Holographic polymer-dispersed liquid crystal memoryfor optically reconfigurable gate array using

subwavelength grating mask

Akifumi Ogiwara,1,* Minoru Watanabe,2 Takayuki Mabuchi,2 and Fuminori Kobayashi3

1Department of Electronic Engineering, Kobe City College of Technology,8-3 Gakuen-higashi, Nishiku, Kobe 651-2194, Japan

2Faculty of Engineering, Department of Electrical and Electronic Engineering,Shizuoka University, 3-5-1 Johoku, Hamamatsu, 432-8561, Japan

3Department of Systems Design and Informatics, Kyushu Institute of Technology,680-4 Kawazu, Iizuka, 820-8502, Japan

*Corresponding author: ogiwara@kobe‐kosen.ac.jp

Received 1 September 2011; revised 10 October 2011; accepted 10 October 2011;posted 18 October 2011 (Doc. ID 153366); published 25 November 2011

Holographic polymer-dispersed liquid crystal (HPDLC) memory formed by a subwavelength grating(SWG) mask is presented for new optical information processing. The SWG structure in a photomaskis formedon theSiO2 plateusing theanisotropic reactive ion etching technique.The configuration contextsfor optically reconfigurable gate arrays (ORGAs) are stored in the HPDLC memory by polarization mod-ulationpropertybasedon the formbirefringence of theSWGplate.The configuration contextpattern in theHPDLC memory is reconstructed to write it for the ORGAs under parallel programmability. © 2011Optical Society of AmericaOCIS codes: 090.2900, 160.3710, 160.5470.

1. Introduction

ORGAs have been worthy of notice as a multicontextfield programmable gate array (FPGA) to realize fastand numerous reconfiguration contexts using an op-tical information processing technique [1–8]. As pre-sented in Fig. 1, the ORGAs consist of laser sources,an optical holographic memory, and a programmablegate array VLSI. Because the ORGAs have a per-fectly parallel programming capability without usingany serial transfer, the performance of a parallel pro-grammable gate array VLSI enables perfect avoid-ance of faulty areas; it instead uses the remainingareas. Moreover, holographic memories are wellknown to have high defect-tolerance because each bitof a reconfiguration context can be generated fromthe entire holographic memory. For that reason,

the damage to some fraction of the component rarelyaffects its diffraction pattern or a reconfigurationcontext. Therefore, ORGAs are extremely robustagainst the components defects, such as a laser array,a gate array, and a holographic memory, and are par-ticularly useful for space applications, which requirehigh reliability [7,8]. Thus, holographic memory tostore numerous contexts and to reconstruct themwith high quality is an important part for the ORGAssystem.

TheHPDLCgrating composed of organicmaterials,such as liquid crystal (LC) and polymer, has been ap-plied for grating formation to obtain both high effi-ciency and resolution in the optical function [9–27].The HPDLC grating formed in the grating mediumwith little absorption and scattering showed the highanisotropic diffraction and transparency [24]. The ho-lographic memory to record image information wasalso formed in HPDLC grating by using polarization

0003-6935/11/346369-08$15.00/0© 2011 Optical Society of America

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modulation property of a spatial light modulator, andthe HPDLC memory demonstrated rigorous record-ingwith high diffraction efficiency based on the polar-ization modulation technique [25]. The configurationcontext pattern embedded in the polymer matrix canbe stored based on the parallel light reaction inducedby the laser light exposure as fine periodic structuresproduced by cured-polymer and separated LC dro-plets phases. We showed in a previous paper thatthe diffraction anisotropy in the HPDLC grating de-pended on the droplet shape and size, which were af-fected by process temperature [23]. The anisotropicvolume grating consisting of LC orientation highly or-dered along the grating vector (P polarization) wasformed by controlling grating formation temperature.The anisotropic volume grating can perform high dif-fraction efficiency depending on the incident polariza-tion state of laser light. Furthermore, the HPDLCmemory more effectively supplies the information ofthe configuration context to utilize in theORGA-VLSIby applying the polarization dependence of theHPDLC grating for switching of the configurationcontext pattern reconstructed from theHPDLCmem-ory [28]. Theoptical performance in theHPDLCbasedon the parallel light processing with high diffractionefficiency and transparency is suitable for optical re-configuration in theORGA system. Thus, theHPDLCgrating is expected for a novel holographic memorydevice to demonstrate the ORGAs under parallelprogrammability.

