Nonlinear optical materials have great potential for optical device applications in the areas of signal processing, phase conjugation, beam amplification, and holographic recording [1, 2]. In particular, nematic liquid crystals (NLCs) have attracted considerable interest in the past decade owing to their large nonlinear electro-optical response induced by relatively low laser intensity, which is attributed to collective molecular reorientation created by a photoinduced space-charge field under an applied dc field [3, 4]. Moreover, their performance (diffraction efficiency and beam-coupling ratio) has been dramatically improved by doping them with charge generators such as laser dyes or carbon materials [5–8]. Recent studies have shown that NLCs doped with methyl-red dye exhibit extraordinary large nonlinearity even without the application of a dc field [9]. Enhancement of orientational grating diffraction efficiency by an applied ac field has also been reported in methyl-red doped NLCs [10–13]. However, these studies have been limited to methyl-red doped NLCs which possess special properties not shared by other doped or undoped NLCs, such as orientational grating formation in the absence of an applied dc field, the writing beams must be p-polarized, etc.. Furthermore, discussions are focused on ac enhancement or switching of formed permanent orientational grating [12, 13].

In this letter, we report the formation of ac electric field assisted photo-induced orientational diffractive grating in fullerene-doped as well as undoped homeotropic NLC cells. High diffraction efficiency and large refractive index modulation were observed in the fullerene-doped cell with low optical intensity. The highest diffraction efficiency obtained is ~30 %, which is ~1.5 times larger than that obtained using a dc field. Scattering noise, due to thermal fluctuation of the director, can also be significantly reduced. More importantly, we demonstrate that the orientational grating formation time is ~100 times shorter, and undesired effect such as electrohydrodynamic (EHD) instability due to the dc field induced flow in the NLC cells is avoided. Unless otherwise noted, “grating” will mean orientational diffractive grating.

The material used was a eutectic mixture of the NLC 4’-(n-pentyl)-4-cyanobiphenyl (5CB) and 4’-(n-octyloxy)-4-cyanobiphenyl (8OCB) of 65 and 35 wt %, respectively. This mixture was then doped with a small amount of fullerene (~0.05 wt %), which is a mixture of C₆₀ and C₇₀ in the ratio ~ 90:10 and has been proved to be a very effective charge generator [14]. The measured absorption and scattering loss of the fullerene-doped NLCs is ~24 cm^-1 at 515 nm Ar-ion laser line. The homeotropic alignment was obtained in a 50 μm -thick cell by treatment of the indium tin oxide-coated cell windows with the surfactant octadecyltrichlorosilane. An undoped 50 μm -thick homeotropic cell the NLCs were used as received, which naturally contain some impurities) was also prepared using the same NLC material to demonstrate that grating can also be formed in undoped NLC cell under the applied ac field and possesses similar advantages. Results obtained for both cells were qualitatively the same, except that the doped cell is more sensitive to the writing beams and yields higher diffraction efficiency, consistent with that reported in Ref. [3]. For this reason, we only report results obtained with the fullerene-doped 50 μm -thick homeotropic cell.

The typical geometry of the experiments is shown in Fig. 1. The writing beams are two coherent laser beams from an Ar-ion laser operated at λ = 515 nm intersecting in the cell, and creating an optical interference pattern with a fringe spacing ʌ ≈107 μm (θ ≈ 0.28°). The 515 nm line is selected because it is well within the absorption band of the fullerene dopants [14], and a relatively high power can be obtained in our laboratory at this wavelength. The two beams are linearly s-polarized (o-ray), with approximately equal power, and the diameter of each beam is D = 6.5 mm. The incident angle β is defined as the angle between the sample normal and the bisector of the two writing beams in air, which was ~40° in our experiments. An ac field of frequency f < 5 kHz and peak-to-peak amplitude V _pp ranging from 0–20 V was applied to induce the charge separation and thus the grating formation. A p-polarized (e-ray) He-Ne laser beam (power of 790 μW , beam diameter of 6 mm) in the incident plane was used to probe the grating. The probe beam was aligned with a small deviation (φ ≈ 3°) from the normal of the grating wavevector.

