Synthetic Metals, 51 (1992) 407-417 407

Optical waveguiding of PMMA doped with (t-Bu)4-Pb-phthalocyanine in anisotropic multilayer (pm) geometries: an m-line study

Mikael Lindgren*,**, Ha ruk i Ohkawa, Ta tsuo Wada and Hi royuk i Sasabe Frontier Research Program, RIKEN, Hirosawa 2-1, Wako-Shi, 350-01 Saitama (Japan)

Abstract

Films (0.5-2 #m thickness) of PMMA doped with (t-Bu)4-Pb-phthalocyanine (Pbpc) in the concentration range 0-100% have been studied as multilayer slab waveguides. Multilayer waveguides were made by spin-coating PMMA/Pbpc solutions onto a polyimide system (PIQ). Using the prism coupling method in an m-line set-up, the guiding TE and TM modes were investigated at two wavelengths, 1064 and 514.5 nm, the latter being in the optical window of Pbpc. The value of the refractive index of PMMA/Pbpc was found to be larger at 1064 nm, and in addition anisotropic, the latter indicating partial ordering. It is suggested that the plane of the Pbpc rings tends to be oriented preferentially parallel to the film plane. The results demonstrate the possibility of using a phthalocyanine/polymer system as an active nonlinear wave- guide device operating in the optical window (2: ~ 515 nm). Dispersion relations for uniaxial three- and four-layered waveguide geometries, and field distributions of the eigenmodes were derived and used to design (simulate) basic optically-nonlinear waveguide applications in organic multilayer structures. It is shown how the unique properties of Pbpc (an optical window with low value of n) enables phase-matched SHG for TE ~ ~ TE 2~ for modes of the same order, giving optimal overlap and high conversion.

Keywords: polymer waveguide, phthalocyanine, nonlinear optics, anisotropic films, phase-matching, m-line method.

Introduction

The an i so t ropy of the re f rac t ive index and its dependence on the d i rec t ion of l ight p ropaga t ion and pola r iza t ion are the most impor t an t mater ia l pa ramete r s to know when designing op toe lec t ron ic devices. Thus, the l ight-guiding proper t ies of a given geomet ry can be calcu- la ted by solving Maxwel l ' s equat ions and applying appropr i a t e bounda ry condi t ions for a given l ight polar izat ion. In this s tudy three- and four- layer slab waveguides of th in polymer films spun on glass subs t ra tes

*On leave from: Institute of Physics and Measurement Technology, LinkSping Univer- sity of Technology, S-581 83 Link6ping, Sweden.

**Author to whom correspondence should be addressed.

0379-6779/92/$5.00 ~) 1992 - Elsevier Sequoia. All rights reserved

408

have been investigated. Such films turn out to be more or less aniso- tropic and, herein, m-line spectroscopy in combination ~vith the prism- coupling method is used to determine the refractive index anisotropy, i.e., for light polarized parallel or perpendicular with regard to the film plane.

Thin films (pro) in multilayers are used to construct experimental models. In this report we are concerned with the characterization of films of PMMA doped with (t-Bu)4-Pb-phthalocyanine (Pbpc) both as single layers and in sandwiched multilayers, together with a commercial poly- imide system, PIQ. The latter offers a variety of techniques in organic waveguide fabrication [1]. Simulations of wave-propagating properties are useful in investigations to determine how nonlinear optical (NLO) effects can be used to control or change the guided light. As an example, the efficiency of energy exchange between modes of different frequency or polarization is critically dependent on phasematching conditions. In this report is is shown, from simulations of waveguiding properties, how the particular refractive index dispersion for a metal -phthalocyanine in conjunction with the optical window can be utilised for the efficient phase matching of second harmonic generation in three- and four-layer slab waveguide structures. This follows from the fact that the refractive index in the optical window (the nonabsorptive region at wavelengths shorter than the low-energy absorption bands) is considerably lower than that at wavelengths on the IR side of all the electronic transitions. Normally, sum-frequency phase matching can only be achieved in relatively an- isotropic systems, usually in single crystalline films where the phase- matched energy exchange is only taking place between modes of different polarization. The extraordinary properties of metal-phthalocyanines al- lows, in addition, TE ~ to TE n~ (or TM ~ to TM n~) conversion.

