Experimental study of an ultrasmall pixel, one ... - OSA Publishing

Experimental study of an ultrasmall pixel, one-dimensional liquid-crystal device Boris Apter,1 Yizhak David,1 Itzhak Baal-Zedaka,1 and Uzi Efron1,2,* 1

Department of Electrical and Electronic Engineering, Holon Institute of Technology, Holon, Israel

2

Department of Electro-Optical Engineering, Ben-Gurion University of the Negev, Beer-Sheva, Israel *Corresponding author: [email protected] Received 5 August 2008; revised 13 October 2008; accepted 14 October 2008; posted 21 October 2008 (Doc. ID 99810); published 20 November 2008

A one-dimensional, ultrasmall pixel liquid-crystal (LC) device is experimentally demonstrated. The device has a one-dimensional array of ten 1 mm long, interdigitated, reflective gold electrodes on a glass substrate and a common transparent electrode on the opposite substrate. The interdigitated electrodes are 2 μm wide, separated by a 1 μm interelectrode gap. Operating as a dynamic, reflective, 3 μm pitch diffractive grating, the device simulates the performance of a reflective, ultrasmall, 3 μm pixel, spatial light modulator (SLM). It was shown that, for a proper choice of LC cell thickness (less than 2 μm), LC material (Merck’s BL006 high-birefringence mixture), and driving conditions, the device can attain relatively high diffraction efficiency, thus demonstrating the practical feasibility of a 3 μm pixel, LC SLM. © 2008 Optical Society of America OCIS codes: 070.6120, 230.2090, 230.3720.

1. Introduction

Spatial light modulators (SLM) [1] play an important role in modern optical technologies. The principal applications of these devices include displays [2], beam steering and switching [3–7], adaptive optics [8,9], optical tweezers [10,11], and dynamic computerbased holography [12–17]. The dynamic holography applications call for relatively large SLM panels (∼10 cm) with ultrasmall pixel sizes of less than 5 μm. Both the attainable diffraction efficiency and the maximum diffraction angle are key parameters of the computer-generated hologram and depend critically on the pixel size of the LC device. To the best of our knowledge, the smallest pixel size of current, commercially available, LC reflective microdisplay is about 8 μm [18]. It should be noted that a pixel size of 8 μm corresponds to spatial resolution of 125 mm−1, which is at least 1 order of magnitude lower than that of a typical holographic plate (∼5000 mm−1 ). 0003-6935/08/336315-10$15.00/0 © 2008 Optical Society of America

It is well known that the principal factor responsible for the resolution limitation of LC displays or the loss of diffraction efficiency of SLMs is the effect of the lateral, or fringing, field between adjacent electrodes (pixels). This effect leads to spatial smearing of the intensity or phase profile of the modulated light. Extensive theoretical and experimental studies of the fringing-field effect in LC devices have been performed in recent years [19–24]. The simplest, but one of the most important, subjects of these theoretical and experimental investigations has been the LC diffraction grating generated by applying a binary voltage profile to the 1D periodic electrode structure. The diffraction from the phase grating generated by the fringing field in a homeotropically aligned LC layer was used to study some fundamental properties of LC materials [25]. Another, similar, LC grating was considered as an efficient device for beam steering and diffractive applications and studied both experimentally [26] and theoretically [27]. This device, as well as the device reported in [25], were based on a single-side driving configuration in which interdigitated transparent electrodes were 20 November 2008 / Vol. 47, No. 33 / APPLIED OPTICS