The feature of the light wave in an SWGwhose per-iod is smaller than the wavelengths of the incidentlight is equally considered as that in anisotropic ma-terial, which is known as form birefringence [29–31].Therefore, the polarization modulation techniquebased on the form birefringent microstructure is ex-pected to store the configuration contexts with highresolution in the HPDLC memory. This paper pre-sents the one-time easily writable HPDLC memoryby the effect of form birefringence of SWG fabricated

on the SiO2 plate for application of optically reconfi-gurable gate arrays.

2. Experimental Procedure

A. Sample Preparation

The LC composites for HPDLC memory were pre-pared using mixed prepolymers (Kyoeisha Chem.), 2-hydroxy-3-phenoxy propyl acrylate, 2-hydroxyethylmethacrylate, and dimethylol tricyclo decane diacry-late with LCmaterials [24]. The mixture ratios of theprepolymers were 80, 5, and 15wt:%, and an LCmaterial (Merck BL024) was added to the aforemen-tioned prepolymer mixture at 25wt:% in the fractionof all ingredients. The xanthene dye (Dibromofluor-esceine) and N-phenylglycine were introduced as aphotoinitiator and a coinitiator, respectively. Then,the mixture of the LC material and prepolymers wasinjected and poured into the 10 μm air gap fabricatedby two glass plates with dimensions of 25mm×20mm× 1mm, where gap thickness was preciselymeasured by interferometry.

B. Optical Setup for Device Fabrication

Figure 2 shows an optical setup for formation ofthe HPDLC memory. The green laser (Nd:YVO4,λ ¼ 532nm) of 50mW for photopolymerization waslinearly polarized at a rotation angle of 45° with re-spect to the grating vector of SWG formed in themask using a λ=4 plate and a polarizer. The colli-mated laser light was divided by a half mirror intotwo parallel beams: the reference beam reflectedby a mirror and the object beam transmitted throughthe SWGmask. After the polarization direction of theobject beam was rotated at 90° by a λ=2 plate, the ob-ject beam was incident to the SWG mask includingconfiguration contexts for a logical circuit. The line-arly polarized light of the object beamwasmodulatedto the circularly polarized light by the form birefrin-gence of a subwavelength grating structure formed

Fig. 1. (Color online) Overview of an ORGA comprising a gate array VLSI, a holographic memory, and a laser diode array.

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at a particular region in the SWG mask. Thus, theholographic pattern corresponding to the configura-tion context was recorded in the LC composites byinterferometric exposure composed of the object andreference beams crossed at 30° on the samples con-sisting of LC composites prepared for the HPDLCmemory as the grating spacing of 1 μm based on spa-tially periodic modulation of the refractive index.Based on the result obtained in a previous paper [23],the temperature condition in device fabrication of thesample was adjusted at 50 °C to obtain high anisotro-pic diffraction in the HPDLC grating using the tem-perature controller with a Peltier element in thissetup. The spatially periodic modulation of the re-fractive index is formed by the periodic distributionof LC-rich and polymer-rich phases. The polarizationdependence of diffraction efficiency is related to theanisotropy formed in the periodic distribution of LC-rich and polymer-rich phases. Diffraction efficiency ismainly dominated by the amplitude of the refractiveindex modulation generated by phase separation be-tween LC-rich and polymer-rich regions, where sucha composition gradient forms a spatially transmis-sive volume grating. Furthermore, the polarizationstate of the diffraction is related to the birefringenceof LC molecules and the morphology of LC droplets.Our previous observations strongly suggested thatby increasing the grating formation temperature, thelayers of LC and cured polymer phases in the grat-ings were well formed and a coalesced LC dropletconfiguration with small droplets was obtained [23].LC molecules are considered to be more strongly or-iented in the small droplets, and consequently, theLC orientation produces a highly polarized diffrac-tion. The optical anisotropy of diffraction in theHPDLC grating formed at a temperature of 50 °C bythe temperature controller in Fig. 2 based on the pre-vious results [23] is consistent with the considerationthat the LC molecules in the droplets are alignedalong the grating vector, or the direction of P polar-ization in other words.

