- Email: [email protected]
Nonlinear optics of conjugated polymers
Svl~thetic Metals. 28 (1989) D645 D653
b645
NONLINEAR OPTICS OF (~ONJU(~ATED POLYMER~ M. Sinclair*, D. McBranch, D. Moses and A.J. Heeger Institute for Polymers and Organic Solids and Department of Physics University of California, Santa Barbara, CA 93106, U.S.A. ABSTRACIWe present the results of two types of measurements of the nonlinear optical properties of conjugated polymers. First, we have used third harmonic generation (THG) to probe the nonlinear susceptibility of polyacetylene. The magnitude of 7~(3~(3c0;o~,co,o~)is (4+2)x10 "10 esu with hro=1.17 eV; the only important component of 7~(3)is that associated with n-electron motion along the polymer backbone.
Comparison of .c_is- and |r~n~,-(CH)x shows that ~(3)ttrans is 15-20 times larger than
~(3)lcis. Second, we have employed time-resolved waveguide modulation to measure the magnitude and sign of the nonlinear refractive index (n2) of polydiacetylene-4BCMU.
We find that n2 is
negative, with magnitude of approximately 107(MW/cm2) 1. The response time of this nonlinearity shows a fast (resolution-limited) decay, followed by a slower (-2.5 ps) decay time. These results are consistent with bleaching of the excitonic absorption as the mechanism of the nonlinearity. INTRODUCTION In conjugated polymers, photoproduction of solitons and polarons is a highly nonlinear resonant
optical process. Photon absorption occurs within the ground state electronic configuration and, within 0.1 ps, a 'new electronic configuration evolves (along with a new absorption spectrum). These processes have been well documented experimentally [1-3] and can be used to estimate the magnitude of the resonant third-order susceptibility of these materials [4]. In the case of transpolyacetylene, it has been estimated [5] that ~(3)-10-8 esu, an impressive number even under resonant conditions. What about nonresonant nonlinear processes? In linear optics, it is well known that the properties of the first-order susceptibility (i.e. the complex dielectric constant) in the nonresonant regime are influenced by the positions and strengths of all the higher lying absorptions (hence, all the higher lying resonant optical processes). So one might expect to find large r,onresonant nonlinear susceptibilities in systems where highly nonlinear resonant processes are observed. Indeed, this expectation has been confirmed by a number of recent investigations [6] of the nonresonant nonlinear optical properties of these materials. In order to gain a fuller understanding of the nature of the nonresonant nonlinear susceptibilities in these materials, we have performed a series of third harmonic generation (THG) experiments [5]. With polarization dependence measurements on aligned samples, we have confirmed that the large
* Permanent Address: Sandia National Laboratories, Albuquerque, NM, 87185 0379-6779/89/$3.50
© Elsevier Sequoia/Printed in The Netherlands
D646 nonlinear susceptibilities observed in conjugated polymers are associated with the extended ~electron systems of the conjugated polymer backbone. For trans-polyacetylene, we have measured the magnitude of the third order susceptibility associated with frequency tripling the Nd:YAG laser to be %11(3)=(4+2)x10-10 esu, where the subscript indicates that component of the Z(3)tensor with all indices parallel to the polymer chain. This value is more than an order of magnitude larger than that of the cis- isomer as measured on the same sample. In addition, we have performed nonlinear waveguide spectroscopy on high quality films of the polymer polydiacetylene-4BCMU [7], to determine both the magnitude and the sign of the nonlinear refractive index (n2).
Our results indicate that n2 is negative in sign and has magnitude =10 "7
(MW/cm2) -1. The decay of n2 shows a fast component followed by a slower (-2.5 ps) decay time. These results are consistent with bleaching of the excitonic transition as the mechanism of nonlinearity in this system.
