debyes [49, 50]. In this case, the transition dipole m o m e n t /Zng is the only adjustable parameter. The fitted value of 7.8 debyes for /Z~g is in good a g r eemen t to the value of 8.4 debyes determined in solution, where local field effects can be included m or e precisely [50 ]. Contributions from cascading are clearly visible but smaller than suggested in a previous work [51]. In this work, the transition dipole m o m e n t tLng Was calculated as 14.5 debyes by integrating over the film absorption data (neglecting local field effects). No frequency degeneracy factor was used. The fit with A/~.g as the only adjustable parameter showed only fair agreement to the measured dispersion of X(3). The evaluated value for the mesomeric m o m e n t of 15 debyes is comparable to the literature value. A large cascading contribution similar to that generated by T alone was found. The discrepancy between these two a p p r o a c h e s demonstrates clearly how different assumptions on local field effects and the frequency degeneracy factor can alter the interpretation of the data. This is under further investigation.
33 LI-O • "A
00.9
v
o
.%:OOo,,.~
o~:
o
-
o
o
~0.8
E
~ 0.7 E0.6 © Zo.5
-10.80
~
OA~i~CA
Oo
ooooc .....
-10.56 -10.52 Incidence ongle
Ein=5 pJ Ein=350
-10.48 (deg)
Fig. 7. Normalized transmitted power through the input grating vs. angle of incidence for a DANS side-chain polymer waveguide at 5 and 350 p~l input intensity onto the grating. The lines are guides to the eye [25]. F i g u r e 7 s h o w s t h e n o r m a l i z e d t r a n s m i t t e d p o w e r t h r o u g h the first c o u p l i n g g r a t i n g as a f u n c t i o n of i n c i d e n c e angle in the n o n l i n e a r g r a t i n g c o u p l i n g e x p e r i m e n t s with 5 a n d 3 5 0 p~J i n p u t p o w e r s o n t o the grating. B o t h a shift of the o p t i m u m c o u p l i n g a n g l e a n d a d e c r e a s e in t h e c o u p l i n g efficiency c a n b e o b s e r v e d w h e n t h e p o w e r o f t h e incident b e a m is i n c r e a s e d . T h e detailed analysis o f b o t h t h e t r a n s m i t t e d a n d o u t - c o u p l e d signal yielded a n e l e c t r o n i c n o n l i n e a r r e f r a c t i v e i n d e x coefficient n~. = 7 × 10 -8 cm2/MW a n d the t w o - p h o t o n coefficient fl e q u a l to 1 - 2 c m / G W at 1064 n m [25]. The n o n l i n e a r i n d e x coefficient o f a r o u n d 2 0 0 t i m e s t h a t of f u s e d silica is in g o o d a g r e e m e n t to the T H G data. F u r t h e r m o r e , the v a l u e f o r fl is c o n s i s t e n t with the two-level m o d e l , w h e r e 2w is l o c a t e d j u s t in the tail of the visible absorption.
6. C o n c l u s i o n s T H G a n d TPA m e a s u r e m e n t s o n c o n j u g a t e d p o l y m e r s with c e n t r o - s y m m e t r i c s t r u c t u r e verified a four-level m o d e l including the g r o u n d state, t h e l o w e s t lying visible b a n d a n d t w o - p h o t o n s t a t e s l o c a t e d b e l o w a n d a b o v e this s t a t e to give the d o m i n a n t c o n t r i b u t i o n to the n o n l i n e a r s u s c e p t i b i l i t y X(3). The d i s p e r s i o n o f X(3)( - 3w; w, to, w) in the DANS side-chain p o l y m e r c o u l d be e x p l a i n e d a d e q u a t e l y with a two-level m o d e l including m i c r o s c o p i c c a s c a d i n g . Direct d e t e r m i n a t i o n of the i n t e n s i t y - d e p e n d e n t r e f r a c t i v e i n d e x n2 in t w o s y s t e m s s h o w e d n e a r - r e s o n a n t v a l u e s of the o r d e r o f 10 - s cm2/MW with low t w o - p h o t o n coefficients ft.
Acknowledgements W e t h a n k W. Krug, E. Miao a n d M. W. B e r a n e k o f t h e B o e i n g A e r o s p a c e a n d E n g i n e e r i n g High T e c h n o l o g y C e n t e r f o r s u p p l y i n g the s t r i p - l o a d e d PDA
34 s a m p l e , G . M e r e d i t h a n d D. D o n a l d o f D u p o n t f o r c o n s i d e r a b l e amounts of poly(4-BCMU), M. L e c l e r c a t t h e U n i v e r s i t y o f M o n t r e a l f o r t h e p o l y ( 3 decylthiophene) a n d W . H . G . H o r s t h u i s , G. R. M 6 h l m a n n , E . W . P. E r d h u i s e n of the Akzo Research Laboratories for the samples of DANS side-chain polymer.
