It is shown that twisted nematic liquid-crystal spatial light modulators behave as ... used between crossed polarizers above the optical threshold; they behave as.
March 1988 / Vol. 13, No. 3 / OPTICS LETTERS
251
Phase-only modulation with twisted nematic liquid-crystal spatial light modulators N. Konforti and E. Marom Faculty of Engineering, Tel-Aviv University, Tel-Aviv 69978,Israel
S.-T. Wu Hughes Research Laboratories, Malibu, California 90265 Received September 28, 1987; accepted December 21, 1987
It is shown that twisted nematic liquid-crystal spatial light modulators behave as phase-only modulators when operated belowthe conventional optical threshold. Thus such devices, when operated in a reflection mode, behave as spatial amplitude modulators when used between crossed polarizers above the optical threshold; they behave as
phase modulators when used between parallel polarizers and operated below that threshold.
Optical and electro-optic characteristics of a twisted nematic liquid-crystal (TNLC) cell' have been studied extensively.2 - 5 These efforts have concentrated primarily on the amplitude modulation of light by the electro-optic effect. In this Letter we demonstrate that a TNLC cell can work as a phase-only
or an
amplitude modulator, depending on the applied voltage.
It has been shown5 that the voltage-dependent opti-
cal transmission of a TNLC cell can be expressed as an
intensity transmission factor for crossed (T 1 ) or parallel (TI1) polarizers given by
T1 =PR I-sin
2
2
24' sin
)'
(la) (lb)
Here 4'is the angle between the incoming polarization of the incident beam with respect to the direction of the director at the input interface, AO is the phase retardation acquired in the liquid-crystal (LC) cell, and PR is the twisted nematic rotatory power given by2 sin2 [0(1 + U2)1/ 2 ]
(2)
1 +U
where 0 is the twist angle of the cell and U =
rdAn/
(Xm).
The phase retardation for parallel aligned cells, as a function of the applied voltage, is4 V-
A_ =
F
m( °
)
V0
1
VO VO
where
ckm(=
and amplitude (4 = 450) modulations.
As a matter of
fact, the parallel-aligned cell provides more phase change than the twisted one for an identical LC layer thickness. It also exhibits an oscillatory behavior for the amplitude-modulation response. However, unlike the twisted cell, which is insensitive to wavelength condition for an amplitude-modulation dAn/» >> 1 is satisfied, the parallel-aligned
as long as cell is high-
ly sensitive to wavelength in the visible spectral re-
T = 1 - T1 .
_
scribed in Eq. (3a) is also expected to hold for the TNLC cells in the voltages just above the threshold. It is known that a parallel-aligned LC spatial light modulator can perform both phase-only (with A = 0)
2'rdAn/X) is the maximum phase shift, Vo
is the threshold voltage, and a and : are known functions of the elastic constants and the dielectric anisotropy of the liquid crystal. From the dynamic response analyses of twisted LC cells,3 the relationship
de-
0146-9592/88/030251-03$2.00/0
gion.
This is the reason why a twisted LC cell is
commonly used for the amplitude modulation of visible radiation. On the other hand, in the infrared region (X - 10 gm), to achieve unity rotatory power would require a relatively thick LC layer, 6 which, in
turn, would result in an undesirably slow response time. Thus the parallel alignment is more attractive than the twisted one for IR applications The theory of the response of a twisted cell to an external field should take into consideration the tilt as well as the twist of the director as a function of the cell
depth.3
With an increase in voltage the tilt angle
increases, as in a normal parallel-cell configuration.
It has been pointed out8 that the optical threshold for the twist effect exceeds the threshold for the onset of deformation; the latter can be identified through a change in the capacitance of the cell. To investigate the just-above-threshold behavior of TNLC cells, we carried out an experiment sketched schematically in Fig. 1. We used an interferometric setup that permits measurement of the response of the cell between crossed polarizers, the transmission being essentially given by Eq. (la). For low voltages, the cell is almost transparent. A linearly polarized laser beam (X = 0.63 ,um, He-Ne
laser) impinges upon the Mach-Zehnder interferometric setup. On traversing the 90° TNLC cell, the light polarization is rotated by 900, and therefore, for © 1988, Optical Society of America
252
OPTICS LETTERS / Vol. 13, No. 3 / March 1988 VJ2 A M
L ~~~.
