February 15, 1994 / Vol. 19, No. 4 / OPTICS LETTERS

High-speed analog refractive-index modulator that usesa chiral smectic liquid crystal

Anat Sneh, Jian-Yu Liu, and Kristina M. Johnson

Optoelectronic Computing Systems Center, Campus Box 425, University of Colorado at Boulder, Boulder, Colorado 80309-0425

Received September 2, 1993

We demonstrate a fast liquid-crystal analog phase modulator composed of a homeotropically aligned electroclinicchiral smectic liquid crystal. Pure phase modulation is obtained by electrical modulation of the refractive indexof the liquid crystal. A refractive-index change of 0.045 can be obtained at a 5-its switching speed with a15-V/tm applied electric field by use of the commercial electroclinic chiral smectic liquid crystal mixtureBDH764E. This results in a 7r phase modulation depth at A = 0.633 ,um in a device of 10-,zm thickness.

Modulation of light by nematic liquid crystals is amature technology offering a host of applicationsincluding data displays, spatial light modulators,1and tunable filters.2 These devices feature a largemodulation depth, good contrast ratio, and low powerdissipation and cost. One major disadvantage ofnematic liquid crystals that limits the applicabilityof these materials is their slow switching speeds(approximately of the order of milliseconds). A morerecent class of liquid crystals, the surface-stabilizedferroelectric liquid crystals3 (SSFLC's), offer orders-of-magnitude-faster switching speeds (approxi-mately of the order of microseconds) and bistability.SSFLC's are basically binary switching devices thatare not capable of either analog intensity or analogphase modulation. SSFLC's are part of the chiralsmectic liquid-crystal (CSLC) class of liquid crystals.Another member of the CSLC family is the nontiltedsmectic A* phase (SmA*). Under the influence ofan applied electric field a molecular tilt is inducedin this phase that is nearly a linear function ofthe applied electric field. This field-induced tilt,called the electroclinic effect, was first described andobserved by Garoff and Meyer.4 Compared withSSFLC devices, electroclinic CSLC's have analogmodulation capability, higher switching speeds(microsecond and submicrosecond response timesare achievable at room temperature), and smallerinduced tilt angles (current maximum measuredvalues are 20-22°). Parallel aligned electroclinicCSLC's are capable of analog intensity modulation;however, phase modulation cannot be obtained in asimple straightforward configuration.5

Early investigations of the electroclinic effect wereperformed by use of the homeotropic alignment.4 6

Garoff and Meyer probed the critical phenomenanear the smectic A* to smectic C* transition by mon-itoring the amplitude and relative electronic phasedelay between the electroclinic response of their sam-ple and an applied electric field. However, molecu-lar tilt angles and response times of the electrocliniceffect in the homeotropic alignment were not pre-sented in their study. Furthermore, the possibilityof obtaining pure phase modulation rather than in-

tensity modulation was not discussed. Anderssonet al. studied the electro-optic properties of theelectroclinic effect in the surface-stabilized parallelaligned geometry.7'8 With this geometry it is easierto detect and measure the electroclinic response toan applied electric field. Large molecular tilt val-ues (.10°) were reported by use of electric fields of-30 V/,um. However, direct phase modulation can-not be obtained with the simple device geometrygiven in Refs. 7 and 8.

In this Letter we report switching-speed and tilt-angle measurements of an electroclinic CSLC celloperating as an analog phase modulator. This de-vice has a similar cell configuration to that of Refs. 4and 6; however, a 2-order-of-magnitude-smaller spac-ing between the electrodes is used. Large tilt an-gles (-10) and fast response times (-2 ,us) arereported for what we believe to be the first time in thehomeotropic alignment. The homeotropic alignmentis shown to have a different effect on the electro-opticproperties of electroclinic CSLC devices, as comparedwith parallel aligned electroclinic devices.

