Dynamic studies of two-beam coupling on the holographic gratings based on liquid crystal±polymer composite lms

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1 1 January 2001 Optics Communications 187 (2001) 193±198 Dynamic studies of two-beam coupling on the holographic gratings based on liquid crystal±polymer composite lms A.Y.-G. Fuh a, *, C.-R. Lee a, C.-C. Liao a, K.-J. Shyu a, P.-M. Liu a, K.-Y. Lo b a Department of Physics, National Cheng Kung University, Tainan 701, Taiwan, ROC b Department of Electronics Engineering, Kung Shan Institute of Technology, Tainan 710, Taiwan, ROC Received 1 June 2000; received in revised form 11 October 2000; accepted 1 November 2000 Abstract This study reports the observation of two-beam coupling (2BC) in polymer-dispersed liquid crystal (PDLC) lms during the formation of a holographic grating. A non-stationary grating e ect causes such a coupling. Based on the model we propose for the dynamic behavior of a PDLC grating, the experimental results agree well with the 2BC theory. Ó 2001 Elsevier Science B.V. All rights reserved. PACS: Hw; Df; Jk Keywords: Two-beam coupling; Liquid crystal; Polymer; Composite lm Photorefractive materials (PRs) have received extensive attention in the recent decade owing to their promise for applications in optical image processing, phase conjugation, optical switching devices, dynamical holography [1,2], and similar areas. Khoo [3] recently reported the molecular reorientational e ect in nematic liquid crystals (NLCs) associated with the PR e ect, while Ono and Kawatsuki [4] and Simoni et al. [5] reported the same e ect in polymer-dispersed liquid crystal (PDLC) lms. PDLCs have received considerable attention owing to their fundamental importance and potential for displays [6,7], other light control applications [8,9], and holographic recording [10±12]. The formed grating/hologram, although permanent, can be electrically [10,11] and optically [12] switchable. This study reports the observation of two-beam coupling (2BC) of the writing beams during the formation of a holographic grating in PDLC lms. The cause of such a 2BC e ect is not due to the PR e ect. Rather, it results from a non-stationary grating e ect. The liquid crystal, pre-polymers used in this experiment were E7 (E. Merck) and NOA65, 1 respectively. At room temperature, the refractive indices parallel and perpendicular to the director axis of E7 are n k 1:736, n? 1:511. The index of * Corresponding author. Tel.: ext ; fax: address: andyfuh@mail.ncku.edu.tw (A.Y.-G. Fuh). 1 The pre-polymer NOA65 was purchased from Norland Products, Inc., New Brunswick, NJ /01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S (00)

2 194 A.-Y.G. Fuh et al. / Optics Communications 187 (2001) 193±198 the NOA65 is n p 1:52. A slight photoinitiator dye, Rose bengal (RB), was added to the E7± NOA65 mixture (1.5 wt.%). This dye, with the presence of a coinitiator in the pre-polymer, forms free radicals, and then initiates polymerization of NOA65 with the exposure of the lm to green± blue light. Drops of the homogeneously mixed E7± NOA65±dye mixture were sandwiched between two indium±tin-oxide (ITO) coated glass slides separated by 36 lm-thick plastic spacers to form a sample. Samples were prepared using various mixing ratios of E7 and NOA65. Fig. 1 shows the experimental setup. Brie y, two writing beams, E 1 and E 2, derived from an Ar laser (k ˆ 514:5 nm) intersected at an angle 2h which varied from 1 to 8. The beams were TE polarized and unfocused, and each had a beam diameter of 4 mm. Meanwhile, they had a roughly equal power 100 mw. During the writing of the grating, an unpolarized He±Ne laser was introduced to the plane determined by beams E 1 and E 2 to probe the writing region of the sample. One of the rst-order di racted beams of the He± Ne probe beam (from D 3 ), and the writing beams (from D 1 and D 2 ) after coupling in the sample, were monitored while the grating formed. To eliminate uctuation of the output power of the writing beams, a wedge glass (WG) slide was positioned before the beam splitter (BS) which gave the two writing beams. The monitored writing Fig. 1. The experimental setup for studying the dynamic 2BC in a PDLC grating: WG: wedge glass, BS: beam splitter, D 1 ±D 4 : photodiode, M: mirror. beam powers were normalized with the beam power splitted from WG (from D 4 ). Fig. 2 shows the measured results for PDLC samples with 0 wt.% (Fig. 2(a)), 20 wt.% (Fig. 2(b)), 40 wt.% (Fig. 2(c)) E7 for the setup with 2h ˆ 1:85. Notably, the signal of the two writing beams shown in Fig. 2(a)±(c) is increasing with time. The reason for this is the decrease of the photoinitiator dye as the photopolymerization proceeds. It is noted that light scattering is negligible initially, since the compound of the sample is a homogeneously mixed (isotropic) solution. As the polymerization proceeds, it is noticeably increasing in sample containing E7 induced mainly by the unaligned phase-separated LC molecules. The scattering intensity, however, is much smaller compared with that of the transmitted writing beam and the rst-order di racted beam. Therefore, no corrections are made for the measured signals to compensate the light scattering e ect. Furthermore, it reveals that the He±Ne probing beam was di racted almost immediately after the Ar laser beams were turned on at t ˆ 0. The 10± 90% rise time is 1.75 s. We believe that it is due to the laser-induced density grating. The two writing beams E 1 and E 2 established a sinusoidal interference light pattern. Since photopolymerization preferably initiates in high-intensity regions, a spatial pattern of monomer concentration occurs across the lm. Consequently, monomer molecules di use towards the high-intensity regions [13]. Meanwhile, the molecular weight of the polymers in the high-intensity regions increases (due to crosslinking) much more than in the low-intensity regions. Therefore, the intensity interference pattern created a refractive index grating that could be associated with the spatially varying molecular weight of the polymer molecules termed the density grating. On the other hand, if the samples contain liquid crystal molecules which are not consumed during polymerization, the chemical potential of liquid crystals increases in the high-intensity regions more than in the low-intensity regions due to the consumption of monomers. Hence, LC molecules di use from the high-intensity regions towards the low-intensity ones to equalize the chemical potential across the writing area. These di usions are then followed by the formation of a

