1. Introduction

Many interesting phenomena associated with nonlinear optics are produced by the light-matter interaction in liquid crystals (LCs) [1–2]. The nematic liquid crystal (NLC) has a very large optical nonlinearity that allows for many optical nonlinear effects, such as focusing, filamentation and undulation. These effects have been experimentally investigated [3]. The molecular reorientation effect can be generated using a low-intensity cw laser [4–5]. Furthermore, director field reorientation can be markedly enhanced by doping a small amount of dye molecules into LCs [6–8]. The intensity-dependent molecular reorientation in NLCs results in self-focusing. Under appropriate conditions, a self-focusing effect balances the natural diffraction of a beam, and the beam remains collimated and its energy is confined in the propagation direction while traveling through the medium. This phenomenon is known as an optical spatial soliton [9]. Peccianti, et al., demonstrated that a spatial soliton can be generated by a low-intensity laser in a planar NLC cell, which applied externally a low voltage for assistance [10–11]. The interaction between spatial solitons, such as crossing, interlacing, and merging of spatial solitons has also been examined. [12].

Notably, The LC is also well known as a type of nonlinear medium with strong temperature dependence. However, little attention has been paid to the role of optical orientation nonlinearity close to temperature of the phase transition [13]. The magnitude of the elastic constant K_i declines rapidly, and the nonlinear optical response is enhanced as the temperature increase approaches T_NI. Bloisi, et al., [14] have investigated the optically induced molecular reorientation as the temperature neared T_NI. They indicated that increasing temperature results in lowering the optical Freedericksz transition (OFT) threshold intensity I _th. Warenghem, et al., demonstrated that quasi-solitons or self-waveguides can be excited by thermal nonlinearity in dye-doped NLCs in a capillary tube [15–16]. Adding amounts of dye to LCs can reduce the threshold of optical Freedericksz transition (Janossy effect) [1]. Temperature variation changes the physical parameters of LCs, such as the elastic constant, refractive index, and viscosity [17]. The thermal nonlinearity induced by the beam intensity affects the refractive index variation. At the critical temperature from the nematic to is otropic phase, a temperature-dependent OFT effect cannot be overlooked.

Most studies of optical nonlinearity induced by the interaction between light and molecules in NLCs only concerned the beam profiles. Notably, the thermally enhanced optical nonlinearity developed at a temperature close to the critical temperature. An optical field combined with thermal effect influences the molecular orientation. This study investigates the evolution of LC configurations in the pump beam route. Optical nonlinearity in LCs associated with the NLC molecular configuration is investigated via conoscopic technique. This study demonstrated optically induced phase transition [1] from the nematic to the isotropic state experimentally.

2. Experiments

This study investigated laser beam evolution in nematic liquid crystal cells at a temperature close to the nematic-isotropic critical temperature. The laser light was collimated to impinge on the side of the NLC cell and pass through the planar NLC medium. The collimated laser light was scattered by the inhomogeneous LC medium along the beam route. Beam evolution was then examined using a microscope and a charge coupled device (CCD) camera. The NLC cells were composed of two indium-tin-oxide (ITO)-coated glass plates. Two Mylar spacers were inserted between the glass plates to maintain a cell thickness of 38 µm. The ITO glass plates were spin-coated with a thin layer of polyimide and rubbed in opposite directions to homogeneously align the LC molecules. The NLC material used in this experiment is 5CB purchased from E. Merck. The extraordinary and ordinary refractive indices (n_e and n_o) are 1.6812 and 1.5540 (measured at a wavelength λ=546.1nm). The range of the nematic phase of the NLC is 22.5^-35.2° C. The NLC was injected into the sandwich-like structure cell. A covered slide was glued perpendicularly to the planar glass plates to avoid distorting the impinging optical wavefront.

Figure 1 presents the experimental setup. A pump beam with power of 50mW from the Nd-YAG laser (λ=532nm) was collimated to a waist of approximately 5µm using a lens (f=5cm) and launched in the side of the cell. The focal point was inside the LC, ~150 µm away from the vertical cover glass. A half-wave plate and a polarizer were inserted between the Nd-YAG laser and sample cell along the beam route to adjust the intensity and direction of pump beam polarization. The director field of the NLC molecules was aligned along the y-axis. The polarization direction of pump beam was set perpendicular to the director of the NLC, i.e., along the x-axis. Experiments were conducted at about 34° C, close to the T_NI. Enhancement of optical nonlinearity was observed.

To make the interaction between the pump beam and NLC molecule clear, a conoscopic technique was utilized to probe the arrangement of the NLC [13]. A polarizer and an analyzer were placed in the front and the back of the cell, respectively, in the path of the probe He-Ne laser beam. Cross transmission axes were +45° and -45°, respectively, to the z-axis. A converging lens with a short focal length was placed above the cell, and the probe beam was focused on the cell. By analyzing the polarization state of output light with an analyzer, the conoscopic fringes were visualized. The shape, intensity and density of fringes depend on the direction of the optical axes and cell thickness. A screen was placed 15cm away from the cell. The conoscopic patterns that formed on the screen were recorded using a digital camera. The evolution of LC configurations caused by the pump beam at a temperature close to the critical temperature was examined based on recorded conoscopic patterns.