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deposited on one side of the cell’s glass substrate, with the other glass substrate serving only as a mechanical support for the homeotropic LC layer. In such a driving configuration, the fringing (lateral) electric fields generated by the interdigitated electrodes results in reorientation of the LC director away from its initial homeotropic alignment. The device with a 8 μm pitch electrode structure has shown relatively high diffraction efficiency [26]. Another class of binary LC diffraction structures is based on a parallel, homogeneous alignment of LC layer and a driving scheme in which patterned addressing electrodes are deposited on one substrate, whereas the opposite substrate is coated with a common uniform electrode [28–30]. In such configurations, the driving voltage is applied across the LC layer, resulting in the reorientation of the LC director away from its initial homogeneous alignment and toward the direction of applied electric field. The diffraction efficiency of a binary LC phase grating with a relatively small pitch size of 6 μm (4 μm electrode width and 2 μm spacing between electrodes) was studied experimentally, as well as numerically simulated [28]. Another LC binary diffractive structure with a relatively long electrode pitch size of 36 μm was also analyzed and experimentally tested [29]. Some researchers noted the asymmetry of the diffraction patterns generated by such devices [28– 30], which is caused, most likely, by the pretilt angle of the LC director. As a new and promising solution for overcoming the fringing-field limitations in LC diffractive devices, a double-sided binary grating structure with patterned electrodes on both sides of LC cell was recently studied [31,32]. However, this approach requires a precise alignment technique and its use in two-dimensional (2D) LC structures should still be assessed. In this paper we investigate practical realization of an ultrasmall pixel LC device, based on a commonly used reflective mode configuration with a patterned electrode array only on one side and a uniform electrode on the opposite side. We show that, with an appropriate choice of LC material and operational mode, it is possible to reduce the fringing-field limitations and achieve sufficient phase modulation in a relatively simple structure based on a commonly used driving configuration. The preliminary results of computer simulation and experimental evaluation of the device were presented in a conference proceedings [33].

thick glass substrate. The 2 μm wide electrodes are separated by 1 μm interelectrode gaps, resulting in a 3 μm pitch of the electrode array. The schematic drawing of the electrode array structure is shown in Fig. 1. The test device was designed so that the chip served as the rear substrate of the LC cell, operating in a reflective mode, with the chip electrodes serving as the reflecting surface for the incoming beam, thus emulating the performance of reflective LC-on-silicon (LCoS) type SLM. The test-device was assembled using two glass substrates: the electrode array chip (overall size 10 mm × 10 mm × 1 mm) and the glass plate (overall size 25 mm × 25 mm × 1:1 mm) uniformly coated with an indium tin oxide (ITO) transparent electrode. Both substrates were spin coated with PIC-05S polyimide, purchased from Cardinal Industries, Inc., and mechanically rubbed to generate the initial parallel homogenous alignment of the LC director, whose orientation was perpendicular to the interdigitated electrodes. The LC cell construction is shown schematically in Fig. 2. At one edge of the electrode array chip, the substrates were mechanically clamped with a rubber pad without any spacers between the substrates. The other edges of the chip were left unclamped. The cell was placed in a specially designed cassette holder (not shown in Fig. 2) that enabled a mechanical pressure tip [35] and mechanically controllable clamping force at one edge to vary the cell gap thickness within the active area of the interdigitated electrodes. The gap was filled with Merck’s high-birefringence BL006 LC mixture by capillary flow through the nonclamped edges of the electrode array chip. 3.

Experimental Setup

The designed ultrasmall pixel LC test device was evaluated with the experimental optical setup shown in Fig. 3. In this setup, the nonpolarized beam of an He–Ne laser (wavelength 632:8 nm) was linearly polarized (by the first polarizer) in the desired direction, spatially filtered, expanded, and split into two probing beams. Both beams focused onto the active area of the LC test device. The first probing beam

2. Design and Preparation of Ultrasmall Pixel LC Test Device

To assess the possibility of practical realization of an LC device with ultrasmall pixels, we performed design and experimental study of a simple test device. As a base component of the device, we used the “IAME-co-IME” electrode array chip [34] purchased from ABTECH Scientific, Inc. The chip contains 5 þ 5 interdigitated, 1 mm long gold electrodes on a 1 mm 6316

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Fig. 1. Schematics of the electrode array.

the active area of the test device varied with a micrometer-adjustable screw-down mechanism. The second probing beam (Probing Beam 2 in Fig. 3), obliquely (30°) incident on the device, was diffracted by it in a reflective mode. The polarization state of the probing beams was adjusted with the first rotatable polarizer. An opaque shutter (not shown in Fig. 3) was used to block one of the probing beams when the other beam was used for measurements. The transmitted and reflected beams were detected with two photodiodes feeding to the measuring and recording equipment (optical power meter and digital oscilloscope). The LC cells were activated by separate function generators with a 1 kHz square-wave voltage signal. The driving voltages applied to the interdigitated electrodes of the test device were adjusted by multiturn potentiometers. 4. Fig. 2. LC cell construction (cell holder is not shown). Top, general view; bottom, cross section.