3 A.-Y.G. Fuh et al. / Optics Communications 187 (2001) 193± Fig. 2. The changes in intensity of the two writing beams, and the rst-order di racted intensity of the probe beam for the samples having (a) 0 wt.%, (b) 20 wt.%, (c) 40 wt.% E7 for the setup with an intersecting angle 2h ˆ 1:85. The inset in (c) is the magni cation for the curing time in the initial 15 s. phase grating associated with the periodic arrangement of polymer-rich in the high-intensity regions and LC-rich in the low-intensity regions. The refractive index in the LC-rich regions is greater than in the polymer-rich regions. Thus, the phase grating termed reverse-di usion grating, is phase shifted 180 with respect to the density grating. Fig. 2(b) (E7 ˆ 20 wt.%) shows how the di racted intensity initially increased because of the rapid formation of the density grating. The intensity then decreased as the reverse-di usion phase grating began to grow. When the gratings were equal in amplitude and opposite in phase, the di racted intensity became zero. Finally, the diffracted intensity increased again, and eventually became saturated when the photopolymerization process was complete. The di usions of both LC molecules and monomers are made easier by reduced viscosity with increasing LC concentration. Thus, the molecular di usion would rapidly quench the density grating. Fig. 2(c) (E7 ˆ 40 wt.%) re- ects this phenomenon, displaying much smaller intensity and width of the same peak that appeared in the early time in Fig. 2(b) (E7 ˆ 20 wt.%). Fig. 2(b) and (c) also reveals that dynamic changes of the writing beam intensity deviated

4 196 A.-Y.G. Fuh et al. / Optics Communications 187 (2001) 193±198 almost as soon as the beams were switched on. This phenomenon indicates that the two beams were coupled with the energy transferred from one beam (beam 1) to the other (beam 2). They then intersected at the turning time t T when the density grating was fully quenched by the reverse-di usion grating. After turning time t T, two beams coupled reversely, i.e. energy transferred, from beam 2 to beam 1. Based on the 2BC theory, the intensities of the writing beams, I 1 and I 2 can be written as a function of the depth (z-axis) of sample [2] 1 m 1 I 1 z ˆI 1 0 exp az ; 1 1 m 1 exp cz 1 m I 2 z ˆI 2 0 exp az ; 2 1 mexp cz where m ˆ I 2 0 =I 1 0 (m ˆ 1 in this experiment), cd is the coupling strength and equals 2pd Dnsin/=k 0 cosh, d is the thickness of the sample (d 36 lm), Dn is the amplitude of the grating, k 0 is the wavelength of the writing beam in vacuum, / is the phase shift between the grating and light interference pattern and a is the bulk absorption coe cient a t ˆ 0 1: cm 1, which was decreasing with time in the present case. The measured results illustrated in Fig. 2(b) and (c) show that the two writing beams coupled during the formation of the grating. We believe that the molecular di usions give a non-zero phase shift angle /. Restated, the grating was nonstationary. Based on Eqs. (1) and (2), before the turning time t T, energy transferred from I 1 to I 2 I 2 > I 1.Att T, Dn 0, and I 1 ˆ I 2. Meanwhile, after t T, the phase shift angle became p / and energy then transferred in reverse (I 2 to I 1 ). Thus, the measured results agree with the theory qualitatively. For the sample without E7 (Fig. 2(a)), the grating was contributed solely from the density grating. Consequently, no turning time existed and the phase shift would not change from / to p / during the curing as in the samples with E7 (Fig. 2(b) and (c)). The measured result (Fig. 2(a)) agrees with this expectation. Notably, the energy coupled from one beam to the other continuously with no intersection throughout the curing time. Fig. 3. The magni cation of Fig. 2(a) for the time from 110 to 130 s. Fig. 2(a) (E7 ˆ 0 wt.%) also reveals that the measured curve of the rst-order di racted intensity has two peaks. This is natural, since the density grating grew and the rst-order di racted intensity of the probe beam presented the shape of the rst-order Bessel function before the sample was cured. Since the sample absorbed the probe beam, the minimum between the two peaks did not reach zero [14]. Fig. 3 is a magni cation of Fig. 2(a) for the time from 110 to 130 s. The sample is cured during this period. Notably, the signal of the two writing beams uctuates correlatively, while the rst-order di racted intensity of the probe beam is constant. The result indicates that the phase shift / uctuates which, in turn, causes the energy transfer between the two writing beams. Fig. 4 shows the measured results of both the coupling strength, cd, the rst-order di racted ef- ciency, g 1, of the nal grating for the sample having 20 wt.% E7 as a function of the grating spacing K (which is calculated from K ˆ k=2 sinh). The nal coupling strength is calculated from Eqs. (1) and (2) together with Fig. 2(b) for the corresponding intersecting angle. The di racted e ciency is de ned as the intensity of the di racted beam divided by that of the probing beam. Notably, both curves for cd and g 1 are similar, and peak at 2h ˆ 2 (which corresponds to a grating spacing 14.7 lm). As mentioned above, the coupling strength cd equals 2pd Dnsin/=k 0 cosh. It is believed that sin/=cosh varies negligibly during