THIRD HARMONIC GENERATION Since trans-polyacetylene is strongly absorbing at the third harmonic (355 rim) of the pump laser, we used the reflection technique of Burns and Bloembergen [8] for measurements of X,(3). Difficulties associated with determining absolute power were avoided by measuring the THG relative to that from a reference with known Z(3) (Silicon) [8]. The sample was attached to the cold finger of a cryostat, adjacent to a piece of intrinsic silicon (cut with a (111) surface). To facilitate focussing and to allow the samples to be moved in and out of the beam, the cryostat was mounted on a translation stage. Relative measurements were taken; the THG signals from the sample and from the silicon were measured without changing any parameters. For anisotropy measurements, aligned films of trans-(CH)x were grown on glass by suspending the the catalyst in a liquid crystal solvent [9]; the reaction was carried out with the liquid crystal oriented in the 1 tesla field of an electromagnet. Infrared studies of samples prepared by this method indicate that, on average, the chains are aligned to within 40 ° [9]. The comparative cis-trans measurements used films prepared on glass by the standard Shirakawa method. When the polarization of the pump beam is parallel to the alignment direction, P(3e) reflected from the trans-(CH)x sample is approximately 2000 times larger than that from silicon under identical conditions. Using the known optical constants of silicon [8] and oriented trans-(GH)x [10], we obtain ZIt(3)=(4+2) x10-10 esu. The estimated error arises from sample inhomogeneity; P(3~) varied somewhat from place to place on the sample. Figure 1 shows the polarization dependence of the reflected third harmonic power P(3~) from an aligned trans-(CH)x film. Assuming perfectly oriented (CH)x chains, and that the only significant component of the tensor is Ztl(3), P(3(o) is expected to vary as Icos3OI 2, where O is the angle between the polarization and the alignment direction. This type of behavior is shown by the dashed line in Fig. 1. Since the polarization dependence of more highly aligned systems (stretch oriented PPV and crystalline polydiacetylene-PTS [5]) accurately follows the cos60 relation, the deviations from the cos60 dependence seen in Fig. 1 arise as result of imperfect alignment. To account for this we have fit the data to a model which allows for a gaussian distribution of alignment directions [5]. The solid line of Fig. 1 represents a best fit obtained in this manner, and corresponds to a chain
D647
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Fig. 1 The polarization dependence of third harmonic generation from an aligned sample of trans(CH)x. The dashed curve shows the type of behavior expected for a perfectly aligned one dimensional system (cos60); the solid line represents the best fit achieved with a gaussian distribution of chain directions. The gaussian which achieves the best fit (shown in the inset) has a FWHM of 40 °. distribution FWHM of 40 °, in good agreement with the previously inferred value. These data confirm the assumption that %(3) is entirely associated with the nonlinear polarizability of the ~-electron system in the conjugated polymer backbone. Polyacetylene can be prepared in two different forms: cis-(CH)x and trans-(CH)x. Trans-(CH)x has a two-fold degenerate ground state and can support solitons as fundamental nonlinear excitations. In cis-(CH)x, this degeneracy has been lifted so that the important nonlinear excitations are confined soliton pairs (polarons and bipolarons) [11]. The implied changes in the nonlinear optical properties due to this change in symmetry can be probed on the same sample; conversion from cis- to trans(CH)x simply requires heating to 150 ° C for about 1/2 hour. Films of cis-(CH)x were synthesized by carrying out the polymerization and subsequent washing, etc, at -78 ° C; in this way nearly 100% cis-(CH)x can be obtained. The cis-(CH)x samples were prepared as thick films (several microns) in a specially constructed glass cell that allowed for measurements without ever raising the sample temperature above -78 ° C.
After completing the
THG measurements on cis-(CH)x, the sample was isomerized in the same cell, and the same sample was remeasured as trans-(CH)x.
This process was carried out for two independently prepared
samples with the same result; P(3~) from ciso(CH)x was between 250 to 500 times smaller than that from lran$-(CH)x, with the range due to variations across the surface o! the sample. The large difference in %(3) between the two isomers of polyacetylene is difficult to explain within the framework of traditional band theory, in which the mechanism is the nonlinear polarizability of the ~-electron system within a rigid band structure. In materials where the rigid band structure concept is valid, calculation of the nonresonant susceptibilities reduces to performing the appropriate sums over the excited state configurations.
The earliest calculations of the nonlinear susceptibilities of
conjugated polymers were simple band structure calculations of this type [12], and produced theoretical predictions of large susceptibilities. Although, for this mechanism, %(3) must strongly depend on the magnitude of the single particle gap (the sixth power), the predicted difference between .¢j$_-and trans-(CH)x is not as large as is observed.
D648 The situation is more complex than these models allow for, since the inherent lattice instabilities in conjugated polymers render the rigid band concept obsolete, and can be expected to influence the nonlinear optical properties of these systems.
However, the contributions of excited state
configurations in which the lattice geometry differs significantly from that of the ground state should be negligible, since the dipole matrix elements connecting these configurations will be small. Recently it has been proposed [5,13] that the effect of the nonlinear lattice dynamics can be included by properly accounting for the lattice configurations present in the ground state. Inclusion of quantum fluctuations of the lattice (which can be described by a correct quantum treatment of the lattice coordinates) yields finite matrix elements between the ground state and excited states containing solitons and polarons. This effect will be more pronounced in materials with degenerate ground states since larger amplitude fluctuations are possible in this case. The predictions of this theory are in qualitative agreement with the results of the cis-trans experiment, as well as the spectral dependence of X(3)(3eo) for trans-(CH)x [14]. Clearly more experimental and theoretical work is needed to test these ideas.
WAVEGUIDE MODULATION Although THG measurements yield important information about the nature of the nonlinearities in conjugated polymers, most device applications will rely on the nonlinear refractive index n2, which is defined by the relation [15] n=no+n2I
(1)
where n O is the linear refractive index and [ is the optical intensity. Thus it is important to develop techniques which can quickly and accurately measure the magnitude and sign of n2. Techniques such as photoinduced absorption [1-3] and reflection spectroscopy probe the nonlinear refractive index, but are usually confined to spectral regions where the material of interest is (at least) moderately absorbing. Four-wave mixing [15] can be used to measure the magnitude of n2 in regions where the material is transparent, but this method normally does not yield any information about the real and imaginary parts of n2, nor does it yield any information about linear optical properties. For materials which can be prepared as very high quality thin films, another technique which can be used to measure the nonlinear refractive index is waveguide modulation [16]. Light can be coupled into an optical waveguide (using a prism or grating) only at very specific angles of incidence, which are determined by the geometry of the experimental arrangement, and the thickness and refractive index of the film under study [17]. When the angle of incidence coincides with one of these resonant angles, the reflectivity of the system decreases dramatically.