References 1 J. P. Hermann and J. Ducuing, J. Appl. Phys., 45 (1974) 5100. 2 C. Sauteret, J.-P. Hermann, R. Frey, F. Prad~re, J. Ducuing, R. H. B a u g h m a n n and R. R. Chance, Phys. Rev. Lett., 35 (1976) 956. 3 G. I. Stegeman, C. T. Seaton and R. Zanoni, Thin Solid Films, 152 (1987) 231. 4 V. Mizrahi, K. W. DeLong, G. I. Stegeman, M. A. Saifi and M. J. Andrejco, Opt. Lett., 14 (1989) 1140. 5 K. Schulten, I. Ohmine and M. Karplus, J. Chem. Phys., 64 (1976) 4422. 6 J. W. Wu, J. R. Heflin, R. A. Norwwod, K. Y. Wong, O. Zamani-Khamiri, A. F. Garito, P. Kalyanaraman and J. Sounik, J. Opt. Soc: Am., Part B, 6 (1989) 707. 7 S. N. Dixit, D. Guo and S. Mazumdar, Mol. Cryst. Liq. Cryst., 194 (1991) 33. 8 C. Cojan, G. P. Agraval and C. Flytzanis, Phys. Rev. B, 15 (1977) 909. 9 G. P. Agraval, C. Cojan and C. Flytzanis, Phys. Rev. B, 17 (1978) 776. 10 F. Kajzar, I. R. Girling and I. R. Peterson, Thin Solid Films, 150 (1988) 209. 11 D. Neher, A. Kaltbeitzel, A. Wolf, C. Bubeck and G. Wegner, in J. L. Br~das and R. R. Chance (eds.), Conjugated Polymeric Materials, NATO ASI Series, Kluwer, Dordrecht, 1990, p. 387. 12 B. Kohler, J. Chem. Phys., 88 (1988) 2788 and refs. therein. 13 B. J. Orr and J. F. Ward, Mol. Phys., 20 (1971) 513. 14 T. K. Yee and T. K. Gustafson, Phys. Rev. A, 18 (1978) 18. 15 Y. Prior, IEEE J. Quantum Electron., QE-20 (1984) 37. 16 Y. R. Shen, Prinviples of Nonlinear Optics, Wiley, New York, 1984. 17 W. E. Torruellas, D. Neher, R. Zanoni, G. I. Stegeman, F. Kajzar and M. Leclerc, Chem. Phys. Lett., 175 (1990) 11. 18 F. Kajzar, J. Messier and R. Rosilio, J. AppL Phys., 50 (1986) 3040. 19 W. E. Torruellas, K. B. Rochford, R. Zanoni, S. Aramaki and G. I. Stegeman, Opt. Commun., 82 (1991) 94. 20 W. L. Smith, in M. J. W e b e r (ed.), CRC-Handbook of Laser Science and Technology, Vol. III, Part 1, CRC Press, Boca Raton, FL, 1986. 21 K. B. Rochford, R. Zanoni, G. I. Stegeman, W. Krug, E. Miao and M. W. Beranek, Appl. Phys. Lett., 58 (1991) 13. 22 G. M. Carter and Y. J. Chen, Appl. Phys. Lett., 42 (1983) 643. 23 G. Assanto, R. M. Fortenberry, C. T. Seaton and G. I. Stegeman, J. Opt. Soc. Am., Part B, 5 (1988) 432. 24 G. Assanto, M. B. Marques and G. I. Stegeman, J. Opt. Soc. Am., Part B, 8 (1991) 553. 25 M. B. Marques, G. Assanto, G. I. Stegeman, G. R. M6hlmann, E. W. P. Erdhuisen and W. H. G. Horsthuis, Appl. Phys. Lett., 58 (1991) 2613. 26 K. B. Rochford, R. Zanoni, Q. Gong and G. I. Stegeman, Appl. Phys. Lett., 55 ( 1 9 8 9 ) 1161. 27 P. D. Townsend, J. L. Jackel, G. L. Baker, J. A. Shelbourne III and S. Etemad, Appl. Phys. Lett., 55 (1989) 1829. 28 K. Lochner, H. Baessler, B. Tieke and G. Wegner, Phys. Status Solidi (b), 88 (1978) 653. 29 F. Kajzar and J. Messier, Polym. J., 10 (1987) 275. 30 T. Hasagawa, K. Ishikawa, T. Kanetake, T. Koda, T. Takeda, H. Kobayashi and K. Kubodera, Chem. Phys. Lett., 171 (1990) 239.
35 31 R. R. Chance, M. L. Shand, C. Hogg and R. Silbey, Phys. Rev. B, 22 (1980) 3540. 32 M. Lequime and J. P. Hermann, Chem. Phys., 26 (1977) 431. 33 B. I. Greene, J. Orenstein, R. R. Millard and L. R. Williams, Phys. Rev. Lett., 58 (1987) 2750. 34 G. M. Carter, J. Opt. Sci. Am., Part B, 4 (1987) 1018. 35 O. Inganfis, W. R. Salaneck, J.-E. 0 s t e r h o l m and J. ~ a s k o , Synth. Met., 22 (1988) 395. 36 F. Kajzar, J. Messier, C. Sentein, R. L. Elsenbaumer and G. G. Miller, Proc. SPIE, 1147 (1989) 36. 37 V. H. Houlding, A. Nahata, J. T. Yardley and R. L. Elsenbaumer, Chem. Mater., 2 (1990) 169. 38 D. Neher, A. Wolf, M. Leclerc, A. Kaltbeitzel, C. Bubeck and G. Wegner, Synth. Met., 37 (1990) 249. 39 T. Sugiyama, T. Wada and H. Sasabe, Synth. Met., 28 (1989) C323. 40 H. J. Byrne and W. Blau, Synth. Met., 32 (1990) 229. 41 R. Dorsenville, L. Yang, R. R. Alfano, R. Zamboni, R. Danieli, R. Ruani and C. Taliani, Opt. Lett., 14 (1989) 1321. 42 P. N. Prasad, J. Swiatkiewicz and J. Pileger, Mol. Cryst. Liq. Cryst., 160 (1988) 53. 43 C. Bubeck, A. Kaltbeitzel, A. Grund and M. Leclerc, Chem. Phys., 154 (1991) 343. 44 G. R. M6hlmann, W. H. G. Horsthuis, C. P. J. M. van der Vorst, A. McDonach, M. Copeland, C. Duchet, P. Fabre, M. B. J. Diemeer, E. S. Trommel, F. M. N. Suyten, P. Van Daele, E. Van Tomme and R. Baets, Proc. SPIE, 1147 (1989) 245. 45 F. Kajzar and J. Messier, Phys. Rev. A, 32 (1985) 2352. 46 A. F. Garito, J. R. Heflin, K. Y. Wong and O. Zamani-Khamiri, in R. A. Hann and D. Bloor (eds.), Organic Materials f o r Nonlinear Optics, The Royal Society of Chemistry, London, 1989, p. 16. 47 C. W. Dirk and M. G. Kuzyk, Phys. Rev. B, 41 (1990) 1636. 48 G. R. Meredith and B. Buchalter, J. Chem. Phys., 78 (1983) 1938. 49 W. Liptay, Angew. Chem., Int. Ed. Engl., 8 (1969) 177. 50 M. S. Paley, J. M. Harris, H. Looser, J. C. Baumert, G. C. Bjorklund, D. Jundt and R. J. Twieg, J. Org. Chem., 54 (1989) 3774. 51 W. E. Torruellas, R. Zanoni, G. I. Stegeman, G. R. M6hlmann, E. W. P. Erdhuisen and W. H. G. Horsthuis, J. Chem. Phys., 94 (1991) 6851.
21
Nonlinear optical probes of conjugated polymers* D. Neher**, W. E. Torruellas***, K. B. Rochford*, M. B. Marques**, R. Zanonittt, G. Assanto and G. I. Stegeman Center f o r Research in Electro-Optics and Lasers, University of Central Florida, 12424 Research Parkway, Orlando, FL 32826 (USA)
Abstract Nonlinear optical properties of conjugated polymers can be measured using various techniques, including third-harmonic generation, two-photon absorption, nonlinear grating coupling and interferometry. These methods will be compared with regard to their suitability for obtaining specific parameters. We illustrate the application of these techniques to the study of ~--conjugated polymeric systems, such as poly(4-BCMU), poly(3-decylthiophene) and 4-dialkylamino-4'-nitrostilbene (DANS) side-chain polymer, all of them regarded as candidates for the realization of all-optical switching devices, and outline relevance and limits of each technique.