C. Microscopic Observation Method

A polarizing microscope (Olympus CX31-P) using anobjective lens of 100× with a numerical aperture of0.80 and a long working distance of 1:2mm was usedto observe the polarizationmodulation property of anSWG mask. The SWG mask was placed between thepolarizer and the analyzer arranged under crossedNicole conditions, and then the form birefringencewas observed at several polarization angles. Thestructure of an SWG mask was investigated by scan-ning electron microscopy (SEM; Hitachi S-4300). ForSEM, the grating sample was cut along the directionparallel to the grating vector, and the cross-sectionalviews of the grating structure were observed byseveral magnifications.

3. Results and Discussion

A. Subwavelength Grating Mask

The grating pattern was fabricated using an SiO2plate with dimensions of 25mm × 25mm × 1mm. Asubwavelength grating composed of both line andspace widths of 200nm was formed in a square re-gion of 40 μm× 40 μm using the electron beam litho-graphy. The anisotropic etching process was appliedto design the ratio of depth to groove to be high. Aneutral magnetic loop discharge (NLD) plasma etch-er (NLD-800: ULVAC) was used for the anisotropicetching process. The NLD plasma was produced withan RF power of 1500W and a bias power of 400W.The working gases were CF4 and CH2F2 with overallpressure of 0:8Pa, and flow rates were 20 and11 sccm, respectively, and the etching time was 120 s.

The effect of form birefringence on the formed grat-ing pattern is important for the formation of HPDLCmemory towrite the configuration context. Therefore,an investigation using the polarization microscopewas conducted in detail as follows. Figure 3 showsimages of the subwavelength grating mask formedin the SiO2 plate observed at the crossed Nicole con-dition byapolarizingmicroscope. TheSWGmaskpat-tern was designed corresponding to the location of

Fig. 2. (Color online) Optical setup for fabricating HPDLCmemory using a laser interferometer with a subwavelength grating mask. Thepolarization modulation conditions, such as linearly polarized and circularly polarized lights, are shown in light passes using differentarrows.

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photodiodes in the ORGA-VLSI chip, shown in Fig. 1.The arrows top of the images represent the directionsof the polarizer (P) andanalyzer (A) in themicroscope.Figure 3(a) shows the image corresponding to the con-text pattern for the OR circuit observed at 45° withrespect to P. Here, OR means logical OR operationfor OR gate. Figure 3(b) shows the image by magnifi-cation of one pixel in Fig. 3(a) observed at 45° with re-spect to P, while Fig. 3(c) shows the same imageobserved at 0° with respect to P. The bright image co-mposed of several pixels for the OR circuit is observed

in Fig. 3(a) when the grating vectors in the SWG aretilted at 45° with respect to P. Figures 3(b) and 3(c)shownbymagnification of onepixel in the context pat-tern show the effect of form birefringence in the fab-ricated SWG. Figure 3(b) shows the bright image ofsquare configuration when the grating vectors in theSWG are tilted at 45° with respect to P, while Fig. 3(c)shows the dark image when the direction of P in thepolarizedmicroscope is placedat0°with respect to thegratingvector of theSWG.Fromthe comparisonof theimages by polarization microscopy, we can confirmthat the SWGmask presents the effect of polarizationmodulation based on the form birefringence of thefabricated grating.

Figure 4 shows SEM cross-sectional views to inves-tigate the internal volume structure formed in theSWGmask in detail. The configurations of Fig. 4 cor-respond to those of the SWGmask used in Fig. 2. Theimage of a whole pixel is shown in Fig. 4(a), and theclose-up view of the grating structure is shown inFig. 4(b). From Fig. 4(b), the period of 400nm com-posed of the equivalent width of line and space is ob-served, and the height of 1:7 μm is estimated; as aresult, the ratio of the height to period defined as

200µm

Fig. 3. Images of subwavelength gratingmask formed in the SiO2

plate observed at the crossed Nicole condition with polarizer (P)and analyzer (A) by a polarizing microscope. (a) The image corre-sponding to the context pattern for the OR circuit observed at 45°with respect to P, (b) the image by magnification of one pixel in (a),and (c) the image observed at 0° with respect to P of (b).

