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Abstract
We report the light beam action on the nematic liquid crystal film with a free surface. It was found that a weak light absorption by the liquid crystal substrate dramatically changes the orienting properties of the light beam; in particular, a thermal gradient field induces an umbilical defect formation.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The light interaction with partially ordered systems such as nematic liquid crystals (NLCs) is very diverse and gives rise to a large variety of optical phenomena [1–4]. Numerous effects can be observed when light field directly or indirectly affects the NLC films: the light-induced reorientation in optically transparent [5,6] and absorbing [7] NLCs, photorefractive [8,9] and photovoltaic [10] effects, etc.
The light field exerts the orientational torque acting on molecular dipoles in NLC. On the microscopic level, this effect results in the rotation of nematic director $\textbf {n}$, a unit vector indicating the preferable alignment of the long molecular axes whose direction coincides with the NLC optical axis. This director rotation usually occurs in the $\Sigma$ plane specified by director $\textbf {n}$ and an extraordinary component of the light field. When an NLC contains a dye additive, the optical response can be enlarged by the two orders of magnitude due to the dye excitation [7]. However, the NLC reorientation occurs within the same $\Sigma$ plane [11].
There are a few exceptions from this rule. One of them is the effect of director oscillations at an oblique incidence of the ordinary light wave on a homeotropic NLC [12,13]. Another one is the axially symmetric director deformation, which can be considered as an umbilical defect [14] or destructing boojum [15,16], formed in a tightly focused light beam [17,18]. The three-dimentional director reorientation resulting in the appearance of an umbilical defect can be achieved in an NLC film by photoinduced modification or induction of external electric fields [19–21]. Similar director distributions are also formed by the local isotropization in dye-doped NLC cells under the light beam irradiation [22].
Here we study the light beam action on the NLC film with one free surface. In particular, the umbilical defect generation due to the light beam action on the NLC film deposited on a glass substrate with the absorbing layer is found and investigated.
2. Experimental
The nematic liquid crystal E7 (Synthon Chemicals, GmbH) with a high clearing point was used in the study. For NLC alignment, we used the 1-mm-thick glass plates coated with surfactant octadecyl chlorosilane (OTS) or having an indium tin oxide (ITO) layer. The OTS is typical orienting material which provides a homeotropic anchoring. For the ITO layer, homeotropic anchoring is formed due to the two-dimensional inhomogeneity [23] with average roughness $\approx$ 3 nm in the surface profile (Fig. 1(a)) measured by an atomic force microscope NTEGRA (NT MDT Spectrum Instruments, Russia; provided by FLNP JINR).
Fig. 1. The 5 $\mu$m $\times$ 5 $\mu$m atomic force microscopy image of ITO surface (a); schematic representation of the sample (b); typical conoscopic image of the NLC layer with a free surface (c); the sketch of experimental setup (d): laser shutter (S), glass plate (GP), unpolarized beam splitter (BS), lens (L), polarizers (A, P, and P1), red light emitting diode (LED), photodiodes (PD1 and PD2). The Nd:YAG and He-Ne lasers emit cw radiation at $\lambda _g$ = 532 and $\lambda _r$ = 632.8 nm, respectively; LED spectrum peaks at $\lambda _{max}$ = 620 nm.
At oblique incidence (angle of incidence is 45$^{\circ }$) of p-polarized light beam at $\lambda _g = 532$ nm, the transmission coefficients (the ratio of transmitted light power to the incident one) measured with the help of a photodiode are $t = 0.986$ and $t = 0.912$ for OTS and ITO coated glass plates, respectively, whereas the corresponding reflection coefficients (the ratio of reflected light power to the incident one) are $r = 0.014$ and $r = 0.060$. Thus we can conclude that ITO coated plate absorbs about 2.8% of light, whereas the absorption of OTS coated plate does not exceed the measurement error ( 0.2%).
The liquid crystal molecules tend to align normally to NLC-air interface [24]. The NLC film placed onto the glass substrate with OTS or ITO coating provided the uniform homeotropic alignment which was verified by the observation of the clear cross in a conoscopic image (Figs. 1(b) and 1(c)). The thickness $L$ of the NLC film was measured by birefringence effect at an oblique light incidence (see Supplement 1 for detailed explanation).
