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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 below
the 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.
2-5These efforts have concentrated pri-
marily 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 volt-
age.
It has been shown
5that the voltage-dependent opti-
cal transmission of a TNLC cell can be expressed as an
intensity transmission factor for crossed (T1) or par-
allel (TI1
) polarizers given by
T1=PR I-sin 224' sin 2 )' (la)
T = 1 -T1.(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
A_ = F m( ° )
V- V01
VO
VO
where ckm
(= 2'rdAn/X) is the maximum phase shift, Vo
is the threshold voltage, and a and : are known func-
tions of the elastic constants and the dielectric anisot-
ropy of the liquid crystal. From the dynamic response
analyses of twisted LC cells,3the relationship de-
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)
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, un-
like the twisted cell, which is insensitive to wavelength
for an amplitude-modulation condition as long as
dAn/» >> 1 is satisfied, the parallel-aligned cell is high-
ly sensitive to wavelength in the visible spectral re-
gion. This is the reason why a twisted LC cell is
commonly used for the amplitude modulation of visi-
ble radiation. On the other hand, in the infrared re-
gion (X -10 gm), to achieve unity rotatory power
would require a relatively thick LC layer,6which, 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.3With an increase in voltage the tilt angle
increases, as in a normal parallel-cell configuration.
It has been pointed out8that 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 interfero-
metric setup. On traversing the 90° TNLC cell, the
light polarization is rotated by 900, and therefore, for
0146-9592/88/030251-03$2.00/0 © 1988, Optical Society of America
252 OPTICS LETTERS / Vol. 13, No. 3 / March 1988
A L SLITD
~~~. Dfields just above the threshold, the twist remains lin-
ear 0(z) = Omz/dj while the tilt follows a sinusoidal
dependence:
y = A(V)sin(7rz/d), (4)
where A(V) < 7r/2
for the purposes of this study.
Since the refractive index exhibited by an aniso-
tropic molecule tilted by an angle -y is given by10
nzy =~
neO(1 + tan
2y \1/2
n.2+2n tan
2l
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, detec-
tor.)
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 whose width is
adjusted to the size of the slit positioned in front of a
silicon photodetector. The measured phase behavior
(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 ob-
tained by utilizing the setup of Fig. 1
after blocking the
reference beam and rotating the analyzer by 900. Fig-
ures 2 and 3 refer to two different LC materials in an 8-
,m-thick cell at room temperature (T - 240C), 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
Vrms
for 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.
The optical transmission characteristic of a TNLC
cell can be understood from Berreman's theoretical
analyses.
3When a TNLC cell is subjected to an exter-
nal voltage, the LC molecules tend to realign parallel
to the applied field, while keeping their twisted orien-
tation, if the voltage is higher than the Freedericksz
transition threshold but lower than the optical thresh-
old. The phase change in this voltage regime is attrib-
uted to the effective birefringence of the twisted ne-
matic 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
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 in-
creasing leakage through the parallel polarizers, as
shown in the bottom traces of Figs. 2 and 3. In this
voltage regime, the amplitude modulation occurs in
company with the phase change.
According to the model presented by Berreman 3for
6
5
4
z3
2
00
(5)
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; electric-
field frequency 10 kHz, sine wave.
5
4
Z 3
z
0
VOLTAG
E, Vrms
Fig. 3. Same as Fig. 2
nematic LC. but for a cell filled with ZLI-1132
VJ2
M
S.F.
M
90°- TN LC
0
March 1988 / Vol. 13, No. 3 / OPTICS LETTERS 253
the total phase shift for small -y is found to be
rd n dz
Ov = 27r 'y
rd/2 nJ n
ce47 |o XF
1 + A2(V)sin
21d 1 dz
n,2 + ne 2A2( V)sin
2 rZ
td/2 F / 2 \I1/2
_47 n, fd[1/n2 1 )_n
A2 (V)sin 2 ]1 dz
fled r r / 2 12
4 E sin 1[ 2 )1/2A(V)
(6)
where E is the complete elliptic integral of the second
kind.
At threshold
~d/2 n
Ov
0= 47r
f edz = 27rned/X. (7)
The upper traces in Figs. 2 and 3 essentially show
the AO5
= OV -Ov
0behavior. From the results ob-
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 modu-
lation 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 ob-
served in the amplitude traces exhibit the same peri-
odicity 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 twist-
ed nematic LC cells do not behave as pure-amplitude
modulators above
the optical threshold, since a signifi-
cant 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-
tion. This is of significance in data-processing appli-
cations, both for direct on-line phase modulation and
for encoding a phase grating or hologram.
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
intensity modulation, a 450 twisted LC layer is em-
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-
age, crossed polarizers are often used. However, for
phase-only modulation, the analyzer should be paral-
lel to the polarizer in order to preserve high transmis-
sion. Both phase- and amplitude-modulation behav-
ior 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 simi-
lar phenomenon was also observed recently in the LC
TV.1
2It 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 inten-
sity regime
has a higher optical threshold. This obser-
vation was recently put into practice'3when a TNLC
light valve was used for a dynamic optical interconnec-
tion 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 experi-
ment.
E. Marom is also with Hughes Research Laborato-
ries, Malibu, California 90265.
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