Fig. 4. SEM cross-sectional views of (a) a pixel region and (b) aclose-up view of grating in subwavelength grating mask.

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aspect ratio is 4.25. Based on the experimental re-sults, the effect of form birefringence in the fabri-cated SWG is described in the following [29].

Effective refractive indices for TE and TM wavesare expressed by

nTE ¼ ff × n21 þ ð1 − f Þ × n2

2g1=2; ð1Þ

nTM ¼ ff × n−21 þ ð1 − f Þ × n−2

2 g−1=2; ð2Þ

where f is a filling factor, which is the ratio of thelinewidth to period (in this case, f is obtained as0.5), and n1 and n2 are refractive indices of air(n1 ¼ 1:0) and SiO2 substrate (n2 ¼ 1:46). Usingthe Eqs. (1) and (2), effective refractive indices arecalculated as nTE ¼ 1:251 and nTM ¼ 1:167. Thephase modulation (δ) of the SWG is expressed by

δ ¼ ðnTE − nTMÞ ×H; ð3ÞwhereH is the height of the grating. The phase mod-ulation (δ) is obtained as 0.143 using the height of1:7 μm for the grating. The phase modulation of fab-ricated SWG approximately corresponds to that of aquarter-wave plate for the incident green laser light(λ ¼ 532nm). The formation of HPDLC memory isconducted by writing the configuration context ofthe OR circuit pattern using the phase modulationproperty of the SWG mask. Though the green light(λ ¼ 532nm) is used to induce a phase separationin the LC composites materials with a photoinitiatorand a coinitiator, the structure shown in Fig. 4(b) isno longer the subwavelength structure for the wave-length less than 400nm. The approach to adjust thegap thickness than 10 μm in the HPDLC gratingstructure is considered to be effective in order to raisethe memory density of the HPDLC memory.

B. Generation of Holographic Memory

Figure 5(a) shows a block diagram of the experimen-tal system. The configuration system comprises a la-ser source, an HPDLC memory, and an ORGA-VLSI.A green laser with the same wavelength at devicefabrication was used as the laser source to recon-struct a context pattern. Figure 5(b) shows a photo-graph of three-dimensional alignment of the HPDLCmemory and the ORGA-VLSI. The HPDLC memory,recorded using the SWG mask designed for an ORcircuit, was placed 100mm in front of the ORGA-VLSI. Figure 5(c) shows the context for the OR circuitreconstructed by the expanded laser beam illumi-nated diagonally at an angle of 30° on the HPDLCmemory, and it was written to the ORGA-VLSI forconfiguration generation. Figure 5(d) shows the con-text pattern for the OR circuit shown in Fig. 3(a),which was reoriented by reversal of right and leftand counterclockwise rotation of 45°. There are dif-ferences in the observation direction and the positionto detect these two figures, that is, Fig. 3(a) is ob-served in fore surface of the SWG mask tilted at 45°

while Fig. 5(c) is observed behind of the pattern re-constructed from the HPDLC memory at horizontalposition. Therefore, Fig. 5(d) is reoriented to adjustthe alignment of array spots with that of Fig. 5(c).The array spots of Fig. 5(d) are identical to thoseof Fig. 5(c), though the spot positioned at the topof left-hand side is missing because it was outer fromobservation region of the polarization microscope.The patterns comprising the white and dark pointssignifying binary states as H and L, can be clearlyobserved, respectively. The positioning adjustmentsof the HPDLC and ORGA-VLSI could be executedby frequently executing configuration proceduresand by monitoring the circuit executions of the con-figured gate array on the ORGA-VLSI.

C. Optically Configuration Using Holographic Memory

The ORGA-VLSI was fabricated using a complemen-tary metal-oxide-semiconductor process chip of4:9mm × 4:9mm, consisting of three metal layersof 0:35 μm. The ORGA-VLSI chip has four logicblocks, five switching matrices, 12 I=Obits, and 68gates. The 340 photodiodes having a size of25:5 μm× 25:5 μm, and a distance of 90 μm was fabri-cated in the chip by an arrangement of 20 × 17.Although the basic part of the VLSI chip is basedon the typical FPGAs, each programming elementof all blocks of the ORGA-VLSI has connection toan optical reconfiguration circuit to detect an opticalconfiguration context. Moreover, the logic block con-sists of a four-input one-output lookup table and adelay flip-flop with a reset function. These functionsare optically reconfigurable using 40 optical reconfi-guration circuits. Similarly, switching matrices canbe reconfigured optically through 12–24 optical con-nections, and each I/O block is also controlledthrough nine optical connections. Thus, the VLSIpart can achieve a perfectly parallel configuration.