For materials with low losses
(absorption and scattering), the angular width of these modes is small. Furthermore, the positions of each mode is very sensitive to the refractive index: any perturbation of the refractive index of the film, caused by the presence of a strong optical field, will shift the angular positions of the reflectance minima. By measuring the amount a mode shifts in response to a known optical field, the magnitude and sign of both the real and imaginary parts of the nonlinear refractive index can be deduced.
I3649 DETECTOR (
)
PROBE
VAVEGUII)E
PUMP / I
F7
CHOPPER
DELAY
Fig. 2. The experimental arrangement for the waveguide modulation measurements.
\
4B0
48 3
f
A86
489
49 2
0 (deg)
Fig. 3. The reflection coefficient in the vicinity of one of the TM modes of a polydiacetylene-4BCMU waveguide.
We have modified this technique in several important ways to allow for time-resolved measurements, and to ease the requirements on sample preparation, To demonstrate the method, we have performed a series of measurements on the conjugated polymer polydiacetylene-4BCMU [7]. Our results indicate that just below the primary absorption band the real part of the nonlinear refractive index is negative in sign, and has a magnitude of approximately 10-7(MW/cm2) -1. The response time of this nonlinearity has two components: a fast (resolution-limited) response time followed by a slower (-2.5 ps) decay. Both of these results are consistent with bleaching of the excitonic absorption as the mechanism of the nonlinearity. Our experimental arrangement (see Fig. 2) uses the focussed light attenuated total reflection (FLATR) method [18] in conjunction with standard pump and probe techniques for the observation and modulation of the guided modes of a thin film. In the FLATR arrangement, the sample is prepared by first depositing 450 A of silver on a clean glass slide. The material to be studied is then deposited
D650 directly on the silver layer.
In this case the sample is a thin film of the conjugated polymer
polydiacetylene-4BCMU, prepared by spin-casting from solution [19]. The uncovered side of the slide is brought into optical contact with the base of a prism (with the same refractive index as the slide) by means of an index-matching fluid. By measuring the reflectivity as a function of the angle of incidence, the positions of the guided modes of the system can be determined. The pump and probe pulses are obtained with a beamsplitter from a synchronously pumped, cavity dumped (4 MHz) dye laser operating at 630 nm.
The output pulses of the dye laser have an
autocorrelation FWHM of 1 ps and a maximum energy of 25 nJ. The probe beam is first spatially filtered and expanded, and is then focussed (through the prism) on the multilayer system (see Fig. 2). The mechanically chopped pump beam is focussed on the back side of the prism and is made to coincide (spatially and temporally) with the probe pulse. After reflection from the sample, the beam profile is measured by scanning a photodiode with a small aperture across the beam. The output of the photodiode is split, and both the cw and the modulated intensity (due to the chopped pump beam) of the reflected light are recorded simultaneously. The sample/prism combination is then translated vertically until the beam strikes an unsilvered portion of the glass (total internal reflection). The beam profile at this spot is then taken to normalize both the cw and the modulated reflectivities. Finally, by varying the relative delay between the pump and probe pulses, the temporal evolution of the induced modulation of the reflected light is measured. Figure 3 shows the angular dependence of the reflected light at the position of one of the TM guided modes of the polydiacetylene film. For a typical film thickness of - lp.m, two TM and TE modes were observable. Although, in principle, the linear optical constants could be determined by fitting the measured positions and widths of these modes to the Fresnel equations for the multilayer system, this procedure has not been completed for two reasons: first, the films are too soft to allow for independent thickness measurements using contact techniques (Dektak); second, due to the
o) dR/dO (o.u.)
~R
(o.u.)
. . . . . . .
//~ J~(~deg)
. . . . . . .
Fig. 4. a) The numerical derivative of the data of figure 3, for comparison with Fig. 4b; b) The measured photo-modulation of the reflectivity in the vicinity of the TM mode shown in Fig. 3.
D651
highly anisotropic nature of the polymer composing the film, some birefringence is expected. Thus, there are more parameters than can be uniquely determined by fitting the data to the Fresnel equations. Work in this area is continuing. The modulation of the reflected beam (AR) due to the pump beam is shown in Fig. 4b. Also shown in Fig. 4 is the (negative) angular derivative of the data in Fig. 3. The close agreement between the two curves indicates that the measured modulation of the probe beam corresponds to a shift of the position of the mode. This implies that n2 is real, since imaginary n2 leads to a width modulation of the mode. By comparing the relative sizes of the modulated reflectivity (=5x10 -4) and the angular derivative of the reflectivity (200/rad), we are able to determine the angular shift of the mode (AOc=3X10 -6 rad). Finally, we can relate the angular shift of the mode to the change in the effective mode index (N) using N=npsinOc
(2)
where np=1.51 is the index of the prism, and Oc=48.7 ° is the coupling angle of the mode. Following this procedure, we obtain AN=-3xl0 6 .