Materials and methods

Chemicals The tert-butyl substituted Pb-phthalocyanines were prepared as re-

ported previously [2]. The polyamic acid/polyimide system, PIQ was ob- tained commercially from Hitachi Chemicals [l(a)]. The optical properties of similar polyimide systems, obtained from Dupont Chemical, have been investigated and reported previously [l(b)-(d)]. PMMA (optical grade) was obtained commercially and used without further purification other than filtering the solutions prior to use. Films for waveguiding were made using the spin-coating technique followed by drying and annealing procedures.

m-Line spectroscopy The method of obtaining the effective refractive index of propagating

TE or TM modes in isotropic systems from so-called m-line measurements

409

using the prism coupling technique was reported some time ago [3]. With this technique, polarized l ight from a laser is coupled into the film with a high index prism, and the air gap between the prism and film is controlled by adjust ing the pressure on the prism head. For weak coupling (maxi- mum airgap allowing a detect ion of m-lines), the presence of the prism is not necessary for the analysis of the mode propagat ion characterist ics [3(b)]. Most measurements were made using high index prisms made from F D l l or FD21, commercially available from Hoya (Japan). Laser experi- ments were carried out on a table equipped with the usual optical accessories, rotat ional stages, and cw low-power ( < 2 - 5 m W ) lasers (514.5 nm Ar, 632.8 nm He-Ne, 1064 nm YAG).

Analysis of anisotropic multilayer structures In the theoret ical analysis it was assumed tha t the thin films had

biaxial anisotropy with the dielectric tensor real and diagonal, and one principal direction perpendicular to the film plane (X-axis), one defined as the direction of propagat ion (Z-axis), and thus, the third defined as the transverse direction [4]. In the analysis of the films, uniaxial symmetry was assumed, so that ny= nz= no, and nx=nE (refractive index for ordinary and extraordinary ray, respectively). The effective indices for propagat ing modes were obtained from the following expressions: Nm = np sin Or,, where np = the refractive index of the prism, and Or, is the angle of incidence at the prism bottom for excitat ion of mode m [3]. Three unknown parameters, such as no, nE and t, can be obtained from these data including both TE and TM modes. The unknown parameters were found by fitting, simultaneously, the dispersion relations associated with the set of experimental data by i terat ions following a s tandard gradient technique [5]. The derivation of dispersion relations and wavefunctions associated with each TE or TM mode in a four-layer s t ructure for a given geometry and set of parameters can be obtained in a similar fashion as in the three-layer problem. The dispersion relations are given in the Appendix.

Resul t s

P/Q The polyamic acid to polyimide conversion is followed by drastic

s t ructural and optical ordering effects, and these features have been studied in detail using the m-line method in combinat ion with X-ray spectroscopy and other methods [ lb-d] . The most important characteris- tics for waveguide implementat ion are demonstra ted in Fig. l(a) and (b), which shows the changes following the refractive index and its birefrin- gence during (slow) annealing. These results have been analysed using the uniaxial approach to the mode dispersions, in contras t to earlier studies [lb, c]. This refined approach does not change the earlier main

1.69

¢~ 1.68 H

1.67

~ 1.66

1.65

150 2OO 250

anneal temp°C

id

:~ .0.04

II

-0.05

gr~

r

.~ -0.06

410

-0.07

1.64 -0.08 ' ' 100 100 150 200 250

(a) (b) anneal temp°C Fig. 1. The changes in the refract ive index (a), and the birefr ingence (b), of the polyimide system, PIQ, during heat t reatment. The analysis was made following a uniaxial approach in refining the m-line method. The four series refers to samples of different ini t ial thickness: 1.7-2.4 pm, that resulted in final thicknesses of 1.4-2.0 ttm. The par t icular sample is 'PIQ 13', as given in the product information [l(a)].

conclusions concerning polyimides [l(b), (c)]. However, it implies that it is necessary in (accurate) characterizat ion of more anisotropic systems [5], and part icularly when designing sensitive parameters such as, e.g., phasematching conditions in waveguiding devices. Multi layer s t ructures consisting of PIQ films spun on phthalocyanine-doped PMMA will be discussed in some detail in the following sections.

(t-Bu)¢-Pb-phthalocyanine in PMMA The nonl inear optical properties of Pbpc are current ly under investi-

gation [2], and here we shall only report on linear optical response. Adopting the m-line technique it was possible to determine the refractive index in the optical window (at 514.5 nm), in addit ion to the region on the IR side of the low-energy optical absorption (1064nm). The refractive indices for TE polarizations (no) at both wavelengths are shown in Fig. 2, together with that obtained from TM-mode excitation at 1064 nm (ne), for films of PMMA of different composit ion (% by weight). It was not possible to obtain m-line data for TM polarization in the optical window at Pbpc concentrat ions above ~20%, the detailed reasons not yet being known.

