Response properties of photoinduced gratings were studied in planar cells of liquid crystal doped with multiwalled carbon nanotubes. The grating formation time deduced from beam-coupling measurements was obtained to be ~30 ms. Absorption spectroscopy implies that the permanent gratings are associated with periodically distributed carbonaceous material adsorbed on the inner surfaces of the cell windows under prolonged illumination to the 514.5-nm beams, giving rise to the persistent light-induced modulation of the easy axis.
©2002 Optical Society of America
Over the last decade we have witnessed tremendous advances in the development and characterization of photorefractive (PR) organic materials including organic crystals, polymer composites, and liquid crystals (LCs) [1,2]. Since Rudenko and Sukhov  first demonstrated the photorefractivity of LCs, many researchers have also concentrated their efforts on this novel class of material. There are several reasons for pursuing the development of PR LCs in particular. Compared with polymeric systems, LCs are intriguing owing both to the low characteristic voltage required for application to the material for the realization of wave mixing and to the high modulation of the refractive index induced with a rather low power density of light beams. Most advantageously, PR LC cells are very easy to fabricate, thanks partially to the prosperity in the display industry.
Khoo  presented a sophisticated theoretical investigation on the mechanisms of the PR effect in nematic LCs. The effect was interpreted to be derived primarily from orientational ordering within an inhomogeneous bulk space-charge field as a consequence of the Carr–Helfrich effect and flow effect. Recently experimental evidences of surface charge mediated PR effects have been reported in LC cells [5,6]. While Zhang et al.  suggested that the PR-like effect in homeotropically aligned LCs is mediated by surface charges rather than bulk currents, Pagliusi and Cipparrone  observed the surface charge induced PR-like gratings in pure LC planar cells. It is clear that a full understanding of photorefractivity in LCs is challenging. This requires additional studies on the relevant issues.
Recently we reported our observations of both self-diffraction and optical amplification by holographic gratings formed in nematic LC films doped with carbon nanotubes [7–9]. Our interest in considering carbon nanotubes as a dopant stems from their novel properties in mechanics, electronics, and nonlinear optics, as mentioned in our earlier publications [7–9] and well documented in Ref. 10. Indeed, our previous studies on the nanotube-doped LC samples have brought about the achievement of a large nonlinear index-change coefficient n 2 ~ 10-1 cm2/W  as well as of high gains ~15 [8,9]. In the present paper, we discuss further the response characteristics of the orientational PR gratings in the same material. The decay time was obtained to be several tens of seconds for a persistent grating. This unexpectedly long decay time constant allowed us to discover the surface phenomenon of the LC cells. It is shown that the prolonged two-wave mixing, employed in the recording of a persistent grating, resulted in an inner-surface alteration of the cell due to the formation of periodically distributed adsorbates at the interface between the aligning layer and the LC material. These carbonaceous deposits may well provide charge-trapping sites, leading to a drastic change in LC anchoring properties during the grating recording.
Glass substrates composed of uniform and transparent indium-tin-oxide films were first spin-coated with polyimide and then rubbed unidirectionally to provide initial planar alignment of LC. Cells were fabricated with pairs of the treated substrates. The nematic LC sandwiched in the 25-μm-thick (d) cells is known commercially as E7 (from Merck), a eutectic mixture of four different cyanobiphenyl and cyanotriphenyl compounds with a positive dielectric anisotropy and nematic-to-isotropic transition at 61 °C. At the room temperature, the refractive indices parallel and perpendicular to the director axis are 1.75 and 1.52, respectively, giving the average index of refraction n of 1.6. A trace (0.02% by weight) of purified, uncapped multiwalled carbon nanotubes (from SES Research) as the dopant was thoroughly sonificated in the LC at ~75 °C before incorporation into a sample. The absorption spectrum of the nanotubes is shown in Fig. 1. Note that it reveals no apparent features in the visible except for a sole, weak continuum attributed to the scattering by the suspended particles. The addition of the dopant is made for creating charge-transfer complexes  in the solution to enhance the nonlinearity of the nematic, thereby promoting the performance of wave-mixing effects [7–9].
To investigate the response properties of our samples we performed a two-wave-mixing experiment, including the asymmetric beam coupling as reported in Ref. 8, in the tilted geometry. The purpose to conduct such an asymmetry is to establish the same PR gratings that were previously observed. Because no significant beam coupling was observed at an applied dc voltage V dc ≤ 3 V , the applied bias in the experiment was set above 3.7 V, the Fréedericksz transition threshold of the sample . Two p-polarized Ar+ laser beams of the 514.5-nm (λ) line were superposed onto the sample on the same 3-mm-diameter spot. The wave-mixing angle α= 0.7° and the incident angle of the two beams, β= 26.2°, inside the LC. The experimental conditions yield a fringe spacing of 27 μm as the grating constant Λ according to the formula
Because the dimensionless parameter  Q = 2πλd/nΛ cos β ≈ 0.1 < 1, the resulting phase grating is in the Raman–Nath grating regime. The total optical loss contributed by reflection, scattering and minute absorption was estimated to be ~16 cm-1 outside the vicinity of the electrohydrodynamic instability (V dc ~ 7 V).