A configuration procedure was confirmed using theoptical reconfiguration systemshown inFigs. 5(a) and5(b). In the configuration system composed of a lasersource, an HPDLC memory, and an ORGA-VLSI, agreen laser with the same wavelength at device fab-rication was used as the laser source to reconstruct acontext pattern. The laser beam was expanded twotimes by two lenseswith 50 and 100mmfocal lengths,and the expanded beam was incident to the HPDLCmemory. The HPDLC memory recorded using anSWG grating mask designed for an OR circuit wasplaced 100mm in front of the ORGA-VLSI, as shownin Fig. 5(b). The context for the OR circuit was recon-structed by the expanded laser beam illuminateddiagonally from the bottom side at an angle of 30°on the HPDLC memory, and it was written to theORGA-VLSI for configuration generation. Both theHPDLC memory and the ORGA-VLSI were placedon xyz-3-stages with 0:5 μm resolution for eachdirection, and adjusted by monitoring the circuitexecutions of the configured gate array on the ORGA-VLSI. The reconstructed intensity from the HPDLC

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memory shown in Fig. 5(c) was incident to the photo-diode arrays inORGA-VLSI placed 100mmbehind it.

After the configuration procedure, the configura-tion period wasmeasured as 20 μs, as shown in Fig. 6.Here, the configuration period is defined as the sum-mation of a refresh period, a configuration irradia-tion period, and a setup and hold time of flip-flops.Each configuration procedure is executed by char-ging the junction capacitance of photodiodes, the op-eration of which means the refresh period, then byturning one laser on, the operation of which meansthe configuration irradiation period, and finally byrising a configuration clock signal, the operation ofwhich includes a setup and hold time of flip-flops.The configuration clock signal is connected to all

configuration flip-flops to keep the state of a pro-grammable gate array on ORGA-VLSI.

As shown in Fig. 6, the output signal became highstate ð1Þ for input1 and input2, which were low ð0Þand high ð1Þ states when the configuration clock sig-nal was raised at 20 μs. At 37:5 μs, the output signalmaintained high state ð1Þ when input1 changed tohigh state ð1Þ from low state ð0Þ. At 93:75 μs, the out-put signal changed to low state ð0Þ when input1 andinput2 changed to low states ð0Þ from high states ð1Þ.At 143:75 μs, the output signal changed to high stateð1Þ from low state ð0Þ when input1 changed to highstate ð1Þ from low state ð0Þ. Thus, we can observe thatORGA-VLSI executed logical OR operation correctlyby HPDLC memory generation for the OR circuit.Though the measured reconfiguration period was

Fig. 5. (Color online) Optical system for the configuration generation by reconstruction using HPDLC memory: (a) block diagram of theexperimental system, (b) alignment of the HPDLC memory placed in front of the ORGA-VLSI, (c) context image for OR circuit recon-structed by HPDLCmemory generation, and (d) the context pattern for the OR circuit shown in Fig. 3(a), which was reoriented by reversalof right and left and counterclockwise rotation of 45°.

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longer than the previous result [8], it was sufficientlyshorter than currently available FPGAs. The time isconsidered to be accelerated by reducing the area forone pixel of the OR circuit pattern formed in the SWGmask since the reconstructed light intensity from theHPDLC memory can be efficiently incident to thephotodiode arrays in ORGA-VLSI. The significanceof the result concerning configuration procedure isthe execution of the parallel programmability usingthe optical information processing technique. There-fore, our proposed polymer-dispersed LC holographicmemory was sufficiently demonstrated for opticallyreconfigurable gate array.

