- Email: [email protected]
Third-harmonic generation in polyphenylacetylene: Exact determination of nonlinear optical susceptibilities in ultrathin films
Volume 163,number 2,3
THIRD-HARMONIC
10November 1989
CHEMICALPHYSICSLETTERS
GENERATION IN POLYPHENYLACETYLENE:
EXACT DETERMINATION OF NONLINEAR OPTICAL SUSCEPTIBILITIES IN ULTRATHIN FILMS
D. NEHER, A. WOLF, C. BUBECK and G. WEGNER Ma.r-Planck-InstitutJiir Polymerforschung,Ackermannweg 10, D-6500 Mainz. Federal Republicof Germany
Received 17July 1989;in final form 16August 1989
Third-harmonicgeneration measurementshave been performed at 10= 1064nm on ultrathin films of polyphenylacetylene.The nonlinearsusceptibilityX2 X( -3~; w, w, o) wasdeterminedtobe (7.0 I! 1.0) x 10-rlesu withthephaseof~rs’equai to 152”f 5” indicating that two- and three-photon resonances contribute to the observed nonlinearity.The influence of back-reflectioneffects was estimated experimentallyby measurementsin different optical configurations.Wefound the experimentaldata couldonly be explained by using an evaluation procedure includingall bound wavesin the layer system.
1. Introduction
Recent optical investigations on organic systems with delocalized x-electron systems have shown strong nonlinear effects combined with response time in the picosecond region [ 11. Integrated devices for optical data processing based on the nonlinear susceptibility xc3) could be realized with thin films of suitable organic materials. Therefore the determination of optical nonlinearities in the thin film geometry is of special interest. For waveguide devices the material should have low absorption and scattering in the desired wavelength region combined with high nonlinearity and should be easy to process [ 2 1. Because two-photon resonances can enhance the nonlinearity without leading to strong absorption the determination of two-photon levels is of particular interest. With this in mind we have investigated x(3) ( -3~; w, w, w) of polyphenylacetylene with third-harmonic generation (THG). This is the most sensitive and accurate method for the determination ofX’3), but care has to be taken in the analysis ofdata. Multiple reflection of the fundamental and harmonic waves has been treated theoretically, but experimental proof of the effects of multiple reflection in multilayer systems on the evaluation of xc3’ has not been published to our knowledge. We have analysed thin films on a transparent substrate in two 116
different optical geometries. The difference in harmonic intensities in the two configurations clearly indicates the influence of back-reflection effects.
2. Polyphenylacetylene
Polyphenylacetylene was polymerized using a [Rh(COD)Cl], catalyst [ 31. The polymer is soluble in methylene chloride. Thin amorphous stable films can be made by casting or spin coating from solution. The absorption spectrum (see fig. 1) shows a broad band (fwhm = 200 nm) with a maximum at 385 nm. The form of the absorption is almost the same in solution as in the solid state. Recent dfwm 0.8 0
0.7
:
0.6
h
0.5
3
;;
0.1 0.0
1
H
=+E +=
:; b
L-7
200
400
600
wavelength [urn1 Fig. 1. Absorption spectrum of an ultrathin polyphenylacetylene film (thickness 37 nm) prepared by spin coating on a fused silica substrate.
0 009-2614/89/$ 03.50 0 Elsevier Science Publishers B.V. ( North-Holland Physics Publishing Division )
Volume163,number2,3
10November1989
CHEMICALPHYSICSLETTERS
experiments on polyphenylacetylene films determined a x$g?,( -w; w, -w, w) value of 5x 10-l’ esu in the transparent region of the absorption spectrum [4]. This is one of the largest non-resonant third-order susceptibilities measured in amorphous polymeric films.
The intensities of these fields compared to the incident intensity can be calculated via the matrix formalism described elsewhere [ 91. In each layer a nonlinear polarisation
P~“(r)=~,X13)[E~(r)+ES(r)13
(4)
is created, leading to four bound source waves oscillating at the harmonic frequency [ 7 I 3. Theory
Et: (r)=E$
The first theoretical treatments of harmonic generation in a parallel slab [ 51 have been extended by including multiple reflections of the generated harmonic waves in the evaluation procedure [ 61. Multiple reflection of the fundamental in a parallel slab was included in the analysis by Krausz et al. [ 71. For the evaluation of our experimental data we used a matrix formalism including all waves in a multilayer sample as briefly described in the appendix. A similar and more extended formalism was proposed by Bethune [ 81. For the treatment of multiple reflection effects we consider a multilayer system of n layers with thickness di, complex dielectric function er and nonlinear susceptibilities xj3) surrounded by vacuum. We confine our considerations to s-polarized light and isotropic media. The surface normal of the layer system should be parallel to the z axis. Assuming a fundamental beam with frequency w and wavevector
E)li(r)=Et’exp{i[k$x-kti(z-z,)]}$,
(1)
propagating with the angle &, relative to the z axis in vacuum, the forward-propagating fundamental wave E$(r) and backward propagating reflected wave E$ (r ) in a layer i between z=zi and z= zi+ 1can be written in the form [ 91: E~(r)=E~exp(i[k~~:x+k~=(z-z,)lj$,
@a)
E$(r)~Ey~exp(i[k&x-k?Jz-z,)]}$.