The NLC cell (the thickness is $L$ = 20 $\mu$m) composed of two plane parallel glass plates with OTS coating was used to compare its optical response with that of the NLC samples with one free surface.
The schematic diagram of the experimental setup is shown in Fig. 1(d). The light beam with the wavelength $\lambda _g$ = 532 nm from the continuous wave (cw) solid-state laser (SSP-LN-532-FN-300-0.5-LED, CNI, China) was focused on the sample by lens L with focal distance $F$ = 100 mm. The angle of light incidence was either 0$^\circ$ or 45$^\circ$. The plane of linear polarization could be rotated by the $\lambda$/2 phase plate. The waist radius of light beam was measured to be $w_0$ = 30$\pm$2 $\mu$m (at a level of e-2) by the “knife-edge” method [25]. The diffraction patterns of passed and reflected light were observed on screens 1 and 2, respectively, and recorded by a USB camera.
Dynamic processes were registered by the PD1 and PD2 photodiodes. The first one is used to measure the transmission of a probe light beam (light power is $P$ $\approx$ 0.2 mW) at wavelength $\lambda _r$ = 632.8 nm from He-Ne laser (LGN-207A, Russia) with the linear polarization in $YZ$-plane. To register the polarization changes of the probe light, polarizer P1 crossed to the initial light polarization was used. The pump beam was suppressed by the red filter. The second photodiode was used to detect the opening and closing of the light shutter interrupting the pump beam.
The textures of illuminated area were observed and recorded using the visualization scheme consisting of a USB-camera with a 10x objective, the light emitting diode LED with a luminescence peak at $\lambda _{max}$ = 620 nm, and crossed polarizers P and A.
3. Results and discussion
Let us start with the NLC layer with a free surface on the OTS-coated glass substrate. In this case, the obliquely incident light beam forms a typical ring-shaped aberrational pattern [6], which enlarges with an increase in the light intensity $I=2P/\pi {w_0}^2$ (Figs. 2(a) and 2(b)). At a small shift of the sample, more rapid than the time of light-induced phase relaxation ($\sim$ 1 s), a part of diffraction pattern, which corresponds to the shifting direction, becomes brighter (Fig. 2(c)). This behavior implies the light beam self-focusing [26]. When passing from p- to s-polarization, the aberrational structure disappears (Fig. 2(d)), thus, the only extraordinary refractive index is affected by light. Therefore we can conclude that the light field induces the NLC director rotation in the same manner as for the conventional NLC cell (Figs. 2(e) – 2(i)). The minor difference in the light beam intensity leading to the same optical response can be explained by a weaker anchoring at NLC-air interface.
Fig. 2. Far-field diffraction patterns on Screen 1 for obliquely incident light beam passed through the NLC film ($L = 19 \pm 1$ $\mu$m) placed on the OTS-coated glass substrate (a-d) and through the conventional homeotropic NLC cell of the same thickness (e-i). Patterns (c) and (g) were obtained at a rapid shift of the sample in the direction showed by an arrow. Patterns (a-c) and (e-g) were obtained in the light beam polarized along the $Z$-axis, patterns (d) and (i) were obtained in the light beam polarized along $X$-axis.
For the NLC films placed on the ITO-coated glass substrate, the nonlinear optical response becomes different from the one described above.
In the case of a relatively thin ($L$ = 7 $\mu$m) NLC film, the diffraction rings were formed at one order of magnitude lower light beam intensities (Fig. 3(a)). The rapid shift of the sample indicates the light self-defocusing (Fig. 3(b)) [26]. The change in the incident light polarization does not affect the diffraction patterns. The light polarization itself remains the same as that for the light passing through the NLC film. An evolution of the pattern in the reflected light observed at Screen 2 begins with the intensity oscillations (see Visualization 1). These oscillations are due to the interference of light reflected from the air-NLC and NLC-substrate interfaces. Thereafter, the steady-state pattern shown in Fig. 3(c) is set in. An irradiated area remains dark in the visualization scheme with crossed polarizers during the entire process of light exposure. The results obtained allow one to conclude that the light beam causes thermocapillary effect which is well-investigated for isotropic liquids [27–29]. Specifically, the local optical heating results in the decrease of the surface tension and following dimple formation at NLC film surface.