1. I n t r o d u c t i o n Since the experimental work of Hermann and Ducuing on finite polyenes [1 ], there has been an increasing interest in investigating the third-order nonlinear susceptibility )((3) of ~--electron conjugated organic molecules. Using third-harmonic generation Sauteret et al. measured values of X(3) exceeding 10 -x° e.s.u, in polydiacetylene (PDA) crystals [2], and numerous later experiments have established the suitability of conjugated organic materials for the realization of ultrafast switching devices in an integrated-optical format. In addition to short response times and large third-order nonlinearities, many of these polymers, in fact, present physical and chemical properties which allow the fabrication of guiding (planar) structures where the optical excitation can be optimized and maintained at high levels over long propagation distances [3 ]. All-optical devices rely on an intensity-dependent index of refraction (or optical Kerr effect), usually expressed as *Invited paper. **Present address: Max-Planck-Institut ftir Polymerforschung, Ackermannweg 10, 6500 Mainz, Germany. ***Present address: Raytheon Research Division, 131 Spring Street, Lexington, MA 02173, USA. tpresent address: Dylor Corporation, RD5, P.O. Box D, Ligonier, PA 15658, USA. ttpresent address: Centro de Fisica da Universidade de Porto (INIC), 4000 Porto, Portugal. *ttPresent address: Center for Laser Research, Oklahoma State University, Stillwater, OK 74078, USA.
0379-6779/92/$5.00
© 1 9 9 2 - Elsevier Sequoia. All rights reserved
22 (1)
n=no +neI
where the nonlinear refractive index coefficient n2 is related to the susceptibility X(a)(- w; ~o, - ~o, to) by 3 n2 - 4no2eo c )((3)( _ to; to, - ~o, w)
(2)
A variation in the refractive index with intensity leads to a nonlinear phase shift experienced by the optical wave upon propagation, and it is on the size of the obtainable phase shift that all-optical switches are based [3]. However, various other nonlinear effects are usually associated with the Kerr dependence in eqn. (1), among them index saturation, two-photon absorption (TPA) and thermo-optic effect. For example, recent investigations demonstrated that TPA can limit all-optical switching [4]. It is therefore of particular importance to investigate all these properties when characterizing organic materials for all-optical switching applications, and to compare them with accepted theoretical models. Various techniques are available for the nonlinear characterization of third-order materials. Unfortunately, none of them is suited to provide a complete set of information on a given material and distinct aspects of the optical nonlinearity have to be probed with different techniques. In the following we will briefly review four of these techniques: third-harmonic generation (THG), two-photon absorption, nonlinear interferometry and nonlinear grating coupling. Finally, the results will be discussed with the aid of simple two- and four-level models which properly describe most v-electron conjugated systems.
2. T h e o r e t i c a l
models
The macroscopic nonlinearity results from an orientational average of the microscopic hyperpolarizibflity. For the case of a one-dimensional 7relectron conjugation along the axis if, the general expression reads: X!3.~l(- w; ~o~, a~, to3)=
(3)
In isotropic materials, the orientational average gives a factor of 1/5. Furthermore in eqn. (3) we assumed the local field tensor re, to be diagonal in the molecular frame. One approach to explaining T in conjugated polymers starts from calculations on finite-size conjugated model compounds like polyenes. These molecules belong to the centro-symmetric C2h group. Here the electronic states have either even parity (~Au states), or odd parity (~Bu states) and the ground state configuration is always SAg. Theoretical calculations, that used a Hamiltonian extended by electron--electron correlation effects [5-7], showed large transition dipole moments between I'A~ and llBu, the lowest lying one-photon allowed transition and from l'Bu and a higher lying two-
23
photon state m~Ag. With increasing length of the conjugated system, this two-photon state approaches the visible lZBu band [7]. Such a three-level model is in quantitative agreement with early calculations on 1D 7r-conjugated polymers using the simple noninteracting nearest-neighbor Htickel Hamiltonian [8, 9]. These calculations suggested that the strong interband transition to the edge of the conduction band and successive intraband transitions inside the conduction band are responsible for the large nonresonant nonlinearity in these polymers, which increases dramatically with the inverse of the sixth power of the gap energy EG. These relations seemed to be verified in various experiments [2, 10, 11]. Close to resonance, the 2lAg state located slightly below the visible 1 ~Bu state [12] m a y contribute to the interaction pathway, although the transition dipole m o m e n t with the 1 iBu state is considerably smaller than that between llBu and m~Au. In conclusion, a three- or four-level system (as shown in Fig. 1) may be sufficient to explain the low frequency dispersion of the nonlinear susceptibility in conjugated polymers. Different treatments of the semiclassical perturbation theory in a discrete level system have been published, namely, an averaging method [13] or a diagrammatic analysis [14]. Nevertheless, both procedures lead to similar expressions [15], in particular in the nonresonant regime, and contain the same dominant terms in the near-resonant case, i.e.: ) ( 3 ( - 0); 031, 0)2, 0)3)(X
e4 _- ~g~--/x_~,~,xjg_,______~x/~__~_g --5 h u ~ ' (0)- 0)~,g+ iFu,g)(~o~+ 0)1 - 0)g,g+ iFg,g)(0)l - ~%g+ iFug)
(4)
The sum extends over all excited states u=nIBu and g the even parity states, including the ground state itself. Note that all transitions from the ground level to lAg states are one-photon-forbidden. gl! ,A I 1.1
A
,A g ! tgu
3-
L
~
4-I
Fig. 1. Schematic diagram of the three- and four-level models, g denotes the ground state (l~Ag) of even parity, g' and ge, excited states with the same parity and u the lowest state with odd symmetry (11B~). The/x t e r m s are transition dipole moments. A and A' are respectively the energy difference between the I IB~ state and the lowest excited two-photon states 2JAg and the second excited two-photon state m~Ag.
