Liquid crystals under the spotlight: light based measurements of electrical and flow properties of liquid crystals

Transcription

1 Invited Paper Liquid crystals under the spotlight: light based measurements of electrical and flow properties of liquid crystals Thomas P. Bennett a, Matthew B. Proctor b, Malgosia Kaczmarek b and Giampaolo D Alessandro a a Mathematical Sciences, University of Southampton, Southampton, England, UK; b Physics and Astronomy, University of Southampton, Southampton, England, UK ABSTRACT Optical light modulation in photorefractive liquid crystal cells depends strongly on the relative voltage drop across the photoconductive and liquid crystal layers. This quantity can be estimated using the Voltage Transfer Function, a generalization of the standard cross polarized intensity measurements. Another advantage of this new measurement technique is that we can use it to estimate dynamical parameters of the liquid crystal and of the device, either through simple black-box models or using a full Ericksen-Leslie theory. In this latter case we can obtain estimates of some of the viscosities of the liquid crystal. Keywords: Liquid crystals, Photorefractive liquid crystals, Optical light modulators, Liquid crystal viscosity, liquid crystal cells 1. INTRODUCTION Liquid crystalline materials find application in a wide range of electro-optical devices such as hybrid two-beam-coupling cells, 1 optical wave guides, spatial light modulators 3 and displays. 4 Of particular interest here are liquid crystal light valves and optically addressed light modulators. The typical design of such devices combines a photoconductor with a liquid crystal layer. 5, 6 Notwithstanding the simplicity of the design, they display a remarkably varied and rich range of phenomena, from pattern formation 7 to slow light. 8 The general working principle of an optically addressed light modulator is easy to explain: a non-uniform light beam illuminates a photosensitive layer and thus induces a non-uniform electric field across the adjacent liquid crystal layer. If the electric field is sufficiently strong it orients the liquid crystal and, hence, creates a refractive index modulation that changes the phase of the incident beam. There are two main ways of creating a photo-induced electric field. In one class of cells, the photosensitive layer is a thin slab of photorefractive crystal, e.g. SBN. 9, 10 The non-uniform illumination creates a space-charge field inside the crystal. Its evanescent component in the liquid crystal layer orients the molecules and induces the phase modulation of the incoming beam. A second class of cells, instead, uses a photoconductive layer to modulate an external voltage applied to the cell (see the left panel of Figure 1 for a schematic diagram). In some designs the photoconductor is a relatively thick (mm) slab of an inorganic crystal, e.g. BSO. 11 In others, that are of interest here, the photoconductor is a thin (typically 100 nm) organic polymer layer. 1 The main advantages of this choice are the low cost of the polymer and the ease of fabrication of the layer. We have built cells using PVK:C 60 as a photoconductive polymer 13 and have shown that optical phase modulation occurs both in the DC and low frequency AC regime 14, 15 (see the right panel of figure for a typical output). In order to understand the role of the polymer layer and have some guidance in the choice of material, it is useful to know the voltage dropped across the liquid crystal as a function of the light intensity. The layers are too thin to measure this voltage directly, but it is possible to use a modification of the standard cross-polarized intensity measurement, the Voltage Transfer Function (VTF), 16 to estimate it. As an added benefit the VTF allows us also to extract dynamical information on the cell and the liquid crystal. In the next section, we introduce this measurement tool which we use in section 3 to measure the effect of light intensity on the voltage dropped across the liquid crystal layer. In section 4 we expand the use of the VTF to extract dynamical information on the cell and show how it can be used to measure some of the viscosities of a liquid crystal. In the conclusion we summarize the main results and discuss briefly what other information can be deduce from VTF measurements. Liquid Crystals XIX, edited by Iam Choon Khoo, Proc. of SPIE Vol. 9565, 95650C 015 SPIE CCC code: X/15/$18 doi: / Proc. of SPIE Vol C-1

