1. Introduction

Spatial solitary waves, or solitons, have been widely investigated in recent years both for basic research interest and for their potentials in signal processing, optical switching and all-optical readdressing [1–6]. In particular, scientists have been searching for suitable optical materials that can easily support this kind of nonlinear effect. In general, in order to induce nonlinear effects in usual optical materials, pulsed laser sources are needed to comply with high peak power requirements. From this point of view, liquid crystals represent a promising alternative, because of their reorientational optical nonlinearities which can be excited at very low optical intensities, about 10⁹ times lower than in conventional nonlinear materials [7,8]. In an uniaxial crystal like a nematic liquid crystal (NLC), a spatial soliton can be realized due to the reorientational response, which causes a dependence of the refractive index on the optical intensity. When a light beam propagates in such a medium, the refractive index increases in the central, and more intense, region of the beam, thus causing a self-focusing effect which can balance linear diffraction [9]. In this case, the beam spot size does not change during propagation and the field distribution represents a particular eigen-solution of the corresponding nonlinear propagation equation. In this scenario, NLCs provide an ideal workbench for investigation of spatial solitons, not only because of the large nonlinearity [7–8] and high nonlocality [10–11], but also because of an electro-optic response, which enables a fine control both of birefringence and walk-off angle [12]; while spatial nonlocality allows both propagation of stable solitons in two transverse dimensions and their long-range interactions [11–12], the high orientational birefringence of the medium allows to create a broadly tunable walk-off as well as redirection of solitons by using an applied voltage bias [12]. All these phenomena have been observed and characterized in suitable NLC cells which have been designed and fabricated “ad hoc”, in order to control many of the parameters which are responsible of the exploited nonlinear effects.

This paper is aimed to give an overview on the design and fabrication process of cells used to observe and investigate optical spatial solitons. The particular dimension of the used glass slabs as well as their peculiar form, along with the director anchoring imposed both on the input interface and in the bulk, represent the key elements for the realization of this goal.

2. Cell design and director configuration

The necessity of availability of NLC cells in which the anchoring on the surfaces is optimized for controlling the director orientation as well as the propagation direction of a spatial soliton inside the cell led us to design and realize suitable cell configurations. We have already noted that, by impinging on a standard sample in waveguide regime with a vertical polarization and an incident angle of about 4°, two waves are formed, which propagate inside the cell with a given, relative angle. In order to increase this angle, we have designed a cell in which the particular director orientation both at the entrance and in the bulk could be suitably controlled. In particular, it was necessary to realize a cell configuration in which the impinging light beam, properly polarized, is able to induce the appearance of the e- and o- waves in the medium with a relative angle larger than fraction of a degree, which represents the limit value previously observed in many nonlinear materials [15–19]. As a result, the realization of a particular cell configuration that allows observation and electric control of the propagation direction of a self-sustaining light filament over about 7° (without acting on the impinging polarization) represents the most important goal of this work.

An important aspect of the designed cells is the possibility of changing the anchoring direction, at the entrance as well as in the bulk, in order to create different configurations of the NLC director orientation; these are responsible for the different, observed optical phenomena. We have considered three different configurations, depending on the director orientation assumed both in the x-y plane at the input interface and in the y-z plane in the bulk. By assuming z as the propagation direction, the first configuration sees the orientation of the director n̂ along the x axis at the input interface; if we assume the angle α between the x axis and the input director orientation as the first parameter to describe the configuration, in this first case we have α=0°. In the same configuration, the orientation of n̂ in the bulk is fixed along the z axis and the angle with respect to this axis is therefore β=0°. We have named this configuration “standard configuration” and, by using the angles α and β, we indicate it as [0°/0°]. In order to illustrate the obtained n̂ orientation a sketch is presented in Fig. 1. Figure 1(a) represents a three-dimensional view of the obtained sample; the director orientation at the input interface as well as in the bulk is represented by the orientation of rod-like molecules.

Figures 1(b) and (c) show the top and side view of the possible n̂ orientations in the first 100 µm of the cell, deduced by experimental observations; these have been made by means of optical microscopy, which allows to determine the exact director orientation imposed by the rubbing direction at the top and bottom substrates. If the same rubbing process is utilized to align the director at the (lateral) input interface, the final director configuration between the entrance surface and the top and bottom ones of the bulk is the result of the minimum energy configuration inherent to the intermolecular forces. Actually, a theoretical approach aimed to represent the real director orientation distribution is under development.

