1. Introduction

Liquid crystals (LCs) are known to respond efficiently to external action induced, e.g., by optical fields. Such light-induced effects in nematic liquid crystals can be very strong due to the ease of reorienting the anisotropic LC molecules with polarized light. This will lead to changes in the refractive index of the material and, at sufficiently high levels of illumination, to a strong nonlinear optical response by the medium.

The optical nonlinearity in conventional LCs may readily be a billion (10⁹) times larger than that in typical organic materials. This high value can still be significantly increased by doping the LC with a small concentration of dye molecules [1,2], comb-polymers and dendrimers [3], or metal nanoparticles [4]. Today, such heterogeneous LC systems have attracted attention due to the possibilities they offer in enhancing some desired properties of existing LCs or in allowing design of novel smart materials with unique properties that the original substances cannot alone provide.

Adding dye molecules in an LC matrix is the most popular method to increase the optical response of an LC system. It has lead to such discoveries as giant optical nonlinearity [5], low-power optical reorientation [6], dye-induced enhancement of optical nonlinearity [7], colossal optical nonlinearity [8,9], and supra-optical nonlinearity [10]. Usually, at low concentrations (less than 1 wt%) the dye does not change the basic matrix properties (elasticity, clearing temperature, refractive index, etc.), but does change the optical properties that can manifest themselves through such effects as the trans-cis photoisomerisation of the azo-dye molecules at irradiation, light-induced adsorption/desorption of the dye [11–13], or photorefractivity [10]. The advantages of the dye doping can even be improved by combining the azo-molecules with polymers. Interesting new effects and properties have been obtained by adding such polymer-dye complexes to LCs to form heterogeneous LC systems [14].

Recently, we proposed and investigated into a new heterogeneous liquid crystalline material [14] in which hydrogen-bonded polymer-azo-dye complexes were doped at a low concentration (c < 1 wt. %) in an LC bulk. The resulting dilute nano-suspension combined the unique anisotropy of liquid crystals with the stability of polymers and the light sensitivity and light-induced mobility of azo-dyes. In this system, we discovered a surprising self-orientation property and a spontaneous anchoring transition from planar to homeotropic alignment to take place, which was caused by the combined effect of the material constituents.

In this paper, we investigate into the nonlinear optical properties of this heterogeneous LC system. The suspension shows a strong nonlinear response at extremely low light powers. We observe formation of aberration rings by self-phase modulation in millisecond time scale and without a clear power threshold. We measure a particularly high value for the nonlinear parameter (up to 10⁻³ cm²/W) when irradiating this homeotropically aligned LC at normal incidence.

2. Materials

The experiments were carried out with a nematic liquid crystal 4-Pentyl-4'-cyanobiphenyl (5CB; PI Chemicals Co., Ltd) doped with a hydrogen-bonded polymer-azo-dye complex. The polymer-dye complex P4VP(CHAB)_0.5 was prepared by mixing the polymer poly-4-vynil-pyridine (P4VP, Mn: 1000 g/mol, Mw: 1200 g/mol; Polymer Source Inc.) and the azo-dye 4-cyano-4'-hydroxyazobenzene (CHAB, BEAM Co.), both separately dissolved in dimethylformamide (DMF, 98%, Fluka). The procedure how to prepare the complex and, further, the complex-doped LC is fully described in [14].

The polymer-dye complex was added to the LC, and the DMF solvent was evaporated away. The resulting LC suspension, 5CB + c % P4VP(CHAB)_0.5 (c < 6 wt. %), was further used and compared with samples of CHAB-doped 5CB without the polymer.

The suspension was put in a sandwich-type symmetrical glass cell, the inner surfaces of which were covered with rubbed polyimide films (polyimide poly(4,4'-oxydiphenylene-pyromellitimide) [15] that usually provide strong anchoring and planar alignment of the LC. The cell thickness was set by Teflon stripes in a range of 20 ÷ 160 μm. The cell was filled starting from isotropic state of the LC (T ≈60 °C) and slowly cooled down to room temperature.

