1. Introduction

Birefringent materials like quartz, calcite and mica are frequently used as optical elements to influence the polarization state of light [1]. A radiation of wavelength λ propagating in such media is separated into an ordinary and an extraordinary component with a relative phase difference φ=2πLΔn/λ, where L is the thickness of the sample and Δn (birefringence) is the difference between its extraordinary (n_e) and ordinary (n_o) indices of refraction. By choosing a suitable value of L, the material behaves as a half-wave (L=λ/2Δn) or a quarter-wave (L=λ/4Δn) plate [2]. In making these waveplates, once Δn is fixed, a strong constraint remains on the thickness L and, in any case, the fabricated device can be only used with a suitable, single wavelength. Furthermore, the sensitivity on L requires very precise fabrication processes which correspond to high prices of the optical elements; therefore, availability of a waveplate suitable for a large interval of wavelengths (achromatic plate) and whose thickness is not a critical factor, would attract a large interest.

Past studies have shown that Nematic Liquid Crystals (NLC) are promising materials to achieve such a result [3][4][5]. The key-feature of NLC is that Δn can be modified (within a given range) by applying an external perturbation (electric, magnetic and/or temperature); an eventual device, based on NLC, could hence be adapted to the actual wavelength used in the experiment. The simplest realization of such a device is obtained by enclosing a NLC with a positive dielectric anisotropy in a cell made of two Indium Tin Oxide (ITO) coated glasses, treated to give a planar alignment to the NLC director n. By applying an external electric field E with direction perpendicular to the glass slabs of the cell, n will reorient along the same direction of E. The effective refractive index of the sample inside the cell can be written as n_eff=n_on_e/(n_e²cos²θ+n_o²sin²θ)^1/2 [6] where θ is the angle between n and E, n_e is the extraordinary refractive index of the NLC and n_o is the ordinary one: depending on the value of θ (determined by the amplitude of the electric field) the value of n_eff can assume all values between n_e and n_o and the birefringence Δn=n_eff - n_o changes consequently. By tuning Δn and keeping fixed the thickness L of the NLC layer, it is, therefore, possible to fulfill the desired phase retardation condition for a large range of wavelengths. This basic embodiment of the device presents however some drawbacks. The orientation of n is, indeed, sensitive to temperature changes [6]. Moreover, the switching times of such devices are usually quite long (2-8 ms) at room temperature [6], thus limiting the fields of possible applications. Some years ago, a NLC modulator with a frame time of about 30 µs has been demonstrated [7] at T≈100 °C; although high-temperature operation reduces the response time significantly, a thermal stability of the NLC has to be considered.

In order to overcame above mentioned problems, the NLC layer is often stabilized by means of polymeric chains. By diluting a small concentration (typically, about 10%) [8] of monomer molecules in the NLC and by exposing the mixture to a low intensity UV light, some polymeric chains grow following the direction of the rubbing channels, made on the glass substrates to induce the planar alignment of the NLC director. The polymeric network increases the robustness of the device and, at the same time, limits the mobility of the NLC molecules: If an electric field is applied, the polymer exerts on the director n a torque which helps it to relax faster back to its original position when the field will be removed. This effect noticeable shortens the response time of the device; on the other hand, however, it increases the switching threshold and, consequently, the operating voltages. Moreover, due to the irregularity of morphology induced by the polymeric network, visible light is strongly scattered. Therefore, these systems are, in fact, suitable only for wavelengths in the infrared range.

In the past, we have exploited a single-step technique for realizing holographic gratings made of polymer slices alternated to homogeneous films of NLC (POLICRYPS) [9], and later the standard POLICRYPS writing process has been performed with a stabilized setup [10]. Several features of these structures make them a valid alternative to existing switchable waveplates. First of all, POLICRYPS are characterized by a sharp morphology which exhibits limited scattering losses when illuminated by visible light. Moreover, the polymer slices confine and stabilize the NLC molecules, influencing also their alignment, as shown by observations at the optical microscope [11]. As a consequence, low operating voltages and short switching times [9] are needed to reorient the director in the NLC films of a POLICRYPS structure. In the following, experiments are reported, which are devoted to investigate the behavior of POLICRYPS when used as phase modulators.

2. Phase Retardation Behavior

Our first aim was to check how good is the alignment of the NLC director within the POLICRYPS structure and to measure the birefringence of the sample. For our experiments, a POLICRYPS grating with a periodicity Λ=1.22µm (deduced by using the standard grating equation [12]) and thickness L=6µm (measured by a standard spectrophotometer before filling the cell) has been realized following the procedure described in [9]. Figure 1(a) shows a view of the sample on the rotation stage, while the typical POLICRYPS morphology, observed between cross polarizers, is shown in Fig. 1(b).

 

Fig. 1. View of the sample on the rotation stage (a) and optical microscope image of a POLICRYPS structure (b).

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The value of L has been chosen to obtain a very low efficiency grating, since, in order to be used as a good phase modulator, the grating should, in principle, transmit all the impinging light; the evaluation has been carried out by means of the commercially available GSolver software [13], which exploits a rigorous coupled wave analysis (RCWA) [14].