(Probing Beam 1 in Fig. 3) normally incident on the device, traversed the LC layer and was diffracted from the interdigitated electrodes. Since the first transmitted diffraction order of the probing beam was phase modulated by the LC layer, it was used for adjusting and measuring the effective thickness of the LC layer (cell gap) within the electrode array area of the test device. To transform the phase modulation of the transmitted light into intensity modulation, the test device was placed between two rotatable polarizers so that the first transmitted diffraction order passed through the analyzer. An additional LC cell was used as a controllable retarder to adjust the overall phase retardation and transmittance of the system. The cell gap thickness within

Experimental Results

Our experimental study was aimed at evaluating the diffraction properties of the designed ultrasmall pixel test device in reflective mode. As noted above, the main factor limiting the diffraction efficiency of the LC devices is the fringing-field effect, which is proportional to the thickness of the LC layer. The cell thickness (i.e., the gap between the device substrates) was, therefore, the physical parameter varied during the experimental evaluation of the device, using a technique based on applying a controllable mechanical pressure on the LC cell. This method was detailed in previous publications [22,35]. The effective thickness of the homogeneously aligned LC layer was estimated and adjusted by measuring the cell’s birefringence, similar to the method reported in [36]. The calibration of the varying cell gap thickness was performed by the following procedure. The laser beam was initially linearly polarized by means of the first polarizer at 45° with respect to the initial,

Fig. 3. Experimental setup. 20 November 2008 / Vol. 47, No. 33 / APPLIED OPTICS

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parallel alignment of the LC director in both the compensator and the test device cells. The second polarizer, which served as an analyzer, was orthogonal to the first polarizer. The multiturn potentiometers were adjusted so that a uniform potential was applied to all interdigitated electrodes of the test device, while the common, transparent ITO electrode was grounded. In this way, a spatially quasi-uniform driving voltage was applied across the LC layer and the test device operated as an electrically controllable retardation plate. The laser beam, transmitted through the LC layer of the test device, was diffracted from its periodic electrode structure, deposited on the rear glass substrate. Since the electrode array was placed behind the LC layer, this diffraction pattern was not affected by the cell retardation. Thus, the grid structure acts only as an output multibeam splitter, allowing the measurement of the cell retardation by using any of the transmissive diffraction orders. Because of the specific design of the experimental setup, it was more convenient to measure the retardation by using the first transmission order. The intensity of the first transmission diffraction order, passed by the analayzer, was monitored by Photodiode 2 (see Fig. 3). During the first step of the gap estimation procedure, all electrodes of the test device were grounded. By applying an appropriate driving voltage to the compensating LC

cell, the overall retardation of the system was thereby adjusted to minimize the intensity of the beam transmitted through the analyzer. In the next step, the test device cell was activated by sweeping a spatially uniform voltage across its LC layer from 0 to 10 Vrms and the intensity transmitted through the crossed polarizer–analyzer pair was recorded against the applied voltage. By counting the resulting output beam intensity cycles, the number of which is proportional to the retardation change, the effective cell thickness d was calculated by using the well-known relationships [37] Δφmax ¼ ð2π=λÞðne − no Þd;

ð1Þ

d ¼ Δφmax λ=½2πðne − no Þd;

ð2Þ

where Δφmax is the maximum phase retardation, λ is the wavelength, and ne and no are the extraordinary and ordinary refractive indexes of the LC. Figure 4 shows the relative intensity, at normal incidence, recorded at various mechanical pressure levels applied to the cell. These curves correspond to four different cell gap thicknesses adjusted to generate maximum phase retardations Δφmax ¼ π, 1:5π, 2:0π, and 2:5π rad in transmissive mode.