In the homeotropic alignment of CSLC's the smec-tic layers are formed parallel to the confining glassplates, as shown in Fig. 1. For a parallel aligned cellthe smectic layers are oriented perpendicular to theplates. When an electric field is applied along they axis (as shown in Fig. 1) a rotation of the molec-ular director in the x-z plane in induced, result-ing in a change of the angle between the molecu-lar director (optic axis) and the incident beam di-rection (z axis). This field-controlled deflection ofthe optic axis modulates the extraordinary indexof refraction, as seen from the known dependenceof the extraordinary index of refraction on the an-gle 6 between the optic axis and an incident beam:

'e(0) = rsin2 + cos2(6)] , (1)

where nO is the ordinary index of refraction andne is the extraordinary index of refraction for 0 =900. Pure phase modulation is induced if light ispolarized along the extraordinary-polarization direc-

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306 OPTICS LETTERS / Vol. 19, No. 4 / February 15, 1994

FxY a

Z I nclIdent Beam Incident BeamElectrodes Electrodes

I/ l vIii X\ LC Molecules LC Molecules

Smectic layers Smectlc layers

Glass Substrates Glass Substrates

(a) (b)Fig. 1. Homeotropically aligned chiral smectic A* cell.(a) Off state (V = 0); the molecules are aligned perpen-dicular to the glass substrates. (b) On state (V 0 0);the molecules tilt in the x-z plane. For clarification theelectrodes appear planar rather than extending down tothe lower substrate, as they actually do.

tion. Homeotropically aligned electroclinic CSLC'sare therefore capable of analog phase or intensitymodulation.

We present measurements made on a homeotropi-cally aligned SmA* liquid-crystal cell prepared as fol-lows. A metal layer of 2.3-ttm thickness is depositedonto an optical flat (A/10) fused-silica substrate. An18-,Am-wide channel is etched in the metal film,which acts both as the electrodes and spacers, permit-ting an electric field to be applied in the x-y plane.We achieve the homeotropic alignment by using cetyl-trimethyl-ammonium-bromide surfactant applied tothe above substrate and a second optical flat. Theliquid crystal used in this study is the commerciallyavailable electroclinic mixture BDH764E,9 which un-dergoes the following phase transitions9:

- ~~89-92°C *73°C 28°CI 59-2, N* 730c SA* SC*

As shown in Fig. 1 and described by Eq. (1), whenan electric field is applied along the y axis a mod-ulation of the extraordinary index of refraction oc-curs, and the cell retardation is modified. In orderto enhance the modulation depth the sample cell istilted around the y axis to form oblique incidence inthe x-z plane (see Fig. 1). This phase modulationis then converted into intensity modulation when thecell is sandwiched between a pair of crossed polariz-ers. We maximize the intensity modulation by rotat-ing the optic axis in the glass substrates plane (x-yplane) to form an angle of 450 with respect to the ori-entation of a crossed-polarizers pair.

We performed the measurements by applying anac square wave across the cell and monitoring themodulated output intensity change as a function ofthe square-wave amplitude. The frequency of theapplied field is 500 Hz to avoid hydrodynamic flowduring the measurements. The intensity readingsare taken with a silicon p-i-n photodiode and a dig-ital storage oscilloscope (Hewlett-Packard 54201A).The sample temperature is controlled to within 0.1 0C

stability, and the accuracy of the temperature read-ings is within 0.5 0C. Typical data obtained for400 oblique incidence from air are shown in Fig. 2.Molecular tilt-angle values are obtained from themeasured intensity change by use of computer cal-culations of expected intensity modulation versusknown tilt angles of the optic axis. The measure-ment error is approximately ±0.3°.

Comparison of the molecular tilt-angle resultsgiven in Fig. 2 with the tilt angles obtained at thesame conditions (i.e., temperature and electric field)with parallel aligned surface-stabilized BDH764Ecells9 shows a smaller electroclinic response forthe homeotropically aligned cells. The differenceis reduced at higher temperatures within the SmA*phase. This may be attributed to the different dis-tribution of the surface anchoring forces relative tothe smectic layers' orientation in the homeotropicalignment (the surface anchoring forces penetrateacross the smectic layers rather than parallel tothem). This geometry of anchoring forces' distribu-tion along with the fact that the anchoring forces inthe homeotropic alignment are weaker than those inthe parallel alignment may cause the cell to appearwarmer when homeotropically aligned. Evidence ofa downward shift in the A*-C* transition tempera-ture of BDH764E as the anchoring forces' strength isreduced is reported in Ref. 10.