(2b)
The indices t (transmitted) and r (reflected) indicate the direction of propagation of the waves. The components of the wavevector in a layer i are given by k”i,X=kr. ,r =k$‘sin% 0 =K 9 k&:= [ E:(k;)2-K2]
“2.
(3)
exp{i[kt:x+kt:(z-z,)]}Zr
I?:: (r)=EF’exp{i[kFixtkt’(z-zi) E~f(r)=E~fexp{i[k~~~-k~:(z-z,)]}$,
,
(5a) (5b)
I}$ ,
(5c) (5d)
with amplitudes p?’ bt -
( 3k$')2x'3' (@I
)2_
(kf)l
b%)’
(6a)
WYr:)3 t
(6b)
3(E32Ec >
(6~)
3E3E:)2
(6d)
9
( 3k$)‘xc3’
EP,: =
(k;,)2_
Et’2 = zzt
(@Z)Z_
(k;)2
( 3k;)2x(3’
E:?:=
(@)I
( 3kf)2x’3’
(@2)2_(kf)2
and wavevectors kb’ ,,x> k:; = 3k$ > I,X= Sk” k:’ = [ (k$*+
(k;:)2]
‘D,
(7a)
kb2 LX= 3kv,,x>
ktl = kG 2
kb2 = [ (kb2)2+ (k”‘ v)*] “2 1,x
(7b)
creating the free transmitted and reflected harmonic waves El, and EF,r described by the wavevector kf. The bound and free propagating waves have the same x components of the wavevectors and are s-polarized in the case of isotropic media. One can group the two bound waves into pairs which have the same wavevector length and can be treated as transmitted and reflected waves of one type: Et’, Et: and Et:, EF:, described by the indices bl and b2. Bound waves of the type b2 are only created if the forward and backward propagating fundamental coexist in space and time. For normal reflection conditions the backward propagating bound waves are negligible, but both the Et{ and EF: wave must be taken into account. This 117
Volume 163,
number2,3
CHEMICAL PHYSICSLETTERS
is particularly valid for polymers with the main absorption band between the fundamental and harmonic wavelength. In this case the strong dispersion of the linear susceptibility leads to n(w)
4. Experimental The experimental configuration was based on the Maker fringe method. Infrared light pulses (A= 1064 nm) of 0.4 mJ energy and 35 ps duration generated by an active/passive modelocked Nd:YAG laser were focused on the sample with the focal region in vacuum. The 1/e* radius of the fundamental beam intensity in these experiments was 60 urn. The beam focus was carefully adjusted onto the sample mounted on a rotation stage. The generated harmonic light pulses were detected by a photomultiplier tube. For referenceweusedX’3)(-30;@,cu,nr)=3.11~10-14 esu for fused silica at 1064 nm [ 61. Thin films of polyphenylacetylene were prepared by spin coating on 1 mm thick fused silica substrates. The thicknesses of the films were determined by an u-step profiler. We calculated the dispersion of the refractive indices by Lorentz-Lorenz and/or iterative Kramers-Kronig analysis of the absorption spectrum [9] from 190 to 800 nm. By comparing with interference cxpcrimcnts we found the real part of the dielectric function e generated by UV absorption to be around 1.820.2. The absorption coefficient at the harmonic frequency (A=354 nm) is 1.15 x IO'cm- ’for ultrathin films. To evaluate the influence of multiple reflection effects, we investigated the sample both with the film in front of (configuration 2) and behind (configuration 1 ) a fused silica substrate. Finally the Maker fringe pattern of the substrate alone was measured after removal of the film without displacement ofthe sample (same position as in configuration 2). This procedure enables us to determine the phase of xt3)
[‘Il.
