Polarization insensitive modulator based on deformed helix ferroelectric liquid crystals. W.Haase' ,F. Podgornov1, E.Pozhidaev2. 'Institute of Physical Chemistry, ...
Polarization insensitive modulator based on deformed helix ferroelectric liquid crystals W.Haase' ,F. Podgornov1 , E.Pozhidaev2 'Institute of Physical Chemistry, Darmstadt University of Technology, Petersenstrasse 20, Darmstadt, D-.64287, Germany 2Lebedev Physical Institute, Leninsky pr. 53, Moscow 117924, Russian Federation
An optical device for modulation ofthe intensity ofunpolarized light was constructed. In comparison with other modulators, this apparatus allows to reduce the loses of energy of light and preserve its angular divergence. The switching time and contrast ratio ofthe modulator are 50}ts and 300, respectively. Keywords: spatial light modulator, FLC, polarization, attenuator
INTRODUCTION Optical modulators are one ofthe most important components in modem optoelectronics. They are widely utilized in optical
communication systems, switching devices, information processing systems, etc. In the same time there are several requirements imposed to the modulators, namely, they should have fast response time, high contrast ratio, low driving voltage and low energy consumption. Moreover, for some applications, it is desirable that modulators could operate with unpolarized light. In the simplest case, an optical modulator represents itself an anisotropic medium placed between two crossed polarizers [1]. By changing the birefringence or by rotating the optical axis of a medium, one can control the transmittance. The main drawback of this type of modulator is that it can transmit , in the best case, only 50% of energy of the incident unpolarized light. However, several polarization insensitive modulators were proposed and investigated. For example, a modulator consisting of two inclined, birefringent slabs and a pinhole was reported [2]. Changing the inclination angles, one can vary the width and the divergence of the light beam and, as a consequence, the intensity of transmitted light. The response time of such
device is limited by the speed of the mechanical components. The other device consists of two inclined and fixed anisotropic plates mounted in tandem and a half wave plate placed between them [3J. Rotation of a X/2 plate also induces the change of the width of light beam and , hence, the transmitted intensity. Nevertheless, both of above mentioned modulators suffer from high angular divergence, backward reflection and low response time. In this report, we present a two channel in-line optical modulator based on DHF effect in ferroelectric liquid crystals. The distinguishing properties of the proposed device are fast response time (about 50 — 100 ts), high contrast ratio, low angular divergence of the transmitted beam and minimal backward reflection.
DEFORMED HELIX FERROELECTRIC LIQUID CRYSTAL EFFECT (DHF EFFECT) There are several electrooptical modes in ferroelectric liquid crystals: SSFLC, DHF, electroclinic effect, V-shaped switching. Among them DHF and V-shaped modes are the most appropriate for applications where gray scale is required. Because of importance ofthe DHF effect for our report, it is worthwhile to give its brief description. As it is known, each smectic layer in ferroelectric liquid crystals has its own direction of spontaneous polarization. Due to helix twisting, average polarization over all layers is equal to zero. The total rotation of the inclination plane, called the helix pitch Po, needs 1 000- 1 0000 smectic layers and it can lay in submicrometer range. A small electric field E applied
along the smectic layers and perpendicular to the helix axes can result in partial unwinding (see fig.1) [4]. This transformation leads to the continuous increase of the effective tilt angle Gjjand effective birefringence zineff until the saturation value is reached. Any DHF cell at U < U (U is the helix unwinding voltage) can be considered as a periodically modulated birefringent structure with a period which is dependent on the applied voltage. The birefringence zineffin this case is the result of spatial averaging over all phase retardations. The maximum value of Llfleff corresponds to a uniform state when the helix is unwound. Light scattering on the helix structure is the inherent property of any DHF cell. Polarization Analysis, Measurement, and Remote Sensing IV, Dennis Goldstein, David Chenault, Walter Egan, Michael Duggin, Editors, Proceedings of SPIE Vol. 4481 (2002) © 2002 SPIE · 0277-786X/02/$15.00
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Maximal intensity of the light scattering appears at U— 0, due to the diffraction on the non deformed helical structure and due to defects. With increasing electric field tn increases and the light scattering decreases, because of the partial helix unwinding in an electric field. The peak of light scattering near UU is due to many defects which appear before the total helix unwinding. The minimal light scattering and maximal birefringence is at U> U, when the helix is totally unwound. It was found [5] that the response time 'r0,10,9 in DHF effect is, under some conditions, almost independent on the voltage and it can be at the order of 150-200 ps at small value of the helix pitch and large tilt angle 9 (4):
0
where y is the rotational viscosity.
.c
a,
E=O
EE dednccbfidd
&iclstorted hthx
Figure 1 : Unwinding of the helix due to the action of an electric field. Ifthe electrical field is higher than E, the helix is totally unwound.
The DHF effect is characterized by very modest driving voltage inducing significant changes of optical properties. This circumstances as well as the absence of any threshold voltage makes the DHF effect most suitable for optical applications [5].