24
3. N o n l i n e a r optical m e t h o d s 3.1. T h i r d - h a r m o n i c
generation
T h i r d - h a r m o n i c g e n e r a t i o n (THG) is widely u s e d to d e t e r m i n e the nonlinear optical susceptibility X(3)(- 3w; co, w, to) of materials b o t h in the solid p h a s e and in solution. THG is insensitive to the t h e r m o - o p t i c effect and, far f r o m r e s o n a n c e s , the value o f X(a)( - 3w; w, oJ, w) can be u s e d to estimate n2, b u t an a c c u r a t e e x t r a p o l a t i o n is v e r y difficult w i t h o u t p r e c i s e i n f o r m a t i o n on all the r e s o n a n t levels in the molecule. The relative simplicity o f this m e t h o d o p e n s the w a y for wide-range tunability of the f u n d a m e n t a l w a v e l e n g t h in o r d e r to d e t e r m i n e the spectral dispersion o f X(3)( - 3w; w, w, ~o). Tunable THG n e a r the e l e c t r o n i c r e s o n a n c e s of the material e n a b l e s o n e to scan t h e electronic levels that p r e s u m a b l y d o m i n a t e the n o n l i n e a r p r o p e r t i e s . In b o t h theoretical m o d e l s outlined a b o v e [13, 14], the n e a r - r e s o n a n t X(3)(-3w; w, w, ~o) f r e q u e n c y d e p e n d e n c e is d o m i n a t e d by only o n e term, i.e., in the fourlevel model: X(3)( - 3oJ; o~, oJ, o~)= 6Ne4
~-~ f
3~
~ 3 ]P~gl2[~ug'lz I f ]' ~g, (3eo-eOug+i/'ug)(2W-Wg,g~-iFg,g)(W-O~g+iFug)
(5)
The s u m m a t i o n e x t e n d s o v e r the g r o u n d state g and the d o m i n a n t e x c i t e d t w o - p h o t o n states and u is the d o m i n a n t o n e - p h o t o n level. While the transition dipole m o m e n t s Pug, f r e q u e n c i e s O~ugand b a n d w i d t h Fug are directly accessible via linear absorption, values for ~ug,, Wg,g and /'g,g can be d e d u c e d b y a fit of the e x p e r i m e n t a l data for X¢3)(-3w; w, w, w). W e included a f r e q u e n c y d e g e n e r a c y f a c t o r of six in eqn. (5) that a p p e a r s w h e n the 48 different t e r m s for T(-oJ4; w3, we, ~o,) c o n v e r t into eight different t e r m s with d e g e n e r a c y six for T ( - 3 w ; w, oJ, o~). This f a c t o r was s u g g e s t e d r e c e n t l y b y Shen [16], although we n e v e r f o u n d it to be u s e d in the data evaluation in c o m m o n literature and it m a y be c a n c e l e d out b y an a v e r a g i n g f a c t o r of 1/3! [15]. In the c u r r e n t setup [17l all THG m e a s u r e m e n t s w e r e p e r f o r m e d in t r a n s m i s s i o n on thin p o l y m e r films spun or cast o n t o f u s e d silica substrates. A Q-switched Nd:YAG laser, g e n e r a t i n g 10 ns pulses at 10 Hz, was f r e q u e n c y doubled to p u m p a dye laser. D o w n - c o n v e r s i o n of the dye laser light in LiIO3 c o v e r e d the 1 . 4 5 - 1 . 7 3 ~ m wavelength region. W a v e l e n g t h s b e t w e e n 1.22 and 1.45 ~ m w e r e o b t a i n e d by Raman shifting the dye laser s o u r c e in a 1 m long He cell. With the same Raman cell we c o n v e r t e d the f u n d a m e n t a l and the s e c o n d h a r m o n i c of the Nd:YAG to 1906, 956, 1367 and 1567 nm. Pulses o f energies ranging b e t w e e n 25 and 2 5 0 p J w e r e f o c u s e d with a lens ( f = 20 cm) o n t o the sample, m o u n t e d on a c o m p u t e r - c o n t r o l l e d r o t a t i o n stage inside a 200 m T o r r v a c u u m cell. The h a r m o n i c light g e n e r a t e d t h r o u g h the sample was d e t e c t e d and r e c o r d e d as a function of the i n c i d e n c e angle. Both the m a g n i t u d e and p h a s e o f X(3)( - 3w; to, w, w) c o u l d be e x t r a c t e d by r e p e a t i n g the e x p e r i m e n t s at the same location on the s u b s t r a t e b u t a f t e r c o m p l e t e removal o f the film. An e x a c t d e t e r m i n a t i o n o f the p h a s e r e q u i r e s
25 that the signal p r o d u c e d by the film is c o m p a r a b l e in m a g n i t u d e to that o f the substrate. With X(3) o f c o n j u g a t e d organic systems typically t h r e e o r d e r s o f m a g n i t u d e larger t h a n t h a t o f fused silica, this is equivalent to a thickness o f the p o l y m e r i c film less t h a n 100 nm. The data w e r e finally fitted using the Simplex m e t h o d and the e x p r e s s i o n derived by Kajzar et al. [18]. Note that, since the thickness o f the films usually did not e x c e e d 100 nm, the p r e c i s e value o f the refractive i n d e x o f the c o n j u g a t e d p o l y m e r at the f u n d a m e n t a l and h a r m o n i c f r e q u e n c i e s has a negligible influence on the c a l c u l a t e d p h a s e and m a g n i t u d e o f X(3)(-3~o; o~, ~o, ~o).
3.2. Two-photon absorption M e a s u r e m e n t s of the dispersion of the t w o - p h o t o n coefficient fl w e r e p e r f o r m e d using the t u n a b l e ns-laser s o u r c e d e s c r i b e d a b o v e [ 19]. W e r e c o r d e d directly the t r a n s m i s s i o n T t h r o u g h a thick p o l y m e r i c s a m p l e as a f u n c t i o n o f the input p o w e r I and fitted the e x p e r i m e n t a l data to the e x p r e s s i o n [20]: T(/) -
To l + [3IL
(6)
A half-wave plate b e t w e e n two c r o s s e d polarizers was u s e d in o r d e r to v a r y the input intensity.
3.3. N o n l i n e a r i n t e r f e r o m e t r y An intensity-driven c h a n g e in the refractive index is always related to a c o r r e s p o n d i n g n o n l i n e a r p h a s e shift after a finite p r o p a g a t i o n length: A~b(/) = ko 1An(~)
(7)
with An(/) =n2I
(8)
for a Kerr-type nonlinearity. T h e i n t e r f e r o m e t r i c d e t e r m i n a t i o n of such a p h a s e c h a n g e can be a c c o m p l i s h e d with high a c c u r a c y and readily related to the n o n l i n e a r coefficient he, p r o v i d e d that electronic and t h e r m a l effects can be s e p a r a t e d . F u r t h e r m o r e , t w o - p h o t o n a b s o r p t i o n can be m o n i t o r e d s e p a r a t e l y b y m e a s u r i n g the t r a n s m i s s i o n t h r o u g h the s a m p l e as a f u n c t i o n o f input power. T h e r m a l p r o b l e m s are r e d u c e d or eliminated b y using s h o r t p u l s e s s e p a r a t e d in time b y m o r e t h a n the thermal r e l a x a t i o n constant. The i n d e x s a t u r a t i o n can b e e v a l u a t e d and t a k e n into a c c o u n t in the data analysis. In o u r e x p e r i m e n t s a c h a n n e l w a v e g u i d e o f a n o n l i n e a r material was p l a c e d in one a r m of a M a c h - Z e h n d e r i n t e r f e r o m e t e r [21 ]. As a high p o w e r s o u r c e we u s e d a m o d e - l o c k e d Nd:YAG laser that p r o v i d e d 60 p s pulses at 1.319 t~m at 76 MHz. The i n t e r f e r e n c e fringes, f o r m e d after the two interf e r o m e t e r a r m s w e r e c o m b i n e d , w e r e e x p a n d e d and a small fraction was d e t e c t e d by a 3 0 0 /zm e InGaAs p h o t o d i o d e . A 4 Hz periodic m o d u l a t i o n o f t h e optical p a t h length in one a r m of the i n t e r f e r o m e t e r i n d u c e d a sinusoidal m o d u l a t i o n o f the fringe pattern, that in t u r n c a u s e d an oscillation o f the signal at the p h o t o d i o d e . An e l e c t r o - o p t i c pulse e x t r a c t i o n s y s t e m was u s e d
26
to provide single pulses at 1 kHz for thermal measurements. In both arrangements, the peak intensity reached 200 MW/cm2 in the waveguide.