Fig. 4. Experimentally recorded intensities for various maximum cell retardations (test-device cell thicknesses): (a) π rad (1:1 μm), (b) 1:5π rad (1:7 μm), (c) 2π rad (2:2 μm), (d) 2:5π rad (2:8 μm). Transmission geometry at normal incidence, λ ¼ 632:8 nm. The voltage applied across the test device is proportional to the time elapsed indicated by the horizontal axis (5 s=division representing 1 V increments). The top wedgelike signal shows the analog voltage as recorded by the scope. 6318


Substituting into Eq. (2) these values of Δφmax, the operational wavelength (λ ¼ 0:6328 μm), and the refractive indices of Merck’s BL006 LC mixture (ne ¼ 1:816, no ¼ 1:53), we calculated the following effective thicknesses d ¼ 1:1, 1.7, 2.2, and 2:8 μm. All of the following diffraction experiments were carried out using these cell thicknesses. In the diffraction experiments, the laser beam was linearly polarized by the first polarizer in a direction perpendicular to the interdigitated electrodes of the test-device, i.e., parallel to the director of the nonactivated, homogeneously aligned LC. The diffraction properties of the device were studied in a reflective mode of operation, with the second probing beam obliquely incident on the device, at a 30° angle. The compensating LC cell was not activated during these experiments. The test device was activated by grounding the common transparent electrode and the even interdigitated electrodes and by applying a 1 kHz square-wave voltage signal to the odd interdigitated electrodes. In this way, a periodic spatial modulation of the effective refractive index for a beam polarized along the initial alignment of the LC director was generated due to the reorientation of the LC director in the generated, periodic electric field, as illustrated by the computer simulation shown in Fig. 5. We used the autronic-MELCHERS 2dimMOS software [38] to simulate the 2D distribution of the LC director. It can be seen from Fig. 5 that applying the driving voltage to the interdigitated, 3 μm pitch electrode structure results in a periodic tilt variation of the LC director with a double period of 6 μm. We consider this 6 μm period as the basic period Λ of the structure, to be used later to identify the diffraction orders m and the diffraction angle αm ,

according to the diffraction grating equation, for a given wavelength λ: sin αm þ sin θ ¼ mλ=Λ;

ð3Þ

where θ is the incidence angle of the probing beam. The diffraction orders are designated as 0 R, 1 R, 2 R… indicating zero and positive/negative mth reflected diffraction orders, correspondingly. We used the following signs conventions (see top part of Fig. 5): The incidence angle θ is positive when measured counterclockwise from the normal to the device and the diffraction angles αm are positive when measured counterclockwise and negative when measured clockwise from the normal. Thus, the positive diffraction orders increase counterclockwise, whereas the negative diffraction orders increase clockwise from the direction of zero order (0 R). Figure 6 shows an example of the beam shape diffracted from the structure in the reflective mode and registered by a digital camera. The effective thickness of the LC layer in this particular example was d ¼ 1:1 μm. As can be seen from Fig. 6, when the test device is not activated (all electrodes are grounded), the diffraction pattern contains only specularly reflected (0 R) and even (2 R, þ4 R, þ6 R, þ8 R) diffraction orders. It is clear, that these even diffraction orders are caused by the background parasitic diffraction from the periodic metallic electrode structure with a period of Λ=2 ¼ 3 μm. We have termed these diffraction orders “even orders,” with respect to the basic period of Λ ¼ 6 μm. According to the grating Eq. (3), for the parasitic even orders −2 R, þ2 R, þ4 R, and þ6 R, we expect the following diffraction angles of −45:31°, −16:8°, −4:48°, and

Fig. 5. (a) Definition of diffraction orders for the interdigitated device. (b) Periodic reorientation of the LC director calculated using the 2dimMOS program [38]. 20 November 2008 / Vol. 47, No. 33 / APPLIED OPTICS