For our experiments, we have arranged the set-up shown in Fig. 2. The focalized light (spot diameter 0.5 mm, power density 1mW/mm²) from a He-Ne laser (λ=633nm) passes through a vertical polarizer before reaching the POLICRYPS. This is used as a retardation plate, whose orientation can be manually adjusted by using a rotation stage with a 0.5deg/div accuracy. The transmitted laser beam passes, then, through a second (horizontal or vertical) polarizer before being detected by a photo-detector.

 

Fig. 2. Experimental setup for the measurement of the POLICRYPS birefringence. P polarizer, A analyzer, I_inc totally incidence intensity, I_out output intensity, I_0T and I_±1T zeroth and the first order transmitted intensities, respectively, α angle between the light polarization direction (y axis) and the grating axis (direction of the POLICRYPS channels) in the yz plane, PD. Photo-detector, OSC oscilloscope.

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As mentioned above, in order to enhance the functionality of the system, we have fabricated a particular sample with a very small diffraction efficiency (almost 3%) at normal incidence. To estimate how good the system works as phase-retarder, we assume, as a reference, the transmitted intensity (zeroth diffracted order, I_0T) immediately after the sample when its optical axis is aligned along the axis of the first polarizer. In this condition, the photo-detector gives a signal of 2.9 V. Then, the output intensity after the second polarizer (I_out), has been measured, at room temperature (T=25 °C), versus the rotation angle α of the sample axis around the direction of the impinging beam. A constant offset of approximately 0.2 mV has been measured when the aperture of the detector was closed; this level was independent of the value of. α. Data have been taken by varying α in steps of 10 deg., both between crossed and parallel polarizers. Results shown in Fig. 3 reveal a behavior typical of a retardation wave plate: both intensities are periodic functions of the rotation angle α (the two curves for I_// and I_⊥ have been drawn by starting from their minimum values, which do not coincide because the sample does not exactly fulfill the half wave plate condition [ΔnL=(m+1/2)λ]. Furthermore, the two behaviours confirm the absence of liquid crystal droplets (with almost the same dimension of the probe wavelength) inside the structure: in that case, indeed, the incidence light would be strongly scattered and would become depolarized, with the consequent impossibility of obtaining zero transmitted intensity.

 

Fig. 3. Experimental data points and theoretical (solid line) behavior of the output intensity versus the rotation angle obtained by placing the sample between crossed (red) and parallel (blue) polarizers. The difference between the level of I_0T and the maximum value reached by I_parall is due to the absorption of the second polarizer. The experimental error is +/- 0.08 mV, estimated as the maximum semi-dispersion of a measure set.

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By using the Jones matrices formalism [15] for a retardation plate, it is possible to calculate the irradiance of both vertically and horizontally polarized light beams passing through the plate:

where I_0T is the total intensity transmitted through the sample. Data have been fitted with Eqs. (1) and (2); the fit procedure has been carried out by writing these equations as:

where A=I₀sin²(φ/2), C=I₀, D=sin²(φ/2), X=α, B and E are arbitrary phases. From the value of A, it is possible to determine the retardation (φ=1.69 rad) and then the birefringence. Using the equation

we have obtained Δn=0.028. In the same way, from the value of D, we obtain Δn=0.027. This value seems to be too low; probably the residual concentration of monomer (NOA 61 by Norland) in the NLC (E7 by Merck) films is not negligible and this reduce the NLC birefringence. By increasing the curing temperature it should be possible to obtain a better phase separation between the polymer and the NLC with a consequent increasing of the birefringence. New materials are, actually, under test in order to work with higher curing temperatures, without inducing the thermo-polymerization process during the curing process. In any case, a strong correlation remains between the birefringence and other parameters, like temperature, fringe spacing and cell thickness; future characterizations will be done in order to investigate these correlations.

We have also checked the possibility of switching the birefringence of our sample by applying an external electric field. Results are shown in Fig. 4.

 

Fig. 4. Birefringence versus the applied electric field (square voltage pulses at 1 Khz).

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Measurements have been performed by placing the sample between parallel polarizers, with its optical axis oriented at 45° with respect to the axes of polarizers. The applied voltage is increased from 0V to 51V (from 0 V/µm – to 7.1 V/µm in our case): due to the director reorientation, the birefringence is turned to zero.

In order to check the NLC stabilization due to the polymeric walls, we have measured the birefringence versus the power of the impinging laser beam. The measurement has been carried out with a green laser beam (λ=532nm), using a POLICRYPS sample with a low diffraction efficiency at the green wavelength. The fringe spacing and the thickness of the sample where Λ=1.22µm and L=7.22µm, respectively. In this case, the birefringence measurement yielded φ=1.88 rad. and Δn=0.020. The power dependence of the birefringence is shown in Fig. 5

 

Fig. 5. Birefringence versus the power of the impinging laser beam (the spot diameter is 1 mm).

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The very small variations, which can be observed, indicate that the stabilization action of the polymeric walls in the POLICRYPS is able to strongly reduce the thermal noise [16] produced by the increasing impinging intensity.

3. Conclusions

We have reported a first investigation of the phase modulator behavior of POLICRYPS. These structures prove to act as good phase retarders, with a birefringence that is independent of the impinging intensity, and can be turned off by applying a suitable external voltage. The study confirms the absence of liquid crystal droplets inside the POLICRYPS structure, since they would cause strong light scattered and depolarization, that have not been observed. Thus, POLICRYPS are good candidates to became electrically controlled and switchable wave plates. Next steps will be the study of the behavior in the telecom range and in a pulsed laser regime.