2 x z ~ Power supply Incident beams PVK:C 60 LC PI Output beams Vrms =8 V f = 0.1 Hz Figure 1. Left: Schematic diagram of a photorefractive liquid crystal cell: the two incoming light beams create an illumination grating across a photoconductive polymer layer (PVK:C 60, in this case). This induces a conductivity grating and, hence, creates a spatially modulated voltage drop across the liquid crystal layer and, hence, a refractive index grating that diffracts the incoming beams. The thin polyimide (PI) layer on the right is used only for alignment purposes. Right: Experimental images of beam diffraction from a 1 µm thick PVK:C 60 -PI cell filled with E7. The images were taken at different points in the amplitude cycle of the applied voltage. [ Configuration at input Director Polarizer 0.8 Light polarisation A 0.6 Polarizer V nm DPSS laser 0. Signal generator 00 5 Vin [Amp15 0 [Amplitude] Figure. Left: Schematic diagram of the experimental apparatus that measures the VTF. A beam from a solid state laser of wavelength λ = 53 nm is linearly polarized at 45 to the rubbing direction of a planar photorefractive liquid crystal cell. An oscillating voltage, of variable frequency and amplitude, is applied to the cell. The output beam passes through a polariser rotated by 90 with respect to the first one. The transmitted light is measured by a photodiode and its digitalised intensity is stored in a file for processing. Right: Typical measurement of the cross-polarized intensity I. The frequency of the applied voltage is fixed at a relatively high value with respect to the cell time constants (1-10 khz) and its amplitude is increased from zero. The quantity plotted is the time-averaged cross-polarized intensity. The two thin rectangular inserts are schematic plots of the liquid crystal alignment through the cell thickness: as the voltage is increased the alignment changes from planar to nearly homeotropic and the birefringence-induced phase lag reduces to zero. Each decrease of π corresponds to one oscillations of I. Proc. of SPIE Vol C-

3 Figure 3. VTF measurements showing the average cross-polarized intensity normalized in the interval [0, 1] as a function of the amplitude (vertical) and frequency (horizontal) of the voltage applied to an E7 cell. The four plots show increasing intensity from left to right: (a) 0.18 mwcm, (b) 1.8 mwcm, (c) 5.7 mwcm, and (d) 68 mwcm. Cell parameters: Liquid crystal E7, thickness 1 µm, PVK:C 60 and PI alignment layers on the input and output facets, respectively.. THE VOLTAGE TRANSFER FUNCTION When a voltage is applied to a planar liquid crystal cell, as the one illustrated in figure 1, the alignment of the liquid crystal molecules may change. A typical experiment to measure the realignment is a cross-polarized intensity measurement: a standard setup is illustrated schematically in the left panel of figure, while the right panel shows a typical result. In a typical experiment the applied electric field oscillates on a time scale much faster than any of the cell time scales so that the liquid crystal responds only to the r.m.s. field amplitude. In a VTF measurement the cross polarized intensity is measured both as a function of the voltage amplitude and of its frequency. Plots for different light intensities are shown in figure 3. From these plots we can derive a considerable amount of information about the cell. For example, a vertical cross-section at high frequency produces a plot similar to the one in the right panel of figure. This can be fitted to estimate the cell thicknessa and pre-tilt, and the liquid crystal splay and bend elastic constants. 17 However, many other properties of the liquid crystal and the cell can be estimated from the VT measurements. In the next section we show how the VTF can be used to understand and optimize the functioning of photorefractive liquid crystal cells, while in section 4 we discuss briefly how it can be used to measure liquid crystal time scales. 3. VTF MEASUREMENTS OF THE PHOTOREFRACTIVE EFFECT As mentioned in the introduction, the key to refractive index modulation in photorefractive liquid crystal cells is the ratio of the voltage dropped across the photosensitive and the liquid crystal layers. We can measure this using the VTF by tracking the lowest boundary between dark and bright regions: this maps approximately the location of the Frederiks threshold, i.e. at this boundary the voltage applied to the cell is approximately the Frederiks threshold voltage irrespective of the amplitude of the voltage applied to the cell. If we consider the left-most panel in figure 3 we can track the behavior of this voltage with frequency. As the polymer layers are much thinner than the liquid crystal layer, at high frequency all of the voltage is dropped across the liquid crystal layer. Moreover the liquid crystal responds to the r.m.s. voltage amplitude. As the frequency is decreased the liquid crystal begins to respond to the voltage amplitude (which is larger by a factor of than the r.m.s. amplitude): hence there is a small bulge downward in the boundary at approximately 10 Hz. However, this effect is more than compensated by the fact that, as the frequency is decreased further and further, more and more voltage is dropped across the resistive load of the polymer layers. In fact, at 0.1 Hz we are unable to observe the Frederiks transition even when the amplitude of the voltage applied to the cell is 3.5 V. At higher light intensities we can expect that the resistance of the PVK layer will be reduced. This has no effect at high frequency (see panels (b-d) of figure 3) where the polymer acts as a capacitance. However, at low frequency we see a significant change in the VTF. For example, in panel (b) we see that the Frederiks transition is now observable even at 0.1 Hz, while in panel (d) there is no difference in the Frederiks transition at low and high frequency, indicating that the voltage is approximately all dropped across the liquid crystal layer. This information is summarized in figure 4. From this plot we see that the light intensity has a significant effect only at frequencies below approximately Hz and that at the lowest frequency plotted it is possible to drop more than half the voltage across the polymer layers. A detailed optimization of the cell parameters requires to take into account of side current and of the electrical properties of the polymer layers. 15 Corresponding author: G. D Alessandro (dales@soton.ac.uk) Proc. of SPIE Vol C-3