As was observed recently, a cell filled with the complex-doped LC is not stable in orientation over time [14], but undergoes a clear anchoring transition from planar to homeotropic alignment without any external action, typically in hundreds of hours. This surprising phenomenon is observed only in the complex-doped LCs, but not in LCs doped either with pure polymer or pure dye at corresponding concentrations. Even in a cell made of bare glass (or quartz) plates without any aligning layers, the complex-doped LC self-orients to a perfect homeotropic alignment immediately after the filling. The samples containing pure LC or dye-doped LC do not show such behavior [14].

In this paper, we use the homeotropically aligned samples, acquired either through the anchoring transition or the self-orientation process, to investigate the nonlinear optical response of the material. In order to facilitate a meaningful reference, samples of pure LC and azo-dye-doped LC were also prepared in homeotropical alignment using layers of polyimide SE-1211 (NISSAN).

3. Experiments and results

We used the simple but powerful method of aberrational self-phase modulation of a light beam [16–18] to study the nonlinear optical properties of the complex-doped LC. Using the experimental setup of Fig. 1 , we observed strong aberrational self-interaction of the laser beam traversing a self-oriented LC cell. In the experiment, a linearly polarized light beam (λ = 457 nm) from a DPSS laser was focused with a 15 cm lens onto the cell. The beam waist was 58 μm at the location of the cell placed in a vertical position. The laser beam was incident perpendicularly to the cell, so that the wave vector of the interacting light, k_light, and the director of the cell, d_LC, were parallel to each other. The incident power was in the range of 0.1 ÷ 9 mW, corresponding to intensities of 0.9 ÷ 85 W/cm².

 

Fig. 1 Experimental set-up. 1 – laser, λ = 457 nm, P < 9 mW; beam waist in focus ≈58 μm; 2 – polarizer; 3 – lens (f = 15 cm); 4 – cell filled with complex-doped LC, homeotropically aligned; 5 – screen. d_LC || k_light (normal incidence).

Download Full Size | PDF

The laser beam has a Gaussian intensity profile, and therefore the light-induced nonlinear change in the refractive index of the medium will be larger at the beam axis and diminish radially towards the beam edge. The different radial parts of the beam will interfere with each other and cause formation of a ring system in the far field seen on a screen. The number N of the aberration rings is related to the thickness-averaged change Δn in the refractive index through the expression

The irradiation of the complex-doped LC with normal incident linear polarized beam led to appearance of system of rings. A typical aberrational ring structure is shown in Fig. 2 . There are several interesting features in the behavior of the system. Despite the normal incidence, no visible threshold for the formation of the aberrational structure was observed. Instead, even at small powers (Figs. 2a-2e) the ring pattern started to appear immediately after switching the beam on. With increasing power, each new ring appeared on the edge of the laser spot. The rings were non-divergent. At higher powers, though, an additional ring structure started to appear which was concentric with the original one, but was clearly divergent (Figs. 2f-2j). At those intensities, the outer rings are unstable, jittering and with exposure time transforming to a system of internal non-diverging rings with one wide outer ring.

 

Fig. 2 Typical structure of the system of aberration rings observed in the far field when irradiating 5CB + 0.5%P4VP(CHAB)_0.5 at normal incidence (a-j) and at 50° angle of incidence with p-polarized light (k-l). The cell thickness is L = 82 μm. Laser beam power: (a) 1.2 mW; (b) 1.5 mW; (c) 1.9 mW; (d) 2.3 mW; (e) 2.7 mW; (f) 3.1 mW; (g) 4.0 mW; (h) 6.4 mW; (i) 7.5 mW; (j) 8.9 mW; (k) 0.5 mW and (l) 2.0 mW.

