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This study is the first to investigate an optically addressed, electrically tunable prism grating based on homogeneously aligned liquid crystals (LCs) with a photoconductive layer. A conductivity-gradient electrode-like grating pattern of the polymer layer results in a spatially periodic gradient of the effective electric-field drop, producing a prism grating with a spatially periodic LC gradient reorientation. The asymmetric diffraction pattern can be adjusted by varying the dc voltage. The first-order diffraction efficiency is 64% at optimal conditions. The proposed prism grating exhibits extremely low diffraction noise in the off state, a high switching contrast inthe on–off state (~1000), simplicity of fabrication, and high controllability at a low voltage range (0 to 0.4 V/μm).
©2012 Optical Society of America
1. Introduction
The application of various liquid crystal (LC) beam steering devices in optical interconnects, optical fiber communication, projection displays, optical data storage, and optical switches are examined [1–6]. These devices have been developed using index matching, optical phased array, and blazed groove profiles, among others [7–10]. The common disadvantage of these devices is the complexity of fabrication. The prism gating shows the highest potential among these beam steering devices because of its high diffraction efficiency, highly asymmetric diffraction pattern, simplicity of fabrication, and high controllability at a low voltage range. Ideally, a well-designed prism grating achieves 100% diffraction efficiency for the 1st-order beam, which corresponds to a 100% beam-steering efficiency.
A prism grating that uses a periodic gradient refractive index nanoscaled polymer-dispersed liquid crystal (GRIN PDLC) was recently developed by Wu et al. [11]. GRIN PDLC gratings exhibit high transparency in the visible region owing to their nanoscaled droplets and polarization independence. However, GRIN PDLC gratings exhibit a relatively high operating voltage (100 Vrms) and a lack of phase change. Another LC prism grating based on polymer-stabilized liquid crystal (PSLC) demonstrates improved performance with high diffraction efficiency (~80%) and a low applied voltage (~0.2 Vrms/μm). However, the PSLC-based prism has ~20% diffraction noise in the voltage-offstate, resulting in significant decay in the light switching contrast of the on–off state (~6) [12]. To enhance the previously developed LC-based prism gratings, this study proposes and demonstrates an optically addressed, electrically tunable LC prism grating based on a homogeneously aligned LC cell coated with a photoconductive layer.
Experimental results show that a UV-addressed prism grating with a spatially periodic LC gradient reorientation can be generated with an applied dc voltage because of a spatially periodic gradient of effective electric-field drop on the LC layer. The asymmetric diffraction pattern can be controlled by varying the voltages on the LC prism grating. A maximun diffraction efficiency of ~64% and a maximum on–off state switching contrast of ~1000 for the proposed prism grating can be achieved. The proposed LC prism grating has the following advantages: high diffraction efficiency, reduced extremely low diffraction noise in the off state (high switching contrast in on–off states), simplicity of fabrication, and high controllability at low voltages.
2. Sample preparation and experimental setups
Figure 1 illustrates the fabrication of an electrically tunable prism grating based on homogeneously aligned LCs with a photoconductive polymer layer. In Fig. 1(a), the photomask with a spatiallyperiodic grayscale has a strip width of 250 μm. An unpolarized UV light from a 7.5 W Hg lamp with an intensity of ~10 mW/cm2 selectively illuminates the photoconductive polymer layer poly(N-vinylcarbazole)(PVK) precoated over the indium tin oxide (ITO) glass substrate through the photomask. The photomask is in contact with the ~0.25 μm thick PVK film during the UV light irradiation. The polyimide films are then coated over the PVK–ITO substrate and another ITO substrate, and both are rubbed in the x direction. Separated by 25 μm plastic spacers, the two substrates are combined to produce an empty cell. The LCs (E7 from Merck, n0 = 1.5216, ne = 1.7462) are injected into the empty cell to form a homogenously aligned LC cell coated with the PVK layer. An external dc voltage is applied on the cell to form the LC prism grating, as shown in Fig. 1(b).
Fig. 1 Schematics of (a) the procedure for the fabrication of the electrically tunable prism grating based on the homogeneously aligned LC cell with a photoconductive polymer layer and (b) the electrically tunable prism grating.
Figure 2 presents the experimental setup for examining the programmable asymmetric diffraction of the formed LC prism grating. An unpolarized He–Ne laser beam (λ = 633 nm) passes successively through a polarizer, a half-wave plate, and an analyzer with a transmission axis fixed in the x direction. The beam then passes through the LC prism grating at an externally applied dc voltage. The transmission axis of the polarizer can be rotated to control the incident intensity of the probe beam. A photodiode with an active diameter of 1.1 cm is linked to a computer and placed approximately 15 cm away from the cell to measure the diffracted intensities of the 0th, + 1st, and −1st orders.
Fig. 2 Experimental setup for examining the programmable asymmetric diffraction effect of the formed LC prism grating. P, polarizer; A, analyzer; λ/2, half-wave plate; D, photodetector.
