1. Introduction

The “Giant Optical Nonlinearity” (GON) [1,2] of liquid crystals is characterized by a nonlinear refractive index n₂≈10^-5 cm²/W, several orders of magnitude higher than the one of nonlinear liquid materials. In the 1990s it has been discovered [3] that in nematic samples doped by anthriquinone dyes, GON occurs at very low pump intensities, corresponding to an enhancement of n2 by two orders of magnitude. Recently, in samples doped with the azo-dye Methyl Red (MR) a nonlinear refractive index n2>1 cm2/W has been measured [4] and even higher values have been detected in photoconducting nematics [5]. In all the samples where an extraordinarily large n2 has been found, the occurrence of a photovoltaic effect has been demonstrated under the same illumination conditions. For this reason all the authors believe the light-induced space charge to play an important role in determining this nonlinear behaviour. However, this role is not yet clear since the measured photovoltage is in the range of millivolts, much lower than the one usually required for director reorientation.

In this paper we report the results of an investigation carried on MR-doped nematic liquid crystals using pump-probe techniques under cw and pulsed regimes. Our experimental data confirm the extraordinarily large nonlinear response and suggest a new explanation for this behaviour. We believe that the huge orientational effect is due to light-induced modification of the anchoring conditions. In this way the strong nonlinear response becomes consequence of the photoalignment process, which affects the bulk director reorientation as widely studied since the beginning of the nineties after the works of Ichimura and coworkers [6] and Gibbons et al [7].

2. Experimental details

Samples were prepared between ITO coated glasses. Cells’ thickness were determined by Mylar spacers. A solution of Dimethyloctadecyl[3-(trimethoxysilyl)-propyl]ammonium chloride and isopropyl alcohol (1:1000) was spin coated on the glasses and placed in a oven at 120 °C for 30 minutes, in order to get homeotropic alignment of the samples. The mixture of 5CB and MR (1% in weight) was introduced by capillarity. The good homeotropic alignment of the cell was checked by optical polarizing microscopy.

Conventional pump-probe geometry was used, with a probe He-Ne laser beam linearly polarized parallel to the polarization of the pump beam, detecting the signal transmitted by a crossed polarizer located behind the sample. The unfocussed pump beam was provided either by a single pulse (τ=4 ns) of the second harmonic (λ=532 nm) of a Q-switched Nd-Yag laser or by a cw beam of an Ar⁺ laser (λ=514 nm). Pump and probe beams were co-propagating at normal incidence on the sample.

3. Results and discussion

In fig.1 typical data obtained for cw excitation are presented, showing the detected signal vs time.

 

Fig.1. Signal vs time in case of cw excitation. The incident pump intensity is 56 mW/cm² and the cell thickness is 23 µm. Signal oscillations are visible both during rising and relaxation (see text). Inset: Signal rise under cw irradiation at lower intensity (I=5.6 mW/cm²). The initial slope can be fitted by assuming S∝E^γ with γ=4.8, as shown by the dashed line.

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The main features of this curve can be understood taking into account that the signal is [8]:

where C is a proportionality constant, α is the absorption coefficient at the probe wavelength, d is the sample thickness, ϕ is the angle between the probe beam polarization direction and the ordinary wave vibration direction and δ is the phase shift between the e-wave and the o-wave.

The oscillations in fig. 1 clearly show that a director reorientation occurs in a direction different from the probe beam polarization giving rise to both ordinary and extraordinary waves inside the liquid crystal [9]. This reorientation leads to a multiple π phase shift between the e- and o-wave, each π corresponding to an extremum of the curve. A careful consideration of the figure reveals the occurrence of a delay between the switch-on of the pump beam and the rise of the signal, which increases on reducing the pump power. Moreover, for long illumination times a memory effect occurs since the induced reorientation becomes not completely reversible and may recover after a few days. These observations suggest that the onset of the phenomenon depends on the impinging energy density rather than on the intensity. For this reason it becomes questionable the meaning of the nonlinear refractive index n2, since the fundamental dependence n=n(I) is no more appropriate.

In order to avoid memory effects caused by a long illumination, we have performed the same experiment using a single pulse excitation of the second harmonic of a Q-switched Nd-YAG laser.

Figure 2 shows the typical results of this investigation.

 

Fig.2. Signal vs time in case of pulsed excitation. The impinging energy density is E=10 mJ/cm² in curves a and c and E=6 mJ/cm2 in curve b. In case of curve c a dc voltage V=12 V is applied across the cell thus creating a field perpendicular to the glass plates. Cell thickness=23 µm. All the curves decay to zero for a longer time.