3.4 Nonlinear grating coupling The geometry of a grating coupler is shown in Fig. 2. A periodic perturbation in the plane of the waveguide provides the appropriate m o m e n t u m along the propagation direction to match the wavevector kx = k0 sin 0 of an incident beam to fl of the confined guided wave throughout the coupling region. In a waveguide with a nonlinear index this condition is altered during the coupling process and along the coupling region, due to the dependence of the guided-wave wavevector on the index of the film forming the guide itself. In a grating coupler realized in a nonlinear waveguide, therefore, the coupling efficiency and the angle for optimum excitation become powerdependent, and such effects can be related to the magnitude and sign of n2. The role of thermal effects can be inferred by the pulse shape in time after the coupler and by analyzing the coupler operation when employing pulses of different duration. TPA mainly affects throughput measurements, i.e., measurements of the guided light after a finite propagation length. The pertinent equations from coupled-mode theory have been analyzed in detail elsewhere [22-24]. In our setup [25], we employed 30 ps pulses from a flashlamp pumped, pulsed actively/passively mode-locked Nd:YAG laser operating at 1064 um at a 10 Hz repetition rate. Our samples had two grating couplers for input and output of a guided-wave field, and during the experiments we monitored both the light transmitted through the input grating and the light out-coupled at the second grating after propagation (typically 1 cm) Z
f z/ n c
ns x~
Fig. 2. Layout o f the nonlinear grating c o u p l i n g geometry. The n o n l i n e a r m e d i u m of t h i c k n e s s h and linear refractive index nf is coated o n t o a s u b s t r a t e having refractive index ns. A grating s t r u c t u r e o f periodicity A is etched into the s u r f a c e of the s u b s t r a t e . The incident b e a m is characterized by the intensity I, the s p o t size w o and w a v e v e c t o r k0, w h e r e a s fl" d e n o t e s the p r o p a g a t i o n c o n s t a n t of the confined waveguide m o d e m . In o u r e x p e r i m e n t s we u s e d a grating periodicity of 0.6 ]zm and a s p o t size of 3.5 ram.
27 as a function of input power. The two output signals are affected to different extents by dispersive (n2) and absorptive (TPA) nonlinearities [24].
4. M a t e r i a l s
All polymeric materials that we addressed in our experiments are soluble, thus allowing the fabrication of amorphous, good quality films by spin-coating or casting. Unlike other polydiacetylenes (PDA) that can be grown only in crystalline form, poly(4-BCMU) is soluble in common organic solvents, allowing the fabrication of low-loss waveguide structures [26, 27]. Optical and electrical probes applied to PDA include photoconductivity [28], THG [29, 30], threewave mixing [31], transient absorption [32, 33], electro-absorption [30] and DFWM [34]. These investigations showed the excitonic nature of the main absorption peak. Two-photon levels slightly below and between 4000 to 9000 c m - i above this peak have been located in different experiments. Nevertheless none of these experiments found both 1A~ states simultaneously. Poly(3-alkylthiophene)s are soluble forms of the insoluble polythiophene. The pronounced thermochroism in solution can be interpreted due to confomml defects along the backbone [35], created by twists between neighboring thiophene units. These may also explain the broad inhomogeneous absorption band. Various THG measurements on this class of materials showed contradictory results [36-39] and no clear evidence for the dominant two-photon level could be found. DFWM measurements [40-43] showed sub-picosecond time response and spectral behavior, that could be explained by an inhomogeneously broadened absorption line. Side-chain polymers containing 4-dialkylamino-4'-nitrostilbene (DANS) as the active moiety were initially developed for electro-optic applications [44]. Nevertheless the strong absorption in the visible peaking around 430 nm should initiate strong third-order nonlinearities. Because of the broken symmetry, no hidden two-photon levels should exist and the two-photon spectrum is expected to follow the shape of the linear absorption peak.
5. R e s u l t s a n d d i s c u s s i o n
5.1. P oly (4-BCMU) a n d poly (3-alkylthiophene) The experimental results of the magnitude and phase of X(3)(-3w; (o, w, o~) of poly(4-BCMU) relative to fused silica are shown in Fig. 3. The magnitude shows a broad maximum around 1500 nm that is due to the three-photon resonance with the excitonic absorption. No pronounced feature that can be associated with a two-photon resonance is visible. The interaction with the two-photon state is strongly reflected in the phase of X(3)(-3w~ co, oJ, w). While a simple two-level model including only the ground state and the l lBu state predicts a negative nonresonant X(a), the measured values
28
50001 4-LEVEL3-AL=EVEL ;000 .
.
.
.
.
.
.
.
-,ooo
cm-1
i-
v
3000 > 0
2000
C12 1000-
(a)
o 4OO
. CY)
(D -C}
...... 3-LEVEL (A:-3OOOcrn-') - - - 3-LEVEL (A'=+4500cm-') ............. ~ 4--LEVEL (A=-3OOOcmU-1, -- . 5':+4500cm-') 300
'.,
i
,,
200 0 (,3 E]
~O_
I O0
900
(b)
1100
WAVELENGTH (nm) 1300
1500
1700
1900
Fig. 3. E x p e r i m e n t a l l y m e a s u r e d magnitude (a) and p h a s e (b) o f X ( m ( - 3w; ~, a~, eo) relative to fused silica as a function of fundamental w a v e l e n g t h for a 3 0 n m t h i c k film o f poly(4BCMU). The solid and broken lines r e p r e s e n t theoretical fits to t h e three- and four-level m o d e l s s h o w n in Fig. 1 [17].