SLITDD
fields just above the threshold, the twist remains linear 0(z) =
Omz/dj
while the tilt follows a sinusoidal
dependence: y = A(V)sin(7rz/d),
S.F.
(4)
where A(V) < 7r/2for the purposes of this study. Since the refractive index exhibited by an aniso-
M
tropic molecule tilted by an angle -y is given by10
2 y \1/2 nzy=~neO(1n.2+2n + tantan 2 l
90°- TN LC
(5)
Fig. 1. Experimental setup used for investigating the phase modulation of 90° twist cells. (S.F., spatial filter; B/S's, beam splitters; M's, mirrors; A, analyzer; L, lens; D, detector.)
6
5
compensation, a quarter-wave plate producing the same rotation is inserted along the other branch. The two beams, after propagating through the analyzer, interfere and form a fringe pattern
4
whose width is
adjusted to the size of the slit positioned in front of a silicon photodetector. The measured phase behavior
z3
(upper traces in Figs. 2 and 3), as well as the amplitude
response (lower traces), are plotted for comparison on the same figures. The amplitude response was obtained by utilizing the setup of Fig. 1 after blocking the reference beam and rotating the analyzer by 900. Figures 2 and 3 refer to two different LC materials in an 8-
2
,m-thick cell at room temperature (T - 240 C), one being BDH-E-7 (Fig. 2) and the other ZLI-1132 (Fig. 3). The driving voltage has a frequency of 10 kHz.
According to Refs. 4 and 9, one finds the threshold voltage of a TNLC cell to be Vo = 0.937 and V = 1.007 Vrmsfor E-7 and ZLI-1132, respectively. The mea-
sured threshold exhibited in our Figs. 2 and 3 for the onset of the phase modulation is in close agreement with these calculations (1.05 V for E-7 and 1.1 V for
1132). On the other hand, the optical threshold in both curves was found to be 1.75 V.
0
0 VOLTAGE,Vrms
Fig. 2. Phase and amplitude response of a BDH-E-7 LC cell. Note the coincidence of the occurrence of the first two
cycles in the phase-response curve with the respective bumps in the amplitude curve. The third cycle is obscured by crossing the optical threshold where nonuniform twisting takes place. The phase change from peak to peak is equal to 2ir. Cell thickness 8 ,um; X = 0.63 ,m; T L 240C; electricfield frequency 10 kHz, sine wave.
The optical transmission characteristic of a TNLC cell can be understood
from Berreman's theoretical
analyses.3 When a TNLC cell is subjected to an external voltage, the LC molecules tend to realign parallel to the applied field, while keeping their twisted orientation, if the voltage is higher than the Freedericksz transition threshold but lower than the optical thresh-
5
old. The phase change in this voltage regime is attrib-
uted to the effective birefringence of the twisted nematic cell, which decreases with voltage owing to the increasing tilt of the LC molecules. No amplitude modulation is expected in this regime because the twist remains uniform and the waveguiding effect still
4
Z
3
z
exists.
However, at voltages above the optical threshold the twist is no longer uniform, and the light becomes less affected by the waveguiding properties of the twist and the controlled birefringence, resulting in an increasing leakage through the parallel polarizers, as shown in the bottom traces of Figs. 2 and 3. In this voltage regime, the amplitude
modulation
company with the phase change.
occurs in
According to the model presented by Berreman 3 for
0
0 VOLTAGE, Vrms
Fig. 3. Same as Fig. 2 but for a cell filled with ZLI-1132 nematic LC.
March 1988 / Vol. 13, No. 3 / OPTICS LETTERS
tion. This is of significance in data-processing applications, both for direct on-line phase modulation and
the total phase shift for small -yis found to be rd n dz 27r 'y
Ov =
rd/2
ce47 |o
nJn
for encoding a phase grating or hologram.
F1 + A (V)sin 2
2
X
It is the purpose of this Letter to demonstrate that conventional TNLC spatial light modulators can be used as pure spatial phase modulators in addition to their use as intensity modulators. For the purpose of
11d dz
intensity modulation, a 450 twisted LC layer is em-
]1 dz
ployed in a reflective-mode LC light valve." The reflective-mode operation allows the incident beam to traverse the LC layer twice, and thus the phase change is doubled. To achieve a good dark state at null volt-
n,2 + ne 2A2( V)sin2 rZ _47 n,
4
253
td/2 F fd[1/n2
/
fled r r /1
E sin [
2
1
2
2
\I1/2
)_nA2(V)sin 2
12 (6) )1/2A(V)
where E is the complete elliptic integral of the second kind. At threshold ~d/2 n Ov 0 = 47rf
edz = 27rned/X.
