Guided Wave Studies of Reflective MTN Liquid Crystal Cell

doi:10.4236/jmp.2012.310195

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Journal of Modern Physics, 2012, 3, 1586-1591

http://dx.doi.org/10.4236/jmp.2012.310195 Published Online October 2012 (http://www.SciRP.org/journal/jmp)

Guided Wave Studies of Reflective MTN

Liquid Crystal Cell

Zhidong Zhang, Libin Si, Wenjiang Ye, Xuan Zhou, Li Jiang

Department of Applied Physics, Hebei University of Technology, Tianjin, China

Email: [email protected]

Received August 18, 2012; revised September 16, 2012; accepted September 22, 2012

ABSTRACT

The fully-leaky guided wave technique has been used to study the reflective 90˚ MTN liquid crystal cell used for LCOS.

The cell is comprised of upper substrate with indium-tin-oxide coating and lower substrate with aluminum coating. Re-

flective angle-dependent signals (Rss, Rpp, Rsp and Rps) were recorded over a range of angles of incidence with the cell

under application of 0 - 7 Vrms ac electric fields. From the recorded experimental data, we found the reflective signals

are quite strong, especially the polarization conversion signals. Fitting the data in reflection with the results of the mod-

eling-program gives the information about the pre-tilt and twist of the director as well as the parameters of different

optical layers. We found that the pre-tilt angle on the upper substrate is different from that on the bottom in the best fits,

which suggests that the indium-tin-oxide and the aluminum coatings have different effects on the alignment layers.

Keywords: Fully-Leaky Guided Wave; Liquid Crystal; MTN Cell; Multilayer Optical Theory

1. Introduction

Reflective-mode liquid crystal displays have some ad-

vantages over transmissive-mode ones such as low power

consumption, outdoors readability, thin profile. In 1996,

Shin-Tson Wu et al. presented a new reflective-mode

display called mixed-mode twisted nematic (MTN) liq-

uid crystal cell [1]. It has favorable features like high

brightness and contrast ratio, fast response time etc., so it

is used for both direct-view displays and reflective-mode

projections. The structure and fabrication processes of

the MTN cell are nearly identical to a conventional TN

cell, but they have two differences: one is that the MTN

cell has a smaller retardation (~0.25 μm), the other is that

the front director of the MTN cell must be aligned at an

angle of β to the polarized direction of the incident light.

In general, the geometric structure of the reflective 90˚

MTNcell used for liquid crystal on silicon (LCOS) is

shown in Figure 1 [2,3].

On the study of liquid crystal displays, it is vitally im-

portant to know the director distribution of a given cell

geometry both with and without applied electric fields. In

recent decades, a series of guided wave techniques have

been developed to explore the director structure in vari-

ous cells [4-18]. These techniques mainly utilize that a

discrete set of guided modes will be excitated in the liq-

uid crystal layer, and the guided modes depend on the

distribution of the director. The newly improved fully

leaky guided wave technique has also been developed to

explore the director distribution of standard liquid crystal

cell [8-18]. A two-pyramid coupling method with match-

ing fluid is used to couple light into and out of the liquid

crystal cell comprised of two standard glass substrates

with transparent indium-tin-oxide (ITO) coatings and

alignment layers, shown in Figur e 2 [19,20].

Use of low-index pyramids increases the angle range

of the incident light allowing the excitation of a number

of fully leaky guided modes. Because the light is directly

coupled out of the cell, weakly guided-modes are sup-

ported over a continuous range of incident, and the varia-

tion of optical intensity with angle of incident shows very

broad optical features. The light is now leaky from the

lower substrate, so the reflective signals are quite weak,

especially the polarization conversion signals. However,

these signals are particularly sensitive to the twist and tilt

of the director, meanwhile, if these signals are too weak,

they will be easily interfered by the noise.

Now the cell used in our study has a lower substrate

with aluminum coating rather than ITO. The aluminum is

a good reflector, so the light will be reflected strongly,

and it also has the function of electrode. Because the cell

is a reflective-mode one, there are only four reflective

signals (Rss, Rpp, Rsp, Rps, the first subscript refers to the

input polarization, the second to the output) in the ex-

periment. By fitting the recorded reflective data to the

model data produced by the modeling-program based on

both the continuum theory of liquid crystals and the mul-

tilayer optical theory, the director distribution may be

Z. D. ZHANG ET AL. 1587

Figure 1. The geometric structure of 90˚ MTN cell used for

LCOS.

