1. Introduction

Different ways of designing variable focal length lenses, based on the flat layers of nematic liquid crystals (NLC), have been proposed [1–7]. Usually, non-homogeneous electric field is used in the NLC-cell [1–6] to create lens-like distribution of the refractive index via the inducing of the suitable configuration of the NLC director (direction of preferred molecular orientation). Surface relief microlenses may be also immersed in the standard NLC-cell [7]. In Refs. [8,9] a small amount (up to 3%) of reactive monomer was mixed with a NLC and in situ polymerized [10] by homogeneous UV irradiation. A distributed electric field was produced by a circular-hole-patterned electrode structure on one [8] or both [9] cell substrates. Strongly focused light induced reorientation and simultaneous UV photopolymerization was used in similar compounds to create microlenses with fixed focal length [11]. Different polymer network structures and their influence on the electrical switching properties of the NLC were studied [10,12]. In particular for the structure of nematic domains, separated by thin polymeric walls, it was established that the threshold field of nematic reorientation increases with increasing the concentration of the polymer network [12]. Recently a pattern irradiation was used to produce regions with different threshold voltage for switching [13]. It was demonstrated that this technique (with a mask in the form of concentric dark and transparent rings) can be used to produce switchable Fresnel lenses.

In this paper, we introduce a technique to create variable focal length lenses. The essence of the idea is the following. The illumination of the mixture of a uniformly preoriented NLC and a few percent of photopolymerizable monomer by one Gaussian-shaped laser beam may induce a non-homogeneous centro-symmetric polymer network formation. The electro-optical response of this system to a uniform electric field will be non-homogeneous (centro-symmetric). Particularly, the threshold field for director reorientation will be maximal in the center of the illuminated spot and minimal in the non-illuminated regions. Then it will be possible to produce a corresponding distribution of the nematic director in the cell by applying a pixel-free (uniform) voltage and, as a consequence, to form a circularly symmetric distribution of the refractive index, with a maximum in the center. Such a cell will represent a LC-lens. The changes of the voltage will vary the profile of the refractive index and, as a first approximation, the focal length of the lens.

2. Materials and sample preparation

We used a monofunctional monomer glycidyl methacrylate, which contains an epoxy group (SR-379, from Sartomer Company):

The same photoinitiation complex (dye, initiator and coinitiator) was used as in [14], in combination with commercially available NLC mixture E7 (Merk) as a non-reactive liquid crystal matrix. These components were mixed and stirred carefully to obtain a homogeneous solution. The concentration of the monomer in the total mixture was 3 wt %. The electro-optical cells from Displaytech or Linkam (both providing parallel alignment of the nematic) were filled with this mixture. The cell thickness was 4μm and 5μm.

3. Experimental set-up

The experimental setup is shown in Figure 1. The photopolymerization of the monomer was initiated by means of a Verdi laser beam (λ=532 nm) having Gaussian intensity distribution. The diameter of the beam was 2.3 mm. The sample was irradiated for 30 minutes at 23.8 mW light power. No electric field was applied during the irradiation. He-Ne laser beam (λ=543 nm) of diameter 0.7 mm was used as a probe at normal incidence on the sample. We measured the intensity (I) of the light transmitted through the cell, which was placed between crossed polarizer and analyzer. A Glan prism was used as a polarizer with polarization direction tilted at 45° with respect to the optical axis of the cell. The intensity (I_max) of light transmitted through the parallel polarizers was measured also to take into account the absorption and reflection losses on polarizers. The movable horizontal stage allowed examining different points of the cell in the X direction. The intensity of the probe beam was attenuated by means of a neutral filter to minimize its influence on the sample. After traversing the sample, the probe beam passed through an analyzer, a 1.8 mm diameter diaphragm, and was registered with a photodiode. The distance between the sample and the diaphragm was 22 cm. The sample reorientation was carried out by a source of sinusoidal signal with 1kHz frequency. The r.m.s. value of the applied voltage was detected with a multimeter.

 

Fig. 1. Experimental set-up. Dashed lines denote elements used in polymerization process only; solid lines denote those used during the electro-optical measurements.

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4. Results

4.1 Electro-optical properties

The dependence of the normalized light transmission T=I/I_max on the applied voltage demonstrated standard threshold behaviour before the polymerization of the cell. In the range of voltages exceeding the threshold value (U_th=0.98 V), the light transmission changes with oscillations: first decreases passing through a minimum at U≈1.3 V, then increases with the maximum at U≈1.95 V and again decreases to the minimal value at higher voltages. Such an oscillation dependence of T upon the external field is typical for the case of a pure planar nematic layer [15]. After the polymerization of the cell the qualitative behaviour of this dependence was preserved.

Figure 2a shows the light transmission before polymerization as a function of the probe beam position X in the sample under different values of applied voltage. The interval of X from 2 mm to 7.5 mm corresponds to the region of the cell, which is filled with the composite material. Here T is different from zero due to the birefringence of the sample. Outside of this region, the empty cell is optically isotropic and T is zero. As can be seen from Figure 2a, T is rather constant everywhere in the filled region at U=0. This optical homogeneity indicates that the orientation of the NLC in the cell is uniform. Under the influence of the electric field, the light transmission varies in every point of the cell. The curves represented in Figure 2a for U=1.01 V and 1.06 V show that T is constant in the filled area, except the small regions near the borders (at X=2.3 and 7 mm), where most likely the edge effects become apparent.

