Switching behaviour of ferroelectric liquid crystals probed by optical second-harmonic generation

Transcription

1 Appl. Phys. B 74, (2002) DOI: /s Applied Physics B Lasers and Optics y.g. fokin 1 t.v. murzina 1 o.a. aktsipetrov 1 s. soria 2, g. marowsky 2 Switching behaviour of ferroelectric liquid crystals probed by optical second-harmonic generation 1 Department of Physics, Moscow State University, Moscow , Russia 2 Laser-Laboratorium Goettingen e.v., Hans-Adolf-Krebs-Weg 1, Goettingen, Germany Received: 16 October 2001/Revised version: 18March 2002 Published online: 6 June 2002 Springer-Verlag 2002 ABSTRACT Ferroelectric properties of thin (1.5 4 µm planar cells of a ferroelectric liquid crystal (FLC) mixture are studied using electro-optic measurements, second-harmonic generation (SHG) and SHG interferometry. A switching behaviour of the FLC cells in external dc electric fields is observed. It is characterised by rotation of the polarisation plane of the transmitted light and by changes in the SHG intensity, phase and anisotropy dependences, which are attributed to a collective motion of the system as a ferroelectric uniform state with C 2 symmetry. PACS Gd; Ky; D 1 Introduction Ferroelectric liquid crystals (FLCs) have been attracting significant attention for several decades, and are known as promising materials for potential applications and as rare examples of two-dimensional (2D) ferroelectrics [1]. Along with the Langmuir Blodgett ultra-thin polymeric films, which have been designed recently as intrinsic 2D ferroelectrics [2], FLCs are another class of improper 2D ferroelectrics [3]. The role of dimensionality in structural phase transitions and ferroelectricity in these materials has been one of the central points of basic theoretical and experimental studies for decades. Optical second-harmonic generation (SHG) is a rather simple, non-invasive and informative method for studying the structure, symmetry and morphology of ultra-thin films [4]. This advantage of SHG stems from its unique sensitivity to the breakdown of inversion symmetry [5]. The latter results in high sensitivity of the SHG probe to the ferroelectric properties of the subsurface layers and ultra-thin films. In particular, SHG allows us to reduce the influence of other sources of electric currents not connected to polarisation switching, like injected charge carriers or impurities, which may complicate electrical studies. The polar order of FLC molecules is equivalent to a non-centrosymmetric arrangement. The SHG signal is pronounced only when the helical structure of the smectic-c* Fax: / , ssoria@llg.gwdg.de (SmC*) phase is suppressed. This suppression occurs when FLC films are constrained in thin cells where the unwinding of the helix is achieved by surface coupling. We have studied ferroelectric properties and the switching behaviour of thin planar FLC cells using electro-optic (EO) and SHG intensity and interferometry measurements. Both techniques are independent and self-contained and lead to equivalent results. However, only SHG is surface-sensitive. SHG intensity and interferometry profiles were observed as functions of the applied field for two combinations of input output polarisations of light in transmission and reflection geometries. For the analysis of the SHG results, the system was assumed to be a ferroelectric uniform state with C 2 symmetry (collective model). Molecules tend to form a uniform orientation to avoid the production of polarisation charge at E = 0. The surface constraint also promotes a uniform alignment. 2 Experimental set-up The output of a Q-switched Nd:YAG laser with a pulse intensity of 1 10 MW/cm 2, a pulse duration of 7ns and a repetition rate of 10 Hz at a wavelength of 1064 nm is used as fundamental radiation. To characterise the general non-linear optical properties of thin FLC cells, the azimuthal anisotropy of the SHG intensity is measured in transmission and reflection geometries at different angles of incidence. The cells are mounted on a rotation stage in air, which stage is arranged in such a way that the smectic layers are almost horizontally oriented, parallel to the y z plane (Fig. 1a). In addition to the SHG intensity measurements, the SHG interference method [6] is used, allowing us to detect the SHG phase. The fundamental and SHG wavelengths are filtered out from each other by using an appropriate set of colour filters and a grating monochromator. A reference branch, which measured the SH signal generated by a z-cut quartz crystal, was used in order to compensate the intensity fluctuations. The interferometry measurements were done by translating a thin crystalline quartz plate a distance of 20 cm in the direction parallel to the fundamental beam. A dc electric field of up to 25 V directed to the cell along the normal (z direction) was applied using indium tin oxide (ITO) electrodes. Figure 1b shows the details of the chevron layer as well as a sketch of the collective switching model.