4. Conclusions

This paper reported the formation of holographicmemory using an SWG mask in LC composites fornew ORGA architecture. The polarization modula-tion properties based on the form birefringence inthe fabricated SWG were investigated by polariza-tion microscopy. The volume structure of an SWGmask was confirmed by the SEM observations thatgrating structure was composed of line and spacewidths of 200nm and the height of 1:7 μm. The func-tion of polarization modulation in the SWG was es-timated to be similar to a quarter-wave plate forgreen laser light (λ ¼ 532nm). The HPDLC memoryfabricated by the SWG mask clearly reconstructedthe configuration context of OR circuit information,and the configuration procedure was confirmed usingthe optical reconfiguration system.

The HPDLC memory can be applied to ORGAs torealize parallel programmability and fast reconfi-guration. The HPDLC is suitable for parallel lightprocessing with photodiode arrays and fast reconfi-guration will be realized.

References1. J. Mumbru, G. Zhou, X. An, W. Liu, G. Panotopoulos, F. Mok,

and D. Psaltis, “Optical memory for computing and informa-tion processing,” Proc. SPIE 3804, 14–24 (1999).

2. J. Mumbru, G. Zhou, S. Ay, X. An, G. Panotopoulos, F.Mok, andD. Psaltis, “Optically reconfigurable processors,” Proc. SPIECR74, 265–288 (1999).

3. J. Mumbru, G. Panotopoulos, D. Psaltis, X. An, F. Mok, S. Ay,S. Barna, and E. Fossum, “Optically programmable gatearray,” Proc. SPIE 4089, 763–771 (2000).

4. M. Watanabe and F. Kobayashi, “Dynamic opticallyreconfigurable gate array,” Jpn. J. Appl. Phys. 45, 3510–3515(2006).

5. N. Yamaguchi and M. Watanabe, “Liquid crystal holo-graphic configurations for ORGAs,” Appl. Opt. 47, 4692–4700(2008).

6. D. Seto andM. Watanabe, “A dynamic optically reconfigurablegate array—perfect emulation,” IEEE J. Quantum Electron.44, 493–500 (2008).

7. M. Nakajima and M. Watanabe, “Optical buffering techniqueunder a space radiation environment,” Opt. Lett. 34, 3719–3721 (2009).

8. A. Ogiwara, M. Watanabe, T. Mabuchi, and F. Kobayashi,“Formation of holographic memory for defect tolerance in op-tically reconfigurable gate arrays,” Appl. Opt. 49, 4255–4261(2010).

9. R. L. Sutherland,V. P. Tondiglia, L.V.Natarajan,T. J. Bunning,and W. W. Adams, “Electrically switchable volume gratingsin polymer-dispersed liquid crystals,” Appl. Phys. Lett. 64,1074–1076 (1994).

10. T. Karasawa and Y. Taketomi, “Effects of materials system onthe polarization behavior of holographic polymer dispersed li-quid crystalgratings,”Jpn.J.Appl.Phys.36, 6388–6392 (1997).

11. A. Ogiwara, Y. Kuratomi, T. Karasawa, A. Takimoto, and S.Mizuguchi, “PS polarization converting device for LC projec-tor using holographic polymer dispersed liquid crystal films,”SID Int. Symp. Dig. Tech. Pap. 30, 1124–1127 (1999).

12. K. Kato, T. Hisaki, and M. Date, “Alignment-controlled holo-graphic polymer dispersed liquid crystal for reflective displaydevices,” Jpn. J. Appl. Phys. 38, 805–808 (1999).

13. J. J. Butler andM. S. Malcuit, “Diffraction properties of highlybirefringent liquid-crystal composite gratings,” Opt. Lett. 25,420–422 (2000).

14. T. J. Bunning, L. V. Natarajan, V. P. Tondiglia, and R. L.Sutherland, “Holographic polymer-dispersed liquid crystals(H-PDLCs),” Annu. Rev. Mater. Sci. 30, 83–115 (2000).

15. C. C. Bowley and G. P. Crawford, “Diffusion kinetics of forma-tion of holographic polymer-dispersed liquid crystal displaymaterials,” Appl. Phys. Lett. 76, 2235–2237 (2000).