Fig. 3. Far-field diffraction patterns on Screen 1 (a, b) and Screen 2 (c) for the obliquely incident light beam passed through the NLC film ($L$ = 7 $\mu$m) on the ITO-coated glass substrate. The pattern (b) is obtained at a rapid shift of the sample in the direction shown by the arrow. The light intensity on beam axis is $I$ = 2.2 kW$/$cm$^2$.
For the thicker NLC film ($L$ = 20 $\mu$m), the far-field diffraction pattern becomes more complicated (Fig. 4(a)). Its asymmetric structure is similar to that observed at the photorefractive effect in NLC cell, when the two profiles of the phase shift with opposite signs overlap each other [19]. In our case, the negative phase shift is related to the dimple formation, whereas the positive one can be associated with a decrease in the nematic order parameter or director reorientation. In contrast to the previous cases, the polarization of the light beam does not remain unchanged: a part of light goes through the crossed polarizer P1 (Fig. 4(b)). At the normal incidence of the light beam, the diffraction pattern (Fig. 4(c)) resembles that for the thinner film (Fig. 3(a)), but a Maltese cross pattern (Fig. 4(d)) is formed when the light passes through the crossed polarizer P1. Here the effect also does not depend on the initial polarization of pump beam.
Fig. 4. Far-field diffraction patterns at Screen 1 for obliquely (a,b) and normally (c,d) incident light beam with $I$ = 1.4 kW$/$cm$^2$ (light polarization is along $Z$-axis, see Fig. 1(d)) passed through the NLC film ($L$ = 20 $\mu$m) on the ITO-coated glass substrate. Patterns (b) and (c) were obtained with polarizer P1 placed in front of Screen 1. Microscope image obtained in the visualization scheme for the oblique incidence of the pump beam (e). Time dependencies (f) of the normalized light power for the probe beam ($\lambda _r$ = 632.8 nm) passed through the sample in crossed polarizers for different pump beam intensites $I$.
The bright Maltese cross appears in the visualization scheme even for the oblique incidence of the pump beam (Fig. 4(e)). This indicates the axially symmetric director distribution with its axis normal to the glass substrate.
To elucidate the process responsible for the director deformation which is visualized in crossed polarizers by the Maltese cross, we first note that variation of the nematic order parameter cannot affect the polarization of incident light exciting the extraordinary wave in the undeformed NLC. At the same time, the thickness modulation can affect the light polarization due to the director alignment at the deformed free surface. However, the time dependence of probe beam transmission in crossed polarizers (Fig. 4(f)) has shown that the characteristic rise and fall times are several tens of milliseconds, which are two orders of magnitude lower than the characteristic time of the thickness variation. From this, we can conclude that the reorientation processes are not caused by thermocapillary convection and thickness variation.
It is interesting to note that the size of director deformation area is not limited by the light beam diameter. This is more clearly seen for relatively thick ($L$ $\approx$ 50 $\mu$m) NLC films. At an increase in the light beam intensity, the deformation area becomes significantly larger than the beam waist $w_0$ (Fig. 5). For example, when the light intensity on the beam axis is $I$ = 3.5 kW$/$cm$^2$, the radius of the deformed area is 6 times larger than $w_0$. Note that the similar pattern corresponding the umbilical defect is formed in the NLC film placed on photovoltaic substrate [20].
Fig. 5. Microscope images recorded with the visualization scheme (a-d) and the corresponding profiles (e) of the light-induced structure images at various light intensities on beam axis: $I$ = 0.71 (a), 1.1 (b), 2.8 (c), 3.5 (d) kW$/$cm$^2$. The thickness of the NLC film is $L$ = 50$\pm$5 $\mu$m.
The phase shift difference between neighboring minima and maxima in the intensity profiles (Fig. 5(d)) corresponds to $\phi = \pm \pi$. If we assume that the NLC director does not reorient on the beam axis, two bright areas between the center and periphery in the reorientation area (Fig. 5(b)) should correspond to phase shift $\phi \approx 2\pi$ at $I = 1.1$ kW/cm$^2$. The same phase shift $\phi \approx 2\pi$ required for the development of one aberrational ring in the NLC film on the substrate without ITO layer (Fig. 2(a)) appears at light intensity one order of magnitude higher $I = 11.2$ kW/cm$^2$.