Download Full Size | PDF

The suspension of 5CB + 0.5% P4VP(CHAB)_0.5 was studied also at different angles of incidence in the range 0 ÷ 50° using p-polarized light. The larger the angle, the more the rings looked like the ones typically observed in orientational nonlinearity (Figs. 2k-2l). This kind of nonlinearity can easily be distinguished from the observed non-diverging case due to the longer time it takes for the rings to form (tens of seconds). The stable, non-jittering rings that were observed in the complex-doped LC at normal incidence gradually disappeared when the angle of incidence was increased, and at 40° those rings disappeared as they were screened by rings formed due to the orientational nonlinearity. The first ring of the orientational nonlinearity appeared at a very low power of 50 μW at 40° angle of incidence. The appearance of orientational nonlinearity in doped LC systems at oblique incidence is a well-known phenomenon which has been rather widely studied [3,19]. In the following we will only consider the case of stable non-diverging aberration structures at normal incidence at low powers when the outer rings do not appear yet (Figs. 2a-2e).

The dependence of the aberration structure on the cell’s thickness (Fig. 3 ) was checked in samples with rubbed polyimide layers after the anchoring transition had taken place and the suspensions appeared to be totally homeotropic.

 

Fig. 3 The number of rings of the aberration pattern as a function of beam power for different thicknesses of the cells filled with 5CB + 0.5% P4VP(CHAB)_0.5 (after anchoring transition). The cell’s thickness: (A) – 23 μm; (B) – 55 μm; (C) – 82 μm; (D) – 160 μm. The data correspond to the non-diverging case.

Download Full Size | PDF

According to Santamato and Shen [20] the large rings arise from spatial self-phase modulation that depends on the laser beam intensity profile, whereas the small rings result from the interference of the spatial self-phase modulation and the wave-front curvature of the incident beam in the sample. The authors observed one or two small rings before the large rings showed up clearly. Lucchetti et al. [21] reported the analysis of these small rings, called by the authors the fine structure, with the help of the Fraunhofer diffraction integral [20,21]. Applying this analysis as well as Kirchhoff diffraction integral [22] to our experimental conditions does not give any reasonable fitting of the observed multiple fine structure rings within the laser beam spot (the non-diverging case). Thus, the observed fine structure cannot be simply explained by the interplay of the wave-front curvature of the beam and nonlinearity in the sample. The fine ring structure, on the other hand, is caused by the phase modulation of the light in the LC composite, and we can introduce an associated effective refractive index change δn_FS through $\Delta \varphi =\frac{2\pi }{\lambda }{\displaystyle {\int }_{-L/2}^{L/2}\delta n_{FS}(r,z)dz}$ [18]. Here r is the radial coordinate counted from the beam axis. The light-induced change of the effective refractive index can then be determined from the relation $\left|\delta n_{FS}\right|=\lambda N/L$, similar to the Eq. (1). Using the experimental data in Fig. 3 the values appear to be in the range of δn_FS = 0 ÷ 0.039. The corresponding effective nonlinear parameter can be calculated as $n_{2,FS}=\delta n_{FS}/I$. The average value of $n_{2,FS}$ appears to be in the range (0.5 ÷ 1) ± 0.04 × 10⁻³ cm²/W depending on the cell’s thickness. This value is two orders larger than the typical nonlinear parameter encountered in orientation nonlinearity of transparent liquid crystals and of the same order of magnitude as the nonlinearity of the Janossy effect in dye-doped LCs [23,24]. For further experiments, the cell thickness was chosen to be about 80 μm as it gave a strong nonlinearity at small powers while still providing good-quality LC alignment.

The nonlinear effect strongly depended on the concentration of the complex (Fig. 4a ). For the sake of simplicity in the sample preparation, in the following experiments we used pure glass cells of 80 μm thickness. Increasing the concentration by a factor of 2 enhanced $n_{2,FS}$ by the same factor. For the highest concentration of 5.3%, however, this was no longer true. This concentration seemed to be high enough to cause phase separation and unstable behavior of the LC alignment. The effective nonlinear parameter was in the range from (2.7 ± 0.1) × 10⁻⁴ cm²/W for LC suspension doped with 0.2% of the complex to (1.36 ± 0.09) × 10⁻³ cm²/W for 1% doping.