(7)
The upper traces in Figs. 2 and 3 essentially show = OV - Ov0 behavior. From the results obthe AO5 tained one can estimate the maximum tilt A(V) for the curves presented in Ref. 3.
It should be pointed out that the phase modulation below the optical threshold, as shown in Figs. 2 and 3,
occurs only for the incident light polarized parallel to the front director of the TNLC cell. For the light polarized normal to the front director, no phase modulation was observed within this voltage regime, i.e., the tilt of LC molecules does not affect the phase of this polarization. The residual amplitude fluctuations observed in the amplitude traces exhibit the same periodicity as in the phase traces since both depend on the same AOk,as indicated in Eqs. (1) (for amplitude re-
sponse) and now derived in Eq. (6) (for the phase response). In addition, the termination of the phase response of the TNLC cells coincides with the onset of the amplitude response when the twist of the LC layer becomes nonuniform. The two effects, the bumps due to molecular tilt and the phase retardation associated with it on the one hand, and the nonuniform twist of the LC layer on the other hand, seem to coalesce into each other at the optical threshold value (lower traces, Figs. 2 and 3).
A careful look at these traces reveals that the twisted nematic LC cells do not behave as pure-amplitude
modulators above the optical threshold, since a significant phase variation is inherently associated with the amplitude change. Although this is not troublesome when such devices are used for display purposes, it cannot be neglected in data-processing applications. On the other hand, below the optical threshold the amplitude variations are insignificant, so that the cells could be considered to provide phase-only modula-
age, crossed polarizers are often used.
However, for
phase-only modulation, the analyzer should be parallel to the polarizer in order to preserve high transmission. Both phase- and amplitude-modulation behavior can be achieved with a conventional TNLC cell at
two different electric field ranges, the lower one being primarily responsible for the phase response. A similar phenomenon was also observed recently in the LC TV.12 It has also been shown in this Letter that the calculated threshold of LC deformation relates to the onset of the phase-modulating regime, while the intensity regime has a higher optical threshold. This observation was recently put into practice'3 when a TNLC light valve was used for a dynamic optical interconnection involving a double-pass configuration through a LC light modulator. The phase-modulation regime was necessary to prevent the occurrence of double diffraction in view of the double-pass transmission through a LC light valve. The ability of hybrid TNLC light valves to provide phase modulation only for a selected polarization was essential in such an experiment. E. Marom is also with Hughes Research Laboratories, Malibu, California 90265. References 1. M. Schadt and W. Helfrich, Appl. Phys. Lett. 18, 27 (1971). 2. C. H. Gooch and H. A. Tarry, J. Phys. D 8, 1575 (1975). 3. D. W. Berreman, Appl. Phys. Lett. 25,12 (1974); J. Appl. Phys. 46, 3746 (1975). 4. L. M. Blinov, Electro-Optical and Magneto-Optical Effects of Liquid Crystals (Wiley, New York, 1983). 5. U. Efron, S. T. Wu, and T. D. Bates, J. Opt. Soc. Am. B 3, 247 (1986). 6. S. T. Wu, U. Efron, and L. D. Hess, Appl. Phys. Lett. 44, 842 (1984). 7. S. T. Wu, Opt. Eng. 26, 120 (1987). 8. M. F. Grebenkin, V. A. Seliverstov, L.M. Blinov, and V. G. Chigrinov, Sov. Phys. Crystallogr. 20, 604 (1976).
9. M. Schadt and F. Muller, IEEE Trans. Electron Devices ED-24, 1125 (1978). 10. M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), p. 679. 11. J. Grinberg, A. Jacobson, W. P. Bleha, L. Miller, L. Fraas, D. Boswell, and G. Myer, Opt. Eng. 14,217 (1975). 12. F. T. S. Yu, S. Jutamulia, T. W. Lin, and X. L. Huang, Opt. Laser Technol. 19, 45 (1987). 13. E. Marom and N. Konforti, Opt. Lett. 12, 539 (1987).
