758 OPTICS LETTERS / Vol. 19, No. 10 / May 15, 1994

High-speed analog achromatic intensity modulator

Jay E. Stockley, Gary D. Sharp, Dave Doroski, and Kristina M. JohnsonDepartment of Electrical and Computer Engineering, University of Colorado at Boulder, Boulder, Colorado 80309-0425

Received October 18, 1993

We report what is to our knowledge the first implementation of a broadband analog intensity modulator composedof two chiral smectic liquid-crystal half-wave retarders. A reflection-mode intensity modulator employing a singleactive device has also demonstrated achromatic transmission. A quantitative theory for chromatic compensationis presented. By optimum selection of liquid-crystal retardance and orientation, intensity transmission isuniform throughout the visible. The chiral smectic liquid-crystal devices used in the implementation are capableof switching in less than 20 ,us.

Broadband high-speed light values have numer-ous applications, including spectroscopy, camerashutters, and displays. The intensity modulatorpresented here was independently suggested byAnderson et al.I and by Sharp.2 In Ref. 1 quali-tative predictions on the behavior of a broadbandintensity modulator were presented. Here we pro-vide a quantitative theory for chromatic compensa-tion and include experimental results for what webelieve to be the first implementation of a broadbandanalog intensity modulator based on chiral smecticliquid-crystal retarders.

The transmission-mode achromatic intensity mod-ulator shown in Fig. 1 employs two identical ac-tive half-wave plates between crossed polarizers.The active material is chiral smectic A (SmA*) liq-uid crystal, which provides intensity modulation bymeans of analog molecular rotation about the devicenormal.3 Commercially available SmA* materialsexhibit switching speeds of the order of 20 jus butare limited to a tilt-angle range of less than ±12°at room temperature. 4 However, the cascading oftwo SmA* half-wave retarders of 11.250 tilt angleprovides ample rotation to change the polarizationof incident light by as much as 900. Moreover, thedual modulator can be made wavelength insensitivein the visible by means of chromatic compensation.

The intensity transmission of the modulator canbe analyzed directly by use of the Mueller calculus.5The output Stokes vector SO containing the powertransmission function is derived according to theequation

SO(A, 01, 02) = PXQ(A, 01, 02 )PySi, (1)

where Si is the Stokes vector for the input source,01 and 02 give the orientations of the retarders withrespect to the input polarization, Q is the Muellermatrix describing the active elements, and P. and P,are x- and 9-oriented polarizers, respectively. Tak-ing the source to be 9 polarized, with unity powerspectral density, we see that the first element ofthe output Stokes vector represents the intensitytransmission function. Substitution of the appropri-ate Mueller matrices into the above equation yieldsthe transmission function

T(A, 01, 0 2 ) = 2 (1 -q22), (2)

where qij are the elements of the Mueller matrix Q.For a modulator consisting of two linear retardersthis matrix is given by

Q(A, 01, 02) = W(M, 02 )W(F, 01) - (3)

Here the W's represent the Mueller matrices for theSmA* half-wave retarders having their optic axes ori-ented at 01 and 02 with respect to the input polariza-tion, as shown in Fig. 1. The chromatic retardanceof the active elements, r, is given by

r'(A) = ir -An(A) AOAn(A,) A0

where AO is the half-wave retardance wavelength andAn is the dispersive liquid-crystal birefringence. Letr = w + 8, where 8 is the wavelength-dependentdeparture from the ideal half-wave retardance.

Multiplication of the matrices in Eq. (3) gives

q22 = sin4(8/2) + cos4(8/2)cos[4(0j - 02)]

+ sin2(8/2)cos2(8/2)[cos(401) + cos(402)]. (5)

With ideal half-wave retarders the active structurefunctions as a pure polarization rotator. The rota-tion depends on only the difference between the ori-entations of the optic axes and is independent of theabsolute orientations. However, transmission atother wavelengths depends critically on the absoluteorientations as well. By a recasting of the orienta-tions in terms of a difference and a mean orientationthis dependence can be clearly demonstrated by thefollowing:

01( - 02a 2 , (01 + 02)ayo = V }

An off state (null in the power transmission) can beobtained for any a0 only when the optic axes arecrossed (the structure appears isotropic), giving 01 =a0 + 450 - a, and 02 = a0 - 450 + a.