 

Fig. 1. Schematic drawing of experimental setup. P: polarizer, M: mirror, λ/2: half-wave plate, L: Lens, LC: liquid crystal.

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3. Results and Analysis

Beam evolution was first inspected by a microscope with a CCD. Figure 2 presents the sequential observation at the temperature 34° C. As shown in Fig. 2(a), the optical beam propagates along the z-axis and focuses inside the LC, ~ 150 µm away from the incident face. At the focus, the temperature increased slightly due to the accumulated energy from the pump beam. This temperature increase caused the OFT threshold to reduce gradually [1]. Thus, the optical nonlinearity due to molecular reorientation was enhanced thermally. At t=1.5 s, an undulate propagation mode with convergent and divergent loops appearing alternately was noted, as shown in Fig. 2(b). A dark spot was formed at the focus. The optical field combined with thermal effect reoriented LC molecules and reduced scattering in the uniform orientation region would form the dark spot. At t=3.0 s, additional dark spots formed and the light beam was extended by several sections in the propagation (z) direction of the LC, as shown in Fig. 2(c). As energy accumulated continuously, the local NLC temperature increased and approached the clear point of phase transition. An increased number of molecules were reoriented at the focus region. At t=5.0 s, the dark spot expanded and combined with neighboring spot in a transient time, as shown in Fig. 2(d). At t=6.0 s, the dark regions connected together and formed a long and narrow dark channel rapidly, as shown in Fig. 2(e). The dark channel may have arisen because the temperature exceeded critical temperature T_NI. The sequential behavior of the light beam in the liquid crystal at the temperature close to the critical point was examined from the microscope in the experiment. This study demonstrates the phenomenon in Fig. 2(e) as the occurrence of the optically induced phase transition from a nematic to isotropic state in the pump beam route.

 

Fig. 2. The temporal sequence of beam evolutions in the NLCs cell at the temperature close to the critical point (T=34° C). Pumping time t=0, 1.5, 3.0, 5.0, 6.0 seconds, respectively.

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The conoscopic technique was applied to probe the sample cell from the top. Figures 3(a)–3(e) showed the conoscopic patterns of the probe beam, which correspond to Figs. 2(a)–2(e) inspected by the microscope, respectively. The conoscopic patterns were on the y-z plane, the cross section of the probe beam. The reorientation of the LC molecules was then inspected, as the pump beam propagated in the NLC cell at the temperature close to T_NI.

 

Fig. 3. Conoscopic patterns of the probe beam which passes through the cell in the route of the pump beam at T=34° C. Figures 3(a)–3(f) were conoscopic patterns that changed with time, corresponding to Figs. 2(a)–2(f), respectively.

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Figure 3(a) presents the initial state of the conoscopic pattern when the sample cell was impinged by the pump beam. No fringes appeared in the route of light propagation because the LC molecules were not reoriented by the pump beam. At t=1.5s, interference fringes appeared around the focus, as shown in Fig. 3(b). The emergence of interference fringes indicated that the refractive index has varied gradually away from the focus. Bloisi, et al., [14] demonstrated that the reduction in LC elastic constants at a temperature close to T_NI caused a rapid decrease in the OFT threshold, such that the optical field easily reoriented LC directors. As the temperature approached T_NI, the ease with which LC molecules reoriented at the focus.

The extent of reorientation of the LC molecule depends on the light intensity profile. In the focus region, the director of molecules was rotated by the light field to the x-axis (polarization direction of the pump beam) at the central portion, and molecular rotation in the neighboring region was relatively less. As the beam narrows at the focus, the central intensity increases. The optical axis of the LC molecule was drawn to the field direction of the pump beam most effectively at the center portion of the focus. The subrays of the beam then experienced the following effective refractive index [18], $n_{\mathrm{eff}}\left(\theta \right)=\frac{n_o{n}_e}{{\left(n_o^2{\cos }^2\theta +n_e^2{\sin }^2\theta \right)}^{\frac{1}{2}}}$ where θ is the angle between the direction of beam polarization and the optical axis. The polarized light experienced increased effective refractive indices at the center portion of beam but small effective refractive indices at the neighborhood. The LC will form a grin lens-like medium at the focus region. The convergent characteristic resulted in the specific mode of the convergent and divergent loops appearing alternately as inspected in Fig. 3(c). Enhanced by the elevated temperature effect at the central portion of the focus, molecules were effectively ordered reoriented. A uniform LC arrangement was retained by the optical field at the focus region; thus, decreased light scattering caused the dark spot inspected at the focus in the microscope visualization (Figs. 2(b) and 2(c)).