2 778 Applied Physics B Lasers and Optics E S E P k ω Y,, Y Y, Θ k 2ω Ψ +E E=0 are transmitted through the structure by elastic stress, and result in an unwinding of the helix and homogeneous ordering in the z direction (perpendicular to the film plane) dictated by the surface. This unwinding takes place if the thickness of the cell is much smaller than the bulk helical period. All the cells are equipped with indium tin oxide electrodes, and coated with a rubbed polyimide layer for the planar alignment. In this study, we have preferentially used cell configurations with identically brushed polyimide coatings. a V FIGURE 1 a Details of the planar aligned FLC cell together with the system of coordinates. b Sketch of the collective switching model: the director field proceeds on the surface of the tilt cone The EO measurements were carried out using stabilised He Ne laser radiation (wavelength λ = 632.8nm) with crossed polariser and analyser. The real-time detection of the transmitted signal was performed by an externally triggered photodiode. Applying a dc electric field in the direction normal to the cell leads to a rotation of the polarisation plane of the transmitted light. 3 Materials and samples The studied FLC quaternary mixture consists of 4.67 wt % (S)-IGS97 in DFT1, which is a mixture of three components, MH11, MH3 and MH2 (50 : 25 : 25 wt %, respectively) (Fig. 2). The primary dipole moment of the FLC molecules is directed perpendicular to the long molecular axes. The SHG measurements are performed in 1.5-, 2-, 3- and 4-µm-thick cells (E.H.C., Tokyo). When a bulk helical SmC* is constrained between the closely spaced substrates, the interaction forces between the LC molecules and the surface plates b -E 4 Experimental results The electro-optic responses were measured at various incident angles. Figure 3 shows the dependence of the transmitted light versus dc electric field, applied to the sample, at normal incidence for crossed polariser and analyser. In this figure, open and closed symbols indicate the transmittance for increasing and decreasing electric fields, respectively. As shown in this figure, the electric field dependence of the transmittance shows a threshold-less, hysteresis-free switching. Asymmetrical character of the switching behaviour can originate from the asymmetrical structure of the chevron and from the surface electroclinic effect that rotates the molecules out of the y z plane. It is possible to distinguish the low-field (< 2V) and the high-field (> 2V) regions, which reveal different transmittance values. The low-field region represents continuous changes in the FLC cell structure induced by a dc electric field, while the high-field region corresponds to the saturation fields. SHG experiments were performed with the purpose of studying the influence of the surface interactions as well as confirming the results deduced from EO studies. These measurements were carried out for the p-in, s-out polarisations combination of the fundamental and SHG waves in order to avoid the contribution to the SHG signal coming from the isotropic ITO electrodes [7]. Figure 4 shows a typical dependence of the p-in, s-out SHG intensity on the azimuthal angle for a 3-µm cell in transmission geometry with and without dc electric field applied to the sample. An anisotropic pattern reveals a four-fold symmetry of the SHG output, which is consistent with the C 2 point-symmetry group that applies 3,0 2,5 Transmitted Intensity [a.u] 2,0 1,5 1,0 0,5 0,0 FIGURE 2 Structure of the FLC molecules and their relative weights in the FLC mixture Applied Voltage (Volts) FIGURE 3 Transmitted intensity versus applied electric field. Open and closed circles correspond to positive and negative applied fields, respectively. The solid line corresponds to the theoretical fit using (1)

3 FOKIN et al. Switching behaviour of ferroelectric liquid crystals probed by optical second-harmonic generation U=0V U=2V FIGURE 4 SHG azimuthal anisotropy from the FLC for the p-in, s-out polarisations combination in transmission, normal-incidence geometry with (open circles) and without (solid circles) electric field. The solid line corresponds to the theoretical fit using (2) to FLCs [8]. In the experiments described below, azimuthal orientation of the cells is chosen to correspond to the maximum of the SHG anisotropic dependences at zero fields. Applying a dc electric field leads to a shift of about 20 in the azimuthal angle domain in the low-field region. In the highfield region the shift corresponds to the tilt angle θ = 32. The non-zero isotropic SHG contribution is attributed to the hyper-rayleigh scattering, which originates from structural inhomogeneity of the FLC cell structure [9]. SHGintensity,arb.un. SHG phase, degrees a 260 b bias, volts FIGURE 5 a Dependence of the SHG intensity and b dependence of the SHG phase versus DC electric field applied to the FLC cell 30 Figure 5a shows the dependence of the SHG intensity on the dc electric field applied to the FLC cell. The experiment is performed in transmission through the FLC cell, which is set at 15 of incidence of the fundamental