Manaila-Maximean et al. Vol. 15, No. 12 /December 1998 /J. Opt. Soc. Am. B 2975

Bistability and multistability in polymer-dispersedliquid-crystal films

Doina Manaila-Maximean, Constantin Rosu, and Rodica Bena

Department of Physics, University ‘‘Politehnica’’ of Bucharest, Splaiul Independentei,313, Bucharest 77206, Romania

Received July 14, 1998

We have obtained polymer-dispersed liquid-crystal (PDLC) films by using poly(methyl methacrylate) and thenematic liquid crystal E7 in a solvent-induced phase separation method. The optical transmission of thePDLC sample is modulated by application to the sample of a control voltage from a reaction block, which elec-tronically sums a feedback signal, an ac electric signal from an ac generator, and a dc bias voltage; the result-ant signal is proportional to the output optical power detected by a photomultiplier. Because the PDLC filmalso exhibits a quadratic electro-optic effect (Kerr effect), which depends on the control voltage, multistabilityis experimentally obtained. The conditions for obtaining a differential gain and hysteresis are also theoreti-cally analyzed; good agreement with the experimental results is observed. © 1998 Optical Society of America[S0740-3224(98)01312-5]

OCIS codes: 190.1450, 190.0190.

1. INTRODUCTIONAn optical bistable system has two possible states for thesame value of an input parameter, usually the inputpower.1 Obtaining a bistable device with hysteresischaracteristics requires that two conditions be fulfilled:the presence of a nonlinear mechanism, such that a physi-cal property depends nonlinearly on the input power, andthe presence of a reaction mechanism. The opticalbistable devices can be intrinsic (all optics) and hybrid(optics and electronics). In the intrinsic systems the non-linear intensity dependence is due to the direct interac-tion of light with matter. In a hybrid system the lightthat passes through an electro-optic modulator is photo-detected. The electrical signal from the photodetector isintroduced into an electronic processing system, whichcontrols the voltage on the electro-optic modulator.2,3 Weobtained bistable and multistable operations in a hybridsystem by using polymer-dispersed liquid-crystal (PDLC)films as electro-optic modulators.

PDLC films have composite structure and consist ofmicrometer-sized liquid-crystal (LC) droplets embeddedin a solid polymer matrix.4,5 PDLC films can be self-supported and flexible because the polymer matrix isplasticized by the dissolved LC molecules.

PDLC devices exhibit an electro-optical effect becauseof optical heterogeneity between the components and theLC domains or among the LC domains. One achievesswitching between an opaque field-off state and a trans-parent field-on state by matching the ordinary refractiveindex of the LC to the refractive index of the polymer ma-trix. The transmittance of the sample varies continu-ously with the applied electric field.6

PDLC films also exhibit a quadratic electro-optic effect(Kerr effect).7 The Kerr effect consists in the appearanceof birefringence from application of an electric field, so thesample behaves as a uniaxial crystal. On a molecularlevel, the Kerr effect for isotropic materials arises from

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contributions of the molecular hyperpolarizability, per-manent dipole moments, and anisotropic polarizability ofthe constituent molecules. In LC’s the reorientation ofthe molecular director also changes the refractive index ofthe system. In PDLC’s the Kerr effect is due mainly tothe collective reorientation of the LC microdroplets whenan external electric field is applied. The change in therefractive index is proportional to the square of the field,and the corresponding phase shift is proportional to thewidth of the PDLC cell.

2. EXPERIMENTWe obtained PDLC films by using as a polymer matrixpoly(methyl methacrylate) and the nematic LC E7, withthe dielectric anisotropy De . 0. The composite film wasprepared by the solvent-induced phase separationmethod. The polymer and the LC were mixed in a ratioof 60/40 by weight polymer/LC and dissolved in chloro-form; the solution, with an approximate concentration of1:6, was homogenized and spread onto indium tin oxide–coated glasses. The thickness of the resultant cell was 20mm. Bistable and multistable operations were performedon this PDLC cell in the experimental setup shown in Fig.1.8

The input on the sample power P1 was modified with avariable polarizer used as an attenuator. After the laserbeam passes through the PDLC sample, its power is P2and it generates in the photomultiplier a voltage U2 thatis proportional to P2 .