Two more configurations have been designed to observe new optical phenomena: By changing the director orientation in the y-z plane (β=45°) we obtained the [0°/45°] configuration (Fig. 2); in Fig. 3 also the configuration [45°/45°] is presented. In both Fig. 2 and 3 the three-dimensional sketch (a), the top view (b) and the side view (c) of the director orientation are shown respectively.

 

Fig. 1. Sketch of the director orientation obtained by using the anchoring conditions imposed both at the input interface and in the bulk (0° in the x-y plane with respect to the x axis and 0° in the y-z plane with respect to the z axis, the so called “standard configuration” [0°/0°]). (a) 3D view of the obtained configuration; rod-like molecules reproduce the anchoring orientation imposed on the substrates (input and bulk). (b) and (c): top and side view of the possible director orientation trend in the first 100 µm of the cell respectively; estimations are deduced from optical microscopy observations.

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Fig. 2. Sketch of the [0°/45°] configuration obtained by changing the director orientation on the substrate in the bulk. (a): 3D view of the obtained configuration; rod-like molecules reproduce the anchoring orientation imposed on the substrates (input and bulk). (b) and (c): top and side view of the possible director orientation trend in the first 100 µm of the cell respectively; estimations are deduced from optical microscopy observations.

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Fig. 3. Sketch of the [45°/45°] director configuration obtained by changing the director orientation both at the input interface and in the bulk. (a): 3D view of the obtained configuration; rod-like molecules reproduce the anchoring orientation imposed on the substrates (input and bulk). (b) and (c): top and side view of the possible director orientation trend in the first 100 µm of the cell respectively; estimations are deduced from optical microscopy observations.

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3. Thin cells fabrication and characterization

In order to observe optical and physical phenomena in liquid crystalline materials, it is convenient to confine them into cells made of glass plates or quartz slabs, separated by Mylar or Kapton spacers (the latter having a higher temperature resistance). The peculiarity of our samples lies in their particular dimensions and form and in the accuracy required during the fabrication process. We use special glass slabs covered by a film of conductive material (Indium-Tin-Oxide or ITO) which allows application of an external voltage. In order to obtain good quality samples with peculiar characteristics, it is necessary to fulfill some important requirements: In fact, a typical sample is obtained by perfectly superimposing two glass slabs, spaced by the Mylar, and filling the internal volume with the nematic liquid crystal (NLC); a previous polymeric treatment of surface is made to induce a suitable anchoring of the NLC (planar in our case). A very low presence of surface scratches is accomplished to prevent inhomogeneous deposition of the polymer used to determine the nematic anchoring; a grinding edge process is also used to obtain smooth and parallel surfaces which we position the glass interfaces to. Then, while performing these steps, a first problem arises: when we launch a focused Gaussian laser beam inside the cell (in a waveguide regime), we have to eliminate the meniscus that is present at the cell entrance, since, acting as a lens, this meniscus would diffract the input beam and cause divergence and losses. This is the reason we introduced glass plates which behave as optical interfaces at the input as well as at the output of the cell. The final cell configuration is shown in Fig. 4.

 

Fig. 4. (a): Sketch of a thin cell with two additional (input and output) optical glass interfaces. (b): Image of the cell obtained by using the fabrication process described in the text.

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3.1 Fabrication process

In order to produce sample cells with the described characteristics, we have implemented a process, whose main steps are:

a.) Glass cutting: accomplished by using a commercial glasscutter, allows to obtain slabs of about 40 mm length and 5 mm width

b.) Glass grinding; first part: based on the utilization of a stepper motor driven by a home-made LabView software and connected to a micrometer movement; an electronic control allows to use the total rotational movement made of 200 steps; in this way the minimum translational step is only 2.5 µm. A particular tip made of “corindone” (Al₂O₃), installed on a rotating machine, enables grinding the edges of two coupled glass slabs, thus reducing their width to 4 mm

c.) Manual grinding of the slabs: by using a particular aluminium support, it is possible to reduce the slab width to 3.5 mm, and, at the same time, to check that the final slabs are parallel with good accuracy. We use three different silicon powder grains, monitoring the typical size of each powder by a SEM (Scanning Electron Microscopy) analysis.

d.) Glass cleaning: necessary to obtain a clean surface which the NLC can be deposited on. At the end of these four steps, we obtain two identical glass slabs of 40 mm length and 3.5 mm width.