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Curve a) is obtained at a pump energy density E=10 mJ/cm², curve b) at E=6 mJ/cm² and curve c) at E=10 mJ/cm² with a voltage V=12 V applied in order to quench any director reorientation (field applied perpendicular to the cell boundaries). The last curve confirms the orientational character of the signal detected in a) and b), which is completely quenched by the applied field. In the case of fig. 2a we can estimate a phase shift π<δ≤3π since two maxima are present. On the contrary curve b), related to a lower energy density, shows the similar reorientation effect leading to sample birefringence, but a maximum phase shift lower than π is obtained. From data of curve a) a light-induced birefringence Δn≅4×10^-2 can be estimated, which confirms the extraordinarily high nonlinear response of the studied material. In fact, even if in this case the effective index ${{\mathrm{n}}_2}^{\text{eff}}$=Δn/I is 1.6×10^-8 cm²/W, by taking into account that the characteristic response time of the reorientation process for a 23 µmcell is of the order of some tens of milliseconds, it is easy to work out the corresponding nonlinear refractive index that is possible to obtain by cw excitation: n₂=${{\mathrm{n}}_2}^{\text{eff}}$ (t/τ), being τ the pulse duration. Under our experimental conditions n₂ of the order of 1 cm²/W has been estimated.

Our experiments clearly show that reorientation affects both polar and azimuthal angles in agreement with the former observations of the director sliding in planar cells [10]. These observations support the idea that the exciting linearly polarized light induces an easy axis in the transversal plane also in the present geometry. However, the induced azimuthal director reorientation cannot be parallel or perpendicular to the pump beam polarisation. In fact, if this were the case, the signal would be zero being ϕ in equation (1) either 0 or π/2. This fact is confirmed by independent measurements performed to study the memory effect, showing that the stable orientation of the director on the surface under long time illumination is never parallel to the pump beam polarisation. Moreover, we are here focussed on the transient effect, which is able to give a nonlinear optical response and the azimuthal orientation will be far from the saturation value since we are using energy densities 2–3 orders of magnitude lower than the one necessary to get a permanent reorientation. The occurrence of an easy axis in the azimuthal plane actually changes the surface conditions, thus making unstable the initial alignment so that a new director orientation is established through the cell due to the elasticity of the medium. In this way, it is easy to explain the observed nonlinear optical behaviour: since the bulk orientation of a liquid crystal is strongly affected by the anchoring conditions, any change of them induced by a light wave will produce a bulk reorientation; this reorientation affects the light propagation itself with the consequent onset of a nonlinear optical response. Moreover, since only a thin layer near the surface has to be excited in order to get the elastic reorientation of the whole sample, a very low intensity will be required to induce the nonlinear response.

The reported data allow ruling out both the effect of the photo-induced electric field and the effect of photo-isomerisation as basic mechanisms of the nonlinearity. In fact any longitudinal space charge field would stabilise the structure under this geometry, whereas the trans-cis conformational change should not be effective to reorient the director under short pulse excitation and, most of all, would have a decay time much slower than the one observed for example in fig. 2a and 2b. (By spectroscopic measurements, we got a recovery time of the trans-cis cycle of about 10 minutes in these compounds). Moreover the additional torque that azo-dye molecules might induce on the liquid crystal director is expected to be lower than the one measured with antraquinone dyes [11], which corresponds to n₂ of the order of 10^-3 cm²/W. Thus it cannot be responsible for the huge nonlinear response that we are dealing with.

It may be questionable if a light induced flow can be the origin of the observed reorientation in the case of pulsed excitation. As a matter of fact, we estimate a temperature rise of the order of 10 K due to the strong light absorption of our samples, which produces a thermal gradient over the 4 mm of the beam diameter on the sample. However, by comparing our experimental conditions to the ones used in a former observation of flow induced reorientation by Khoo et al. [12], we remark that in our case the induced thermal gradient is about two orders of magnitude lower. Additionally the previously observed flow build-up was slower (of the order of few milliseconds) than the signal rise that we observe.

The fast build-up of the observed signal (fig. 2) should not be considered “a priori” in contradiction with the surface induced reorientation. In fact, under fast excitation we expect a fast surface reorientation as well, whereas the speed of propagation of such reorientation in the bulk will decrease roughly as z², being z normal to the cell boundaries. Since the signal can be observed also for thin samples (3µm), we believe that the effective reoriented layer can be much smaller than the sample thickness, thus making possible a fast response. On the other hand, a reorientation confined only to a thin layer close to the surface is sufficient to detect a signal. However, the dynamics of the observed process needs to be investigated in details in order to figure out the complex mechanism of light induced surface modifications.