By means of Eq. 1 and the approximation An=AN, we
calculate an order of magnitude estimate of n2=-10-7(MW/cm2) 1. This result is consistent with bleaching of the exeitonic absorption (possibly due to phase space filling effects [20]) as the mechanism of the nonlinearity, since a reduction of the oscillator strength of this transition will cause a decrease in the real part of the refractive index for energies below the exciton energy. For a simple bleaching of the exciton transition, the fractional changes in the real and imaginary part of the refractive index (n='q+i~) would be equal.
However, at energies below the
transition where the material is nonabsorbing (as in the present case), the absolute magnitude of the change in the real part of the refractive index would be several orders of magnitude larger than that of the imaginary part.
This explains the lack of evidence for any change in K (which would be
observable if present in the same magnitude). Although the value of n2 obtained in this experiment is somewhat lower than has been reported for the related polymer polydiacetylene-PTS [21], it is not unreasonable, since the measurements on PTS were performed with the optical field polarized parallel to the chain direction of the crystalline sample, and thus take full advantage of the nonlinear n-electron system. In the present case, the polymer chains are randomly aligned (probably in the plane of the substrate), and the projection of the polarization of the TM optical field on the average chain direction will be much smaller. The (normalized) time evolution of the modulation of the probe beam (at - 48.50 on Fig. 3b) is shown in Fig. 5. The rise and initial decay of this waveform are resolution limited. At later times the decay is slower and fitting the data to a single exponential yields a 2.5 ps decay time. Even though the PDA-4BCMU samples used in this experiment are transparent (co is less than 100 cm 1 at 630 nm), the observation of a slower decay indicates that the measured n 2 is (at least partially) resonant in nature.
In a truly nonresonant measurement the time decay would be the (symmetric)
autocorrelation of the laser pulse and no decay time would be resolvable. Furthermore, a decay time of 2.0 ps following resonant excitation has been observed in polydiacetylene-PTS [20]. Future work will concentrate on extending the waveguide modulation experiments further into the nonresonant regime.
D652
AR (o...)
I-4.0
2.0
O0
20
4.0
6.0
time (ps)
Fig. 5. The (normalized) time decay of the photo-modulated reflectivity at = 48.5 ° following picosecond excitation.
In conclusion, we have presented the results of two types of measurements of the nonlinear optical properties of conjugated polymers.
From THG experiments on polyacetylene, we find
X(3)(3co;co,(o,co)=(4_+2)xl0 "10 esu for the trans- isomer.
This value is more than an order of
magnitude larger than that of the cis- isomer as measured on the same sample. This large nonlinearity is entirely associated with the extended =-electron system of the conjugated ploymer backbone. From time-resolved waveguide modulation experiments, we have measured the nonlinear refractive index of the polymer polydiacetylene-4BCMU.
We find that n2 is negative and of order 10-7
(MW/cm2) -1. This nonlinearity shows a resolution limited response followed by a slower (2.5 ps) decay. These results can be explained by bleaching of the excitonic absorption as the mechanism of the nonlinearity. ACKNOWLEDGEMENT This research was supported through Office of Naval Research, Contract #N00014-86-K-0514. REFERENCES 1 C.V. Shank, Y. R. Yen, R.L. Fork, J. Orenstein and G.L. Baker, Phys. Rev. Left. 49, 1660 2
(1982). Z. Vardeny, J. Strait, D. Moses, T.C. Chung and A.J. Heeger, Phys. Rev. Lett. 49, 1657
3
(1982). L. Rothberg, T.M Jedju, S. Etemad and G.L. Baker, Phys. Rev. Lett. 57, 3229 (1986).
4
A.J. Heeger, D. Moses and M.Sinclair, Synth. Met. 15, 95 (1986).
5
M. Sinclair, D. Moses K. Akagi and A.J. Heeger, Phys. Rev. B (in press).
6
Nonlinear Ootical Prooerties of Polymers. Ed. by A.J. Heeger, J. Orenstein and D.R. Ulrich, Materials Research Society Symposium Proceedings, 109 .Materials Research Society Pittsburgh PA, 1988).
7 8
M. Sinclair, D. McBranch, D. Moses, and A.J. Heeger, Appl. Phys. Lett. (submitted). W.K. Burns and N. BIoembergen, Phys. Rev. B4, 3437 (1971).
9
K. Akagi et al, Synth. Met. 17, 563 (1987).
D653
10
These values were obtained by reflectance from highlly oriented Durham polyacetylene; G. Leising (private communication).