118
10 NovemberI989
5. Results Third harmonic generation measurements on a 37 nm thick film of polyphenylacetylene in the above configurations are shown in fig. 2. The refractive indices of this film were determined to be n(w) = 1.72&0.05 and rz(30)= 1.65&0.05. The optical density at 3w was 0.18. The harmonic intensity in
configuration 1 (film on the backside of the substrate) is clearly enhanced compared to the intensity in configuration 2. The interference pattern in the latter case shows additional oscillations for incident angles between - 10” and IO”. They arise from the interference between the forward propagating fundamental wave and the fundamental reflected at the backside of the substrate (effective reflection coefficient around 0.18). Signal enhancement via the E:bwave is only possible if these fundamental waves overlap in the film. (In our configuration, focus radius around 60 pm, substrate thickness I mm, this is only true for small incidence angles.) In addition the back reflection of the fundamental at the filmsubstrate interface (reflection coefficient 0.09) leads to a small enhancement. In configuration 1 the forward propagating fundamental wave overlaps in the film with that reflected at the film-vacuum interface (reflection coefficient 0.26) over the whole region of the incidence angle and leads to the observed enhancement. In the substrate both the coherence length relative to the free harmonic wave and the amplitude of the generated EF2 wave is small and only the EF'contribution is dominant. Additional small oscillations occur from multiple reflections in the substrate [ 61 but are normally not visible. We analysed the data with two different assumptions: (a) all reflection effects are taken into account, but only the EF: wave is used and (b) the full formalism is used. A formalism similar to assumption (a) is used by several authors for the evaluation of xc31(-3~;w, to,w) [11-131. The determined xC3) values are summarized in table 1 together with the phase ofXt3). We set the transmission of the backwards propagating fundamental wave from the substrate into the film equal to zero for the fit under assumption (b) and configuration 2. This simulates the reflection behavior for incidence angles greater than 10”. In all cases only data points with I$I> 10"were taken into
Volume 163,number 2,3
CHEMICALPHYSICS LETTERS
r
10 November 1989
A)
Fig. 2. Third-harmonic intensity as a function of the incidence angle for (A) 37 nm thick film of polyphenylacetylene at the backside of a 1 mm thick fused silica substrate; (B) the sample as in (A) but with the film in front of the substrate; (C) Maker fringe pattern of the substrate alone after the in situ removal of the film. The experimental datapoints are shown with error bars. The scale is the same in all subfigures. The solid line represents the theoretical tit including all bound waves.
Table
1
Evaluationof the experimentaldata shown in fig. 2 with the two different assumptions noted in the text Film backside (configuration
assumption (a) assumption (b)
Film frontside (configuration 2)
I)
xc’) ( 10-‘2esuj
phase (xl’)) (deg)
$3) (LO_‘2 esu)
phase (x”) (deg)
4.6kO.4 2.7f0.3
167 153
3.0+0.3 2.7kO.3
167?5 153+5
account. As the table shows, only the evaluation ineluding all waves can explain the data in all contigurations. This demonstrates that the observed dif-
ference in harmonic intensity is mainly due to the different amplitudes of the bound waves Eb” in both configurations (as discussed above). Particularly in 119
Volume163.number2,3
CHEMICAL PHYSICSLETTERS
configuration 1 the neglect of the bound waves Ekf (and @:) leads to large errors in the determination ofx(3’. The magnitude of such errors depends on film thickness, refractive indices and absorption and cannot in general be predicted Individual investigations on the dispersion of xc3) could be strongly influenced by the dispersion of n(w). On the other hand the signal enhancement in contiguration 1 can be useful in analysing thin films with relatively low xt3). We found similar contributions from back-reflection effects in all thin film systems, even in systems with the harmonic field generated by the substrate was negligible compared to that produced by the film. We note here that, for film thicknesses small compared to the coherence length of the bound waves relative to the free propagating harmonic, the nonlinear behavior of an ultrathin film can be modelled by a nonlinear polarisation sheet [ 141 embedded in the film medium allowing back reflection effects to be more easily included in the analysis. Nevertheless absorption of the harmonic and fundamental waves is difficult to include in this model and therefore this analysis is confined to nonabsorbing films and is not applicable in our case. In addition the magnitude of the evaluated phase of xc3) depends on the analysis procedure, although the differences are not large. If we assume that the nonlinear susceptibility xc3’( -30; w, w, o) is described by only one term [ 111: x(3)( -3w. , w>0 , w) -1 cc (3w-w,,+iT,)(20-w,,,+ir,,,)(w-w,,)
(8) with g denoting the ground state, n the visible absorption band and g’ the two-photon level, the visible absorption spectrum would lead to a phase of approximately 90”-120”. The observed phase of around 152” points to a two-photon level with a maximum between 350 and 450 nm. This conjecture was supported by further investigations on substi-
120
10November
1989
tuted polyphenylacetylenes [ 151. The high nonlinear susceptibility reported by Prasad [ 41 is probably enhanced by this two-photon level. If we assume that the polymer is oriented randomly in the plane of the ultrathin film the nonlinear susceptibility parallel to the polymer backbone x$it?,( -3~; w, w, w) is given by [ 161
(9) which is equal to (7.0+ 1.0) x lo-” esu. The above assumption was supported by polarisation-dependent absorption measurements; nevertheless it might be an oversimplification and the given value of xLztE?,should be considered as the lower limit.
6. Conclusion Our investigations show that all propagating and generated waves must be included in an analysis of third harmonic generation measurements on ultrathin films. Otherwise the determined xc3) values can be in error by a factor of two. The nonlinear susceptibility of polyphenylacetylene was determined to esu. be xgi x (-3w; w, w, o)=(7.0fl.0)Xi0-*2 This relatively large value is enhanced via a threephoton resonance with the visible absorption band and probably a two-photon level at around 350-450 nm. In data processing applications in the interesting wavelength region around 850 nm this two-photon level could enhance the third-order susceptibility.
Acknowledgement We thank A. Kaltbeitzel for useful discussions, J. Swalen for advice on the refractive index evaluation, B. May for help with the fit routine, D. Lupo for helpful comments on the manuscript and H.J. Menges for considerable technical support. This work is supported by the BMFT under project 03M4008E9.