beam. The application of the dc electric field results in a drastic decrease (increase) of the SHG intensity for fields of approximately +2( 2) V/µm, and no hysteresis is observed. No switching was observed in reflection geometry under the same conditions, either. The dependence of the SHG phase versus electric field, shown in Fig. 5b, demonstrates a switching behaviour similar to the intensity switching (Fig. 5a), but relatively inverted to the sign of the electric field. Figure 6 shows the dependence of the SHG intensity versus translation of the reference-crystal position for two different applied biases. SHG intensity 15 mm (40 degr) U=+8V U=-6V reference crystal position, mm FIGURE 6 SH interferograms for 2 V/µm (solid circles) and 2V/µm (open circles) measured in transmission geometry at room temperature for the p s combination of polarisations at 15 of incidence 5 Discussion The transmittance T is described by T = sin 2 ( 2 ( ( ) )) Θ + θ app sin 2 π neff d, (1) λ where Θ is the angle of incidence, θ app is the apparent tilt angle, d is the cell thickness, n eff is determined by the molecular distribution and λ is the light wavelength. The electro-optic transmittance change is regarded as a function of θ app (V ),wherev is the applied voltage. However, n eff is also a function of V, since it is determined by the molecular distribution. As seen in (1), the amplitude and the phase of the T Θ curve give n eff and θ app at a given electric field, respectively. From Fig. 3 it is clear that there is a quantitative difference between the data and the theory for the negative values of the applied electric field, but it is still in good agreement. When discussing the results obtained in non-linear experiments, we need to estimate the characteristic thickness of the samples that participate in SHG. The coherence lengths of SHG in reflection from and in transmission through the FLC cell are l cor = π/(k 2ω ± 2k ω ), k 2ω and k ω being wave vectors of the SH and fundamental wavelengths, respectively. 4,4 4,0 3,6 3,2 2,8

4 780 Applied Physics B Lasers and Optics The ordinary refractive indices were taken as n o (ω) = 1.47 and n o (2ω) = 1.52, and the extraordinary refractive indices as n e (ω) = 1.58 and n e (2ω) = 1.62 (reflectivity measurements conducted by the authors). This gives thickness values of about 90 nm and 5 µm, as the corresponding effective refractive indices are n 2ω = 1.54 and n ω = 1.49 [10]. This means that about layers of LC molecules participate in the SHG process in reflection from the sample, while for the transmission geometry the whole cell takes part in SHG. Therefore, a few sub-surface layers of FLC molecules placed close to the upper window of the cell are the ones responsible for SHG in reflection geometry. The fact that the SHG intensity, phase and anisotropy in reflection geometry do not depend on external electric fields is evidence of the immobility of the sub-surface FLC molecules, which is due to the strong stabilising influence of the cell walls, i.e. it shows the appearance of the electroclinic effect. Based on the SHG experiments for the reflection geometry, the thickness of the sub-surface layer stabilised by the electroclinic effect can be estimated to be at least 90 nm. The molecules in the studied FLC form an asymmetric chevron structure. In this structure, the molecular directors of the neighbouring layers are tilted by the same angles with respect to the z axis. In the case of the same volumes of the upper and lower halves of the chevron structure, the in-plane component of the dipole moment of the FLC becomes zero, and the film possesses only the z component of the dipole moment. Thus, in transmission geometry at normal incidence no SHG would be observed, but experiments performed proved the presence of SHG in this case. That is why the FLC samples studied are considered to have the asymmetric chevron structure and the chevron cusp should not be at the centre of the cell thickness. Nevertheless, in both cases, the FLC structure can reveal the C 2 point-symmetry group, which is observed experimentally. Applying an electric field to the cell leads to collective motion of the molecules. Each of them moves along the surface of the cone with the angle θ. In the first approximation this angle is a linear function of the applied electric field in the lowfield region, and saturates in the high-field region, reaching a maximum value equal to the tilt angle θ = 32 (see Fig. 3). Since all the molecules rotate in phase, applying an electric field can be considered as a rotation of the sample coordinate system around the x axis, and the shift of the anisotropy dependence should correspond to the tilt angle θ. Thus, the anisotropy dependence of the SHG intensity for the p s polarisations combination I ps (2ω) can be approximated by the formula I ps (2ω) =I isotr + E 4 p{ sin φ cos 2 φ cos 2 α(2χ xxy χ yyy ) sin 2α(χ yxz sin 2 φ + χ xyz cos 2 φ) + sin φ ( χ yzz sin 2 α + χ yxx cos 2 α sin 2 φ )} 2 where I iso is the isotropic (incoherent) component of the SHG, E p is the amplitude of the p-polarised component of the incident