16. R. L. Sutherland, V. P. Tondiglia, L. V. Natarajan, and T. J.Bunning, “Evolution of anisotropic reflection gratings formedin holographic polymer-dispersed liquid crystals,” Appl. Phys.Lett. 79, 1420–1422 (2001).

17. J. J. Butler, M. S. Malcuit, and M. A. Rodriguez, “Diffractiveproperties of highly birefringent volume gratings: investiga-tion,” J. Opt. Soc. Am. B 19, 183–189 (2002).

18. R. L. Sutherland, “Polarization and switching properties ofholographic polymer-dispersed liquid-crystal gratings. I.Theoretical model,” J. Opt. Soc. Am. B 19, 2995–3003 (2002).

19. R. L. Sutherland, L. V. Natarajan, V. P. Tondiglia, S.Chandra, C. K. Shepherd, D. M. Brandelik, and S. A. Siwecki,

Fig. 6. (Color online) Implementation results of an OR circuit. The OR circuit was configured and could be executed correctly as seen inthe downside three signals, which are two input signals and one output signal of the OR circuit, respectively. The configuration period wasmeasured as 20 μs.

1 December 2011 / Vol. 50, No. 34 / APPLIED OPTICS 6375

“Polarization and switching properties of holographic polymer-dispersed liquid-crystal gratings. I. Experimental investiga-tions,” J. Opt. Soc. Am. B 19, 3004–3012 (2002).

20. M. E. Holmes andM. S. Malcuit, “Controlling the anisotropy ofholographic polymer-dispersed liquid-crystal gratings,” Phys.Rev. E 65, 066603-1 (2002).

21. Y. Lu, F. Du, and S. T. Wu, “Polarization switch using thickholographic polymer-dispersed liquid crystal grating,” J. Appl.Phys. 95, 810–815 (2004).

22. R. L. Sutherland, V. P. Tondiglia, L. V. Natarajan, andT. J. Bunning, “Phenomenological model of anisotropic volumehologram formation in liquid-crystal-photopolymer mixtures,”J. Appl. Phys. 96, 951–965 (2004).

23. A. Ogiwara, H. Kakiuchida, M. Tazawa, and H. Ono, “Analysisof anisotropic diffraction gratings using holographic polymer-dispersed liquid crystal,” Jpn. J. Appl. Phys. 46, 7341–7346(2007).

24. A. Ogiwara, M. Minato, S. Horiguchi, H. Ono, H. Imai,H. Kakiuchida, and K. Yoshimura, “Diffraction properties ofanisotropic volume gratings formed in polymer-dispersedliquid crystal,” Jpn. J. Appl. Phys. 47, 6688–6694 (2008).

25. A. Ogiwara and T. Hirokari, “Formation of anisotropicdiffraction gratings in a polymer-dispersed liquid crystal by

polarization modulation using a spatial light modulator,”Appl. Opt. 47, 3015–3022 (2008).

26. A. Ogiwara, H. Kakiuchida, K. Yoshimura, M. Tazawa,A. Emoto, and H. Ono, “Effects of thermal modulation ondiffraction in liquid crystal composite gratings,” Appl. Opt.49, 4633–4640 (2010).

27. A. Ogiwara, “Effects of anisotropic diffractions on holographicpolymer-dispersed liquid-crystal gratings,” Appl. Opt. 50,594–603 (2011).

28. T. Mabuchi, M. Watanabe, A. Ogiwara, and F. Kobayashi,“Optically reconfigurable gate array with a polymer-dispersedliquid crystal holographic memory,” in 2011 NASA/ESAConference on Adaptive Hardware and Systems (IEEE, 2011),pp. 44–49.

29. I. Richter, P.-C. Sun, F. Xu, and Y. Fainman, “Design consid-erations of form birefringent microstructures,” Appl. Opt. 34,2421–2429 (1995).

30. H. Kikuta, Y. Ohira, and K. Iwata, “Achromatic quarter-waveplates using the dispersion of form birefringence,” Appl. Opt.36, 1566–1572 (1997).

31. G. P. Nordin and P. C. Deguzman, “Broadband form bire-fringent quarter-wave plate for the mid-infrared wavelengthregion,” Opt. Express 5, 163–168 (1999).

6376 APPLIED OPTICS / Vol. 50, No. 34 / 1 December 2011