On the other hand, the cross section (y-z plane) of the probe beam from the top shows conoscopic patterns at each focus. At the center of the focus region on the y-z plane, the high excitation of the LC molecular reorientation generated by the optical field was expected due to the increased intensity of the pump beam and the higher temperature compared to the surroundings. The director of the molecule will be perpendicular to the glass plate at the center of focus. According to continuum theory, the orientations of molecules vary depending on boundary conditions. The angle between the director of molecules and glass plate (y-axis, rubbing direction) decreased from the central part down to the periphery of the focus region. Figure 4(a) shows the circular symmetrical arrangement of molecular directors at the focus. Figure 4(b) presents the coincident part of the conoscopic pattern in Fig. 3(c). The distribution of molecular directors at the focus region formed the fringe pattern with elliptical arcs concentric with the focus. The continuously accumulated energy caused additional LC molecular excitation by the optical field in the focus region. The number of elliptical arcs increased with time until the director was completely reoriented (90°) in the central portion. Via the probe with the conoscopic method, the model of LC reorientation due to the pump beam was constructed at a temperature close to T_NI.

 

Fig. 4. (a). Inferred LC configuration at the focus region (y-z plane) where the molecules has been reoriented by the pump beam in the NLC cell at 34° C. (b). The coincident part of the conoscopic pattern in Fig. 3(c).

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The optically induced phase transition from the nematic to isotropic state was demonstrated in this study. The primary characteristic of the phase transition from the nematic to isotropic state is the sudden jump from an optically anisotropic matter to an isotropic matter, i.e., two refractive indices, n_e and n_o, of the liquid crystal to the one refractive index of the isotropic state, n_iso≈(n_e+2n_o)/3 [1]. The isotropic phase can be recognized using the conoscopic technique. As the birefringence of the sample is lost, it is the situation that the sample is placed between two polarizers that cross each other in the conoscopic technique. The interference patterns on the screen were the black palette where the isotropic phase formed. Although LC at the focus is apt to exceed the critical temperature as a result of the increased temperature at the focus, the isotropic state did not appear first at the focus. In the experiment, Fig. 3(d) indicates that the isotropic melting state formed first at the intersection of two concentric elliptical domains of interference pattern.

This study addressed the evolution phenomenon of phase transition observed from Fig. 3(c) to Fig. 3(d) in terms of the proposed LC orientation model in Fig. 5 and Fig. 6 as follows. Figure 5(a) expresses the orientation arrangement of LC in two domains, as the light beam was incident from the left side. Figure 5(b) presents the coincident part of the conoscopic pattern in Fig. 3(c). The concentric elliptical arcs map the variation of director orientation. The angle between the molecular director and y-axis is determined based in light intensity. The light intensity at the foci decreased progressively away from the center portion. Two domains of LC with their own reorientations of the LC molecules merged together, Fig. 6(a) shows the moleculer competition in orientation. Figure 6(b) presents the coincident part of the conoscopic pattern in Fig. 3(d). The induced disorder in molecular orientation decreased the order parameter (S) and suppressed the critical temperature. The effect of induced disorder caused the phase transition from the nematic to isotropic state; the isotropic state was first observed at the intersection of two domains.

 

Fig. 5. (a). Inferred LC configuration at two domains (y-z plane) where the molecules has been reoriented by the pump beam in the NLC cell at 34° C. (b). The coincident part of the conoscopic pattern in Fig. 3(c).

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Fig. 6. (a). Inferred the molecular competition in orientation at the intersection of two domains (y-z plane). (b). The coincident part of the conoscopic pattern in Fig. 3(d).

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At foci of the beam, the optical field excited the director of LC molecules and reoriented the molecules. Then the optic field retained their orientation order and kept the nematic state at the focus region. The director of LC molecules was hardly disturbed when the temperature was slightly over the critical point. The isotropic phase appears at each intersection of the two domains was condensation seed. While the ignition occurred, the isotropic state spread through seeds rapidly (Fig. 3(e)). Finally, the nematic states were transformed into isotropic states along the route that the pump beam propagated, and formed a long and narrow isotropic phase channel rapidly. Results of this study demonstrated that the optically induced phase transition in the restricted geometrical space from the nematic to isotropic state in NLC cells.

4. Conclusions

This study investigated the propagation of a beam in an NLC cell at a temperature close to the T_NI. The thermally enhanced optical nonlinearity produced LC reorientation was examined at the focus. The pump beam traversed in the liquid crystals with the formation of the grin lens-like media at the foci and extended the undulate loops in several sections. Under the appropriate energy of the pump beam, the isotropic phase formed due to the competition induced disorder in the LC director at the intersection of the two domains. Such optically induced phase transition from the nematic to isotropic state initiated the formation of a narrow isotropic phase LC channel along the propagation direction. The conoscopic technique demonstrated that the LC arrangement is affected by the pump beam. By analyzing the conoscopic patterns, we interpret the evolution mechanism of the pump beam that propagating in NLCs at the temperature neared the nematic-isotropic critical point.