c o n v e r t to a p h a s e c l o s e to 0 °, e m p h a s i z i n g an e x c i t a t i o n p a t h w a y that i n c l u d e s higher l o c a t e d t w o - p h o t o n levels as the i n t e r m e d i a t e state [45]. This results s h o u l d be c o m p a r e d to t h e d i s p e r s i o n o f t h e TPA coefficient fl that is s h o w n in Fig. 4. Both the THG and TPA results w e r e fitted by applying the m e t h o d o f averaging by Orr and Ward [ 13 ] for a three- and four-level m o d e l , respectively. A m a g n i t u d e o f 3.11 x 10 -14 e.s.u. [46] and a p h a s e o f 0 ° w a s a s s u m e d for )((3)(_ 3(o; ~o, co, w) in f u s e d silica. The transition-dipole m o m e n t ~ug w a s
29 6000
5000
40OO (..9
E o
5000
2000
1000
0 700
900
1100
1500
WAVELENGTH (nm)
1500
Fig. 4. Two-photon absorption spectrum for a 70 /~m thick sample of poly(4-BCMU). The solid line shows the predictions of the four-level model [17]. TABLE 1 Fitting parameters used in the four-level fit for both THG and TPA data. The values for Am,x, Fug and p~g were calculated from the linear absorption data. The linewidth (Fg,g= Fg-g),transition dipole moments (~ug', P*u~')and energy differences (zi, A') were obtained from the least-square fits to the experimental data
(nm) Po~(4-BCMU) THG 545 TPA 545
(cm - 1)
(cm - 1)
(cm - l)
(cm- 1)
(debye)
(debye)
(debye)
4000 4000
1550 1550
-3000 -2000
4500 4500
13 13
12.5 7.5
17.5 17.5
3000
- 500
5000
17
6.0
11.5
Po~(3-decylthiophene) THG 510 3000
calculated by integrating the visible absorption line (assuming local field c o n t r i b u t i o n s t o b e n e g l i g i b l e ) . In t h e c a l c u l a t i o n s p u b l i s h e d o r i g i n a l l y [ 1 7 , 19] t h e p r o d u c t o f t h e l o c a l f i e l d f a c t o r s in e q n . ( 5 ) w a s s e t e q u a l t o s i x a n d n o f r e q u e n c y d e g e n e r a c y f a c t o r w a s i n c l u d e d ( t h i s is e q u i v a l e n t t o s e t t i n g the local field factor equal to one and using the frequency degeneracy factor o f s i x ) . T h e f i t t e d p a r a m e t e r s f o r /Zug,, /~u~, A a n d A' a r e s u m m a r i z e d in T a b l e 1. T h e g o o d a g r e e m e n t b e t w e e n t h e p a r a m e t e r s e v a l u a t e d f r o m b o t h m e a s u r i n g t e c h n i q u e s is r e m a r k a b l e . T h e f i t t e d v a l u e s f o r tzug, a n d /.Lug- a l s o d e m o n s t r a t e t h e d o m i n a n c e o f t h e n o n l i n e a r i t y b y t h e h i g h e r l y i n g m~Ag state as predicted by theory. A s i m i l a r l e v e l s t r u c t u r e c a n b e e x t r a c t e d f r o m t h e d i s p e r s i o n of)((3)( _ 3o~; co, ~o, oJ) o f p o l y ( 3 - d e c y l t h i o p h e n e ) t h a t is p l o t t e d in F i g . 5 t o g e t h e r w i t h
30 600
2000-
===== ~--
> o_
{3
1500
Experimenfal
- -
4-level
fit
- - ........
3-level 3-level
fit fit
v
DATA A=-1500cm-1 A=+7OOOcm-1
500 X
"s
-
• • • • • Experimenfo] ........ 3-level flf --3-level fit - 4-level
DATA A=+7OOOcrn-1 A=-1500cm-1
400
W U3 1000
5o0 "
¢.y
3: ,-.
///
".
.,.
..
200 500 -
",,
//
".... 100-
O, ......... 700
(a)
, ......... 11 O0
~ ......... 1500
WAVELENGTH (nm)
0 ,. 700
j,,
1900
(b)
.
.
.
.
.
.
.
.
[
.
1100
.
.
.
.
.
.
.
.
,
.
.
.
.
.
.
.
1500
.
.
, ,
1900
WAVELENGTH (nrn)
Fig. 5. Magnitude (a) and p h a s e (b) of ~ a ) ( _ 3w; co, ~, ~) for a 50 n m thick film of p o l y ( 3 d e c y l t h i o p h e n e ) relative to that of fused silica. Experimental data points and theoretical fits to the three- and four-level m o d e l s are s h o w n [15].
theoretical calculations using the three- and four-level models as described above. The shoulder around to= 1100 nm in the dispersion of )((3)(_ 3(o; (o, to, oJ) clearly indicates a two-photon resonance with a state below the 1 lBu state. The corresponding fit parameters are summarized in Table 1. Again the best agreement between theory and the experimental data points is only possible within the four-level model, although the dispersion is dominated by the interaction with the higher energy mlAg. The interferometric measurements on poly(4-BCMU) channel waveguides yielded an electronic contribution to n 2 ( e l e c t r o n i c ) = 5 × 1 0 - s cm2/MW, an estimated thermal contribution n2(thermal) = - 8 x 1 0 - ' 1 cm2/MW and a twophoton coefficient /it < 0 . 2 cm/GW. Note, in particular, the positive sign of the electronic contribution in correspondence to the results of the THG experiments. The nonlinear index coefficient n2 of around 5 × 1 0 - a cm~./MW (or 150 times n~. of fused silica) is distinctly lower than a nonresonant value of about 1000 times the nonlinear susceptibility of fused silica, predicted from the THG results at 1904 /zm. The low value for fl suggests that the actual linewidth of the low-lying two-photon state is smaller than that assumed for the four-level fit. Although the electronic contribution is considerably larger than the thermo-optic effect, the latter accumulates at high repetition frequencies due to its long relaxation time in t h e / z s timescale and therefore dominates the intensity-dependent phase shift if no pulse selection is used.
5.2. DANS side-chain p o l y m e r Figure 6 shows the magnitude and phase of )((a)(-3~o; w, w, w) as a function of the fundamental wavelength. Because of the broken symmetry, the dispersion can be explained within a simple two-level model [47].
31
2000 ....
no c a s c a d i n g cascading
1500
-~ lOOO
.k Of
500 -
i
(a)
0
500 1 "
---
400~
no
]-
cascading
cascading
d
300
'~
200
T
1°I° oi 800 .
(b)
.
I±~ .
.
1000
.
.
.
.
1200
.
.
.
.
1400
WAVELENGTH
.
.
.
1600
.
1800
2000 •
(nm)
Fig. 6. Magnitude (a) and p h a s e (b) o f X(a)(- 3to; to, to, to) a s a function of w a v e l e n g t h for a 75 n m thick film o f DANS s i d e - c h a i n p o l y m e r [51]. The solid line through the data p o i n t s is the theoretical fit explained further in the text.