e.) Polymer deposition: a very thin “polyimide” layer is deposited on the surfaces of the two glass slabs, by means of a spin-coater (CaLCTec s.r.l.). The polymer is a solution of 20 wt% LQ1800 (by Hitachi Chemical), prepared by dissolving one part of LQ1800 in four parts of 1-Methyl-2-Pyrrolidone; the thickness of the polymer layer can be varied by changing the percentage of LQ1800 in the polyimide solution. The deposition process is ended by a thermal polymerization carried out at 140 °C for one hour, and at 250 °C for a further hour.

f.) Rubbing process: the glass slabs are positioned on a vacuum translation stage while a cylinder, covered by a cotton velvet, is placed on the top of the slabs. By rotating the cylinder in the opposite direction with respect to the translation, it is possible to induce a preferred planar direction in the polymer molecules, with a particular tilt angle. The NLC director turns out, then, to have the same direction of the polymer molecules, thus assuming a planar anchoring with a “pre-tilt” angle of about 3°-5° degrees. This procedure is also necessary to eliminate disclinations that are often observed in a planar NLC cell without pre-tilt angle when an external voltage is applied.

g.) Sample assembly: after the rubbing process has been completed, we close the cell to prepare the final sample. In order to avoid the formation of possible “bend” or “splay” distortions in the volume, the correct way of overlapping the two slabs is by opposing the rubbing directions; then we close with a glue the two slabs separated by Mylar (or Kapton) spacers of 75 µm. Finally we glue the two optical interfaces at the (lateral) input and output of the cell. These are two glass slabs, without ITO deposition, that are positioned in such a way that the pre-tilt angle is seen in the same direction when going through the sample starting from the input point.

3.2 Surface characterization and alignment measurements

Controlling the thickness of the polyimide layers deposited on the glass surfaces is very important. The presence of scratches on these surfaces could affect the uniform deposition of the polymer on the slabs and, consequently, the correct alignment of the liquid crystal director in the sample. Indeed, we have performed an Atomic Force Microscope (AFM) thickness measurement on a cut previously made in the deposited polymer. Two measurements have been carried out, in layers obtained by deposition of LQ1800 at 20% and 2% in weight respectively. In the first case, the measured thickness was about 50nm, while in the second case it was about 5nm; both values are lower than the dept of scratches that, during the manual grinding process, can be made on by silicon powder grains. Indeed, when these scratches are present, an AFM measurement of their depth has given values of about 2µm, two order of magnitude higher than the polymer layer; consequently, during the spin-coating process, the polymer deposition tends to follow the scratched surface trend, giving no reliability of a uniform polymer deposition.

A further important measurement made on the slab surfaces is the value of the pre-tilt angle. The technique is based on the crystal rotation method [13, 14], and experimental data have been fitted by using the expression:

where Δφ represents the phase defference between extraordinary and ordinary waves versus the incident angle θ and the pre-tilt angle θ₀ ; d is the sample thickness and λ the wavelength of the impinging probe beam; n is defined by the equation

The values of the extraordinary and ordinary refraction indices n_e and n_o depend on the particular liquid crystal used to fill the cell. In the case of E7 by Merck, at 23°C, they are n_o=1.52 and n_e=1.73 at the wavelength λ=633 nm.

In the particular case θ=θ ₀=0°, we find the well known expression $\Delta \phi =2\pi d\frac{\Delta n}{\lambda }$, with Δn=n_e-n_o. At 20 wt% of LQ1800, we have measured a pre-tilt angle of about 4.5°, obtained by making four rubs in opposite directions. On the other hand, by making four rubs in the same direction, we have obtained, in similar samples, a pre-tilt angle of about 8°; furthermore, we have also found that the value of the pre-tilt angle slightly depends on the percentage of polyimide deposited on the surface.

4. Experimental check

Realization of the described planar NLC cells have allowed observation and characterization of optical spatial solitons [12, 20–25]. A spatial soliton is a self-confined beam whose transverse intensity profile remains unchanged during the propagation. The self-confinement behavior of an x-polarized Gaussian beam is obtained by using the “standard configuration” [0°/0°], under the application of an external ac voltage (f=1Khz V_RMS=2.3V) (Fig. 5); the planar anchoring in the z-direction imposed in the cell allows the reorientation of the NLC director in the x-z plane only. The particular nonlinear response of NLC relies, then, on optically-induced molecular reorientation, which extends away from the excitation regions thanks to elastic intermolecular forces. In this sense, the response is spatially nonlocal, because the refractive index perturbation is in general non-zero even where no electromagnetic perturbation is present. These aspects represent the main features exploited to create the refractive index waveguide which is responsible for the soliton formation. Figures 5(a) and 5(b) represent the color-coded images acquired by a high resolution CCD camera from the top of the sample and processed by a software, implemented in Matlab language, which enhances the difference between regions of different intensity. In Fig. 5(a) the focused beam with an impinging power of about 3,7 mW diffracts in a linear regime; Fig. 5(b) represents the formation of the spatial soliton.