Ellipsometry studies of the thin-film properties of related metal- or metal-free phthalocyanines have been reported, indicat ing par t icular preferential or ientat ions of the phthalocyanine rings depending on film

411

production conditions [6]. In this study vacuum deposition techniques were used for sample preparation. It is interesting to note our m-line results for Pbpc also indicate a marked uniaxial anisotropy, see Fig. 2, al though the film preparation technique is quite different. The refractive index for the TE-mode (no) is considerably larger than that for the TM-mode (both no and nE contribute) at higher concentrations of Pbpc, and it is suggested that the Pbpc rings prefer an orientation with the molecular plane parallel to the substrate.

It was possible to use a prism coupler and guide light in the films. Streaks were clearly observed up to 15% Pcpb content at 514.5 nm. Above 10%, the losses at 514.5 nm became higher than 6 dB cm -1.

It was found that PMMA/Pbpc could be spin-coated onto PIQ without losing the waveguide quality of PIQ. Selected four-layer films of known layer thickness and refractive index were investigated using the m-line method and simulated m-line spectra were satisfactorily reproduced (all measured indices effectively fell within +_0.001 of the expected value), giving us complete confidence in the analytical approach to anisotropic multilayer systems. (The thickness of the PIQ layer was measured before spin-coating the final PMMA/Pbpc layer. The thickness of the PMMA/ Pbpc layer could be determined from the absorbance of the final film by comparing the absorbance of the low-energy band for Pbpc with a 'cali- bration curve' compiled from m-line and optical absorption data of three- layer waveguides. The refractive indices were taken from curves as in Fig. 2, or measured separately in three-layer films.)

1.85"

.~ 1.65'

g~

H

1

i " ~ N

nO(1.064) hE0 .O64) nO(0.5145)

m

N

1.45 . . . . . . . , • 0 20 40 60 80 100

% of (t-Bu)4-Pb-Phth in PMMA

Fig . 2. R e f r a c t i v e i n d e x of ( t - B u ) 4 - P b - p h t h a l o e y a n i n e a t w a v e l e n g t h s of 1064 a n d 514.5 nm.

412

W a v e g u i d e s i m u l a t i o n s

Frequency conversions, such as second harmonic generat ion (SHG), are the most established concepts in the characterizat ion of nonl inear behaviour, part icularly among organic materials [4(c)]. The SHG process is depicted in Fig. 3 where the vertical scale indicates the 'density of accessible excited states' compiled from an optical absorption curve of PMMA/Pbpc (in l inear energy units). Both virtual photon states are near the band centred on 720 nm, and the SHG photons are 'de-excitated' from the so-called 'optical window' (~515 nm), the frequency region of low absorption. The combinat ion of these effects makes the system promising in device applications. In order to reach high conversion factors it is necessary that the generated wave and the pumping wave are phase- matched, which means that their wave-vector mismatch (for SHG), Ak =k2o~-2k~, (=n2o~-n~), is equal to zero [4(c)]. Pbpc discussed in the previous section was shown to have an optical window which allowed waveguiding, and, furthermore, the refractive index in the optical window was found to be lower than on the IR side. The simulat ion of the dependence of the effective index on thickness gives a guideline on how to

Energy

ca. 510mn

ca, 720rim

2,

(o

Density of States

Fig. 3. Schematic showing the SHG process where the doubled frequency photons are created in the optical window. The ver t ical axis shows the 'density of photon-states ' compiled from an optical absorpt ion curve re-scaled to be l inear in frequency units.

413

achieve the phase-matching conditions. The experimentally determined refractive indices of Pbpc shown in Fig. 2 may be used to illustrate the SHG condition, albeit remembering that the frequency doubling is not perfect. Furthermore, the SHG is assumed to be activated by applying an external electric field to the centrosymmetric film, e.g., in the transverse direction.