The results on the director field deformation imply the existence of an orientational torque due to the heat diffusion from an absorbing layer to the bulk of NLC and glass substrate. The NLC director rotation occurs faster than the thermocapillary dimple formation caused by the hydrodynamic flows. Hence we can neglect the hydrodynamic effects and assume that the temperature distribution itself can cause the NLC director reorientation.
The effect of molecular orientation was intensively studied for the isotropic liquids [30–32]. In liquid crystals, the thermo-orientational effect was previously observed in the cell with spatially periodic heating electrodes [33]. Following the theoretical model of thermo-orientational effect [34], the orientational torque caused by the temperature gradient can be introduced as
Equations (2) with boundary conditions (3) were solved numerically using the straight line method in the spatial region ($0<\rho /L<2.5$, $0<z/L<1$) with a uniform grid 251$\times$51. We used typical elasticity, viscosity, and thermal conductivity parameters for cyanobiphenyl NLC [35]. Parameters ${\alpha _a}{\left ( {g{P_0}L} \right )^2}/K = 60$ and ${\lambda _a}/{\lambda _ \bot } = 0.52$ were chosen to fit the nonlinear phase shift estimated from comparison of the number of peaks in experimental image for $I$ = 3.5 kW$/$cm$^2$ (Fig. 5(d)) and in the one calculated by Jones matrix approach (Fig. 6(c)) . Due to the low thermal conductivity of the air, the temperature gradient ${\boldsymbol{\nabla} T}$ has the transverse (radial) component which can be much larger than the longitudinal component (Fig. 6(a)). At the same time, the NLC director tends to by oriented along ${\boldsymbol{\nabla} T}$. Because of the homeotropic boundary conditions, the director field ${\textbf {n}}$ is mainly deformed in the middle layer of NLC film (Fig. 6(b)). The axially symmetric director distribution corresponds to an umbilical defect, similar to the one caused by photorefractive and photovoltaic effects [19,21]. It is clearly seen that the temperature spreading causes the large deformation area which exceeds the light beam size. The calculated director deformation area is less than the experimental one because of simplification of the thermal outflow into the bulk of the glass substrate by fitting $g$ parameter.
Fig. 6. The steady-state temperature gradient (a) and director field (b) distribution calculated numerically for the NLC film on the ITO-coated glass substrate ($L$ = 50 $\mu$m and $I$ = 3.5 kW$/$cm$^2$). The light transmittance through the NLC film in crossed polarizers (c).
The considered mechanism allows us to conclude that the NLC director orientation is not of a threshold type, i.e. it should also occur for lower light intensities and sample thicknesses. However, for relatively thin NLC films, the director reorientation is suppressed due to high values of elastic torque $\sim K/L^2$. The effect of NLC thickness on the dimple formation due to thermocapillary effect is not obvious and requires the further study.
Finally, we need to emphasize a crucial role of a free surface in the effective NLC director orientation by the temperature gradients. At light intensities comparable with the light-induced Fréedericksz threshold, the light absorption at ITO layer in conventional NLC cell is not enough for director deformation because of significant heat transfer on the both substrates [1]. Moreover, the temperature gradient in such system should be oriented almost normally to the substrates and can not cause the orientational deformation in homeotropic NLC cell. At the same time, we do not fully exclude the effect in conventional NLC cells, but it should be much weaker. Our preliminary studies show that the light-induced umbilical defect with the size of light beam waist is formed in highly absorbing NLC cell with a large thickness ($L \sim 100$ $\mu$m).
4. Conclusion
The NLC film with a free surface represents an unusual optical system, whose optical response is mainly determined by thermodynamic processes in anisotropic media and their environment. In particular, the air environment prevents the heat outflow and the axially symmetric temperature gradient is formed. Even a weak absorption leads to the director reorientation due to the temperature gradient. The light beam intensities required for the director rotation are an order of magnitude lower for NLC with an absorbing layer in comparison with a direct action of light beam on the induced dipoles. The light-induced director reorientation forming an umbilical defect does not depend on the light polarization and interaction geometry. The thermo-orientational action of light beam is highly nonlocal: the area of director deformation can be several times larger than the light beam diameter.
Funding
Russian Science Foundation (20-72-00178).
Disclosures
The authors declare no conflicts of interest.
Data Availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 and Visualization 1 for supporting content.
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