The second configuration [0°/45°] represents the suitable condition to observe the appearance of two distinct waves, the extraordinary and the ordinary one. Owing to the high birefringence of the NLC and due to the particular director orientation induced by the substrate alignment, the walk-off angle (γ) between the e-wave and the o-wave turns out to be about 7°. In fig. 6 (a) the e- and o-waves, excited by an x-polarized beam, are shown: beam 1 is the e-wave and beam 2 the o-wave; in fact, experimental observations show that, by increasing the impinging optical power, the only beam undergoing some change in its propagation direction is the number 1. This is due to rotations and oscillations of the walk-off plane in the same direction of the bulk director orientation [12]. Furthermore, by applying an external voltage, the director reorientation in the bulk causes the superposition of the two waves and the formation of a single light filament whose transverse intensity profile remains unchanged during propagation: this is a spatial soliton (Fig. 6 (b)). In this particular configuration, the o-wave is linearly polarized in a direction perpendicular to n̂, hence reorientation is inhibited below the Freèdericksz threshold, which is about one order of magnitude higher than the power levels utilized in the present experiments; therefore, only the e-wave contributes to the soliton formation. Furthermore, in order to maximize the portion of soliton-trapped energy with respect to the impinging one, while increasing the bias, the input polarization has to be rotated in order to follow the director reorientation; in this way, it is possible to reduce the o-wave power (that propagates along the ẑ axis). By changing the polarization direction of the impinging beam (from x̂ to ŷ) it is also possible to “switch off” the spatial soliton because of the change of the refractive index experienced by the beam.

 

Fig. 5. Color-coded images acquired from the top of a cell with standard configuration [0°/0°] (a): an x-polarized focused beam diffracts in a linear regime. (b): formation of the self-induced waveguide (spatial soliton) obtained by applying an external ac voltage.

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Fig. 6. Color-coded images acquired from the top of a cell with the [0°/45°] director configuration. (a): By impinging with an x-polarized beam, both e-wave (beam 1) and o-wave (beam 2) excitations are obtained. (b): By applying an external ac voltage, an optical waveguide (spatial soliton) is obtained.

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The third director configuration [45°/45°] is the most suitable to control the soliton steering over angles larger than 7°. In fact, by rotating the input polarization at 45° in the x-y plane, it is possible to create the e-wave only, which transports, now, the whole impinging energy. The induced light filament results very narrow and its propagation direction is about 7° deviated with respect to the input beam wavevector. In this condition, the routing of the created soliton is realized by applying an external voltage; now, the result is obtained without changing the input polarization direction, which is fixed at 45°. The experiment is well described in reference [26].

 

Fig. 7. Color-coded images acquired from the top of a cell with the [45°/45°] director configuration. (a): By putting the input polarization at 45° in the x-y plane, it is possible to produce the e-wave only, at an angle (γ) of about 7° with respect to the input beam wavevector. (b): Application of an external ac voltage is used to control the walk-off angle γ, thus steering and routing the created solitary wave from 7° to 0°.

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5. Conclusions

In conclusion, we have designed and characterized particular configurations of NLC cells, utilized to observe the behavior of a linearly polarized focused beam, launched inside the cell in a waveguide regime. By controlling the anchoring angle of the NLC director, both at the input interface and in the bulk, it is possible to induce several non linear effects in the light beam propagating inside the cell.

We have presented three different cell configurations, which enabled us to observe and characterize three distinct optical phenomena. In the first (standard) configuration, a self-confinement effect is obtained under the action of an external ac voltage. In the second configuration, the excitation of both e- and o-waves is obtained in the linear regime; by applying an external voltage, the modification of the internal birefringence causes the superposition of the two waves, thus forming an optical spatial soliton. In the last configuration, by impinging with a particular polarization, it is possible to obtain that only the extraordinary wave propagates as an optical spatial soliton. Furthermore, a complete control of the walk-off angle can be obtained over values larger than 7°, by application of an external voltage.