11
Handbook of Conductine Polymers, Ed. by T.A. Skotheim, (Marcel Dekker, New York and
12
C. Flytzanis, Nonlinear Ootical Prooerties of Oroanic and Polymeric Materials, Ed. D.J.
Basel, 1986). Williams, American Chemical Society Symposium Series, 233 (Amer. Chem. Soc., Wash., D.C., 1983). 13
J. Yu, H. Matsuoka and W.P. Su, Phys. Rev. B (in press).
14
S. Etemad, G.L. Baker, L. Rothberg, and F. Kajzar, in Nonlinear Ootical Prooerties of P01ymer$, Ed. A.J. Heeger, J. Orenstein and D.R. Ulrich, Materials Research Society Symposium Proceedings, 109, (Materials Research Society, Pittsburgh, PA, 1988).
15
Y.R. Shen, The Princioles of Nonlinear Ootics. (Wiley-lnterscience, New York, 1984).
16
G.M. Carter, Y.J. Chen and S.K. Tripathy, Appl. Phys. Lett. 43, 891 (1983).
17
D. Marcuse, Theory of Dielectric Ootical Wavegvides. (Academic Press, New York, 1974).
18
E. Kretschmann, Opt. Commun. 26, 41 (1978).
19
G.L. Baker, N.E. Schlotter, J.L. Jackel, P. Townsend and S. Etemad, March Meeting of the American Physical Society, New Orleans, 1988.
20
B.I. Greene, J. Orenstein, R.R. Milland, and L.R. Williams, Phys. Rev. Lett. 58, 2750 (1987).
21
G.M. Carter, M.K. Thakur, Y.J. Chen, and J.V. Hryniewicz, Appl. Phys. Left. 47,457 (1985).
b645
NONLINEAR OPTICS OF (~ONJU(~ATED POLYMER~ M. Sinclair*, D. McBranch, D. Moses and A.J. Heeger Institute for Polymers and Organic Solids and Department of Physics University of California, Santa Barbara, CA 93106, U.S.A. ABSTRACIWe present the results of two types of measurements of the nonlinear optical properties of conjugated polymers. First, we have used third harmonic generation (THG) to probe the nonlinear susceptibility of polyacetylene. The magnitude of 7~(3~(3c0;o~,co,o~)is (4+2)x10 "10 esu with hro=1.17 eV; the only important component of 7~(3)is that associated with n-electron motion along the polymer backbone.
Comparison of .c_is- and |r~n~,-(CH)x shows that ~(3)ttrans is 15-20 times larger than
~(3)lcis. Second, we have employed time-resolved waveguide modulation to measure the magnitude and sign of the nonlinear refractive index (n2) of polydiacetylene-4BCMU.
We find that n2 is
negative, with magnitude of approximately 107(MW/cm2) 1. The response time of this nonlinearity shows a fast (resolution-limited) decay, followed by a slower (-2.5 ps) decay time. These results are consistent with bleaching of the excitonic absorption as the mechanism of the nonlinearity. INTRODUCTION In conjugated polymers, photoproduction of solitons and polarons is a highly nonlinear resonant
optical process. Photon absorption occurs within the ground state electronic configuration and, within 0.1 ps, a 'new electronic configuration evolves (along with a new absorption spectrum). These processes have been well documented experimentally [1-3] and can be used to estimate the magnitude of the resonant third-order susceptibility of these materials [4]. In the case of transpolyacetylene, it has been estimated [5] that ~(3)-10-8 esu, an impressive number even under resonant conditions. What about nonresonant nonlinear processes? In linear optics, it is well known that the properties of the first-order susceptibility (i.e. the complex dielectric constant) in the nonresonant regime are influenced by the positions and strengths of all the higher lying absorptions (hence, all the higher lying resonant optical processes). So one might expect to find large r,onresonant nonlinear susceptibilities in systems where highly nonlinear resonant processes are observed. Indeed, this expectation has been confirmed by a number of recent investigations [6] of the nonresonant nonlinear optical properties of these materials. In order to gain a fuller understanding of the nature of the nonresonant nonlinear susceptibilities in these materials, we have performed a series of third harmonic generation (THG) experiments [5]. With polarization dependence measurements on aligned samples, we have confirmed that the large
* Permanent Address: Sandia National Laboratories, Albuquerque, NM, 87185 0379-6779/89/$3.50
© Elsevier Sequoia/Printed in The Netherlands
D646 nonlinear susceptibilities observed in conjugated polymers are associated with the extended ~electron systems of the conjugated polymer backbone. For trans-polyacetylene, we have measured the magnitude of the third order susceptibility associated with frequency tripling the Nd:YAG laser to be %11(3)=(4+2)x10-10 esu, where the subscript indicates that component of the Z(3)tensor with all indices parallel to the polymer chain. This value is more than an order of magnitude larger than that of the cis- isomer as measured on the same sample. In addition, we have performed nonlinear waveguide spectroscopy on high quality films of the polymer polydiacetylene-4BCMU [7], to determine both the magnitude and the sign of the nonlinear refractive index (n2).
Our results indicate that n2 is negative in sign and has magnitude =10 "7
(MW/cm2) -1. The decay of n2 shows a fast component followed by a slower (-2.5 ps) decay time. These results are consistent with bleaching of the excitonic transition as the mechanism of nonlinearity in this system.