Figure 2. Pyramid-coupled cell geometry.

determined accurately.

2. Theory

When the guiding layer is anisotropic liquid crystal in a

waveguide geometry, the eigenmodes of the waveguide

will not be pure TE (s-polarized) or TM (p-polarized)

polarizations except for some special, high-symmetry

structures [20]. Consider a uniformly aligned uniaxial

nematic liquid crystal layer sandwiched by two glass

plates with refractive index ng (see Figure 3). The liquid

crystal is specified by indices parallel and perpendicular

to the director, the optical axis N, ne and no, respectively,

and we assume ne > no. The director of the liquid crystal

layer is tilted by θ from the z-axis and twisted by φ from

the -y axis as shown in Figure 3. The x-y plane is the

plane of the glass surfaces and x-z plane is the plane of

incidence. For a commercial-like cell, it is expected that

ne > n

g and no ≈ n

g [8]. The short semi-axis OB of the

ellipse BOF, formed by the intersection of the plane per-

pendicular to the wave front and the index ellipsoid of

the liquid crystal, gives the ordinary index no, and the

major semi-axis OF gives the extraordinary index e

Figure 3. Schematic of liquid crystal waveguide.

the Snells’ law, we have



Because the upper and lower substrates have the same

refractive index, there are no critical angles and all of the

guided modes will be leaky from both the substrates

(called fully-leaky). We consider that the angle of inci-

dence of polarized light in the upper substrate is



, and

the angle of refraction in the liquid crystal layer is βo for

the ordinary light and βe for the extraordinary light. From

sin sin



(1)



sin sin



 (2)



From the index ellipsoid, it gives

222 2

sin cos







(3)

where ψ is the angle between the optical axis, the director,

and wave-front normal for the extraordinary light in the

liquid crystal layer, which is given by the follow formula

[20]





coscos cossin sinsin

 



 (4)



If the optical axis lies along the x-axis, the TE modes

depend only on no, while TM modes depend on both no

and ne; if the optical axis lies along z-axis, the TE modes

will still sense no, and TM modes will sense no and ne; if

the optical axis is along y-axis, the TE modes are given

by ne while TM modes are given by no. For these three

special cases, the eigenmodes propagating in liquid crys-

tal waveguide geometry are pure TE or pure TM modes.

If the optical axis is rotated out of the y-axis to some ar-

bitrary angle in the x-y plane or y-z plane, or both, e.g.

the optical axis is at a general position as shown in Fig-

ure 3, the eigenmodes are no longer pure TE or TM

modes. It is found when a linearly polarized light (p or s

light) enters such a waveguide, the light will produce

polarization conversion [8], the output light having some

of the orthogonal polarization components present. In

general the polarization conversion signals are specifi-

cally sensitive to the tilt and twist of the director, so these

signals are very useful to study the director distribution.

For either form of incident light, two eigenmodes will be

excited in the liquid crystal layer, one with the E field

along the short semi-axis OB in the ellipse BOF, the oth-

er with the E field along the major semi-axis OF in the

ellipse BOF. So we can decide the polarization conver-

Z. D. ZHANG ET AL.

1588



sion signal from the angle of Ω between -y axis and OB

when either pure s or pure p light enters the liquid crystal

layer. From Figure 3 we have [20]

respectively. Two substrates were separated with 3.1 μm

diameter spacers. The light of pyramid-coupling is

shown in Figure 2, but in our study there are only reflec-

tive signals. The matching fluid (made by CARGILLE

LABS, USA) allows the cell to be rotated with respect to

the pyramid.

sincossin c

cos

1cos cossin

os sin

sin sin

















(5)

The experiment arrangement is shown in Figure 4.

Two apertures collimate the light beam from He-Ne laser

(λ = 632.8 nm), and the mechanical chopper modulates

the laser beam at 1.86 kHz to allow the phase-sensitive

detection. The variable attenuator modulates the intensity

of incident light, and the quarter wave plate changes the

polarization state of the laser beam from linear to circular.