Volume 163, number 2,3
CHEMICAL PHYSICS LETTERS
10 November 1989
Appendix In the following we briefly explain the data analysis via a matrix formalism. As explained in the main text the forward and backward propagating fundamental waves in layer i generate four bound waves Et:, Et: and Et:, Et: leading to the free harmonic waves Ei,, and Et,. We now consider two neighbouring layers i and i+ 1 with all waves included. The boundary conditions at z=z,+~ are (Ala)
(Alb) for the total fields oscillating at 30~leads to a linear equation system that can be written in a standard matrix form: E:=
(-M,w&‘+Mi,~~i+
C
I,&+I)
t.42)
+M,,f+~+,,J$+,
b=bl,b2
with the summation over both types of bound waves. The forward and backward propagating waves of each type are written in the form of a two-component vector:
Ef=
(z!‘),E,6=($l),
j=i,it 1, b=bl, b2.
(A3)
The transform matrices in (A2) are given by
( I;,f-i,b
hf4,b
Mi,f-i+
M
em
[it
+Pf+$6) -i93
ev( l,b=
-“f-i+ “f-
I
exp[i( -9f+9!)
M+i,b = +
---!--_ ti.f-i+
1 fi,fdr+
Lb ex!d
ri,f-i+
1,b
(
ri,f,i+
I,f exp(
exp[i(-d-v!)l
ri,f-+l+l,b
+$I
>’
exp[i(+9f-9P)l ew(
-id)
’
exp( ti9f)
+id)
exp ( - i9;) I,f
ri,f-r,b I
rl,f-i+
I,f exp(
-ief)
exp( + i9f)
>’
(Ada) Wb) (A4c)
with the formal transmission t,,- and reflection r,_,-coefficients
(A51 and the propagation phases cpf=k;,,d,,
q$=k;,d,,
b=bl, b2.
(Ah)
For a system comprising tow active layers i= 1, 2 surrounded by vacuum i=O, 3 the equation describing the
free propagating wave in front of the sample takes the form: Eb= ,=& +M
O.f-1,f
[(Mo,r-l,b- Mo,r-,,J%_,,b )E: + %,r_, ,,AM,,r+z,b- M l,r-&‘b,f-2,b )E; 1 M I,f-2,f M 2,f+3,f Ef3
*
(A7)
The equation determining the field E;,, of the free forward propagating harmonic wave in vacuum behind the sample is then given by (A7) with the forward propagating field E g,, and the backward propagating field ES,, both set equal to zero. This formalism allows the determination of the harmonic intensity I& (proportional to (E:,,)2) without knowledge of the unknown field E’,,r and without any approximations. The above equation can easily be extended to a multilayer system with n> 3. 121
Volume 163, number 2,3
CHEMICAL PHYSICS LETTERS
References [ 11 D.S. Chemla, I. Zyss, eds., Nonlinear optical properties of organic molecules and crystals (Academic Press, New York, 1987). [2] G.I. Stegeman, R. Zanoni, K. Rochford and C.T. Seaton, in: Nonlinear optical effects in organic polymers, eds. J. Messier, F. Kajzar, P. Prasad and D. Ulrich, NATO ASI Series (KIuwer, Dordrecht, 1989). [3] A. Furlani, C. Napoletano, M.V. Russo and W.J. Feast, PolymerBull. 16 (1986) 311. [4] P.N. Prasad, in: Nonlinear materials for non-linear optics, eds. B.A. Hann and D. Bloor, Special Publication No. 69 (Roy. Sot., London, 1989). [5] N. Bloembergen and P.S. Pershan, Phys. Rev. 128 (1962) 606. [6] F. Kajzar and J. Messier, Phys. Rev. A 32 (1985) 2352. [ 71 F. Krausz, E. Wintner and G. Leising, Phys. Rev. B 39 (1989) 3701.
122
IO November 1989
[8]D.S.Bethune,J.Opt.Soc.Am.B6(1989)910. 191J. Swalen. J. Mol. Electron. 2 (1986) 155. [ iOjC. Bubeck, A. Kaltbeitzel, R.W. ienz, D. Neher, J.D. Stenger-Smith and G. Wegner, in: Nonlinear optical effects in organic polymers, eds., J. Messier, F. Kajzar, P. Prasad and D. Ulrich, NATO ASI Series (Kluwer, Dordrecht, 1989). [ I 1] F. Kajzar, J. Messier and C. Rosilio, J. Appl. Phys. 60 ( 1986) 3040. [ 121 M. Sinclair, D. Moses, A.J. Heeger, K. Vilhelmsson, B. VaIk and M. Salour, Solid State Commun. 6 1 (1987) 221. [ 131 T. Kaino, K. Kubodera, S. Tomaru, T. Kurihara, S. Saito, T. Tsutsui and S. Tokito, Electron. Letters 23 (1987) 1095. [14]J.E.Sipe,J.Opt.Soc.4m.B4 (1987)481. [ 151 D. Neher, M. Ixclerc, A. Wolf, C. Bubeck and G. Wegner, to be published. [ 161 F. Kajzarand J. Messier, Thin Solid Films 132 (1985) 11.