4 V th (I,!)/V th (0,1) Hz 0.6 Hz 0.53 Hz 1.07 Hz.17 Hz 4.41 Hz 8.94 Hz Hz Pump intensity (mw/cm ) Figure 4. Frederiks transition (normalized to its value in the dark and at high frequency) as a function of frequency for different light illumination levels for an E7 cell. This plot was obtained from the data used for figure 3. V th(0, ) was approximated with the lowest illumination intensity threshold value at highest frequency (1 khz). However, a simple RC circuit model 14 of the photorefractive cell indicates that the largest voltage modulation across the liquid crystal layer is achievable when its impedance is similar to that of the polymer layers. In the case of the cell used in figures 3 and 4 this is achieved at approximately 0.5 Hz and at light intensities of the order of 1 mw/cm. 4. VTF AND LIQUID CRYSTAL TIME SCALES The VTF is a multi-frequency scan of the light response of the liquid crystal cell. It therefore contains also information on the time scales scales both of the liquid crystal and of the electrical components of the cell. It is therefore possible to use it to estimate these parameters both for standard and photorefractive liquid crystal cells. A first approach is to use a simple black-box model 16 which comprises two parts. The first is a high pass filter that describes the electrical response of the cell as a simple RC filter with cut-off frequency ω VT = 1/(C K R L ), where C K is the effective capacitance of the polymer layers and R L is the resistance of the liquid crystal layer. Applied voltages with frequency ω ω VTF are dropped across the liquid crystal, while lower frequency voltages are dropped across the polymer layers. The second component models the mechanical response of the liquid crystal: it is a low pass filter with cut-off frequency ω LC. The liquid crystal dynamics follows the time evolution of signals with frequency ω ω LC, but responds only to the average of signals with frequency larger than this value. The two cut-off frequencies can be fitted to the VTF data and give values that are a good indicator of the electrical and viscous time scales of the cell. While these are not accurate enough to determine physical parameters of the liquid crystals they offer a quick and easy testing procedure for new polymer and liquid crystalline materials. A second approach 18 to the analysis of the cell dynamics is based on a Ericksen-Leslie model of the liquid crystal alignment and flow. 19 The alignment and flow equations for a planar cell uniform in the x and y directions, of thickness d in the z-direction and with director constrained to lie in the (x, z)-plane are θ γ 1 t = [K 1 cos (θ) + K 3 sin (θ)] θ z + K 3 K 1 [ g(θ) v ] z z + m(θ) θ = 0, t ( ) θ sin(θ) + ɛ aɛ 0 z ( φ(z, t; ω) z ) sin(θ) m(θ) v z, (1) () with m(θ) = 1 [(α 3 α ) + (α 3 + α ) cos(θ)], (3) Proc. of SPIE Vol C-4