0146-9592/94/100758-03$6.00/0 © 1994 Optical Society of America

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May 15, 1994 / Vol. 19, No. 10 / OPTICS LETTERS 759

Achromatic Intensity ModulatorTransmission-mode Geometry

Polarizer

Plate

Fig. 1. Schematic for a broadband analog intensitymodulator based on a dual SmA* polarization rotator.The angles 01 and 02 are the absolute orientations of theretarder optic axes with respect to the incident 9-polarizedlight.

Substitution of Eqs. (6) into Eq. (5) simplifies theintensity transmission function of Eq. (2), as follows:

T(A, ao, a) = sin2(4a) - sin2(8/2)sin2 (4a)- (1/2)sin2 8 sin 2(2a)

X [cos(4a) + cos(4ao)].

range. In both cases the transmission spectrum isnearly flat for each value of a over a 250-nm band.

The simulation used to obtain the theoreticalresults assumed half-wave retarders at a designwavelength of 520 nm. The broadband intensitymodulator used to obtain the experimental resultswas built with two SmA* liquid-crystal devices em-ploying British Drug House 764E electroclinic mate-rial designed as zero-order half-wave retarders at awavelength of 520 nm (Ref. 4) (1.6-,um gap). Thesedevices were parallel aligned with polyvinyl alcoholon indium tin oxide-coated substrates. As shown inFig. 1, the two retarders were oriented to tilt in op-posite directions and placed between crossed polariz-ers. The structure was illuminated with a tungsten-filament source. Electric fields varying from -25 to+25 V/,Lum were applied to the devices to change themolecular tilt angle and hence the parameter a.

0.E

P

-2:1

_RI

(7)

Chromatic compensation centers around minimizingthe loss that is due to 8 in the fully on state (a =22.50). By examination of the above equation thisoccurs in general for a0 = ±450. Substituting thisorientation into Eq. (7), we obtain the achromatictransmission function

T(A, a) = sin2(4a) - sin2(8/2)sin2(4a)+ sin2 8 sin4 (2a). (8)

The transmission equation consists of the ideal term[sin2 (4a)] followed by the sum of two chromatic terms.Physically the orientations have been selected suchthat the second retarder doubles the polarization ro-tation of the first while suppressing the ellipticityinduced by the first. In Eq. (8) the transmission isideal at a = 0 and has a loss in transmission ofsin4(8/2) for the extreme tilt condition (a = 22.50).At intermediate tilts chromatic compensation occursthat provides a substantially flat output spectrum.

Figure 2 demonstrates the theoretical advantageof the dual SmA* modulator over that of a singlehalf-wave retarder. The bandwidth for a 3% lossfor the on state of the dual modulator is greaterthan 200 nm, whereas for a single half-wave retarderit is 74 nm. This is because the dual modulatorhas a fourth-order wavelength-dependent loss term,whereas the single retarder has a second-order lossterm.

Figure 3 compares the theoretical (solid curves)and experimental (dashed curves) output transmis-sion spectra of the dual modulator for linearly polar-ized light parameterized by the difference angle a.Although a few representative values of a are shown,the intensity modulation is analog throughout this

450 500 550Wavelength (nm)

600 650

Fig. 2. Theoretical comparison of the bandwidth of theon state of the dual SmA* modulator with the transmis-sion of a single SmA* half-wave retarder between crossedpolarizers and oriented at 456 with respect to the incidentpolarization.

I

EI

E

.7

a = 22.5°…-_ - - _ _ __ -

0.8

0.6

0.4 __-~~~--__ a-1.5

0.2_

0.0 . _._ . . . . . ,I,,..I....I.

450 500 550 600Wavelength (nm)

650 700

Fig. 3. Comparison of theoretical (solid curves) and ex-perimental (dashed curves) transmission spectra for theanalog intensity modulator parameterized by the differ-ence angle a.