THIRD-HARMONIC
10November 1989
CHEMICALPHYSICSLETTERS
GENERATION IN POLYPHENYLACETYLENE:
EXACT DETERMINATION OF NONLINEAR OPTICAL SUSCEPTIBILITIES IN ULTRATHIN FILMS
D. NEHER, A. WOLF, C. BUBECK and G. WEGNER Ma.r-Planck-InstitutJiir Polymerforschung,Ackermannweg 10, D-6500 Mainz. Federal Republicof Germany
Received 17July 1989;in final form 16August 1989
Third-harmonicgeneration measurementshave been performed at 10= 1064nm on ultrathin films of polyphenylacetylene.The nonlinearsusceptibilityX2 X( -3~; w, w, o) wasdeterminedtobe (7.0 I! 1.0) x 10-rlesu withthephaseof~rs’equai to 152”f 5” indicating that two- and three-photon resonances contribute to the observed nonlinearity.The influence of back-reflectioneffects was estimated experimentallyby measurementsin different optical configurations.Wefound the experimentaldata couldonly be explained by using an evaluation procedure includingall bound wavesin the layer system.
1. Introduction
Recent optical investigations on organic systems with delocalized x-electron systems have shown strong nonlinear effects combined with response time in the picosecond region [ 11. Integrated devices for optical data processing based on the nonlinear susceptibility xc3) could be realized with thin films of suitable organic materials. Therefore the determination of optical nonlinearities in the thin film geometry is of special interest. For waveguide devices the material should have low absorption and scattering in the desired wavelength region combined with high nonlinearity and should be easy to process [ 2 1. Because two-photon resonances can enhance the nonlinearity without leading to strong absorption the determination of two-photon levels is of particular interest. With this in mind we have investigated x(3) ( -3~; w, w, w) of polyphenylacetylene with third-harmonic generation (THG). This is the most sensitive and accurate method for the determination ofX’3), but care has to be taken in the analysis ofdata. Multiple reflection of the fundamental and harmonic waves has been treated theoretically, but experimental proof of the effects of multiple reflection in multilayer systems on the evaluation of xc3’ has not been published to our knowledge. We have analysed thin films on a transparent substrate in two 116
different optical geometries. The difference in harmonic intensities in the two configurations clearly indicates the influence of back-reflection effects.
2. Polyphenylacetylene
Polyphenylacetylene was polymerized using a [Rh(COD)Cl], catalyst [ 31. The polymer is soluble in methylene chloride. Thin amorphous stable films can be made by casting or spin coating from solution. The absorption spectrum (see fig. 1) shows a broad band (fwhm = 200 nm) with a maximum at 385 nm. The form of the absorption is almost the same in solution as in the solid state. Recent dfwm 0.8 0
0.7
:
0.6
h
0.5
3
;;
0.1 0.0
1
H
=+E +=
:; b
L-7
200
400
600
wavelength [urn1 Fig. 1. Absorption spectrum of an ultrathin polyphenylacetylene film (thickness 37 nm) prepared by spin coating on a fused silica substrate.
0 009-2614/89/$ 03.50 0 Elsevier Science Publishers B.V. ( North-Holland Physics Publishing Division )
Volume163,number2,3
10November1989
CHEMICALPHYSICSLETTERS
experiments on polyphenylacetylene films determined a x$g?,( -w; w, -w, w) value of 5x 10-l’ esu in the transparent region of the absorption spectrum [4]. This is one of the largest non-resonant third-order susceptibilities measured in amorphous polymeric films.
The intensities of these fields compared to the incident intensity can be calculated via the matrix formalism described elsewhere [ 91. In each layer a nonlinear polarisation
P~“(r)=~,X13)[E~(r)+ES(r)13
(4)
is created, leading to four bound source waves oscillating at the harmonic frequency [ 7 I 3. Theory
Et: (r)=E$
The first theoretical treatments of harmonic generation in a parallel slab [ 51 have been extended by including multiple reflections of the generated harmonic waves in the evaluation procedure [ 61. Multiple reflection of the fundamental in a parallel slab was included in the analysis by Krausz et al. [ 71. For the evaluation of our experimental data we used a matrix formalism including all waves in a multilayer sample as briefly described in the appendix. A similar and more extended formalism was proposed by Bethune [ 81. For the treatment of multiple reflection effects we consider a multilayer system of n layers with thickness di, complex dielectric function er and nonlinear susceptibilities xj3) surrounded by vacuum. We confine our considerations to s-polarized light and isotropic media. The surface normal of the layer system should be parallel to the z axis. Assuming a fundamental beam with frequency w and wavevector
E)li(r)=Et’exp{i[k$x-kti(z-z,)]}$,
(1)
propagating with the angle &, relative to the z axis in vacuum, the forward-propagating fundamental wave E$(r) and backward propagating reflected wave E$ (r ) in a layer i between z=zi and z= zi+ 1can be written in the form [ 91: E~(r)=E~exp(i[k~~:x+k~=(z-z,)lj$,
@a)
E$(r)~Ey~exp(i[k&x-k?Jz-z,)]}$.