5 and g(θ) = 1 (α 3 + α ) cos(θ) α 1 8 cos(4θ) + 1 ( α 3 + α 4 + α 5 + α ) 1. (4) 4 In these equations θ(z, t) is the angle that the director field makes with the x-axis, v is the x-component of the velocity, K 1 and K 3 are the splay and bend elastic constants, ɛ 0 is the vacuum permittivity and ɛ a = ɛ ɛ the dielectric anisotropy of the nematic, with ɛ and ɛ the component of permittivity along and orthogonal to the director respectively. The rotational viscosity γ 1 is related to the Leslie viscosity coefficients α i, i = 1,..., 5 by γ 1 = α 3 α. It is possible in principle, but not feasible in practice, to fit many of the parameters in these equations to the VTF data. We are developing a computationally effective approach that will allow us to determine some of the viscosity coefficients, in particular γ 1 and α 4 + α 5, from an appropriate selection of the VTF data. 5. CONCLUSIONS In this paper we have used a novel measurement technique, the Voltage Transfer Function, to determine the voltage dropped across the liquid crystal layer in a polymer-based photorefractive liquid crystal cell. The VTF measures the cross-polarized intensity as a function of applied frequency and voltage for a given value of the light intensity. By tracking the Frederiks transition as a function of frequency at different light illuminations we have been able to draw curves that show the partitioning of the voltage applied to the cell across the polymer and liquid crystal layers. This analysis not only shows that our understanding of the working principles of a photorefractive cells are correct, but it also gives us a handle to optimize the polymer layer properties to obtain maximum refractive index modulation. As an added benefit, the VTF contains also a considerable amount of dynamical information about the photorefractive cell and on the liquid crystal itself. It is possible to use this to extract the time constants of the liquid crystal cell using a very simple black-box model. We are also developing a thorough analysis of the time response of the liquid crystal based on an Ericksen-Leslie model which we expect will allow us to determine some of the viscosities of the liquid crystals, namely γ 1 and α 4 + α 5 in the case of a planar cell. In conclusion, the VTF is a versatile tool to characterize the response of liquid crystal cells and materials that can be used to obtain both electrical and physical properties of a device and its component materials. We have explored some uses in this paper, but others are also possible. For example, by measuring the VTF at different wavelengths of the illuminating beam we can measure the cell and photoconductor wavelength response. This Swiss-knife versatility of this simple-toperform experiment make the VTF a truly remarkable measurement tool. ACKNOWLEDGMENTS We would like to thank our collaborators over the years that have helped us develop and test some of the ideas mentioned in this paper, in particular James Bateman and Mark Herrington. REFERENCES [1] M. Kaczmarek, A. Dyadyusha, S. Slussarenko, and I. C. Khoo, The role of surface charge field in two-beam coupling in liquid crystal cells with photoconducting polymer layers, J. Appl. Phys. 96, pp , Sept [] A. d Alessandro, B. Bellini, D. Donisi, R. Beccherelli, and R. Asquini, Nematic Liquid Crystal Optical Channel Waveguides on Silicon, IEEE J. Quant. Elect. 4(10), pp , 006. [3] J. Beeckman, K. Neyts, and P. J. M. Vanbrabant, Liquid-crystal photonic applications, Opt. Eng. 50(8), p. 0810, 011. [4] F. S. Y. Yeung and H. S. Kwok, Truly bistable twisted nematic liquid crystal display using photoalignment technology, Applied Physics Letters 83(1), pp , 003. [5] K. Komorowska, A. Miniewicz, and J. Parka, Holographic grating recording in large area photoconducting liquid crystal panels, Synth. Met. 109(1-3), pp , 000. [6] U. Bortolozzo, S. Residori, and J. P. Huignard, Beam coupling in photorefractive liquid crystal light valves, J. Phys. D: Appl. Phys. 41(), p. 4007, 008. [7] S. Residori, Patterns, fronts and structures in a Liquid-Crystal-Light-Valve with optical feedback, Phys. Rep. 416(5-6), pp. 01 7, 005. Proc. of SPIE Vol C-5

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