wave, φ is the azimuthal angle of the sample rotation, Θ is the angle of incidence and χ ijk are the independent components of the non-linear susceptibility. (2) In transmission geometry the whole cell takes part in SHG. In this geometry the threshold-less switching proceeds via a collective motion of the director field around the surface of the cone with a tilt angle θ, as shown in Fig. 1b. If the smectic layer is of chevron type, the molecules can choose one-half of the azimuthal angle of the cone, since molecules have a tendency to align themselves parallel to a substrate surface, as illustrated in Fig. 1b (E = 0). The saturation of the SHG intensity at high voltages takes place when the molecular tilt angle comes close to its maximal value (Fig. 5a). The same factors drive the field dependence of the SHG phase (Fig. 5b), as this also depends on the molecular orientation. Moreover, this dependence has the same characteristics as in the case of SHG intensity. The phases of the second-harmonic wave are extracted from the dependences of SHG intensity versus translation position of the reference crystal (Fig. 6), which are approximated by the formula I 2ω ( ) 2 E ref + E samp = Iref + I samp + 2α I ref I samp ( cos d 4π(n ) 2ω n ω ) + ϕ samp ϕ ref (3) λ ω where E ref, E samp, I ref and I samp are amplitudes and intensities of the SHG waves from the reference and from the sample, respectively, α is the mutual coherence of the interfering SHG waves (0 <α<1), ϕ samp is the phase of SHG from the sample, which depends on applied electric field, and ϕ ref is the constant phase of SHG from the reference. The observed switching behaviour is a result of the effect of polar surface anchoring. It is well known that polar surface interaction stabilises a twisted state in which a splay deformation of P exists, P being the polarisation. Then the polarisation space charge ϱ ( P [11]) is produced. Hence, molecules tend to form a uniform orientation to avoid the production of polarisation charge at E = 0. The surface constraint induces a small but finite value of the spontaneous polarisation as well as a finite tilt (6 8 ) close to the solid interface. The formation of a splayed structure can induce a macroscopic rotation of the smectic layers with respect to the rubbing direction, which fixes the molecular direction at the surface (surface electroclinic effect). The collective motion of the director field is determined by the coupling of the applied electric field to the Goldstone (phase) mode [11]. Molecules change their orientation continuously due to induced non-zero torque (P E) and, as a consequence, a threshold-less switching occurs [12]. 6 Conclusions The switching behaviour of thin planar FLC cells is studied by means of optical SHG and linear electro-optical methods. Applying an external dc electric field to the FLC cell leads to the ordered collective motion of the molecules in the chevron structure of the cell. The switching mechanism is a consequence of the boundary conditions and the resulting surface electroclinic effect. This results in a rotation of 32 of the polarisation plane of the transmitted light and drastic changes in the SHG intensity, phase and shift of the anisotropy dependence. Further investigations are in progress in our laboratories and will be reported in the near future.

5 FOKIN et al. Switching behaviour of ferroelectric liquid crystals probed by optical second-harmonic generation 781 ACKNOWLEDGEMENTS We thank I. Musevic, G. Heppke and T.V. Misuryaev for their invaluable assistance and helpful discussions. Financial support from the European network Grant No. ERB FMRXCT (SILC) and RFBR Grant Nos and is gratefully acknowledged. REFERENCES 1 D.C. Ulrich, S.J. Elston: In The Optics of Thermotropic Liquid Crystals, ed. by S.J. Elston, R. Sambles (Taylor and Francis, London 1998) Chapt. 9 2 A. Bune, V. Fridkin, S. Ducharme, L. Blinov, S. Palto, A. Sorokin, S. Yudin, A. Zlatkin: Nature 391, 874 (1998) 3 R. Macdonald, F. Kentischer, P. Warnick, G. Heppke: Phys. Rev. Lett. 81, 4408 (1998) 4 T.F. Heinz: In Nonlinear Surface Electromagnetic Phenomena, ed. by H.-E. Ponath, G.I. Stegeman (North-Holland, Amsterdam 1991) p N. Bloembergen, R.K. Chang, S.S. Jha, C.H. Lee: Phys. Rev. 174, 813 (1968) 6 R. Stolle, G. Marowsky, E. Schwarzberg, G. Berkovic: Appl. Phys. B 63, 9544 (1996) 7 O.A. Aktsipetrov, I.M. Baranova, Y.A. Il inskii: Sov. Phys. JETP 64, 167 (1986) 8 I. Drevensek, R. Blink: Condens. Matter News 1, 14 (1992) 9 Yu. Fokin, T.V. Murzina, S. Soria, G. Marowsky, O.A. Aktsipetrov: Surf. Sci C, 722 (2002) 10 I.Ch. Khoo, S.-T. Wu: Optics and Nonlinear Optics of Liquid Crystals (World Scientific, Singapore 1993) 11 I. Muševič, R. Blinc, B. Žekš: The Physics of Ferroelectric and Antiferroelectric Liquid Crystals (World Scientific, Singapore 2000) Chapts. 4 and P. Rudquist, J.P.F. Lagerwall, M. Buivydas, F. Gouda, S.T. Lagerwall, N.A. Clark, J.E. Maclennan, R. Shao, D.A. Coleman, S. Bardon, T. Bellini, D.R. Link, G. Natale, M.A. Glaser, D.M. Walba, M.D. Wand, X.H. Chen: J. Mater. Chem. 9, 1257 (1999); D.S. Hermann: Mol. Cryst. Liq. Cryst. 358, 167 (2001)