(2b)
The indices t (transmitted) and r (reflected) indicate the direction of propagation of the waves. The components of the wavevector in a layer i are given by k”i,X=kr. ,r =k$‘sin% 0 =K 9 k&:= [ E:(k;)2-K2]
“2.
(3)
exp{i[kt:x+kt:(z-z,)]}Zr
I?:: (r)=EF’exp{i[kFixtkt’(z-zi) E~f(r)=E~fexp{i[k~~~-k~:(z-z,)]}$,
,
(5a) (5b)
I}$ ,
(5c) (5d)
with amplitudes p?’ bt -
( 3k$')2x'3' (@I
)2_
(kf)l
b%)’
(6a)
WYr:)3 t
(6b)
3(E32Ec >
(6~)
3E3E:)2
(6d)
9
( 3k$)‘xc3’
EP,: =
(k;,)2_
Et’2 = zzt
(@Z)Z_
(k;)2
( 3k;)2x(3’
E:?:=
(@)I
( 3kf)2x’3’
(@2)2_(kf)2
and wavevectors kb’ ,,x> k:; = 3k$ > I,X= Sk” k:’ = [ (k$*+
(k;:)2]
‘D,
(7a)
kb2 LX= 3kv,,x>
ktl = kG 2
kb2 = [ (kb2)2+ (k”‘ v)*] “2 1,x
(7b)
creating the free transmitted and reflected harmonic waves El, and EF,r described by the wavevector kf. The bound and free propagating waves have the same x components of the wavevectors and are s-polarized in the case of isotropic media. One can group the two bound waves into pairs which have the same wavevector length and can be treated as transmitted and reflected waves of one type: Et’, Et: and Et:, EF:, described by the indices bl and b2. Bound waves of the type b2 are only created if the forward and backward propagating fundamental coexist in space and time. For normal reflection conditions the backward propagating bound waves are negligible, but both the Et{ and EF: wave must be taken into account. This 117
Volume 163,
number2,3
CHEMICAL PHYSICSLETTERS
is particularly valid for polymers with the main absorption band between the fundamental and harmonic wavelength. In this case the strong dispersion of the linear susceptibility leads to n(w)
4. Experimental The experimental configuration was based on the Maker fringe method. Infrared light pulses (A= 1064 nm) of 0.4 mJ energy and 35 ps duration generated by an active/passive modelocked Nd:YAG laser were focused on the sample with the focal region in vacuum. The 1/e* radius of the fundamental beam intensity in these experiments was 60 urn. The beam focus was carefully adjusted onto the sample mounted on a rotation stage. The generated harmonic light pulses were detected by a photomultiplier tube. For referenceweusedX’3)(-30;@,cu,nr)=3.11~10-14 esu for fused silica at 1064 nm [ 61. Thin films of polyphenylacetylene were prepared by spin coating on 1 mm thick fused silica substrates. The thicknesses of the films were determined by an u-step profiler. We calculated the dispersion of the refractive indices by Lorentz-Lorenz and/or iterative Kramers-Kronig analysis of the absorption spectrum [9] from 190 to 800 nm. By comparing with interference cxpcrimcnts we found the real part of the dielectric function e generated by UV absorption to be around 1.820.2. The absorption coefficient at the harmonic frequency (A=354 nm) is 1.15 x IO'cm- ’for ultrathin films. To evaluate the influence of multiple reflection effects, we investigated the sample both with the film in front of (configuration 2) and behind (configuration 1 ) a fused silica substrate. Finally the Maker fringe pattern of the substrate alone was measured after removal of the film without displacement ofthe sample (same position as in configuration 2). This procedure enables us to determine the phase of xt3)
[‘Il.
118
10 NovemberI989
5. Results Third harmonic generation measurements on a 37 nm thick film of polyphenylacetylene in the above configurations are shown in fig. 2. The refractive indices of this film were determined to be n(w) = 1.72&0.05 and rz(30)= 1.65&0.05. The optical density at 3w was 0.18. The harmonic intensity in
configuration 1 (film on the backside of the substrate) is clearly enhanced compared to the intensity in configuration 2. The interference pattern in the latter case shows additional oscillations for incident angles between - 10” and IO”. They arise from the interference between the forward propagating fundamental wave and the fundamental reflected at the backside of the substrate (effective reflection coefficient around 0.18). Signal enhancement via the E:bwave is only possible if these fundamental waves overlap in the film. (In our configuration, focus radius around 60 pm, substrate thickness I mm, this is only true for small incidence angles.) In addition the back reflection of the fundamental at the filmsubstrate interface (reflection coefficient 0.09) leads to a small enhancement. In configuration 1 the forward propagating fundamental wave overlaps in the film with that reflected at the film-vacuum interface (reflection coefficient 0.26) over the whole region of the incidence angle and leads to the observed enhancement. In the substrate both the coherence length relative to the free harmonic wave and the amplitude of the generated EF2 wave is small and only the EF'contribution is dominant. Additional small oscillations occur from multiple reflections in the substrate [ 61 but are normally not visible. We analysed the data with two different assumptions: (a) all reflection effects are taken into account, but only the EF: wave is used and (b) the full formalism is used. A formalism similar to assumption (a) is used by several authors for the evaluation of xc31(-3~;w, to,w) [11-131. The determined xC3) values are summarized in table 1 together with the phase ofXt3). We set the transmission of the backwards propagating fundamental wave from the substrate into the film equal to zero for the fit under assumption (b) and configuration 2. This simulates the reflection behavior for incidence angles greater than 10”. In all cases only data points with I$I> 10"were taken into
Volume 163,number 2,3
CHEMICALPHYSICS LETTERS
r
10 November 1989
A)
Fig. 2. Third-harmonic intensity as a function of the incidence angle for (A) 37 nm thick film of polyphenylacetylene at the backside of a 1 mm thick fused silica substrate; (B) the sample as in (A) but with the film in front of the substrate; (C) Maker fringe pattern of the substrate alone after the in situ removal of the film. The experimental datapoints are shown with error bars. The scale is the same in all subfigures. The solid line represents the theoretical tit including all bound waves.