A plot of the effective index for a three-layer guide consisting of 72% Pbpc in PMMA on quartz is shown in Fig. 4(a), and represents phase-matching curves for TE(1064)---~ TE(514.5). The arrow indicates the phase-matched condition between 0'th order modes. Similar plots to those shown in Fig. 4(a) can be constructed, revealing SHG phase- matched conditions between modes (all combinations of TE and TM) of the same order in films with Pbpc content from ~ 15%. The efficiency is demonstrated by the large overlap between the interacting modes since the electric field distribution curves are essentially identical. Integration of the modes reveals overlaps always better than 90% for TE modes (far from the critical cut-off thickness). The analysis of TM modes is more complicated since both the Ez and Ex compo- nents have to be accounted for. Simulations yield less efficient con- vers ion- -a total overlap between 30 and 60% at a phase-matched con- dition.

Four-layer structures allow an additional degree of freedom in phase-matching guided-wave geometries. Using PMMA/Pbpc as one layer, phase-matching between modes of the same order is achieved, as in the three-layer case, see Fig. 4(b). The occurrence of two layers decreases the conversion efficiency since only the response integrated over the active layer contributes. The field distribution of TE modes for a four-layer structure consisting of PIQ and PMMA/Pbpc is shown in Fig. 5. The presence of the 'NLO-passive' layer is to allow a variety of possible advantages in the design of optoelectronic devices. Some exam- ples which might involve polyimide systems are: (i) formation of channel waveguide patterns from lithographic methods; (ii) decreasing the propa- gation loss; (iii) fabrication of grating structures for in and out coupling; (iv) being electrooptically active, allowing fine adjustment of phase- matching conditions, etc.

S u m m a r y and conc lus ions

(t-Bu)4-Pb-phthalocyanine/PMMA films have been examined in view of possible (nonlinear) waveguide applications involving optical frequen- cies within the optical window. The refractive index and its anisotropic features have been determined for wavelengths in the optical window (514.5 nm) as well as at near IR (1064 nm) by refining the m-line method. A preferential orientation of the Pbpc rings (parallel to the film plane) may be concluded by comparison with a recent ellipsometry study [6].

414

(a)

1.65"

1.55"

1.45 0.000

TE#1~TE#0 (514.5 nm)TE#1

0.200 0.400 0.600 0.800 1.000 Thickness (microns)

1.7

TE#0(514.Snm) . .

.~ 1.6

r~ ~ / / TE#1 ( 5 1 4 ~ ~

0.0 1.0 (b) Thickness of Phth-Layer (microns)

Fig. 4. Phase-matching curves to illustrate 'near ' TE °' ) TE ~' conversion (a) in a three- layer Pcpb structure, (b) in a four-layer PIQ-PMMA/Pbpc structure. The Pbpc content in PMMA is 72% and PIQ is in the precursor state. The simulations use experimentally determined refractive index data measured at 1064 nm and 514.5 nm. Refractive index of Pbpc is taken from Fig. 2, and parameters for PIQ were measured separately: no = 1.612 (at 1064 nm), no = 1.69 (at 514.5 nm). In the four-layer structure the PMMA/Pbpc layer is varied while the PIQ layer is a constant 0.4 #m. Substrate values for quartz ns = 1.4469 (1064 nm), ns = 1.4616 (514.5 nm). Cladding index = 1.0 (air).

The fact that the refractive index in the optical window is considerably smaller than at IR wavelengths enables phase matching of certain sum- frequency nonl inear optical properties in waveguided geometries. TE ~ > TE 2~ mode conversion between 0th order modes has been demon- strated through simulations. The possibility of extending the single waveguide to multiple-layered waveguides suggests a variety of design- routes for guided nonl inear and optoelectronic devices based on purely organic materials.

415

x-axis

-Ey mode #0 +Ey -Ey

Cladding

(a) (b)

mode #1 +E

Fig. 5. Electric field distribution for the: (a) 0th order; (b) 1st order TE modes at 514.5 nm in the four-layer structure as simulated in Fig. 4. Thicknesses of PIQ and PMMA/Pbpc layers are set equal to 0.4 pm.

References

1 (a) Hitachi Chemical Company Ltd., Product Information: Hitachi Heat-Resistant Fine Polymer PIQ; (b) R. Reuter, H. Franke and C. Feger, Appl. Optics, 27(21) (1988) 4565; (c) H. Franke, G. Knabke and R. Reuter, SPIE, 682(1986) 191-195; (d) C. Feger, Polym. Eng. Sci., 29 (1989) 347.