The reaction block combines three signals: the reac-tion signal from the photomultiplier (U2), the dc biasvoltage (Ubdc), and an ac sinusoidal control signal (Ug);the resultant signal is Uc , which is the control voltage ap-plied to the sample.

We measured the transmittance of the sample as afunction of the control voltage for maximum incident light

1998 Optical Society of America

2976 J. Opt. Soc. Am. B/Vol. 15, No. 12 /December 1998 Manaila-Maximean et al.

power and output power P2 while varying input power P1for various control voltages Uc .

3. RESULTS AND DISCUSSIONSA. Theoretical Conditions for Multistable OperationTo demonstrate the existence of optical differential gainand hysteresis in the PDLC sample we analyzed the de-pendence of the transmittance of the sample on controlvoltage Uc . The transmittance of the sample is

T 5 P2 /P1 . (1)

The dependence of input power P1 on the angle a be-tween the polarization directions of the laser beam and ofthe polarizer is of the form

P1 5 P10 sin 2 a, (2)

where P10 is the maximum emerging from the attenuatorpower. Figure 2 shows the dependence P1(a).

When the reaction loop is interrupted, the transmit-tance of the sample satisfies, at Uc 5 constant, the fol-lowing conditions:

T 5 U2~Uc!/U1 5 U20~Uc!/U10 , (3)

where

U1 5 l P1 . (4)

U1 is the voltage from the photomultiplier, correspondingto P1 ;

U2 5 l P2 (5)

is the photomultiplier signal corresponding to P2 ; U10 isthe maximum of U1 ; and U20 is the corresponding voltageprovided by the photomultiplier (for P1 5 P10).

When the reaction loop is established, the control volt-age is

Uc 5 gU2 1 Ubdc , (6)

where g is the gain of the reaction block.To find the conditions for multistable operation we

have to solve the following system of equations:

Fig. 1. Experimental setup for obtaining multistable operation:L, He–Ne laser with 10-mW maximum power; At, polarizer(which acts as a variable attenuator); P1 , input (incident) poweron the sample; P2 , output (emerging) power; Ph, photomulti-plier; RB, reaction block; G, ac generator; U2 , reaction voltagefrom the photomultiplier; Ubdc , bias dc signal; Ug , ac sinusoidalcontrol voltage; Uc , control voltage applied on the sample; G, a.c.generator.

U2 5 U1 3 U20~Uc!/U10 ,

Uc 5 gU2 1 Ubdc . (7a)

Because U1 has the same dependence on a as P1 (U15 U10 sin 2 a), the result is

U2 5 U20~Uc! 3 sin 2 a,

U2 5 ~Uc 2 Ubdc!/g. (7b)

It follows that

~Uc 2 Ubdc!/~g sin 2 a! 5 U20~Uc!. (8)

Equation (8) can be solved graphically as the intersec-tion of the following functions:

f ~Uc! 5 U20~Uc!, (9)

which was experimentally plotted when the reaction loopwas interrupted, and

g~Uc! 5 ~Uc 2 Ubdc!/~g sin 2 a!. (10)

Equation (10) represents a straight line passing throughpoint (Ubdc , 0), with a variable slope m 5 (g sin 2 a)21.When the incident power upon the sample varies fromzero to P10 [and correspondingly U1 P (0, U10)], varyinga in the interval (0, p/2) causes the slope m to vary in therange (`, g21).

Figure 3 plots the dependence of the maximum signalof the photomultiplier on the control voltage Uc [Eq. (9)]and some particular cases of the straight lines that resultfrom Eq. (10).

We observe from Fig. 3 that when P1 P (0, P10) themaximum domain of the control voltage for obtainingmultistability is (Ubdc , Uc max). Uc max is the solution ofequation system (7b) and corresponds to incident powerP10 (when a 5 p/2).