Table
1
Evaluationof the experimentaldata shown in fig. 2 with the two different assumptions noted in the text Film backside (configuration
assumption (a) assumption (b)
Film frontside (configuration 2)
I)
xc’) ( 10-‘2esuj
phase (xl’)) (deg)
$3) (LO_‘2 esu)
phase (x”) (deg)
4.6kO.4 2.7f0.3
167 153
3.0+0.3 2.7kO.3
167?5 153+5
account. As the table shows, only the evaluation ineluding all waves can explain the data in all contigurations. This demonstrates that the observed dif-
ference in harmonic intensity is mainly due to the different amplitudes of the bound waves Eb” in both configurations (as discussed above). Particularly in 119
Volume163.number2,3
CHEMICAL PHYSICSLETTERS
configuration 1 the neglect of the bound waves Ekf (and @:) leads to large errors in the determination ofx(3’. The magnitude of such errors depends on film thickness, refractive indices and absorption and cannot in general be predicted Individual investigations on the dispersion of xc3) could be strongly influenced by the dispersion of n(w). On the other hand the signal enhancement in contiguration 1 can be useful in analysing thin films with relatively low xt3). We found similar contributions from back-reflection effects in all thin film systems, even in systems with the harmonic field generated by the substrate was negligible compared to that produced by the film. We note here that, for film thicknesses small compared to the coherence length of the bound waves relative to the free propagating harmonic, the nonlinear behavior of an ultrathin film can be modelled by a nonlinear polarisation sheet [ 141 embedded in the film medium allowing back reflection effects to be more easily included in the analysis. Nevertheless absorption of the harmonic and fundamental waves is difficult to include in this model and therefore this analysis is confined to nonabsorbing films and is not applicable in our case. In addition the magnitude of the evaluated phase of xc3) depends on the analysis procedure, although the differences are not large. If we assume that the nonlinear susceptibility xc3’( -30; w, w, o) is described by only one term [ 111: x(3)( -3w. , w>0 , w) -1 cc (3w-w,,+iT,)(20-w,,,+ir,,,)(w-w,,)
(8) with g denoting the ground state, n the visible absorption band and g’ the two-photon level, the visible absorption spectrum would lead to a phase of approximately 90”-120”. The observed phase of around 152” points to a two-photon level with a maximum between 350 and 450 nm. This conjecture was supported by further investigations on substi-
120
10November
1989
tuted polyphenylacetylenes [ 151. The high nonlinear susceptibility reported by Prasad [ 41 is probably enhanced by this two-photon level. If we assume that the polymer is oriented randomly in the plane of the ultrathin film the nonlinear susceptibility parallel to the polymer backbone x$it?,( -3~; w, w, w) is given by [ 161
(9) which is equal to (7.0+ 1.0) x lo-” esu. The above assumption was supported by polarisation-dependent absorption measurements; nevertheless it might be an oversimplification and the given value of xLztE?,should be considered as the lower limit.
6. Conclusion Our investigations show that all propagating and generated waves must be included in an analysis of third harmonic generation measurements on ultrathin films. Otherwise the determined xc3) values can be in error by a factor of two. The nonlinear susceptibility of polyphenylacetylene was determined to esu. be xgi x (-3w; w, w, o)=(7.0fl.0)Xi0-*2 This relatively large value is enhanced via a threephoton resonance with the visible absorption band and probably a two-photon level at around 350-450 nm. In data processing applications in the interesting wavelength region around 850 nm this two-photon level could enhance the third-order susceptibility.
Acknowledgement We thank A. Kaltbeitzel for useful discussions, J. Swalen for advice on the refractive index evaluation, B. May for help with the fit routine, D. Lupo for helpful comments on the manuscript and H.J. Menges for considerable technical support. This work is supported by the BMFT under project 03M4008E9.