With typical experimental parameters f = 50–100 Hz and V _pp = 15 V, clearly visible diffraction spots were generated using a total input writing power as low as P _t = 160 μW. With reference to Fig. 1, if the probe beam is an o-ray, no diffraction is observed; if the probe beam is an e-ray, diffraction is always observed, irrespective of the polarization of the writing beams. This polarization dependence shows that refractive-index change of the e-ray is caused by reorientation of the director in the incident plane (i.e. the grating is an orientational grating) [15]. Furthermore, no diffraction was observed with P _t as high as 100 mW if no ac field was applied; nor was the diffraction observed at β = 0. These results show that the grating formation requires an applied electric field (with a component along the direction of the grating wavevector) to facilitate the charge separation process and modulate the refractive index at the correct wavevector. These experimentally observed features are consistent with those of photorefractive orientational grating in NLCs [15]. However, unlike using a dc field, in which we observed ~30% stable coupling gain (loss) (the experimental method is the same as that described in Ref. [5]), we did not observe stable two-beam coupling in our experiment using the ac field. Instead, the energy coupling exhibits an interesting oscillatory behavior, namely, back and forth, the beam which initially loses energy will gain energy later (but generally, one beam gains energy and the other loses, and the sum of the energy of the two beams is approximately a constant). We also found that the oscillation period τ was always longer than that of the applied ac field. For example, as shown in Fig. 2, for f= 50 Hz, τ is ~15 s (the diffraction efficiency that will be discussed below is stable). Even though the underlying mechanism of this behavior is unknown, the grating formation can be understood by considering the space-charge field in the NLC cell, similar to that under an applied dc field [11]. The difference is that drift of charge carriers is likely to be the major contribution to the ac space-charge field formation, which in turn induces the grating, so long as the period of the space-charge field is sufficiently larger than the director relaxation time that is approximately several seconds [16]. For low frequencies (f ~0.5-2 Hz), the diffracted power was modulated and followed the variations of the ac field. For f > 5 kHz, the ac field cannot lead to the grating formation because the movements of the charges cannot follow the variation of the ac field, similar to that reported in methyl-red doped NLCs [10–13].

 

Fig. 1. Experimental geometry. Writing beams, s-polarized Ar-ion 515 nm laser line; probe beam, p-polarized He-Ne 633 nm laser line.

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Fig. 2. Dynamics of two-beam coupling with V _pp = 10 V, and f = 50 Hz. Upper curve, the beam that gains energy; lower curve, the beam that loses energy; middle curve, the half of the sum of intensities of the two beams.

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A typical diffraction pattern obtained by using P _t = 5.4 mW, V _pp = 15 V, and f = 40 Hz is shown in Fig. 3(a). Diffraction spots up to the 4^th-order can be clearly seen. When the ac field is switched off, the diffraction decays to an insignificant level in ~1 s. On the other hand, the diffraction decays in ~3–4 min after blocking the two writing beams as long as the ac field is maintained. These results are similar to those observed in C₆₀-doped NLCs under an applied dc field [17], except that a persistent grating was not observed in the present work for illumination time as long as 40 min and P _t = 100 mW. The slow decay after blocking the writing beams suggests that the Carr-Helfrich effect [18] may also contribute to the space-charge field as described in Refs. [17] and [19] (Note that we have observed none of the features of surface effects described in either Ref. [15] or Ref. [20], suggesting charge separation is not concentrated at the interface). Compared with a dc field, the scattering noise due to thermal fluctuation of the director was greatly reduced after the ac field was applied, which can be clearly seen in Fig. 3. This feature may have potential for noise reduction in various applications utilizing NLCs.