THIRD HARMONIC GENERATION Since trans-polyacetylene is strongly absorbing at the third harmonic (355 rim) of the pump laser, we used the reflection technique of Burns and Bloembergen [8] for measurements of X,(3). Difficulties associated with determining absolute power were avoided by measuring the THG relative to that from a reference with known Z(3) (Silicon) [8]. The sample was attached to the cold finger of a cryostat, adjacent to a piece of intrinsic silicon (cut with a (111) surface). To facilitate focussing and to allow the samples to be moved in and out of the beam, the cryostat was mounted on a translation stage. Relative measurements were taken; the THG signals from the sample and from the silicon were measured without changing any parameters. For anisotropy measurements, aligned films of trans-(CH)x were grown on glass by suspending the the catalyst in a liquid crystal solvent [9]; the reaction was carried out with the liquid crystal oriented in the 1 tesla field of an electromagnet. Infrared studies of samples prepared by this method indicate that, on average, the chains are aligned to within 40 ° [9]. The comparative cis-trans measurements used films prepared on glass by the standard Shirakawa method. When the polarization of the pump beam is parallel to the alignment direction, P(3e) reflected from the trans-(CH)x sample is approximately 2000 times larger than that from silicon under identical conditions. Using the known optical constants of silicon [8] and oriented trans-(GH)x [10], we obtain ZIt(3)=(4+2) x10-10 esu. The estimated error arises from sample inhomogeneity; P(3~) varied somewhat from place to place on the sample. Figure 1 shows the polarization dependence of the reflected third harmonic power P(3~) from an aligned trans-(CH)x film. Assuming perfectly oriented (CH)x chains, and that the only significant component of the tensor is Ztl(3), P(3(o) is expected to vary as Icos3OI 2, where O is the angle between the polarization and the alignment direction. This type of behavior is shown by the dashed line in Fig. 1. Since the polarization dependence of more highly aligned systems (stretch oriented PPV and crystalline polydiacetylene-PTS [5]) accurately follows the cos60 relation, the deviations from the cos60 dependence seen in Fig. 1 arise as result of imperfect alignment. To account for this we have fit the data to a model which allows for a gaussian distribution of alignment directions [5]. The solid line of Fig. 1 represents a best fit obtained in this manner, and corresponds to a chain
D647
--
,, '
"'1 ......
I'"
, ' ~ 4
~
,,, --s,
,\
/ ~
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J
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• 4-
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Fig. 1 The polarization dependence of third harmonic generation from an aligned sample of trans(CH)x. The dashed curve shows the type of behavior expected for a perfectly aligned one dimensional system (cos60); the solid line represents the best fit achieved with a gaussian distribution of chain directions. The gaussian which achieves the best fit (shown in the inset) has a FWHM of 40 °. distribution FWHM of 40 °, in good agreement with the previously inferred value. These data confirm the assumption that %(3) is entirely associated with the nonlinear polarizability of the ~-electron system in the conjugated polymer backbone. Polyacetylene can be prepared in two different forms: cis-(CH)x and trans-(CH)x. Trans-(CH)x has a two-fold degenerate ground state and can support solitons as fundamental nonlinear excitations. In cis-(CH)x, this degeneracy has been lifted so that the important nonlinear excitations are confined soliton pairs (polarons and bipolarons) [11]. The implied changes in the nonlinear optical properties due to this change in symmetry can be probed on the same sample; conversion from cis- to trans(CH)x simply requires heating to 150 ° C for about 1/2 hour. Films of cis-(CH)x were synthesized by carrying out the polymerization and subsequent washing, etc, at -78 ° C; in this way nearly 100% cis-(CH)x can be obtained. The cis-(CH)x samples were prepared as thick films (several microns) in a specially constructed glass cell that allowed for measurements without ever raising the sample temperature above -78 ° C.
After completing the
THG measurements on cis-(CH)x, the sample was isomerized in the same cell, and the same sample was remeasured as trans-(CH)x.
This process was carried out for two independently prepared
samples with the same result; P(3~) from ciso(CH)x was between 250 to 500 times smaller than that from lran$-(CH)x, with the range due to variations across the surface o! the sample. The large difference in %(3) between the two isomers of polyacetylene is difficult to explain within the framework of traditional band theory, in which the mechanism is the nonlinear polarizability of the ~-electron system within a rigid band structure. In materials where the rigid band structure concept is valid, calculation of the nonresonant susceptibilities reduces to performing the appropriate sums over the excited state configurations.
The earliest calculations of the nonlinear susceptibilities of
conjugated polymers were simple band structure calculations of this type [12], and produced theoretical predictions of large susceptibilities. Although, for this mechanism, %(3) must strongly depend on the magnitude of the single particle gap (the sixth power), the predicted difference between .¢j$_-and trans-(CH)x is not as large as is observed.
D648 The situation is more complex than these models allow for, since the inherent lattice instabilities in conjugated polymers render the rigid band concept obsolete, and can be expected to influence the nonlinear optical properties of these systems.