3. Results and discussion
Time-evolved asymmetric-beam-coupling scans were obtained. Typical examples for two 45-mW writing beams with various voltages applied have been presented in an earlier work . The formation time of the steady-state refractive-index grating was deduced from the time-evolved beam-coupling data and calculated using the simplest single-carrier model that allows the rising signal to be fitted with a single exponential function :
where g(t) represents the beam-coupling ratio of the probe beam , the intensity of the transmitted probe beam in the presence of the pump beam divided by that without the presence of the pump beam, at time t, g denotes the steady-state beam-coupling ratio, and τ is the formation time. Fig. 2 shows that, for a constant grating spacing, the grating formation time decreases as the applied dc voltage is increased, presumably owing to the increased efficiency of charge-carrier redistribution in the field and effective mobility of carriers. For a 1-mW signal beam coupled with a pump of 40 mW, the shortest rise time of 34 ms, accompanied by the greatest beam-coupling ratio of 1.99, occurs at 14 V; further increase of the applied voltage causes the rise time to become slightly longer (inset in Fig. 2), probably as a result of the tight confinement of the average director axis along the dc-field direction. It is worth mentioning that the grating formation time based on the two-beam coupling can be further slightly decreased by decreasing the fringe spacing and increasing the pump/probe ratio. In any case, the decay time obtained from the same experiment was measured to be of similar scale.
The PR performance including the dynamic properties depends strongly on the sample history. For a fresh sample written with a transient grating, the decay time obtained experimentally was found to follow well-known orientational relaxation dynamics :
where γ is the viscosity coefficient and K the elastic constant. With material properties of γ~ 10-2 N s m-2 and K ~ 10-11 N and experimental conditions for d ≈ 25 × 10–6 m and Λ ~ 27 × 10-6 m, one gets τ d ~ 10-1 s, which is close to our observation of τ d ~ 0.5 ± 0.3 s. Beyond the transient-grating regime, decay time constants from measurements of self-diffraction efficiencies were observed to possess two distinct time components. We believe that the surface charge, proposed by Zhang and co-workers , along with space charge governs the grating properties in this stage of grating formation. Such suggestion stems from our speculation that the weaker but much longer component for the relaxation (~30 s) arises from a charge accumulation and discharge process of the LC capacitor .
The persistent-grating stage can be achieved in our experiment for a 20-minute illumination at a total writing intensity of 1.2 W/cm2. In order to investigate the formation of the persistent grating (Fig. 3) under writing of prolonged illumination or, more precisely, sufficient energy density and, in the hope, to realize how the electric charges are possibly kept at the interface, we have obtained the visible spectra of the fresh samples prior to and after 20-minute illumination by a single cw 514.5-nm laser beam at an intensity of 1.2 W/cm2. (During laser irradiation, no external field was applied across the cells.) The reason we elect to apply such simple, conventional absorption spectroscopy, instead of adopting more sophisticated approaches such as micro-Raman or micro-photoluminescence measurements, is for its ease and yet direct.
As shown in Fig. 4, no significant change is observed in the absorption of the pristine E7 sample before and after laser exposure, whereas changes in the broad continua are obvious for the nanotube-doped E7 cell. We obtained similar spectral results for cell substrates of the tested samples, suggesting that the surface alteration would take place during the beam writing in a two-wave-mixing experiment. By examining under a microscope the cell substrates taken apart from a persistently encoded, nanotube-doped LC sample, we have observed the surface-sustained continuum phenomenon in the LC bulk: The stripes in good order that resemble the interference pattern are ruined during the mechanical interaction with air disturbances and recover when the applied airflow seizes. The deposits in the illuminated zones, which may be attributed to nonuniform accumulation of simply original carbon aggregates, nanotube complexes, or of photochemical products of multiwalled carbon nanotubes depending on the illumination conditions and surface chemophysical properties of the polymeric aligning layer, can serve to trap charge carriers during the later stages of the phase-grating formation. The resulting internal electric field then modulates the LC director-axis reorientation and, in turn, the refractive index to create a phase grating that can diffract a light beam. Although the deposited carbonaceous material itself could very well constitute a surface grating, our observation of substantial polarization dependence for these persistent gratings verifies the additional contribution from LC reorientation . Due to a previous study of evident C60 photopolymer produced from a C60-containing chlorobenzene solution with a 514.5-nm Ar+ laser beam , we reason that high-power-density writing beams would create more stubborn photoproducts at the interface between the alignment layer and LC and result in a persistent grating with high degree of depolarization as observed by Khoo .
To conclude, we have studied the time constants of holographic gratings in the transient, intermediate and permanent regimes in films of nematic LC doped with multiwalled carbon nanotubes. The refractive-index grating is generated as a result of reorientation variation of the director axis of the mesophase caused by the photoinduced internal electric field. The incorporation with carbonaceous dopants, such as carbon nanotubes as a photocharge generator, provides a prominent function in the formation of the phase grating via the periodical redistribution of the doping material upon illumination to a light pattern at the interface between the LC and the aligning layer. The carbonaceous adsorbates may act as traps of photoinduced surface charges, cause the light-induced modulation of the easy axis in the LC bulk, and sustain the permanent grating through the continuum effect of the LC. Further experiments are being carried out on polarization dependence to clarify the photoinduced mechanisms at various grating formation stages and the origin of the persistent grating after prolonged illumination. It can be of interest to discover whether nanotubes can be turned by light in a similar fashion to photochromic molecules.
This work is supported primarily by the National Science Council of the Republic of China under grant NSC-89-2112-M-033-015 and NSC-90-2112-M-033-005, and partially by the Ministry of Education of the Republic of China.
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