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(desired) orders by applying an appropriate driving voltages to the odd interdigitated electrodes of the test device. This effect is illustrated in Fig. 7 which shows the normalized intensities of the 0 R, 1 R, and 2 R orders recorded at different cell thicknesses when the driving voltage was continuously swept from 0 to 10 Vrms . As can be seen, it was possible to minimize the intensities of the 0 R (specularly reflected) and 2 R (even, parasitic) orders and maximize the intensities of the 1 R (odd, desired) orders (generated due to the activation of the LC phase grating), by varying the driving voltage in the range of

Fig. 6. Reflective diffraction patterns recorded by digital camera, for nonactivated (top) and activated (bottom) states of the test device.

þ7:63°, respectively, with respect to the basic period of Λ ¼ 6 μm. The measured diffraction angles of these orders were −44°, −17°, −5°, and þ7°, respectively. This rather good agreement between the expected and measured diffraction angles confirms the origin of the even orders as the parasitic background diffraction from the metal electrodes. In the activated state, when a nonzero voltage is applied to the odd interdigitated electrodes (V odd ¼ 3:8 Vrms in the example presented in Fig. 6), with the even electrodes still grounded, an additional diffraction due to the generated LC phase grating takes place. The diffracted light is consequently redistributed between the zero (0 R) order, even (2 R, þ4 R, þ6 R, þ8 R), and odd (1 R, 3 R, þ5 R, þ7 R) diffraction orders. These odd orders are caused by the diffraction from the phase diffraction grating generated due to the periodic modulation of the LC refractive index. Although the grating Eq. (3) predicts the generation of diffraction orders ranging from −4 R to þ14 R from the test device (for an incident angle θ ¼ 30°, grating period Λ ¼ 6 μm, and wavelength λ ¼ 632:8 nm), only the orders shown in Fig. 6 are actually observed and registered due to the structural limitations of our experimental setup and the low intensities of the higher orders. The grating Eq. (3) predicts for the odd orders of −3 R, −1 R, þ1 R, þ3 R, and þ5 R the following diffraction angles (with respect to the basic period Λ ¼ 6 μm): −54:73°, −37:3°, −23:24°, −10:58°, and þ1:57°, respectively. The measured diffraction angles of these odd orders were found to be −53°, −37°, −24°, −11°, and þ1:5°, respectively. Again, this rather good agreement between the calculated and measured diffraction angles confirms the premise that the odd orders are generated due to the periodic spatial modulation of the LC refractive index. To the best of our knowledge, a similar type of combined diffraction from both the periodic metal structure and the LC phase grating in transmissive mode was first reported in [25]. As pointed out above, the diffracted light can be redistributed between the even (parasitic) and odd 6320


Fig. 7. Normalized diffraction intensities versus driving voltage. Effective thickness of the LC cell: (a) 1:1 μm, (b) 1:7 μm, (c) 2:2 μm, (d) 2:8 μm.

2:5 Vrms to 4:4 Vrms . This, as shown below, results from the voltage-generated phase modulation, which allows the reflective-mode diffraction pattern extreme to be attained within the voltage range used for the various LC cell thicknesses. For analysis, we used a simplified diffraction model where the mth diffraction efficiency from a thin sinusoidal phase grating [39] is proportional to ηm ¼ J 2m ðΔφref =2Þ;

ð4Þ

where J m is the Bessel function of the first kind and Δφref is the peak-to-peak phase modulation in the reflective mode. In this simplified model, we neglect the patterned structure of the reflective surface of our device, which is treated as uniform. The peakto-peak phase modulation in the reflective mode is given by Δφref ¼ 4πdΔneff ðθ; VÞ=ðλ cos θÞ;