However, the contributions of excited state
configurations in which the lattice geometry differs significantly from that of the ground state should be negligible, since the dipole matrix elements connecting these configurations will be small. Recently it has been proposed [5,13] that the effect of the nonlinear lattice dynamics can be included by properly accounting for the lattice configurations present in the ground state. Inclusion of quantum fluctuations of the lattice (which can be described by a correct quantum treatment of the lattice coordinates) yields finite matrix elements between the ground state and excited states containing solitons and polarons. This effect will be more pronounced in materials with degenerate ground states since larger amplitude fluctuations are possible in this case. The predictions of this theory are in qualitative agreement with the results of the cis-trans experiment, as well as the spectral dependence of X(3)(3eo) for trans-(CH)x [14]. Clearly more experimental and theoretical work is needed to test these ideas.
WAVEGUIDE MODULATION Although THG measurements yield important information about the nature of the nonlinearities in conjugated polymers, most device applications will rely on the nonlinear refractive index n2, which is defined by the relation [15] n=no+n2I
(1)
where n O is the linear refractive index and [ is the optical intensity. Thus it is important to develop techniques which can quickly and accurately measure the magnitude and sign of n2. Techniques such as photoinduced absorption [1-3] and reflection spectroscopy probe the nonlinear refractive index, but are usually confined to spectral regions where the material of interest is (at least) moderately absorbing. Four-wave mixing [15] can be used to measure the magnitude of n2 in regions where the material is transparent, but this method normally does not yield any information about the real and imaginary parts of n2, nor does it yield any information about linear optical properties. For materials which can be prepared as very high quality thin films, another technique which can be used to measure the nonlinear refractive index is waveguide modulation [16]. Light can be coupled into an optical waveguide (using a prism or grating) only at very specific angles of incidence, which are determined by the geometry of the experimental arrangement, and the thickness and refractive index of the film under study [17]. When the angle of incidence coincides with one of these resonant angles, the reflectivity of the system decreases dramatically.
For materials with low losses
(absorption and scattering), the angular width of these modes is small. Furthermore, the positions of each mode is very sensitive to the refractive index: any perturbation of the refractive index of the film, caused by the presence of a strong optical field, will shift the angular positions of the reflectance minima. By measuring the amount a mode shifts in response to a known optical field, the magnitude and sign of both the real and imaginary parts of the nonlinear refractive index can be deduced.
I3649 DETECTOR (
)
PROBE
VAVEGUII)E
PUMP / I
F7
CHOPPER
DELAY
Fig. 2. The experimental arrangement for the waveguide modulation measurements.
\
4B0
48 3
f
A86
489
49 2
0 (deg)
Fig. 3. The reflection coefficient in the vicinity of one of the TM modes of a polydiacetylene-4BCMU waveguide.
We have modified this technique in several important ways to allow for time-resolved measurements, and to ease the requirements on sample preparation, To demonstrate the method, we have performed a series of measurements on the conjugated polymer polydiacetylene-4BCMU [7]. Our results indicate that just below the primary absorption band the real part of the nonlinear refractive index is negative in sign, and has a magnitude of approximately 10-7(MW/cm2) -1. The response time of this nonlinearity has two components: a fast (resolution-limited) response time followed by a slower (-2.5 ps) decay. Both of these results are consistent with bleaching of the excitonic absorption as the mechanism of the nonlinearity. Our experimental arrangement (see Fig. 2) uses the focussed light attenuated total reflection (FLATR) method [18] in conjunction with standard pump and probe techniques for the observation and modulation of the guided modes of a thin film. In the FLATR arrangement, the sample is prepared by first depositing 450 A of silver on a clean glass slide. The material to be studied is then deposited
D650 directly on the silver layer.
In this case the sample is a thin film of the conjugated polymer
polydiacetylene-4BCMU, prepared by spin-casting from solution [19]. The uncovered side of the slide is brought into optical contact with the base of a prism (with the same refractive index as the slide) by means of an index-matching fluid. By measuring the reflectivity as a function of the angle of incidence, the positions of the guided modes of the system can be determined. The pump and probe pulses are obtained with a beamsplitter from a synchronously pumped, cavity dumped (4 MHz) dye laser operating at 630 nm.
The output pulses of the dye laser have an
autocorrelation FWHM of 1 ps and a maximum energy of 25 nJ. The probe beam is first spatially filtered and expanded, and is then focussed (through the prism) on the multilayer system (see Fig. 2). The mechanically chopped pump beam is focussed on the back side of the prism and is made to coincide (spatially and temporally) with the probe pulse. After reflection from the sample, the beam profile is measured by scanning a photodiode with a small aperture across the beam. The output of the photodiode is split, and both the cw and the modulated intensity (due to the chopped pump beam) of the reflected light are recorded simultaneously. The sample/prism combination is then translated vertically until the beam strikes an unsilvered portion of the glass (total internal reflection). The beam profile at this spot is then taken to normalize both the cw and the modulated reflectivities. Finally, by varying the relative delay between the pump and probe pulses, the temporal evolution of the induced modulation of the reflected light is measured. Figure 3 shows the angular dependence of the reflected light at the position of one of the TM guided modes of the polydiacetylene film. For a typical film thickness of - lp.m, two TM and TE modes were observable. Although, in principle, the linear optical constants could be determined by fitting the measured positions and widths of these modes to the Fresnel equations for the multilayer system, this procedure has not been completed for two reasons: first, the films are too soft to allow for independent thickness measurements using contact techniques (Dektak); second, due to the
o) dR/dO (o.u.)