 

Fig. 4 (a) The number of rings of the aberration pattern as a function of the beam power for different concentrations c of the complex in self-orienting 5CB + c % P4VP(CHAB)_0.5. The cells are made of pure glass. (b) The dependence of the induced refractive index change on the beam power in: (A) self-orienting 5CB + 0.5% P4VP(CHAB)_0.5, (B) homeotropically aligned 5CB + 0.25% CHAB. The cell thickness is 80 μm, and the data correspond to the non-diverging case of the aberration structure.

Download Full Size | PDF

We compared the nonlinear properties of the complex-doped LC samples to the nonlinearity observed in the dye-doped LC (Fig. 4b). For the comparison we used 5CB + 0.5% P4VP(CHAB)_0.5. The complexation degree in the complex P4VP(CHAB)_0.5 is 0.5 that corresponds to approximately 50 wt. % concentration of the dye in the complex. Therefore, to compare the LC doped with 0.5% of the complex to that doped with the dye, one should have the same concentration of the dye in the LC, i.e. 0.25%: 5CB + 0.25% CHAB. The complex-doped LC appeared to have a larger change in the effective refractive index at the same intensity and dye concentration. The effective nonlinear parameter $n_{2,FS}$ was (8.5 ± 0.2) × 10⁻⁴ cm²/W compared to (5.6 ± 0.4) × 10⁻⁴ cm²/W in the dye-doped LC for the same 80 μm thickness of the cell. As for pure LC and polymer-doped LC, no aberration rings were formed at normal incidence for laser powers in the range of 0 ÷ 9 mW.

To study the dynamics of the rings formation and relaxation of the ring structure, we switched the incident beam on and off within a time of 0.14 ms using a mechanical shutter and tracked the intensity of a probe beam from a diode laser (λ = 650 nm) passing through the irradiated area using a photodiode that was connected to an oscilloscope and measured the signal in the spot centre. The probe beam was not focused and was of very low power (0.5 mW) so that it could not cause any changes in the cells. The intensity of the probe beam (within the aperture of the detector) changed because of its diffraction in the LC modified by the pump beam. The rise time obtained from the exponential growth fitting of the signal after switching the beam on was measured to be 6.54 ± 0.04 ms in an 80 μm glass cell at 2 mW laser power. The relaxation time of the ring structure obtained from the exponential decay fitting of the signal after switching the pump beam off was 5.67 ms. The rise time for a cell with dye-doped LC was 8.76 ms and the relaxation time 7.74 ms, i.e., 1.3 times longer than for the complex-doped LC. We also observed that for increasing cell thickness, the rise and relaxation times also got increased.

4. Discussion

The effective dielectric constant and therefore the refractive index of an LC are determined by the molecular orientational ordering, i.e., the director and the order parameter [25]. Light can affect both of these parameters. Therefore, there can be several mechanisms responsible for the observed optical nonlinearity: orientational mechanism connected with the light-induced director change, and thermal and conformational ones causing the light-induced order parameter change.

In the following, we only consider the non-diverging case of self-phase modulation. The orientational nonlinearity can be excluded from the consideration, since we did not observe a threshold behavior that would be normal for our experimental geometry. Also, the rise/relaxation times were a couple of orders less than would be expected for orientational nonlinearity [26].

No aberration rings were observed in the pure LC or polymer-doped LC samples at the low intensities that produced a clear ring structure in the complex-doped sample. There were also no rings at red laser irradiation, which means that the absorption in the dye is important. The absorption spectra of the complex-doped LC were measured before and at laser irradiation leading to the ring pattern formation. It appeared that the amplitude of the absorption band corresponding to the trans-isomer of the CHAB azo-dye is decreasing immediately at irradiation showing the presence of trans-cis isomerization. We suggest the complex-doped LC to have the same mechanism of optical nonlinearity as some of the azo-dye-doped LCs or azobenzene LCs [10,25,27–29] initiated by laser-induced changes in the order parameter of the liquid crystal. The mechanism proposed in those publications was photo-stimulated conformational changes of the liquid crystal or azo-dye molecules caused by trans-cis isomerization of the molecules. The molecules in the trans-form are more rod-like and they follow the orientation of the LC director, while the photo-excited cis-form molecules are bent creating disorder near the transformed azo-dye. Thus, the conformers induce a change in the order parameter ΔS that leads to a change in the refractive indices and in the birefringence. The conformers act as impurities reducing the orientational order. Also the linear polarizability of the excited conformer differs from that of a molecule in the ground state, and gives a contribution to the bulk susceptibility. The trans-cis isomerisation is a fast process, and thus the resulting changes in the order parameter and the refractive index can be rapid [28,29], in the range of milliseconds. Therefore, we suggest the mechanism of the observed nonlinearity to be conformational.