In Figure 2b, the same dependences after the photopolymerization process are presented. One can see that the optical homogeneity of the cell is more or less preserved for U=0. However, the applied voltage produces non-homogeneous changes of the light transmission dependences. Thus at U=1.01 V and 1.06 V, the curves have clearly expressed peak with a maximum at X_c=4.3 mm. Here also, the same non-homogeneities close to the edges persist, which we will not consider hereafter. The Gaussian intensity distribution of the polymerizing beam is also presented in Figure 2b. One can see that the center of the Gaussian beam coincides with the position X_c, and the form of the observed peaks reproduces approximately those of the polymerizing beam. However, the width of the peak on the light transmission dependence does not correspond to the width of the polymerizing beam. The peak amplitude decreases with increasing the applied voltage and disappears completely for higher values (see Figure 2c). Here, the curves coincide at every point of the cell that indicates an uniformization of the cell (homeotropic alignment of NLC).

 

Fig. 2. Light transmission as a function of the probe beam position in the sample under different values of applied voltage U. (a) before polymerization; (b) after polymerization; (c) before and after polymerization for U=1.87 V. Thickness of the cell is 4μm.

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Figure 3 shows the dependence of the phase difference δF=φ(X_c)-φ(X_h) on applied voltage, φ being the induced phase difference of ordinary and extraordinary waves at the given point; X_c and X_b are the coordinates of the center and the border of the photopolymerized spot, respectively (see Figure 2b). φ has been calculated from the relation:

The maximum difference δF is achieved at the voltages lightly above the threshold value. This difference decreases with voltage increasing and becomes zero for higher voltages.

4.2 Visualization of the non-homogeneous character of nematic reorientation in the polymerized sample

In Figure 4, optical micrographs of the polymerized sample at different values of applied voltage are presented. The observation has been done by polarizing microscope in the geometry of crossed polarizers using a polychromatic source of light. At zero voltage, the sample is optically homogeneous. The color of the picture is defined by the refractive index dependence upon the wavelength of light. Under an applied voltage, exceeding the threshold value, the color of the picture is changed due to changes of the refractive index in the cell. Increasing voltage is expressed in the color changes towards the UV region. In the irradiated area of the cell, the circular symmetric formation appears. One can see, that color changes in the center of this formation are delay with respect to changes in borders of the sample. At high voltage, the difference between center and borders of the polymerized spot becomes negligible.

 

Fig. 3. Induced maximal phase difference δF in the cell with thickness of 4μm versus applied voltage.

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Fig. 4. Polymerised area of the sample viewed between crossed polarizers of microscope at different values of applied voltage. The initial optical axis of the cell is oriented at 45° with respect to the polarizers. Thickness of the cell is 5μm.

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In attached movie (Fig.5), the transformation of the sample’s optical microscope image under action of the uniform electric field is presented. One can see, that field induced color changes in the sample have a non-uniform centro-symmetric character. This demonstrates the non-uniform phase modification resulted by the non-uniformity of the stabilizing polymer network. During voltage growth (from start to the middle of the movie), the color changes are distributed from borders of the sample towards its center. Visually, it is expressed by the narrowing spot in the center of the sample. On the contrary, the decrease of the voltage (from middle of the movie to the end) induces color changes towards outside, and the image transformation looks like expanding spot.

5. Discussions

The presented centro-symmetric character of the electro-optical response of the cell (see Figure 2b) indicates a similar distribution of the effective refractive index in the polymerized area. Such a distribution is due to the centro-symmetric character of nematic reorientation, which depends strongly on the structure of the polymer network induced by the Gaussian beam. Since the polymerization rate is proportional to the intensity of exposed light, the polymerization appears to start from the center of the irradiated spot and to propagate in the plane of substrates, with circular symmetry [16]. As a consequence and due to the diffusion of monomers to the brighter regions [13], the density of the polymer network is maximal in the center of irradiated spot and decreases to the outer regions, and as a result, the pattern network structure forms in the gel. Higher voltage is necessary to reorient the nematic confined in polymer network with higher concentration [12]. Thus the retardation of the nematic reorientation is observed in the center of polymerized area with respect to the edges. At much higher values of applied voltage, the influence of the polymer network becomes negligible compared to the electric field, and the nematic reorients uniformly practically in all the volume of the cell (see Figure 2c).

 

Fig. 5. Field induced transformation in the optical image of the lens-like distributed polymer-stabilized liquid crystals. The voltage is increased from 0.5V to 2.65V and then is decreased to 0.5V again. The initial optical axis of the cell is oriented at 45⁰ with respect to the crossed polarizers. Thickness of the cell is 5μm. [Media 1]

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It should be noted that the maximal induced phase difference δF is small in general (see Figure 3). Very likely, the reason of that is still the weak influence of the polymer network on the reorientation of the nematic. The effective focal length f of the obtained lens may be estimated to be at the order of 30 m by expression f=πa²/λδF, where a=X_c-X_b≈0.7 mm is the radius of the lens. In general, the radius of the lens does not correspond to the width of the laser profile (see Figure 2b) and depends on the intensity of the polymerizing beam and time of exposure. To analyze such dependences, it is necessary to have more detailed investigations of kinetics of the curing process, which apparently has a non-linear character.

Obviously, the lensing operation is polarization dependant. However, this dependence may be easily overcome for the normally incident light using two crossed cells.

6. Conclusion

In this paper, we have created and investigated spatially symmetric polymer-stabilized liquid crystal samples using a Gaussian-shaped polymerizing beam. Such a structure can be used for the creation of electrically controllable focal length lenses. Presently we are looking for ways to increase the magnitude of the maximal phase shift for effective focusing of light, by means of varying the composition of the mixture, thickness of the samples as well as the parameters of exposition (beam intensity and time of exposition). The focusing properties of obtained lenses will then be measured and presented.