In order to estimate what could be expected under our picture, we can get the equilibrium director orientation by minimization of the elastic free energy under the usual boundary conditions [1], thus obtaining the tilt angle θ(z).

Under the one elastic constant approximation, considering that the impinging light affects only one surface, we get [1]:

being c an integration constant, L₁ the extrapolation length of the entrance surface, ${{\theta }^{*}}_{\mathit{1}}$ the orientation of the easy axis and θ ₁ the actual director orientation at this surface. Here the strong anchoring condition (θ ₂=θ (d)=0) on the surface opposite to the light entrance has been considered. This approximation is justified by the strong absorption coefficient (α≅10³ cm^-1 for the ordinary wave), which reduces by about one order of magnitude the intensity of the exciting light on the second boundary. Since during reorientation also the extraordinary wave appears, α will increase as well being the e-wave absorption higher than the one of the o-wave. For homeotropic cells ${{\theta }^{*}}_{\mathit{1}}$≈0, however, since the pump beam induces an easy axis in the transversal plane [10], the surface conditions change and make unstable the initial alignment. As a first approximation we may suppose ${{\theta }^{*}}_{\mathit{1}}$=HE, being H a constant factor. In this way from (2) we get:

After that it is straightforward to calculate the variation of the refractive index averaged along the cell thickness. In the limit of small reorientation [1], under the usual approximations we obtain:

i.e. δn independent on the thickness d. As a consequence the phase shift becomes linearly dependent on d.

In order to check the validity of this hypothesis, we have performed additional measurements on samples of different thickness (d=3 µm, d=6 µmand d=23µm) using pulsed excitation.

From expression (1) we should expect the main dependence of S on d to be in the last term, which includes the phase shift. The exponential term plays a very little role for the probe beam, since at λ=633 nm we have measured an absorption coefficient α≅34 cm^-1 for the ordinary wave, then, for a cell 23 µm thick, αd≅7,8×10^-3≪1 and e^-αd≅1. The second term should also exhibit a weak dependence on d since ϕ is strictly related to the reorientation angle in the transversal plane, which is determined by the impinging energy density, at a fixed pump beam polarization [10]. Therefore we can consider S=Asin²(δ/2), where A is a constant factor. Under these experimental conditions we have measured S induced by pulsed irradiation for a fixed value of the impinging energy in samples of different thickness. In order to evaluate the phase shift from these measurements we have considered the last maximum of the signal corresponding to a thickness of 23 µm. Since we are monitoring the signal relaxation, the last maximum corresponds to δ=π that is sin²(δ/2)=1, which means S=A. In this way we were able to calibrate the signal vs δ. By using this method, it has been possible to plot δ vs d, as shown in fig.3.

 

Fig.3. Phase shift δ vs d. The experimental data (symbols) are satisfactory fitted by assuming a linear dependence of δ on the thickness d (full line). The value δ=3π corresponding to d=23 µm may be overestimated.

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These data show a clear linear dependence of δ on d in excellent agreement with the result of eq. (4). As a matter of fact, eq. (4) has been calculated in the small reorientation approximation, which is certainly not the case for the 23 µm sample where δ ≤3π. However, this result can be an additional confirmation that the effect depends only on the surface conditions, since in this case the phase shift δ should be independent on sample thickness, even for strong director reorientation.

Expression (4) may give additional insights on the effect. In fact, according to eq. (1), for small reorientation we expect S∝(δ/2)² while δ is proportional to δn, therefore S∝(δn)², i.e. S∝(HE)⁴. The S vs t curves obtained by cw excitation allow us to check this dependence. The first part of these curves corresponds to low values of the irradiation time, that is to low values of the impinging energy. Therefore, from the initial slope it is possible to get the dependence of the signal on E, in case of small reorientation. In the inset of fig.2 we report the result obtained with a pump intensity of 5.6 mW/cm². It is quite amazing that we get S∝E^γ with γ=4.8, pretty close to our estimation. However, we obtained bigger values for γ (up to 8) at higher pump energies; therefore the dependence of S on E must be analysed more carefully.

4. Conclusions

In conclusion we have shown that the extraordinarily large nonlinear response of dye-doped liquid crystals can be explained as due to light-induced modifications of the anchoring conditions. We have called this phenomenon SINE (Surface Induced Nonlinear Effect) to remind that it occurs “without”(=sine in latin language) a direct optical or electrical torque on the director in the bulk. This behaviour is typical of liquid crystals because of their collective properties, however it may fall in a new category of optical nonlinearities controlled by surfaces.