1. Introduction

Currently carbon nanotubes are the focus of intense interest worldwide because of their exotic physical and electrical properties. Due to their small diameter (in nm), high mechanical strength, high thermal and chemical stability, excellent heat conduction, and band gaps that can be controlled by diameter selection, carbon nanotubes may well provide a fundamental structural and electronic component for the emerging field of nanotechnology [1]. Compared with singlewall carbon nanotubes for which semiconducting phases exist, multiwall carbon nanotubes composed of several cylindrical graphite layers are known to be most metallic.

Over the past decade it has been demonstrated to be of interest to incorporate fullerenes and their derivatives as guests into optical condensed materials to exploit novel optoelectronic devices. Similarly, it can be expected that carbon-nanotube doping in liquid crystals will particularly receive much attention in the near future, since it can combine the merits of both host liquid crystals and guest nanotubes. Liquid crystals possess many unique physical, optical, and electro-optical properties. Among the various mesophases of liquid crystals, nematics are known to possess a large birefringence (Δn~0.3) spanning from the visible to infrared spectral region; their large Kerr-like optical nonlinearity associated with the director axis reorientation by optical fields has made them a very attractive material for a wide spectrum of photonic applications [2]. On the other hand, carbon nanotubes as a dopant can provide high photosensitivity and large nonlinear optical responses and, in turn, enhance the photorefractivity of the liquid crystals [3–5]—an attractive feature useful for a variety of applications in real-time processing, beam amplification, self-pumped phase conjugation, four-wave mixing, optical computing, and dynamic holography [6–9]. Photorefractivity is characterized by spatial modulation of the index of refraction owing to the light-induced redistribution of charge in an optically nonlinear medium, in which the index grating gives rise to an energy exchange; i.e., beam coupling, between two incident coherent beams. Extended from our concentration on self-diffraction properties of refractive-index gratings formed in nematic liquid crystals doped with carbon nanotubes [3], we have recently observed efficient coherent light amplification with very high gains of the order of 10³ cm^-1 [4] and discovered the cenerio pertaining to the surface-sustained permanent gratings [5] in the doped liquid-crystal films. This current paper serves as a supplement to [4] by presenting some new relevant experimental results for systematic comparison.

2. Experimental

We studied the two-beam-coupling effect in liquid-crystal cells (thickness d=25 µm) filled by a capillary action with E7 (from Merck) doped with a trace of open multiwall carbon nanotubes of 18–25 carbonic monolayers (from SES Research). Planar alignment of the liquid crystal was provided by polyimide cast onto two transparent indium-tin-oxide (ITO)-coated glass plates and rubbed in a unidirectional manner. More detailed information on sample preparation can be found in [4].

A two-beam-coupling experiment with a setup similar to that described in [3] was performed in order to examine the gain properties of the photorefractive grating in the liquid-crystal sample. The two p-polarized writing beams, each controlled by means of a neutral-density filter, were derived from a linearly polarized cw Ar⁺ laser (Spectra-Physics Stabilite 2017-04S) beam operating at the 514-nm line, intersecting in the sample with a spot diameter of ~3mm. The unperturbed liquid-crystal director axis was set to coincide with the plane of incidence. With adequate selection on the wave-mixing angle (0.7°) and incident angle (β=26.2°) inside the liquid crystal, the grating spacing was controlled to be 27 µm. Because the grating is of Raman-Nath type, wave-mixing effects with multiorder self-diffractions are allowed as long as an adequate external dc voltage was applied across the sample such that the local total field strength (including the internal charge field) exceeds the electric Fréedericksz threshold field.

The external dc electric field, produced by a bias voltage varying from 0 to 20 V, was applied across the sample thickness. The intensities of the incident probe and pump beams, I ₁₀ and I ₂₀, respectively, the intensities of the transmitted beams without the presence of the companion beam, I ₁ and I ₂, and the intensity of the probe beam after the sample in the presence of the pump beam, I ₁₂, were measured with two identical silicon detectors (Newport 818-SL) and a dual-channel optical meter (Newport 2835-C) interfaced with a personal computer. An iris diaphragm was used for each detector to reduce the amount of entrancing scattered laser among the diffracted beams.