3. Results and discussion
Figure 3(a) depicts the variations in the + 1st-order diffraction efficiency (η1) of the LC prism grating with an increased dc voltage (V) at various UV exposure times tUV from 3 h to 9 h. As tUV increases from 3 h to 7 h, the peak value η1 increases. When tUV exceeds 7 h, the peak value of η1 decays. The + 1st-order diffraction efficiency reaches ~64% at tUV = 7 h and V = 10.5 V. The mechanism for the formation of the prism grating is described as follows: When an external dc voltage is applied on the LC cell coated with a PVK layer, the effective voltage drop on the LC layer (VLC in the steady-state regime is expressed as [13]
where dPVK (σPVK) and dLC (σLC) represent the thicknesses (conductivities) of the LC layer and the PVK layer, respectively. Equation (1) indicates that the voltage drop on the LC layer depends on the ratio of σLC to σPVK. If the PVK film is conductive (σPVK >> σLC), the largest external voltage drop on the LC layer occurs. If the PVK film is nonconductive (σPVK < σLC), only a fraction of the external voltage can drop on the LC layer. PVK is a satisfactory insulator in dark conditions and under visible light illumination and becomes conductive upon UV exposure. PVK exhibits superior photoconductivity as a charge-transporting polymer with a good hole conductivity and a high concentration of active charge transport sites (carbazole groups) [14]. The change in conductivity of the PVK film exposed to UV light can be described quantitatively by a power-dependence relation [15]:where σPVK(dark) is the conductivity of PVK in dark conditions, I is the intensity of PVK exposure to UV light, and β and γ are the material parameters of the PVK. Apparently, the conductivity of the PVK film monotonically and nonlinearly (γ ≠ 1) increases when the intensity of UV irradiation increases. An electrode-like grating pattern of the PVK layer with a spatially periodic nonlinear gradient of conductivity may form aas the PVK film on the LC cell is irradiated with UV light through the photomask grating with a spatially periodic gradient of transmittance. As the external dc voltage is applied on the cell, a spatially periodic nonlinear gradient of an effective voltage drop on the LC layer is obtained. This can form a spatially periodic nonlinear gradient of LC orientation in the cell, which leads to an electrically programmable prism grating effect.Fig. 3 (a) Variations in the 1st-order diffraction efficiencies (η1) caused by the increased dc voltage (V) with various UV exposure times; (b) voltage-dependent diffraction efficiencies of the 0th, + 1st, and −1st orders with a 7 h UV exposure time of 7 h.
To examine the electrically controlled asymmetric diffracted characteristics of the prism grating at different voltages, the voltage-dependent diffraction efficiencies of the 0th, + 1st, and −1st orders at tUV = 7 h are measured [Fig. 3(b)]. The maximum peak value of the + 1st-order diffraction efficiency at 64%, can be obtained. The 0th, + 1st, and −1st order diffraction efficiencies of the prism grating are defined as follows:
where D0 and ± 1 are the diffracted intensities of the 0th- and ± 1st-order beams, respectively, and Dtotal is the total diffraction intensity of all orders. At V = 0 (off-state), η0 approaches 100% and η ± 1 ≅ 0%. As the applied voltage is increased, the 0th order dramatically decays and concomitantly the diffractions for high orders, including the ± 1st order, occur at V < 3.5V. When the applied voltage is increased from 3.5 V to 10.5 V, η1 significantly increases to a maximum value of ~64%, and η-1 is maintained at ~3.4%. A diffraction pattern with a highly asymmetric efficiency ratio of η+1/η-1 ≅ 21 appears. The negligible diffraction noise of the + 1st order in the off state (0 V) in the proposed prism grating exhibits a potentially high switching contrast in the on (10.5 V) and off (0 V) states (~1000), which is significantly superior to that of the PSLC prism grating (~6) developed by Wu et al. [12]. When the applied voltage exceeds 10.5 V, η1 gradually decays. The prism effect of the diffraction grating weakens because the gradient of the LC reorientation gradually disappears. The behavior of the prism grating is similar to that of a conventional grating when the voltage exceeds 24.5 V because the diffraction efficiencies of + 1 and −1 orders are almost equal. At V ≥ 35.5 V, the high orders almost disappear with a concomitant ~100% efficiency of the 0th order. Thus, the effect of the prism grating disappears.To obtain the dependence of the photoconductivity of the PVK film on tUV, a separate experiment based on a PVK-coated 90° twisted nematic (TN) cell is conducted. The PVK film is pre-irradiated by the UV light with 10 mW/cm2. As presented in Fig. 4(a) , the transmission of a He–Ne laser probe beam through the TN cell depending on the applied voltage is measured. The TN cell is placed between the parallel polarizers, and the rubbing direction of the front substrate of the TN cell is parallel to the transmission axis of the polarizer. Figure 4(b) indicates that the threshold voltage for the Freedericksz transition of the TN cell decreases with increasing tUV. This result reflects the increase in effective voltage drop on the TN layer and thus the raise in PVK conductivity with increasing tUV (according to Eq. (1)). The monotonic increase in PVK conductivity with increasing tUV is coincidental to that of the maximum diffraction efficiency of the LC prism grating with increasing tUV for tUV ≤ 7 h. For tUV > 7 h, this maximum diffraction efficiency decreases with increasing tUV instead. This behavior occurs because the photoconductivities for weak- and strong-exposure regions of the PVK film through the photomask grating become non-negligible and saturated, respectively, through long exposure. This phenomenon results in the decay of the PVK layer conductive gradient, hence the decrease in the diffraction efficiency.