2 (a) M. Hosoda, T. Wada, A. Yamada, A. F. Garito and H. Sasabe, Mater. Res. Soc. Symp. Proc. 175, 1990, Mater. Res. Soc.; (b) T. Wada, Y. Matsuoka, A. Shigehara, A. Yamada, A. F. Garito and H. Sasabe, Mater. Res. Soc. Int. Meet. Adv. Materials 12, 1989, Mater. Res. Soc.; (c) H. Sasabe, T. Wada, M. Hosoda, H. Ohkawa, M. Hara, A. Yamada and A. F. Garito, SPIE, 1337 (1990) 62-71.

3 (a) P. K. Tien and R. Ulrich, J. Opt. Soc. Am., 60 (1970) 1325; (b) R. Ulrich, J. Opt. Soc. Am., 60 (1970) 1337.

4 (a) P. K. Tien, Appl. Opt., 10 (1971) 2395; (b) S. Yamamoto, Y. Koyamada and T. Makimoto, J. Appl. Phys., 43 (1972) 5090; (c) J. Zyss and D. S. Chemla, in D. S. Chemla and J. Zyss (eds.), Nonlinear Optical Properties of Organic Molecules and Crystals, Vol 1, Academic Press, New York, 1987, Ch. II, p. 1; (d) G. I. Stegeman and C. T. Seaton, J. Appl. Phys., 58 (1985) R57.

5 M. Lindgren, unpublished results. 6 M. K. Debe and D. R. Field, J. Vac. Sci. Technol., A9 (1991) 1265.

Appendix

The dispersion relations for anisotropic four-layer structures are given below. The refractive indices of the two guiding layers of interest are different and therefore there will be two expressions for the mode dispersion and eigensolutions in the description of both the TE

416

and TM modes. This originates from the relat ive magni tudes of the absolute refract ive indices of the two waveguide layers and the effec- tive index of guiding modes, nia is the refract ive index for l ight in film a polarized along the direct ion i = x, y and z, with x being perpen- dicular to the film plane, z the direct ion of propagation, and, y the trans- verse direction, a = s or c represents substrate or c ladding layer, respec- tively, ta stands for film thickness, ko" N = fl with k0 = 2~/,t (value for vacuum), fl is the wave vector along the propagat ion direct ion in the film.

The dispersion relat ions for the TE modes:

Case 1, N < nyi

[ (Ts ) ] ~2 tanI(z2, t 2 _ t a n _ ~ ( 7 ~ (1) tan ~ 1 t l - t a n -1 ~ - - - a l \a~/J

where

(~2 2 2 = k o ( n y i - N 2) and 7~.c = k 2 ( N 2 - n~,c)2

Case 2, ny 2 < N < n~l a2 -~ 72 -- ko( N2 _ ny2)2

t a n [ ~ t t - t a n - ~ ( ~ ) l = 72( ] - k exp(--272t2) ~ \ 1 + k exp(-272t2) (2)

where

k \ 7 ~ - ~ /

The dispersion relat ions for TM modes:

Case 1, N < nxi

[ tan al tl - t an - 1 ___. _ _ _

\ nsoh / J

where

2 2 ( N2) ot~ = konzi 1 -k-~- and

nxi

Case 2, nx2 < N < nxl

a2 -* 72 - ko n z2 2~- - i \ l ~ x2

[ tan ~,t,-- \~;/J'n%¢--''=

where

(n272--rt227c ~ k = \n27~ 2 + n2z27c,]

n 2 - - ~ a n | ~ 2 ~2 --

nz2~l L \ n2c°~2]J

72,c k ~ ( N 2 2 = - ns,c)

n ~ 2 ( ' 1 - k e x p ( - 2 ? 2 t 2 )

n22~1 \1 ~ k exp( - 2 7 2 t 2 ) ]

(3)

(4)

417

The second dispersion relat ion of each case can be regarded as being due to a single layer guided mode in film 1, that is, the other layer acts as a cladding with an exponential decay of the field distr ibution away from the guide-layer, compare Fig. 5(a) and (b). The dispersion relations for TE and TM modes in three-layer s t ructures are obtainable from these by sett ing t2 = 0. The field distr ibutions are found as l inear combinations of harmonic or hyperbolic functions in guiding and cladding regions, respec- tively, with the expansion coefficients given by the appropriate boundary conditions, as in the three-layer case [4]. Analogous expressions for multi-layer s t ructures are easily obtained as in the three- and four-layer cases.