Volume 163, number 2,3
CHEMICAL PHYSICS LETTERS
10 November 1989
Appendix In the following we briefly explain the data analysis via a matrix formalism. As explained in the main text the forward and backward propagating fundamental waves in layer i generate four bound waves Et:, Et: and Et:, Et: leading to the free harmonic waves Ei,, and Et,. We now consider two neighbouring layers i and i+ 1 with all waves included. The boundary conditions at z=z,+~ are (Ala)
(Alb) for the total fields oscillating at 30~leads to a linear equation system that can be written in a standard matrix form: E:=
(-M,w&‘+Mi,~~i+
C
I,&+I)
t.42)
+M,,f+~+,,J$+,
b=bl,b2
with the summation over both types of bound waves. The forward and backward propagating waves of each type are written in the form of a two-component vector:
Ef=
(z!‘),E,6=($l),
j=i,it 1, b=bl, b2.
(A3)
The transform matrices in (A2) are given by
( I;,f-i,b
hf4,b
Mi,f-i+
M
em
[it
+Pf+$6) -i93
ev( l,b=
-“f-i+ “f-
I
exp[i( -9f+9!)
M+i,b = +
---!--_ ti.f-i+
1 fi,fdr+
Lb ex!d
ri,f-i+
1,b
(
ri,f,i+
I,f exp(
exp[i(-d-v!)l
ri,f-+l+l,b
+$I
>’
exp[i(+9f-9P)l ew(
-id)
’
exp( ti9f)
+id)
exp ( - i9;) I,f
ri,f-r,b I
rl,f-i+
I,f exp(
-ief)
exp( + i9f)
>’
(Ada) Wb) (A4c)
with the formal transmission t,,- and reflection r,_,-coefficients
(A51 and the propagation phases cpf=k;,,d,,
q$=k;,d,,
b=bl, b2.
(Ah)
For a system comprising tow active layers i= 1, 2 surrounded by vacuum i=O, 3 the equation describing the
free propagating wave in front of the sample takes the form: Eb= ,=& +M
O.f-1,f
[(Mo,r-l,b- Mo,r-,,J%_,,b )E: + %,r_, ,,AM,,r+z,b- M l,r-&‘b,f-2,b )E; 1 M I,f-2,f M 2,f+3,f Ef3
*
(A7)
The equation determining the field E;,, of the free forward propagating harmonic wave in vacuum behind the sample is then given by (A7) with the forward propagating field E g,, and the backward propagating field ES,, both set equal to zero. This formalism allows the determination of the harmonic intensity I& (proportional to (E:,,)2) without knowledge of the unknown field E’,,r and without any approximations. The above equation can easily be extended to a multilayer system with n> 3. 121
Volume 163, number 2,3
CHEMICAL PHYSICS LETTERS
References [ 11 D.S. Chemla, I. Zyss, eds., Nonlinear optical properties of organic molecules and crystals (Academic Press, New York, 1987). [2] G.I. Stegeman, R. Zanoni, K. Rochford and C.T. Seaton, in: Nonlinear optical effects in organic polymers, eds. J. Messier, F. Kajzar, P. Prasad and D. Ulrich, NATO ASI Series (KIuwer, Dordrecht, 1989). [3] A. Furlani, C. Napoletano, M.V. Russo and W.J. Feast, PolymerBull. 16 (1986) 311. [4] P.N. Prasad, in: Nonlinear materials for non-linear optics, eds. B.A. Hann and D. Bloor, Special Publication No. 69 (Roy. Sot., London, 1989). [5] N. Bloembergen and P.S. Pershan, Phys. Rev. 128 (1962) 606. [6] F. Kajzar and J. Messier, Phys. Rev. A 32 (1985) 2352. [ 71 F. Krausz, E. Wintner and G. Leising, Phys. Rev. B 39 (1989) 3701.
122
IO November 1989
[8]D.S.Bethune,J.Opt.Soc.Am.B6(1989)910. 191J. Swalen. J. Mol. Electron. 2 (1986) 155. [ iOjC. Bubeck, A. Kaltbeitzel, R.W. ienz, D. Neher, J.D. Stenger-Smith and G. Wegner, in: Nonlinear optical effects in organic polymers, eds., J. Messier, F. Kajzar, P. Prasad and D. Ulrich, NATO ASI Series (Kluwer, Dordrecht, 1989). [ I 1] F. Kajzar, J. Messier and C. Rosilio, J. Appl. Phys. 60 ( 1986) 3040. [ 121 M. Sinclair, D. Moses, A.J. Heeger, K. Vilhelmsson, B. VaIk and M. Salour, Solid State Commun. 6 1 (1987) 221. [ 131 T. Kaino, K. Kubodera, S. Tomaru, T. Kurihara, S. Saito, T. Tsutsui and S. Tokito, Electron. Letters 23 (1987) 1095. [14]J.E.Sipe,J.Opt.Soc.4m.B4 (1987)481. [ 151 D. Neher, M. Ixclerc, A. Wolf, C. Bubeck and G. Wegner, to be published. [ 161 F. Kajzarand J. Messier, Thin Solid Films 132 (1985) 11.