Fig. 4 (a) Normally black operation of the TN cell. (b) Variation in the transmission of the TN cell at an applied voltage with various exposure time to UV light.
To understand qualitatively the connection between the experimental results shown in Fig. 3 and the model addressed in Fig. 1(b), this study presents a simple setup (inset of Fig. 5 ) to measure the variation of the transmission of the homogeneously aligned LC cell coated with the PVK layer. The LC cell is pre-irradiated uniformly by the UV light with 10 mW/cm2 for 7 h. The experimental result shows several oscillations of the transmission with an increase in voltage. A complete oscillation indicates that the probe beam through the cell undergoes a 2π phase shift. At V = 7 V, the transmission of the probe beam undergoes five complete oscillations. This transmission is more frequent than that of the 1st-order diffraction efficiency with an increase in voltage (only one complete oscillation). This large discrepancy is primarily caused by the formed periodic gradient distribution of the LC director for the prism grating in the presence of the applied voltage. In the above discussion regarding the formation mechanism of the voltage-controllable prism grating, the periodic gradient of the LC director in the grating is spatially nonlinear along the y axis at V > 0. Based on the diffraction theory of thin grating [16], the diffraction efficiency of the probe beam through the prism grating is contributed by the effective interference among those transmitted secondary wavelets with a spatially periodic gradient of phase shift by going through the grating regions with a spatially periodic gradient of director orientations (along the y axis). Considering that the phase oscillations for those transmitted secondary wavelets have no correlation with the increase in the applied voltage, the effectively constructive interference among these wavelets and thus the formation of the diffraction maximum can occur only at two specific voltages in the present case. To understand the quantitative relationship between the experimental results in the variation of the diffraction efficiency of the prism grating with the applied voltage with the model presented in Fig. 1(b), a simulated calculation must be performed using the exact diffraction theory of thin grating [16]. A related study will be conducted in the future.
Fig. 5 The variation of the transmission of the homogeneously-aligned LC cell coated with the PVK layer with applied voltages. The LC cell is pre-irradiated uniformly by the UV light with 10 mW/cm2 for 7 h.
Figure 6 shows the variation in the diffraction pattern and the corresponding structure of the prism grating under a polarizing optical microscope with crossed polarizers when the applied voltage increased from 0 V to 35.5 V. The direction of the grating vector for the prism grating was + 45° and −45° from the crossed polarizer and analyzer, respectively. Figure 4(a) shows that no grating structure was generated at V = 0, which indicates a negligible 1st-order diffraction noise in the off state. As the voltage increases from 1.5 V to 10.5 V [Figs. 4(b) to 4(d)], the asymmetric prism grating structure and the corresponding asymmetric diffraction pattern become increasingly apparent. This result is consistent with the increase in the + 1st-order diffraction efficiency from 0% to 64% [Fig. 3(b)]. At V = 10.5 V, a spatially periodic distribution LC gradient reorientation induced by the periodic distribution of an optimal UV-induced conductivity gradient of the PVK layer results in a diffraction distribution with the highest + 1st-order diffraction efficiency. As the voltage increases from 10.5 V to 35.5 V, the structure of the prism grating gradually disappears. This result indicates a remnant + 1st-order diffraction with a considerably weak efficiency.
Fig. 6 Voltage-dependent diffraction patterns and structures of prism grating under a microscope with crossed polarizers.
4. Conclusion
This study proposes an electrically tunable prism grating based on an LC film coated with a photoconductive polymer layer. The periodic distribution of a refractive index gradient is determined by exposing the photoconductive layer to UV light through a periodically grayscale photomask. The experimental results indicate that an optically addressed, electrically tunable prism grating with a spatially periodic LC gradient reorientation can be formed by applying various dc voltages. The formation of the prism grating results from a spatially periodic gradient of an effective electric field drop on the LC layer. The maximum efficiency of ~64% for the + 1st-order diffraction and a high switching contrast of on–off states at ~1000 for the present prism grating can be achieved. In addition, the present LC prism grating has advantages such as easy fabrication and high controllability at a low voltage range (0 to 0.4 V/μm).
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