Furthermore, the large second-order nonlinearity requires the inclusion of the local cascading effect [48]: 1 X(s)(-3to; to, w, to)= -~ Nf3'~fof'~f'~[,),(-3w; w, to, to) + 2 f l ( - 3 w ; 2w, to)cfl(-2to; w, w)]
(9)
32 6e 4
y ( - 3 t o ; to, oJ, to)= - ~
[ - / z ~ g D , l + P~ngA~ng 2 2 D 111 ]
2e3 2 fl(-2o~; to, w)= -~-/.£ngA/.tngD21 e3
(10)
2
fl(-3~o; 2o~, ~o)= ~ t~ngAtL.gD22 where N is the n um ber density of molecules, tLng is the transition dipole m o m e n t between the ground and first excited state, At~,g is the difference between the excited state and ground state dipole moments, often called mesomeric m o m e n t and the D terms are resonant denominators that have been calculated using the diagrammatic model [14]. We included a factor of six in the expression for T and two for f l ( - 2 t o ; to, to) as frequency degeneracy factors, f is the local field factor according to the Lorentz-Lorenz model: f~=
[n(to)l 2 + 2 3
(11)
and c the local field cascading factor [48]: 87r ([n(2~0)] 2 - 1)([n(2o012 + 2) c - -~ N 3[n(2~o)12
(12)
Because of the strong d e p e n d e n c e of these factors on the refractive index n at 2~o, we calculated the refractive index dispersion from a Kramers-Kronig analysis of the absorption spectrum. For the fit of the nonlinear data we assumed a num ber density of 1 × 1021 cm -2. The width (Fng=6000 cm -1) and position (Am~=450 nm) of the excited state were calculated from the absorption spectrum after correcting for dispersion effects. The value for the mesomeric m om ent was set to 18 debyes [49, 50]. In this case, the transition dipole m o m e n t /Zng is the only adjustable parameter. The fitted value of 7.8 debyes for /Z~g is in good a g r eemen t to the value of 8.4 debyes determined in solution, where local field effects can be included m or e precisely [50 ]. Contributions from cascading are clearly visible but smaller than suggested in a previous work [51]. In this work, the transition dipole m o m e n t tLng Was calculated as 14.5 debyes by integrating over the film absorption data (neglecting local field effects). No frequency degeneracy factor was used. The fit with A/~.g as the only adjustable parameter showed only fair agreement to the measured dispersion of X(3). The evaluated value for the mesomeric m o m e n t of 15 debyes is comparable to the literature value. A large cascading contribution similar to that generated by T alone was found. The discrepancy between these two a p p r o a c h e s demonstrates clearly how different assumptions on local field effects and the frequency degeneracy factor can alter the interpretation of the data. This is under further investigation.
33 LI-O • "A
00.9
v
o
.%:OOo,,.~
o~:
o
-
o
o
~0.8
E
~ 0.7 E0.6 © Zo.5
-10.80
~
OA~i~CA
Oo
ooooc .....
-10.56 -10.52 Incidence ongle
Ein=5 pJ Ein=350
-10.48 (deg)
Fig. 7. Normalized transmitted power through the input grating vs. angle of incidence for a DANS side-chain polymer waveguide at 5 and 350 p~l input intensity onto the grating. The lines are guides to the eye [25]. F i g u r e 7 s h o w s t h e n o r m a l i z e d t r a n s m i t t e d p o w e r t h r o u g h the first c o u p l i n g g r a t i n g as a f u n c t i o n of i n c i d e n c e angle in the n o n l i n e a r g r a t i n g c o u p l i n g e x p e r i m e n t s with 5 a n d 3 5 0 p~J i n p u t p o w e r s o n t o the grating. B o t h a shift of the o p t i m u m c o u p l i n g a n g l e a n d a d e c r e a s e in t h e c o u p l i n g efficiency c a n b e o b s e r v e d w h e n t h e p o w e r o f t h e incident b e a m is i n c r e a s e d . T h e detailed analysis o f b o t h t h e t r a n s m i t t e d a n d o u t - c o u p l e d signal yielded a n e l e c t r o n i c n o n l i n e a r r e f r a c t i v e i n d e x coefficient n~. = 7 × 10 -8 cm2/MW a n d the t w o - p h o t o n coefficient fl e q u a l to 1 - 2 c m / G W at 1064 n m [25]. The n o n l i n e a r i n d e x coefficient o f a r o u n d 2 0 0 t i m e s t h a t of f u s e d silica is in g o o d a g r e e m e n t to the T H G data. F u r t h e r m o r e , the v a l u e f o r fl is c o n s i s t e n t with the two-level m o d e l , w h e r e 2w is l o c a t e d j u s t in the tail of the visible absorption.
6. C o n c l u s i o n s T H G a n d TPA m e a s u r e m e n t s o n c o n j u g a t e d p o l y m e r s with c e n t r o - s y m m e t r i c s t r u c t u r e verified a four-level m o d e l including the g r o u n d state, t h e l o w e s t lying visible b a n d a n d t w o - p h o t o n s t a t e s l o c a t e d b e l o w a n d a b o v e this s t a t e to give the d o m i n a n t c o n t r i b u t i o n to the n o n l i n e a r s u s c e p t i b i l i t y X(3). The d i s p e r s i o n o f X(3)( - 3w; w, to, w) in the DANS side-chain p o l y m e r c o u l d be e x p l a i n e d a d e q u a t e l y with a two-level m o d e l including m i c r o s c o p i c c a s c a d i n g . Direct d e t e r m i n a t i o n of the i n t e n s i t y - d e p e n d e n t r e f r a c t i v e i n d e x n2 in t w o s y s t e m s s h o w e d n e a r - r e s o n a n t v a l u e s of the o r d e r o f 10 - s cm2/MW with low t w o - p h o t o n coefficients ft.
Acknowledgements W e t h a n k W. Krug, E. Miao a n d M. W. B e r a n e k o f t h e B o e i n g A e r o s p a c e a n d E n g i n e e r i n g High T e c h n o l o g y C e n t e r f o r s u p p l y i n g the s t r i p - l o a d e d PDA
34 s a m p l e , G . M e r e d i t h a n d D. D o n a l d o f D u p o n t f o r c o n s i d e r a b l e amounts of poly(4-BCMU), M. L e c l e r c a t t h e U n i v e r s i t y o f M o n t r e a l f o r t h e p o l y ( 3 decylthiophene) a n d W . H . G . H o r s t h u i s , G. R. M 6 h l m a n n , E . W . P. E r d h u i s e n of the Akzo Research Laboratories for the samples of DANS side-chain polymer.