3. Results and discussion

The net gain constant were calculated using the well-known formula [6]:

where the beam-coupling ratio of the probe, g=I ₁₂/I ₁, the intensity ratio of the pump and signal beams, m=I ₂₀/I ₁₀=I ₂/I ₁, the interactive length L=d/cos β, and the total optical loss, including scattering, reflection and absorption, α<33 cm^-1. To allow a significant coupling between two incident beams to occur, we usually set the applied voltage V _dc>~3.7 V, the threshold voltage. Interestingly, for a bias dc voltage of 3 V, temporary gains of one beam still took place at the expense of the intensity of the companion beam. See Fig. 1.

 

Fig. 1. Energy exchange between two incident beams of 45 mW at V _dc=3 V.

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Fig. 2 illustrates the voltage dependence of the net gain constant of a 1-mW incident probe beam in the company of a pump beam at various powers.

 

Fig. 2. Net exponential gain coefficient of the 1-mW probe beam as a function of the applied voltage. The incident pump-beam power is fixed at ◈ 60 mW, ● 100 mW, △ 140 mW, and ▼ 200 mW.

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Photorefractive gains as high as 10³ cm^-1 are obtained with a 140-mW pump at an optimal applied voltage of 14 V. This dramatic enhancement from our previous observation [3] is due to the addition of the novel dopant; i.e., carbon nanotubes, as an efficient photocharge generator. The gain-constant curves rise with increase of the bias voltage, saturate at ~14 V, and drop slowly and steadily at higher voltages. One can also see from Fig. 2 that, for a given applied voltage, the gain increases rapidly with increase of pump power. This is so because for a large pump-to-probe ratio, the side diffractions are much weaker in magnitude than the probe, allowing the probe beam to gain more from the pump beam. It is noticeable, however, that the probe amplification eventually tends toward a saturated value as can be seen in the figure where the gain becomes worsened when the pump power increases from 140 mW to 200 mW. This dependence is exactly in consistence with the multiwave-mixing process in a thin nonlinear medium [10]. Similar behaviors can be found for a 5-mW probe beam as shown in Fig. 3. Note that the abscissa remains unchanged and the ordinate has been changed to a logarithm scale for readability.

 

Fig. 3. Voltage dependence of the gain coefficient for the 5-mW probe beam coupled with the input pump beam of various powers: ◈25 mW, ●75 mW, △125 mW, and ▼175 mW.

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Fig. 4. Comparison between different total writing powers of identical pump-to-probe ratio. The incident pump and probe powers are ◈ 20 and 1 mW, ● 100 and 5 mW, △ 40 and 1 mW, and ▼ 200 and 5 mW, respectively.

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To facilitate the comparison to better understand the influence of the pump-to-probe ratio and that of the total incident power on the net photorefractive gain, we obtained Fig. 4 for fixed pump-to-probe ratios of 20 and 40.

For a fixed pump-to-probe ratio at a given applied dc voltage, it is clear that the gain of the probe is increased as the total incident power becomes larger. Compared with the total power of the writing beams, the pump-to-probe ratio is a stronger factor influencing the gain constant. Scrutinizing the data presented in Fig. 4 enables one to see that the gain actually follows a quadratic dependence on the pump power for a common probe. Similar behavior of such dependence has previously been observed in a 25-µm-thick fullerene-doped nematic film [11].

4. Conclusions

In summary, we have reported the results of a study carried on films of nematic liquid crystals doped with multiwall carbon nanotubes with the aim of further investigating the two-beam-coupling effect that has been discovered recently. The coherent-beam amplification depends on the applied dc voltage, the total incident intensity of the writing beams, and, in particular, on the pump-to-probe ratio. The present results suggest that such doped liquid-crystal films might be promising candidates for applications in adaptive optics [12]. A test on holographic storage performance [13] is especially preferred for this photorefractive medium. Studies along these lines are currently being pursued in this laboratory.