 

Fig. 3. Diffraction pattern with P _t = 5.4 mW, (a) f = 40 Hz, V _pp = 15 V; (b) V _dc = 2.0 V. The numbers indicate the orders of the diffracted spots with the transmitted incident probe beam being labeled 0.

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Following the convention in the literature, let the first-order diffraction efficiency η be the ratio of the first-order diffracted probe intensity to the incident probe intensity. Figure 4 shows evolution of η during the grating formation and relaxation processes under applied ac and dc fields, in which we see that the grating formation time is ~1 s for V _pp = 20 V, and f = 100 Hz, which is ~100 times shorter than that using a dc field in our experiment as well as those reported in Ref. [20]. As the grating formation time is largely determined by the formation time of the space-charge field, we expect that a higher field can further reduce it, which is not the case using a dc field, because of EHD instability. We have found that EHD instability and thus dynamic scattering sets in at V _dc = 2.8 V, which undermines the grating formation.

 

Fig. 4. Evolution of first-order diffraction efficiency under applied ac and dc fields with P _t = 5.4 mW. V _ac, V _pp = 20 V, and f = 100 Hz; V _dc = 2 V.

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We also expect larger orientational electro-optical response and thus higher diffraction efficiency by applying a higher ac field, which was indeed achieved by using V _pp = 20 V, f = 50 Hz, and P _t = 11.6 mW with η ~30 %, approaching the maximum value 33 % as predicted in Raman-Nath regime. On the contrary, the maximum diffraction efficiency that we obtained under an applied dc field was < 20 %. As the diffraction is in the Raman-Nath regime (i.e. ʌ² ≫ dλ), the effective nonlinear index coefficient n ₂ can be estimated by the relationships η ≈ (πΔnd / λ)² and n ₂ = Δn/I _t , where Δn is the amplitude of the refractive-index modulation, and I _t is the total intensity of the writing beams. Using the value η = 6% for P _t = 0.3 mW under V _pp = 20 V and f = 50 Hz, we obtain Δn = 0.76 ×10^-3, and thus n2 = 0.9 cm²/W, which is comparable to one of the largest n ₂ value obtained in carbon nanotube doped NLCs [8] and ~1000 times larger than that in C₆₀-doped NLCs using a dc field [17]. Another mechanism leading to the higher diffraction efficiency is likely to be the fact that high applied ac field provides better and more uniform homeotropic alignment in the cell compared to that achieved using surfactants, which was indeed verified by using a cross-polarized optical microscope, under which more uniform dark field was observed when an ac field was applied (V _pp > 4 V,f~10 Hz-5 kHz), showing better homeotropic alignment in the cell.

Figure 5 shows η as a function of V _pp for various frequencies with P _t = 26 mW. For f< 500 Hz, η exhibits similar behavior: η increases as V _pp increases and reaches a maximum at V _pp ≈ 16 V . For f = 1 kHz, η is generally lower. Further increase of f(> 1 kHz) will yield lower diffraction efficiency. As mentioned above, an applied ac field with f > 5 kHz cannot induce the grating formation because no space-charge field can be formed.

 

Fig. 5. First-order diffraction efficiency versus V _pp at various frequencies.

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In summary, we report ac field assisted grating formation in fullerene-doped and undoped NLCs. The electrohydrodynamic instability and dynamic scattering, which occurs above an applied dc field V _dc > 2.8 V, can be effectively suppressed, and thus allows application of a higher field that is not possible for an applied dc field, resulting in higher diffraction efficiency and faster response. Besides, scattering noise due to thermal fluctuation of the director is effectively reduced. The fullerene-doped cell exhibits first-order diffraction efficiency almost as high as the theoretical limit (33%) and effective nonlinear refractive index coefficient as large as 0.9 cm²/W with only 24 cm^-1 absorption and scattering loss. The larger, faster, and noise-reduced photorefractive response in NLCs using an applied ac field is potentially useful for various optical signal processing and storage applications.