References 1 J. P. Hermann and J. Ducuing, J. Appl. Phys., 45 (1974) 5100. 2 C. Sauteret, J.-P. Hermann, R. Frey, F. Prad~re, J. Ducuing, R. H. B a u g h m a n n and R. R. Chance, Phys. Rev. Lett., 35 (1976) 956. 3 G. I. Stegeman, C. T. Seaton and R. Zanoni, Thin Solid Films, 152 (1987) 231. 4 V. Mizrahi, K. W. DeLong, G. I. Stegeman, M. A. Saifi and M. J. Andrejco, Opt. Lett., 14 (1989) 1140. 5 K. Schulten, I. Ohmine and M. Karplus, J. Chem. Phys., 64 (1976) 4422. 6 J. W. Wu, J. R. Heflin, R. A. Norwwod, K. Y. Wong, O. Zamani-Khamiri, A. F. Garito, P. Kalyanaraman and J. Sounik, J. Opt. Soc: Am., Part B, 6 (1989) 707. 7 S. N. Dixit, D. Guo and S. Mazumdar, Mol. Cryst. Liq. Cryst., 194 (1991) 33. 8 C. Cojan, G. P. Agraval and C. Flytzanis, Phys. Rev. B, 15 (1977) 909. 9 G. P. Agraval, C. Cojan and C. Flytzanis, Phys. Rev. B, 17 (1978) 776. 10 F. Kajzar, I. R. Girling and I. R. Peterson, Thin Solid Films, 150 (1988) 209. 11 D. Neher, A. Kaltbeitzel, A. Wolf, C. Bubeck and G. Wegner, in J. L. Br~das and R. R. Chance (eds.), Conjugated Polymeric Materials, NATO ASI Series, Kluwer, Dordrecht, 1990, p. 387. 12 B. Kohler, J. Chem. Phys., 88 (1988) 2788 and refs. therein. 13 B. J. Orr and J. F. Ward, Mol. Phys., 20 (1971) 513. 14 T. K. Yee and T. K. Gustafson, Phys. Rev. A, 18 (1978) 18. 15 Y. Prior, IEEE J. Quantum Electron., QE-20 (1984) 37. 16 Y. R. Shen, Prinviples of Nonlinear Optics, Wiley, New York, 1984. 17 W. E. Torruellas, D. Neher, R. Zanoni, G. I. Stegeman, F. Kajzar and M. Leclerc, Chem. Phys. Lett., 175 (1990) 11. 18 F. Kajzar, J. Messier and R. Rosilio, J. AppL Phys., 50 (1986) 3040. 19 W. E. Torruellas, K. B. Rochford, R. Zanoni, S. Aramaki and G. I. Stegeman, Opt. Commun., 82 (1991) 94. 20 W. L. Smith, in M. J. W e b e r (ed.), CRC-Handbook of Laser Science and Technology, Vol. III, Part 1, CRC Press, Boca Raton, FL, 1986. 21 K. B. Rochford, R. Zanoni, G. I. Stegeman, W. Krug, E. Miao and M. W. Beranek, Appl. Phys. Lett., 58 (1991) 13. 22 G. M. Carter and Y. J. Chen, Appl. Phys. Lett., 42 (1983) 643. 23 G. Assanto, R. M. Fortenberry, C. T. Seaton and G. I. Stegeman, J. Opt. Soc. Am., Part B, 5 (1988) 432. 24 G. Assanto, M. B. Marques and G. I. Stegeman, J. Opt. Soc. Am., Part B, 8 (1991) 553. 25 M. B. Marques, G. Assanto, G. I. Stegeman, G. R. M6hlmann, E. W. P. Erdhuisen and W. H. G. Horsthuis, Appl. Phys. Lett., 58 (1991) 2613. 26 K. B. Rochford, R. Zanoni, Q. Gong and G. I. Stegeman, Appl. Phys. Lett., 55 ( 1 9 8 9 ) 1161. 27 P. D. Townsend, J. L. Jackel, G. L. Baker, J. A. Shelbourne III and S. Etemad, Appl. Phys. Lett., 55 (1989) 1829. 28 K. Lochner, H. Baessler, B. Tieke and G. Wegner, Phys. Status Solidi (b), 88 (1978) 653. 29 F. Kajzar and J. Messier, Polym. J., 10 (1987) 275. 30 T. Hasagawa, K. Ishikawa, T. Kanetake, T. Koda, T. Takeda, H. Kobayashi and K. Kubodera, Chem. Phys. Lett., 171 (1990) 239.
35 31 R. R. Chance, M. L. Shand, C. Hogg and R. Silbey, Phys. Rev. B, 22 (1980) 3540. 32 M. Lequime and J. P. Hermann, Chem. Phys., 26 (1977) 431. 33 B. I. Greene, J. Orenstein, R. R. Millard and L. R. Williams, Phys. Rev. Lett., 58 (1987) 2750. 34 G. M. Carter, J. Opt. Sci. Am., Part B, 4 (1987) 1018. 35 O. Inganfis, W. R. Salaneck, J.-E. 0 s t e r h o l m and J. ~ a s k o , Synth. Met., 22 (1988) 395. 36 F. Kajzar, J. Messier, C. Sentein, R. L. Elsenbaumer and G. G. Miller, Proc. SPIE, 1147 (1989) 36. 37 V. H. Houlding, A. Nahata, J. T. Yardley and R. L. Elsenbaumer, Chem. Mater., 2 (1990) 169. 38 D. Neher, A. Wolf, M. Leclerc, A. Kaltbeitzel, C. Bubeck and G. Wegner, Synth. Met., 37 (1990) 249. 39 T. Sugiyama, T. Wada and H. Sasabe, Synth. Met., 28 (1989) C323. 40 H. J. Byrne and W. Blau, Synth. Met., 32 (1990) 229. 41 R. Dorsenville, L. Yang, R. R. Alfano, R. Zamboni, R. Danieli, R. Ruani and C. Taliani, Opt. Lett., 14 (1989) 1321. 42 P. N. Prasad, J. Swiatkiewicz and J. Pileger, Mol. Cryst. Liq. Cryst., 160 (1988) 53. 43 C. Bubeck, A. Kaltbeitzel, A. Grund and M. Leclerc, Chem. Phys., 154 (1991) 343. 44 G. R. M6hlmann, W. H. G. Horsthuis, C. P. J. M. van der Vorst, A. McDonach, M. Copeland, C. Duchet, P. Fabre, M. B. J. Diemeer, E. S. Trommel, F. M. N. Suyten, P. Van Daele, E. Van Tomme and R. Baets, Proc. SPIE, 1147 (1989) 245. 45 F. Kajzar and J. Messier, Phys. Rev. A, 32 (1985) 2352. 46 A. F. Garito, J. R. Heflin, K. Y. Wong and O. Zamani-Khamiri, in R. A. Hann and D. Bloor (eds.), Organic Materials f o r Nonlinear Optics, The Royal Society of Chemistry, London, 1989, p. 16. 47 C. W. Dirk and M. G. Kuzyk, Phys. Rev. B, 41 (1990) 1636. 48 G. R. Meredith and B. Buchalter, J. Chem. Phys., 78 (1983) 1938. 49 W. Liptay, Angew. Chem., Int. Ed. Engl., 8 (1969) 177. 50 M. S. Paley, J. M. Harris, H. Looser, J. C. Baumert, G. C. Bjorklund, D. Jundt and R. J. Twieg, J. Org. Chem., 54 (1989) 3774. 51 W. E. Torruellas, R. Zanoni, G. I. Stegeman, G. R. M6hlmann, E. W. P. Erdhuisen and W. H. G. Horsthuis, J. Chem. Phys., 94 (1991) 6851.