If we increase incident power P1 by increasing a start-ing with the zero value, the operation point given by Eq.(9) will reach point A, where the condition for the firstjump is fulfilled. In this case we have

Fig. 2. Dependence of the input power P1 on the angle betweenthe polarization directions of the laser beam and of the polarizer.

Manaila-Maximean et al. Vol. 15, No. 12 /December 1998 /J. Opt. Soc. Am. B 2977

dU1 /dUc 5 0. (11)

From Eqs. (3) and (7b), the result is that

U1 5 U10 3 ~Uc 2 Ubdc!/gU20~Uc!, (12)

and the jump condition becomes

dU20 /dUc 5 U20~Uc!/~Uc 2 Ubdc!. (13)

Graphically, this means that the straight line given byEq. (10), which passes through point (Ubdc , 0), will betangent at the curve given by Eq. (9) (see Fig. 3). Afterthe jump, the operation point becomes A8.

If when the power is increased the jump condition isfulfilled only once, the operation will be bistable. Whenthe jump condition is fulfilled in several points, multista-bility is obtained.

Fig. 3. Graphic analysis of the multistability operation condi-tion.

Fig. 4. Experimental dependence of the maximum signal of thephotomultiplier on control voltage Uc for maximum incidentpower without a reaction loop.

The hysteresis phenomenon appears because the pointsat which the jump condition is fulfilled have different val-ues when the input power is increased or decreased. InFig. 3 the operation point jumps from A to A8 when theinput power is increased and from B to B8 when the inputpower is decreased.

B. Experimental ResultsIn Fig. 4 we plot the dependence of the signal of the pho-tomultiplier on control voltage Uc for maximum incidentpower and without a reaction loop.

In Figs. 5(a) and 5(b) we represent the experimental de-pendencies of output power P2 on input power P1 forUbdc 5 0 [Fig. 5(a)] and for Ubdc Þ 0 [Fig. 5(b)], when theinput power is increased and decreased. Because thetransfer curve U2 5 U2(Uc) is slightly varying with thefrequency in the 20-Hz–20-kHz frequency range, we per-

Fig. 5. Experimental dependence of output power P2 on inputpower P1 for (a) Ubdc 5 0 V, (b) Ubdc 5 0.1 V.

2978 J. Opt. Soc. Am. B/Vol. 15, No. 12 /December 1998 Manaila-Maximean et al.

Fig. 6. Theoretical dependence of output power P2 on inputpower P1 for (a) Ubdc 5 0 V, (b) Ubdc 5 0.1 V.

Table 1. Values of Input Power P1 (mW) At WhichJump Conditions Are Fulfilled

Incident Power P1

Jump Order

1 2 3

Increasing powerExperimental value 0.32 1.9 4.12Theoretical value 0.78 2.05 4.1

Decreasing powerExperimental value 0.28 0.76 1.34Theoretical value 0.39 0.76 1.22

formed experimental measurements at only one fre-quency of the voltage Ug , v 5 176 Hz. We observedmultistable operation and significant hysteresis, whichare important for applications in electro-optic devices.

Solving the system of Eqs. (7b) for Ubdc 5 0 and forUbdc Þ 0, we obtained the theoretical dependencies of theoutput power versus input power represented in Figs. 6(a)and 6(b), respectively.

In Table 1 we present the theoretical and experimentalvalues of input power P1 at which the jump conditions arefulfilled for increasing and decreasing power P1 incidentupon the sample. The data presented in Table 1 showgood agreement between the theoretical and experimen-tal results, especially at large incident powers.

4. CONCLUSIONSWe obtained PDLC films experimentally, using a nematicLC. These devices combine the electro-optical propertiesof the LC with the mechanical resistance and flexibility ofthe polymer used as a support matrix. We analyzedtheoretically the conditions for obtaining differential gainand hysteresis and reported experimentally multistableoperation controlled by ac voltages. Good agreement be-tween the theoretical and the experimental results wasfound.

The hysteresis that we observed had a significant mag-nitude, which is useful for electro-optic applications, be-cause the device is less sensitive to electric noise, and forpotential applications as multilevel memory.

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