5 A.-Y.G. Fuh et al. / Optics Communications 187 (2001) 193± Fig. 4. The measured results of the coupling strength, cd, and the rst-order di racted e ciency, g 1, of the nal grating for the sample having 20 wt.% E7 as a function of the grating spacing. the formation of grating in the present case. Thus, cd is proportional to Dn. Assuming Dn 1, the di racted e ciency g 1 is proportional to (Dn) 2 [14]. Also, the increase of the di raction e ciency with the increase of the grating spacing is due to the increasing visibility of the interference fringes set up by the two writing beams. But with further increasing in spacing, the gratings are expected to loose light-di racting power. Thus, the measured result shown in Fig. 4 is reasonable. A separate work proposes a model to explain the dynamical behavior of a PDLC grating [15]. The theory derived from this model allows the determination of the amplitude of the transient and nal gratings. The amplitude of the nal grating Dn is estimated to be for the PDLC sample with 20 wt.% E7 for the setup with 2h 1:85. The phase shift / is then calculated to be 3.9. In conclusion, this work has observed 2BC in PDLC lms during the writing of a holographic grating. The cause of such a coupling e ect is believed to be associated with the non-stationary grating e ect. Meanwhile, the initial energy ow between the two beams is not always from one beam to the other. This is expected, since the geometry of the grating writing is symmetrical in this case. Meanwhile, the nal coupling strength, cd, and grating amplitude Dn can be deduced. Similar experiments with m 6ˆ 1, i.e. I 1 0 6ˆI 2 0, are underway. Acknowledgements The authors would like to thank the National Science Council (NSC) of the Republic of China for nancially supporting this research under contract no. NSC M References [1] P. Gunter, J.P. Huignard (Eds.), Photorefractive Materials and Their Applications, Springer, Berlin, [2] P. Yeh, Introduction to Photorefractive Nonlinear Optics, Wiley, New York, [3] I.C. Khoo, IEEE J. Quant. Electron. 32 (1996) 525. [4] H. Ono, N. Kawatsuki, Opt. Lett. 22 (1997) [5] G. Cipparrone, A. Mazzulla, F. Simoni, Opt. Lett. 23 (1998) [6] J.W. Doane, N.A. Vaz, B.-G. Wu, S. Zumer, Appl. Phys. Lett. 48 (1986) 269. [7] J.L. Fergason, SID Int. Symp. Dig. Tech. Paper, 16, 1985, p. 68. [8] B.-G. Wu, J.L. West, J.W. Doane, J. Appl. Phys. 62 (1987) 3925.

6 198 A.-Y.G. Fuh et al. / Optics Communications 187 (2001) 193±198 [9] A.Y.-G. Fuh, C.-Y. Huang, B.-W. Tzen, Jpn. J. Appl. Phys. 33 (1994) 1088 (Part 1). [10] V.P. Tondiglia, L.V. Natarajan, R.L. Sutherland, T.J. Bunning, W.W. Adams, Opt. Lett. 20 (1995) [11] A.Y.-G. Fuh, M.-S. Tsai, C.-Y. Huang, T.-C. Ko, L.-C. Chien, Opt. Quant. Electron. 28 (1996) [12] A.Y.-G. Fuh, M.-S. Tsai, C.-J. Huang, T.-C. Liu, Appl. Phys. Lett. 74 (1999) [13] T.J. Bunning, L.V. Natarajan, V. Tondiglia, R.L. Sutherland, D.L. Vezie, W.W. Adams, Polymer 36 (1995) [14] H.J. Eichler, P. Gunter, D.W. Pohl, Laser-induced Dynamic Gratings, Springer, Berlin, 1986, p. 99. [15] A.Y.-G. Fuh, M.-S. Tsai, C.-R. Lee, Y.-H. Fan, Dynamical studies of gratings formed in polymer-dispersed liquid crystal lms doped with a guest-host dye, Phys. Rev. E 62 (2000) 3702.