Volume 7 Issue 1 - December 19, 2008
Two-dimensional grating structure induced by light-field of single laser beam in a dye-doped cholesteric liquid crystal film
Hui-Chen Yeh1, Guang-Hao Chen1, Ting-Shan Mo2, and Chia-Rong Lee1,*

1Institute of Electro-Optical Science and Engineering, National Cheng Kung University 
2Department of Electronic Engineering, Kun Shan University of Technology
crlee@mail.ncku.edu.tw

J. Chem. Phys. 127, 141105 (2007)

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Generally, a planar cholesteric liquid crystal (CLC) can be formed by adding chiral material into the nematic liquid crystal within a cell with homogeneous surface alignment. The CLC has a structure with a spatially-periodic rotation of the LC director along the normal of the cell. The distance for which the director rotates 360 degree is called the pitch(P0) of the CLC. Especially, when the CLC material is constricted in a cell with a thickness of d, it can be regarded as lamellar phase with a thickness of a layer equal to half of the pitch at large scales (d >> P0). Two-dimensional (2D) grating structures in such lamellar phase can frequently produced with the applications of mechanical stresses, electric fields and magnetic fields. The formation of the 2D grating structures with CLC layer undulations may be explained as follows. Because of the homogeneous alignment of LCs near the cell substrates, the CLC layers can be confined between the two flat plates parallel to the layers. When an external field is applied to the plates, the LC molecules and thus the CLC layers tend to reorient. However, surface anchoring forces may suppress the layers to rotate free such that the layers to periodically undulate with a tilt in the 2D space of the cell plane.

Although these external forces can induce 2D grating structures in a CLC system, no work has examined such gratings induced by light-field. This work investigates 2D grating structures produced by the light-field of single beam in dye-doped cholesteric liquid crystal (DDCLC) films. The helical pitch of CLCs increases during the illumination of a green beam in virtue of trans-cis isomerization and a coexistent thermal effect. When the green beam is switched off, metastable 2D grating structures present as the CLCs relax. The formation of the grating based on layer undulations is attributable to the action of the restored strain normal to the layers caused by a decrease in the pitch of the CLC structure. The lifetime of the grating strongly depends on the intensity of the green beam. Red-beam-induced cis-trans back isomerization strongly lowers the grating lifetime.

The nematic liquid crystal, chiral dopant and azo dye are BL009 (no=1.5266, Δn=0.2915 at 25°C), CB15, and D2 (all from Merck, Germany), respectively, in the present work. The empty cell is made by combining two indium-tin-oxide (ITO)-glass substrates. Homogeneously aligned films, polyvinyl alcohol (PVA), are coated onto the two substrates and rubbed in the same direction. The cell thickness (d) is 38μm. The DDCLC mixture is injected into thes empty cell to produce a DDCLC cell. The concentration of the chiral dopant is 35.7wt% of the CLC mixture, where the corresponding pitch (P0) and ratio of d/P0 is 0.38μm and 100, respectively. The concentration of the dye in the DDCLC mixture in the cell is 1 wt%.

One linearly polarized green beam (EG), originated from an Ar+ laser (wavelength514.5nm), is pre-expanded and pre-collimated via an expander with a magnification power of 10, and then passes through a diaphragm with an 0.5cm-diameter aperture to illuminate normally the DDCLC cells with a green intensity of IG=70–880mW/cm2 for a constant green pumped duration of tG=120s. One very weak (~1mW/cm2) linearly polarized He-Ne laser beam (wavelength633nm) is used to probe the formation of 2D grating structures. The 2D grating structure in the cell may form when the CLCs self-organize for a few seconds after the green beam is switched off. Experimental results show that the characteristics of the formed 2D gratings, such as lifetime and grating spacing, depend strongly on the green beam intensity for a constant green pumped duration. The variation in helical pitch during grating formation can be observed under a polarizing optical microscope (POM). Figure 1(a) shows an image of the formed 2D grating obtained under a POM without an analyzer with IG=200mW/cm2 and tG=120s.
Figure 1. (a) A formed two-dimensional (2D) grating under a polarizing optical microscope (POM) without an analyzer in dye-doped cholesteric liquid crystal (DDCLC) cell with P0=0.38μm (Cell 6) for IG=200mW/cm2 and tG=120s. Grating spacing is ~9.5μm under the POM. (b) Corresponding 2D diffraction pattern and (c) model of undulations of layers in the 2D grating, in which EG and R represent the polarization direction of the linearly polarized green beam and the rubbing direction of the cell, respectively.

Figure 1(b) presents the corresponding diffraction pattern of the probe beam from this 2D grating. Spacing of the 2D grating (Fig. 1(a)) is ~9.5μmunder the POM. The diffracted intensity of the second orders in the diffraction pattern exceeds that of the first orders along the x- or y-axis (Fig. 1(b)), indicating that 2D grating formation is attributable to 2D spatially periodic layer undulations in the CLC structure, in which the grating spacing near the two substrate surfaces is double that in the cell bulk. Figure 1(c) presents a model of layer undulations in the 2D gratings, which are similar to those in a pure CLC system to which an electric field is applied. Diffraction from the two surface gratings and bulk grating contributes to the mth-orders and (2m)th-orders, respectively, of the resultant diffraction pattern, where m=0, 1, 2…. Surface component spacing of the 2D grating is determined from the diffraction pattern using the diffraction condition

mλ= Λsinθ,                         (1)

where m is the diffraction order, Λ is grating spacing, and θ is diffraction angle. For the first-order diffraction (m=1) (Fig. 1(b)), experimental values λ=633 nm and θ = 4.2° are substituted into Eq. (1), yielding a grating spacing Λ of ~9.6μm, which agrees closely with the spacing measured under the POM.