ð5Þ

where d is the LC cell thickness, θ is the angle of incidence, Δneff ðθ; VÞ is the voltage-angle-dependent, peak-to-peak modulation of the LC layer’s effective birefringence at the oblique incidence or reflection angle, θ, and λ is the vacuum wavelength. The square of the oscillating Bessel function J 21 , which describes the intensity of the þ1 R= − 1 R diffraction orders, peaks at the following values of its argument: ðΔφref =2Þpeak ¼ 1:841; 5:331; 8:536; 11:706…ðradÞ: ð6Þ As shown below, these values correspond to a certain fraction of the maximum phase modulation attainable by the full (10 Vrms ) voltage swing applied to the LC cell in reflection, at the various thicknesses used. Therefore, full sweeping of the voltage causes the diffraction efficiency of the various cell thicknesses to peak at some intermediate voltage levels. To qualitatively analyze this effect, we can approximate the peak-to-peak modulation of the effective birefringence in Eq. (5) by 0 ≤ Δneff ðθ; VÞ ≤ ne − no :

ð7Þ

Substituting into Eq. (5) the upper estimate of Δneff ðθ; VÞ ¼ ne − no ¼ 0:286, an angle of incidence θ ¼ 30° and the operating wavelength λ ¼ 0:6328 μm, we obtain the following estimates of the maximum attainable values of the Bessel function argument ðΔφref =2Þ for different thicknesses of the LC cell, within the 0–10 Vrms operating range of the driving voltage, as follows: d ¼ 1:1 μm;

ðΔφref =2Þmax ≈ 3:6 rad;

d ¼ 1:7 μm;


d ¼ 2:2 μm;


d ¼ 2:8 μm;

ðΔφref =2Þmax ≈ 9:2 rad:

Comparing these values with the theoretical Bessel function arguments from Eq. (6), we conclude that, with a voltage swing of 10 Vrms, the first-order diffraction could peak once for the thinnest cell, twice for the two intermediate cells, and three times for the thicker cell. Such an estimate is supported by the earlier, single-pass, phase calibration experiments, which indicate, as an example, that the thinnest cell of about 1:1 μm thickness should yield a double-pass, 2π rad modulation at a voltage activation level of about 3 V [Fig. 4(a)]. However, due to the effect of the fringing field on the phase modulation and its dependence on the spatial period, we could expect significant deviations from the above estimates of the peak voltages, which are based on uniform cell activation, not subject to the fringing-field effects. Similar results for a transmissive LC diffractive structure with a doubled period of spatial modulation, compared to that of the present study, were reported in [28]. The experimental reflective diffraction patterns versus voltage activation across the various LC cell thicknesses are shown in Fig. 7. As expected, we observe the peaking of the odd, þ1 R and −1 R, diffraction orders, which results from the voltage-activated phase grating in the LC. Now, using the simplified expression of the grating diffraction efficiency, we would expect, based on Figs. 4(b)–4(d), to have additional first-order diffraction peaks for the LC cells at higher activation voltage, as their thickness is increased. While we do observe the rise of a second peak at a higher voltage for the next thicker cell of 1:7 μm [Fig. 4(b)], this second rise is actually reduced and weakened with further increase in the cell thickness to 2.2 and 2:8 μm, with no appearance of additional diffraction peaks. This observation points to the effect of the fringing field, which is known to reduce the effective spatial field modulation across the LC device [19–21]. In fact, the fringing-field effect has been shown to limit the electric field modulation and device resolution at pixel aspect ratios (pixel width to cell thickness) below 3∶1 [40,41]. Indeed, the effective pixel aspect ratios for the thicker cells of 1:7 μm and above used in this work are all below 3∶1. The asymmetry in the intensities of the positive and negative orders, which is clearly seen, is the result of the differences in the effective birefringence experienced by the negative and positive diffraction orders due to the difference in their angular tilt from the normal. Qualitatively, it can be seen (Fig. 5) that the positive diffracted orders are closer to the normal than their negative counterparts. This, in turn, means that the effective birefringence is larger in this case than for the negative orders. (It should be noted that the positive nematic LC used is aligned 20 November 2008 / Vol. 47, No. 33 / APPLIED OPTICS