DESCRIPTION OF THE MODULATOR The proposed attenuator (see Fig. 2) consists oftwo polarization beam splitting prisms (PSP) mounted in tantem, two right angle prisms (RAP), and two halfwave ferroelectric liquid crystal cells operating in asymmetric DHF (Deformed Helix Ferroelectric Liquid Crystal) mode. Polarization beamsplitting prisms and right-angle prisms are arranged in such a way that they form two channel scheme. This scheme allows to transmit unpolarized light through the device without significant attenuation of the intensity. All
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losses inside this scheme are connected only with absorption, reflections and scattering in the constituting optical components. The first polarization beam splitting prism decomposes the incident unpolarized beam onto two beams with orthogonal linear polarizations The beams going through the device combine on the second PSP. The situation changes remarkably when azimuths of both beams are modulated by ?J2 LC cells. In this case, the beams spatially split on the second PSP, so that, on the output of the device, two partially polarized beams appear. In other words, intensity of each of them is lower then intensity of the incident unpolarized light. It means, in turn, that transmittance of the attenuator could be governed by the phase retardation introduced by the cells. In our case, it is necessary that optical indicatrices be inclined at the same angle. Only in such case the outgoing beams are unpolarized. To derive mathematical expression ofthe attenuator transmittance, Jones calculus could be utilized.
4
3
2
1
6 Figure 2: Optical setup ofthe modulator 1,2 —polarization beam splitting prisms; 3,4 — right angle prisms; 5,6 — liquid crystal cells
But beforehand, it is necessary to take into account the following simplifications: losses due to absorption and reflection are negligibly small, the light is monochromatic and the beams in both channels are completely polarized. Let us suppose that Jones vector ofthe incident unpolarized beam has the form
E.inc =1
a
b exp( 17(t)))
(1)
where a=b=/ (t) — random function. The action ofthe polarization beam splitting prisms on the incident light can be described by the following matrices:
=11 o
\o 0)
2
=o
(2)
Here indices 1 and 2 denote the number ofthe channel.
As follows from (1) and (2) , light in the first channel has linear vertical polarization and in the second channel — linear horizontal polarization. Transformation of the state of polarization in each channel is described [6,7] by the equation: Etran = PR(—co)T(IT)R(co)PE,nc
(3)
where R(ço) is the matrix of rotation of optical axis of half wave cell at the angle çP ,R(—ço) - matrix of inverse rotation, T(IT) - matrix describing the phase retardation caused by a X/2 cell. Substituting (1), (2) and (3) one can obtain expressions of the Jones vector of beams transmitted through each channel:
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1 ,(
E'
E2
=
0 0
bcos2(c,2)exp(if) + bsin2(ço2)exp(—iF)
As is clear from these formulas that when ço2 the going light will be partially polarized. The phase difference between two orthogonal components of light is a random function and , in the same time, amplitudes of that components are different. For our case, it is more important , however, to consider the case when q = • Here, the transmitted light is completely
unpolarized. The transmittance of the device can be derived from the formula:
T=(EE +E2E)/I. After substituting
l,
expression for Jones vectors and assuming that, I =
= p2
= P,Fi = "2
,we get:
T =sin2(2ço). This formula indicates that the simultaneous in-plane rotation of the optical axes of both LC cells results in modulation of the intensity ofunpolarized light. One of the possibilities to have in-plane rotation of the optical axis is to use ferroelectric liquid crystal cells operating in DHF mode [8]. In addition to in-plane switching, DHF mode has another advantage, namely, gray scale. For assembling the modulator we selected prisms with dimensions 20 mm x 20 mm x 20 mm. Polarization splitting prisms have extinction ratio 1 : 100. Of course, this ratio is not high enough and, therefore, it limits contrast of our device. The most important elements of this device are liquid crystal cells. We made two DHF cells operating as half wave plates at 2 650 nm. This cells have a thickness approximately 1 .7um and are filled with FLC PBH —9 ( An 0.15 ). The attractive feature of the DHF LC effect for the attenuator is that under applying electric field the optical axis of a cell undergoes inplane rotation. In our experiment we used driving DC voltage varying in the range from -3 V till +3 V which allowed us to rotate optical axis up to 45° . As follows from theory of DHF effect [6] the dependence of the transmittance on the applied voltage has hysteresis behavior (see Figure 3). The contrast ratio at maximum was about 300.
1,0
a
0,8
0,6
E 0,4
02
Applied DC voltage, v
Figure 3: Dependence of the transmission on the applied voltage
SUMMARY The proposed modulator has high contrast ratio, low response time. Due to the absence of polarizers no significant absorption of light takes place, and it can be used for fast effective shattering the light beam of very high intensity in schemes of protection the devices from power light beams, like continuous laser generation, focused sun and lamp light.
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ACKNOLEGEMENT We acknowledge financial support from the Volkswagen Foundation
REFERENCES [1] A.Kaprinen, S. Lottholz, R.Myllyla, G.Andersson, M.Matuszczyk,K.Skarp,I.Dahl, S.T.Lagerwall. Ferroelectrics, 114, 93, 1991 [2] K.Bennett, R.L.Byer. Applied Optics,19, 2408, 1980. [3] H.Lotam, A.Eyal, R.Shuker. Opt. Lett., 16, 9, 690 1991. [4] A.Biradar, S.S.Bawa, C.P.Sharma, S.Chandra. Ferroelectrics, 122, 81, 1999. [5] Y.Yamamoto, IEEE J.Quantum Electron., QE-16, 11, 1251, 1980. [6] D.Kliger, J.Lewis, C.Randall. Polarized Light in Optics and Spectroscopy, Academic Press Inc., 1990. [7] J.Gerrard, M.Burch. Introduction in matrix methods in optics, Wiley Interscience Publication, 1975. [8] L.Beresnev,V.Chigrinov,D.Dergachev, E.Pozhidaev, J.FUnfschiling, M.Schadt. Liquid Crystals, 5, 1171, 1989.
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