~R
(o.u.)
. . . . . . .
//~ J~(~deg)
. . . . . . .
Fig. 4. a) The numerical derivative of the data of figure 3, for comparison with Fig. 4b; b) The measured photo-modulation of the reflectivity in the vicinity of the TM mode shown in Fig. 3.
D651
highly anisotropic nature of the polymer composing the film, some birefringence is expected. Thus, there are more parameters than can be uniquely determined by fitting the data to the Fresnel equations. Work in this area is continuing. The modulation of the reflected beam (AR) due to the pump beam is shown in Fig. 4b. Also shown in Fig. 4 is the (negative) angular derivative of the data in Fig. 3. The close agreement between the two curves indicates that the measured modulation of the probe beam corresponds to a shift of the position of the mode. This implies that n2 is real, since imaginary n2 leads to a width modulation of the mode. By comparing the relative sizes of the modulated reflectivity (=5x10 -4) and the angular derivative of the reflectivity (200/rad), we are able to determine the angular shift of the mode (AOc=3X10 -6 rad). Finally, we can relate the angular shift of the mode to the change in the effective mode index (N) using N=npsinOc
(2)
where np=1.51 is the index of the prism, and Oc=48.7 ° is the coupling angle of the mode. Following this procedure, we obtain AN=-3xl0 6 .
By means of Eq. 1 and the approximation An=AN, we
calculate an order of magnitude estimate of n2=-10-7(MW/cm2) 1. This result is consistent with bleaching of the exeitonic absorption (possibly due to phase space filling effects [20]) as the mechanism of the nonlinearity, since a reduction of the oscillator strength of this transition will cause a decrease in the real part of the refractive index for energies below the exciton energy. For a simple bleaching of the exciton transition, the fractional changes in the real and imaginary part of the refractive index (n='q+i~) would be equal.
However, at energies below the
transition where the material is nonabsorbing (as in the present case), the absolute magnitude of the change in the real part of the refractive index would be several orders of magnitude larger than that of the imaginary part.
This explains the lack of evidence for any change in K (which would be
observable if present in the same magnitude). Although the value of n2 obtained in this experiment is somewhat lower than has been reported for the related polymer polydiacetylene-PTS [21], it is not unreasonable, since the measurements on PTS were performed with the optical field polarized parallel to the chain direction of the crystalline sample, and thus take full advantage of the nonlinear n-electron system. In the present case, the polymer chains are randomly aligned (probably in the plane of the substrate), and the projection of the polarization of the TM optical field on the average chain direction will be much smaller. The (normalized) time evolution of the modulation of the probe beam (at - 48.50 on Fig. 3b) is shown in Fig. 5. The rise and initial decay of this waveform are resolution limited. At later times the decay is slower and fitting the data to a single exponential yields a 2.5 ps decay time. Even though the PDA-4BCMU samples used in this experiment are transparent (co is less than 100 cm 1 at 630 nm), the observation of a slower decay indicates that the measured n 2 is (at least partially) resonant in nature.
In a truly nonresonant measurement the time decay would be the (symmetric)
autocorrelation of the laser pulse and no decay time would be resolvable. Furthermore, a decay time of 2.0 ps following resonant excitation has been observed in polydiacetylene-PTS [20]. Future work will concentrate on extending the waveguide modulation experiments further into the nonresonant regime.
D652
AR (o...)
I-4.0
2.0
O0
20
4.0
6.0
time (ps)
Fig. 5. The (normalized) time decay of the photo-modulated reflectivity at = 48.5 ° following picosecond excitation.
In conclusion, we have presented the results of two types of measurements of the nonlinear optical properties of conjugated polymers.
From THG experiments on polyacetylene, we find
X(3)(3co;co,(o,co)=(4_+2)xl0 "10 esu for the trans- isomer.
This value is more than an order of
magnitude larger than that of the cis- isomer as measured on the same sample. This large nonlinearity is entirely associated with the extended =-electron system of the conjugated ploymer backbone. From time-resolved waveguide modulation experiments, we have measured the nonlinear refractive index of the polymer polydiacetylene-4BCMU.
We find that n2 is negative and of order 10-7
(MW/cm2) -1. This nonlinearity shows a resolution limited response followed by a slower (2.5 ps) decay. These results can be explained by bleaching of the excitonic absorption as the mechanism of the nonlinearity. ACKNOWLEDGEMENT This research was supported through Office of Naval Research, Contract #N00014-86-K-0514. REFERENCES 1 C.V. Shank, Y. R. Yen, R.L. Fork, J. Orenstein and G.L. Baker, Phys. Rev. Left. 49, 1660 2
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