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along the grating vector). Thus, a higher phase modulation versus voltage is expected for positive orders as compared to their negative counterparts, leading to the appearance of the þ1 R diffraction peaks at a lower voltage, relative to those of the −1 R order, as seen in Fig. 7. It should be emphasized that this asymmetry is mainly affected by oblique incidence (30° angle of incidence) of the probing beam on the device. A secondary effect contributing to this asymmetry is probably the pretilt angle of the LC director [28]. Figure 8 shows the angular scans of the intensity distributions in the far-field diffraction patterns recorded by rotating the photodiode, using a slit aperture (Photodiode 1 in Fig. 3). The driving voltage applied to the odd electrodes of the test-device was adjusted to attain a maximum intensity of the −1 R order. According to the sign conventions above, we show in Fig. 8 the positive and the negative diffraction angles, appearing to the left (counterclockwise) and to the right (clockwise) of the zero order, respectively. All curves in Fig. 8 are normalized to the maximum intensity of the zero reflected order 0 R in the nonactivated state. To estimate the diffractive efficiency of the test device, we have defined and calculated two different parameters. The first parameter is the total diffraction efficiency of the odd orders in the activated state: ηtotal odd ¼

X I m odd =I i ;

ð8Þ

m

where I m odd is the intensity of the mth odd diffraction order and I i is the intensity of the incoming beam. This diffraction efficiency is a measure of the modulation efficiency of the device, as the even diffraction orders are caused by reflection from the static electrode pattern. The second parameter is the modulated diffraction efficiency: ηmodulated

X ¼ I m odd =I total refl ;

ð9Þ

m

where I m odd is again the intensity of the mth odd diffraction order and I total refl is the total intensity of the light reflected from the device in its nonactivated state. Using the results of intensity measurements (Fig. 8), we calculated the dependences of the total diffraction efficiency ηtotal odd and the modulated diffraction efficiency ηmodulated on the effective thickness of the LC cell. The results of these calculations are shown in Fig. 9. As can be seen, the total diffraction efficiency of the odd orders is about 20% in the cell thickness range studied. We attribute this relatively low level of total diffraction efficiency to the small fill factor of the electrode array. Since the fill factor of our test device is only 66.7% (2 μm electrode width divided by 3 μm array pitch), a significant amount of the incoming light is redirected into parasitic reflected and transmitted diffraction orders. Neverthe6322


Fig. 8. Angular distributions of diffraction intensities scanned for nonactivated state (thin curves) and activated state (bold curves) of the test device. Effective thickness of the LC cell: (a) 1:1 μm, (b) 1:7 μm, (c) 2:2 μm, (d) 2:8 μm.

less, the modulated diffraction efficiency is quite high, about 60%, and characterizes the high attainable efficiency of electro-optical spatial light modulation in this 6 μm period or 3 μm equivalent pixel size, ultrasmall pixel LC SLM. Undoubtedly, increasing the fill factor will result in increasing both the total diffraction efficiency and the modulated diffraction efficiency. As observed, both efficiencies gradually decrease with increasing cell thickness. This efficiency reduction, similar to the absence of higherorder diffraction peaks, can be attributed to the smearing or widening of the phase grating profile,

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10. 11. Fig. 9. Total diffraction efficiency of the odd orders (bottom curve) and modulated diffraction efficiency (top curve) versus effective thickness of the LC cell.

caused by the fringing-field effect, which is proportional to the thickness of the LC cell [20,21].

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5. Conclusions

The practical realization of an ultrasmall pixel LC SLM was studied in a simple test device operating as a controllable reflective diffraction grating. The test device based on a patterned electrode array activating a LC cell represents the equivalent of 1D, 3 μm pixel array. A high modulation of the diffraction efficiency of up to 60% was attained in the reflective diffractive mode of operation, using a high-birefringence LC material, showing that the use of a 3 μm pixel array in the visible range is feasible with a careful design of the modulator. It is important to emphasize that the device structure is based on a commonly used driving configuration that does not require precision technique for the alignment of the two LC substrates. A main drawback of the studied test device is the parasitic diffraction from its electrode structure. This can be overcome in future devices by increasing the pixel fill factor.

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The authors gratefully acknowledge the support of the Israeli Science Foundation (ISF). 21.

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