Thermal effects can also be responsible for the observed phenomena in addition to conformational nonlinearity. It could be that light-induced heating of the complex causes the change in the refractive index of the LC due to a decrease of the order parameter in the vicinity of the dopant. We cannot totally exclude such thermal nonlinearity despite the fact that the measured relaxation time is almost 10 times longer than the thermal relaxation times estimated for LCs with absorbing dopant [4,30]. First, the thickness dependence of the relaxation time speaks for a thermal mechanism; second, the shorter thermal times cannot be measured as they become screened by the higher values of the conformational times; third, the thermal conductivity coefficient of an LC with a polymer-dye complex can be much smaller in addition to a higher specific heat capacity, which can lead to an increase in the relaxation time.

We also observed that for the complex-doped LC the number of rings increased with temperature at the same intensity. This also speaks for conformational and thermal nonlinearities in the medium [25], since with increasing temperature the derivative dS/dT grows when approaching phase transition, and thus making the order parameter contribution larger.

We performed an additional experiment to study the self-phase modulation in the complex-doped LC for irradiation with circularly polarized light. We found that at the same intensity, the circularly polarized beam produced a larger change in the refractive index than the linearly polarized beam. At the moment we cannot explain this fact completely but evidently it is connected to the presence of the polymer-azo-dye complex.

The enhancement of the nonlinearity in the complex-doped LC compared to an azo-dye-doped LC can be explained by the lower mobility of the azo-dye molecules in the LC suspension due to their bonding to the polymer. In [10] it was shown that diffusion of the dye and its light-induced reorientation perpendicular to the polarization direction can decrease the influence of refractive index change due to order parameter changing. The observed effective nonlinear parameter of up to 10⁻³ cm²/W in the complex-doped LC is lower than that observed in the case of colossal optical nonlinearity [8–10,31], but it can still be of great importance since the studied LC suspension possesses the unique self-orienting property giving interesting perspectives for a variety of LC devices. The combination of the nonlinear and self-orientating properties can be of great advantage, e.g., in environments where aligning by orientants or rubbing is restricted by the small size or special shape of a surface and where controlling by light is preferable. We can see such potential applications in fibres, micro-lens arrays, in microfluidic devices, metamaterial structures, etc.

5. Conclusion

In this work, we have presented results on the interaction of light with a self-orienting liquid crystal suspension containing H-bonded polymer-azo-dye complexes at low concentration. A fast (< 10 ms) nonlinear optical response was observed with the effective nonlinear parameter reaching values of up to 10⁻³ cm²/W at very low light powers (< 10 mW) at normal incidence. As plausible explanation to the findings, we suggested conformational and thermal mechanisms that cause the light-induced order parameter to change in the complex-doped LC.

The studied self-oriented suspension appeared to be a very efficient light-induced nonlinear material that does not require any additional aligning processing or treatment, and as such gives perspectives for a range of optical applications. The strong and fast nonlinear optical response together with the self-orientating property make this LC material more attractive than a conventional dye-doped LCs for use in light-controlled optical devices where the small size or special shape of a surface impose restrictions for the use of traditional alignment (rubbing technique etc.). Microfluidic devices, micro-lens arrays, metamaterial and photonic band-gap structures can be areas of possible application of these complex-doped LCs.