760 OPTICS LETTERS / Vol. 19, No. 10 / May 15, 1994

a = 22.5'

1.0 .r= 17.5'

I0.6 H

n 0.4. _

76

E

0.2 F

. . .. .. _L -

- - - - - - --= 6.0' … __ X_.

0.0p -,n 1-- -,°-°- -, - --i - a = 0.0'500 550 600 650

Wavelength (nm)700 750

Fig. 4. Experimental transmission spectrum for the re-flection-mode analog intensity modulator with a singleSmA* device and a compound achromatic quarter-waveretarder. Normalized intensity measurements are pa-rameterized by the difference angle a.

Experimental results compare well with theoreticalpredictions. The transmission intensity for the onstate (a = 22.50) should ideally be unity. However,Fresnel losses at the (noncoated) interfaces of the de-vices and transparent electrode losses result in peaktransmission between 85% and 90% for the exper-imental implementation. If these loss mechanismsare set aside, the measurements are within the ex-perimental error of the theoretical predictions. Thespectral contrast of the dual-modulator implementa-tion is approximately 1000:1 over the 250-nm band-width, where spectral contrast is defined as the ratioof the maximum to minimum intensities at a givenwavelength.

Achromatic intensity modulation by use of a sin-gle SmA* device can be achieved with a reflection-mode geometry consisting of a polarizer, an SmA*retarder, a passive quarter-wave retarder, and a mir-ror. This geometry was suggested by the authorsof Ref. 1. However, their design called for a zero-order quarter-wave retarder, which limits the the-oretical bandwidth because of its chromatic nature.We have implemented the structure, using an achro-matic quarter-wave retarder consisting of three lay-ers of stretched polymer. The passive achromaticquarter-wave retarder and the mirror serve to rotatethe polarization leaving the liquid-crystal retarder on

the initial pass. This changes the coordinate sys-tem so that the reflected optical field encounters theSmA* device with its optic axis reoriented, which isanalogous to the function of the second half-wave re-tarder of the dual modulator discussed above.

The experimental transmission spectrum of polar-ized light for the reflection-mode achromatic inten-sity modulator parameterized by a is shown in Fig. 4.The solid curve near the bottom of the figure is theresponse of the quarter-wave retarder in the absenceof the liquid-crystal device. The dashed curve imme-diately above that is the transmission of the off state.This results were normalized for Fresnel losses pro-ducing an on state transmission of 95%. The re-sponse was highly achromatic, varying only a few per-cent over a bandwidth of 250 nm. The contrast ratiofor this configuration was nominally 50:1.

In summary, we have reported the implementa-tion of a broadband analog intensity modulator witha wavelength range of 250 nm. The transmission-mode intensity modulator, composed of two SmA*liquid-crystal half-wave retarders, has a contrastratio of 1000:1. The off state is nearly ideal, andthe on state exhibits a maximum 6% variation intransmission from 450 to 700 nm. We can achievea simpler implementation in the reflection mode byemploying a single electroclinic device, a passiveachromatic quarter-wave plate, and a mirror. Re-sults for the reflection mode device indicated highlyachromatic behavior over a bandwidth of 250 nm inthe visible and a contrast ratio of 50:1.

We are grateful for technical discussions with ChanOh, Robert Obremski, and Wilbur Kaye of BeckmanInstruments and the support of Beckman Instru-ments Diagnostic Systems Group.

References

1. G. Anderson, I. Dahl, L. Komitov, S. Lagerwall,K. Skarp, and B. Stebler, J. Appl. Phys. 66, 4983(1989).

2. G. Sharp, "Chiral smectic liquid crystal tunable opticalfilters and modulators," Ph.D. dissertation (Universityof Colorado at Boulder, Boulder, Colo., 1992).

3. S. Garoff and R. B. Meyer, Phys. Rev. Lett. 38, 848(1977).

4. The British Drug House mixture BDH 764E is avail-able from Merck Ltd., WestQuay Road, Poole BH151HX, England.

5. W. A. Shurcliff and S. S. Ballard, Polarized Light (VanNostrand, Princeton, N.J., 1964), pp. 87-95.