By examination of Eq. (1) it is evident that thelargest modulation depth is obtained when the off-state angle 6(E = 0), defined here as 00, is 45°.For an 80 electroclinic tilt obtained at a temperaturejust above the A*-C* transition temperature (280C)with 15 V/,um, and based on the BDH764E index-of-refraction values,1" the refractive-index modulationobtained for 00 = 450 is 0.045. The resulting phasemodulation AO is given approximately by

Ad = Av An(6)cos(0O)l, (2)A

where A is the operating wavelength, An(6) is theextraordinary index-of-refraction modulation, and Iis the device thickness. For A = 0.633 ,-m, An(6) =

0

z

-J

-Iu 0 To A

6 -0

0 A

2 Oil .

u.A8

0-0

T=23 0CT=25 0CT=27 00T=29 00T=31 00T=40 00

5 10 15 20

FIELD [V/gm]

Fig. 2. Induced molecular tilt angle as a function ofapplied electric field at various temperatures. The tiltvalues were computed from measured intensity changevalues taken with the cell tilted by an angle of 400 withrespect to the optical beam direction.

To

February 15, 1994 / Vol. 19, No. 4 / OPTICS LETTERS

25

U)

w=LW

C/)z0ELCa)cc

20

;15

10

5-

0 0 5 10

FIELD [V/4tm]15 20

Fig. 3. Optical response (10-to-90%) rise time versusapplied electric field at various temperatures below andwell above the A*-C* phase-transition temperature.The response becomes field independent when thetemperature is well within the linear region of theelectroclinic effect.

0.045, and 00 = 450, obtaining ir phase modulationrequires a device thickness of 10 ,um. In general, atemperature change of 1.5-2 0C would result in a 10%change in the amount of phase modulation obtained.

Another way to obtain a high off-state angle Ooto increase the modulation depth is to align themolecules in a tilted position with respect to theglass substrates. In this case normal incidence isemployed instead of oblique incidence. This can beachieved by use of a suitable surface treatment, e.g.,oblique evaporation of SiOx.l2 We used antiparalleloblique evaporation of SiO. at an 80' angle of in-cidence to pretilt the liquid-crystal molecules. Pre-liminary results that we obtained with BDH764E insample cells prepared with lateral electrodes showedmolecules pretilts from the surface of 300 ± 50. Thiswas measured conoscopically by the moving isogyremethod."3 The expression for the phase modulationin this case is similar to the one given in relation (2);however, the cos(00) term is set equal to 1.

We studied the switching speed of the homeotrop-ically aligned electroclinic CSLC device-by applyingan ac electric field at a 1-kHz frequency and mea-suring the 10-to-90% response times at varying fieldstrengths (see Fig. 3). At 15 V/,-m and T = 40 0Cthe response time is 2.5 ,us. As this figure shows,the dependence of the liquid-crystal switching speedon the electric field decreases as the temperature in-creases into the more linear region of the electrocliniceffect. Brodzeli et al. observed the switching speedof a homeotropically aligned SmC* to be faster thana parallel aligned SSFLC, possibly because of weakersurface anchoring forces.'4 Our measurements ofthe electroclinic response times in both configura-tions agree with these observations. For example,parallel alignment of BDH764E by use of rubbed ny-lon 6 produces switching times that are roughly twoto three times slower than those obtained with thehomeotropic alignment.'"

In summary, we have demonstrated a microsecond-switching analog phase modulator, using homeotrop-ically aligned electroclinic CSLC's. , The electro-optic

properties of this device have been characterized,showing large tilt angles of as much as 100 andswitching speeds of less than 8 I-s with a 15-V/pumapplied electric field. A 7T phase modulation depthcan be obtained at A = 0.633 /,tm, with a devicethickness of 10 -m and oblique incidence insidethe liquid crystal of 45°. Homeotropically alignedelectroclinic CSLC modulators can be implementedin a large variety of applications, including diffrac-tive optics, adaptive optics, optical interconnections,spectroscopy, wavelength-division multiplexing, andthree-dimensional displays.

We gratefully acknowledge the support of the Na-tional Science Foundation/Faculty Award for Women1536740, the IBM T. J. Watson Research Center,and Beckman Instruments, Inc. We also thankDave Doroski for preparing the liquid-crystal cells,Fu-Yuan Wang for his design and construction of ahigh-voltage pulse generator, and Kenneth Marshallof the Laboratory for Laser Energetics, University ofRochester, for supplying the index-of-refraction dataon the BDH764E.

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15. A. B. Davey and W. A. Crossland, Ferroelectrics 114,101 (1991).l

. T=25'C0 T=31 'C\ T=40'C

307