Figure 2. Curves of the reflection spectrum of CLCs for Cell 6 in dark (curve (a)) and under green beam illumination with IG=200, 440 and 770mW/cm2 (curves (b), (c) and (d), respectively) for tG=120s.
The reflection spectrum of the DDCLC cell is obtained to clarify the mechanism of 2D grating formation. Figure 2 displays the experimental results. The reflection band of the CLCs is red-shifted under illumination with a green beam with IG=200, 440, and 770mW/cm2, curves (b), (c) and (d) in Fig. 2, respectively, for tG=120s. The low transmitted intensity in each curve in the short wavelength region is due to the peak of the absorption of D2 in the green region. A high green intensity corresponds to a largered-shift in the reflection band of the CLCs, implying that pitch elongation increases as green beam intensity increases (Fig. 2). Pitch elongation under green beam irradiation is caused by photo-induced trans-cis isomerization and the coexistent thermal effect. The increases of the cis-isomer concentration and the temperature with green beam intensity, thus, enhance the elongation of the pitch. After the green beam is switched off, the cis-isomers will thermally back cis-trans isomerized to the original trans-state and the cell temperature relaxes to room temperature (TR) via thermal relaxation, recovering CLC pitch. As everyone knows, the elastic energy of a CLC system is associated with helical pitch. Elastic energy increases by elongating the pitch. The descent in pitch causes elastic energy to be released, and, in turn, a restored strain in the normal direction of the cell substrates may be induced, producing elastic instability under the confinement of the surface alignment, thereby resulting in the metastable 2D grating structure. After the cis-isomers have all thermally isomerized back to the trans-state and the temperature has relaxed back to TR, the CLC pitch no longer changes and the induced strain vanishes, resulting in the disappearance of the grating.

To clarify the influence of the coexistent thermal effect on the formation of 2D grating structures, an additional experiment with two steps is performed. First, a thermocouple is used to measure the temperature of the cell at the pumped spot after illumination with the green beam for 120s. Temperature increases from 25°C to 29, 32.5 and 37°C when green beam intensity is 200, 440, and 770 mW/cm2, respectively. Second, the cell is then placed in a hot stage, in which cell temperature is set at 29, 32.5 and 37°C. Figure 3 displays cell reflection spectrums at these temperatures. Experimental results show that the red-shift of the reflection band clearly increases when temperature increases from 25°C to 29°C, 32.5°C and 37oC, as demonstrated by curves of (b), (c), and (d) (Fig. 3). Therefore, the influence of the coexistent thermal effect on pitch, and, thus, on formation of the 2D grating structures are significant.

Figure 4(a) (Fig. 4(b)) displays the variation in 2D grating lifetime with green beam intensity for tG=120s without (with) irradiation by the pumped red beam with intensity IR=500mW/cm2, after the green beam is turned off. The lifetime of the 2D grating increases as green beam intensity increases (Fig. 4(a)). The experimental results can be explained as follows. The conce-ntration of the cis-isomer produced by trans-cis isomerization and the coexistent thermal effect can both increase as green beam intensity increases, thereby increasing pitch. Accordingly, the time that the pitch and temperature take to recover to their original values increases once the green beam is turned off, yielding the experimental results (Fig. 4(a)). Figure 4(b) shows a tendency similar to that in Fig. 4(a); however, lifetime declines under irradiation from the pumped red beam after the green beam is turned off. The strong red beam can rapidly induce the transfor-mation of cis-isomers to trans-isomers and, in turn, accelerates the pitch recovery to its original value, causing grating lifetime to decline.
Figure 4. Variation of 2D grating lifetime with green pumped intensity in Cell 6 (a) without and (b) with illumination of one pumped red beam with an intensity of 500mW/cm2 after the green beam is switched off.
Figure 3. Curves of the reflection spectrum of CLCs for Cell 6 at 25, 29, 32.5 and 37°C (curves (a), (b), (c) and (d), respectively) without green beam illumination.


In summary, this study demonstrates photo-induced 2D grating structures on the DDCLC film under green beam illumination. The helical pitch of the DDCLC films is increased by trans-cis isomerization of azo dyes and the coexistent thermal effect during green beam irradiation. When the green beam is switched off, 2D gratings appear when the CLC structure relaxes. Both thermal cis-trans back isomerization and the rmal relaxation induce recovery of the CLC pitch. The mechanism of the formation of gratings is attributable to the elastic instability arising from restored strain established by pitch recovery. Irradiation with one strong red beam on formed 2D gratings in DDCLC cells can generate photo-induced cis-trans back isomerization, thereby reducing significantly grating lifetime.
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