The glass is a thick plate to reflect ~5% of the incident

light into a reference detector, the signal from which is

used to compensate for drift in source intensity. Three

rotatable polarizers determine the specific polarization

state of the incident light and reflective light. The com-

puter-controlled rotating table sets the angular position of

the 90˚ MTN cell relative to the incident light and also

positions the reflective light detector so that it collects

the reflective signals; that means the reflectivity detector

must rotate through twice the angle of the 90˚MTN cell

[8]. In order to obtain better reflective polarization con-

version signals which are more sensitive to the twist and

tilt of the director, the cell is rotated against the pyramids

to set the rubbed direction(in x-y plane, see Figure 3)

twisted from the y direction by about 30˚.

Obviously, only when Ω equals 0 or π/2, there is no

polarization conversion. This corresponds to one of three

cases: (1) φ = π/2, (2) θ = 0, (3) φ = 0 and θ = π/2. In a

true liquid crystal cell, the liquid crystal layer is sand-

wiched between two glass substrates with ITO coatings,

alignment layers etc. The liquid crystal layer is further

treated as a multilayer optical system when we use the 4 ×

4 matrix method [21,22] to model the optical property of

the system. Controlling a linearly polarized light (p or s

light) with different incident angles, this will lead to dif-

ferent optical field distributions and optical waveguide

modes, so we can obtain four sets of reflective angle-

dependent signals (Rss, Rpp, Rsp, Rps). Based on the con-

tinuum theory, the director distribution can be predicted,

then we model the angle-dependent optical properties by

multilayer optical theory of the 4 × 4 matrix method.

Adjusting the pre-tilt angle and the total twisted angle,

we obtain the best fits between the theory predictions and

the recorded experiment data, so the director distribution

in the liquid crystal cell is determined accurately.

3. Experiment Controlling the cell to rotate through 20˚, at each angle

of incidence, fully-leaky guided modes were set-up in the

liquid crystal layer and the intensity of reflective light at

this angle was recorded. The measurement was repeated

with 1 kHz rms ac voltages of 0 - 7 V applied across the

The experimental 90˚ MTN cell is made by Shenzhen

Live Digital Technology Co., Ltd., which used low-index

(1.52) glass substrate with ITO-coating and the same

(instead of silicon) substrate with aluminum-coating,

Figure 4. Schematic of the experiment installation.

Z. D. ZHANG ET AL. 1589

cell, perpendicular to the substrates. All the measure-

ments were conducted on a monodomain at room tem-

perature 25˚C.

4. Results

In order to obtain the director distribution of the reflec-

tive 90˚ MTN cell and the information about the parame-

ters of different optical layers, the experiment data for Rss,

Rpp, Rsp and Rps are recorded both with and without ap-

plied electric fields. A typical set of experimental data

(crosses) is shown in Figure 5. We note that the polari-

zation-conserving and the polarization-conversion sig-

nals are quite strong, especially the polarization-conver-

sion signals are far stronger than that of the transmissive

TN cell. The reason is that the aluminum coating on the

glass substrate also is a good reflector except for an elec-

trode. According to the numerical modeling of F. Z.

Yang [8], Rsp and Rps will be different unless the director

parallels to the substrate, i.e., θ = 90˚. From Figures 5(c)

and (d), we see that there are differences between Rsp and

Rps, which implies a small tilt angle of the director on

both substrates. The recorded data are fitted to the pre-

dictions produced by the modeling-program, and the fi-

nal fits are given by the full curves in Figure 5.

These parameters for the cell obtained by fitting are as

follows: for the glass substrates n = 1.517 at λ = 632.8

nm; for the ITO εI = 3.25 + i0.079 and d = 30 nm; for the

aluminum εAl = −63.5 + i26.813 and d = 28 nm; for the

alignment layers εPI = 2.05 + i0.005 and d = 35 nm; for

the liquid crystal K11 = 13.1 pN, K22 = 10 pN, K33 = 22.3

pN, ε = 2.1650 + i0.0008, ε// = 2.4359 + i0.001 and d =

3.13 μm, for the tilt angle from z axis θ = 85.5˚ on the

upper substrate and θ = 86.2˚ on the lower substrate, the

corresponding tilt(the tilt angle is between the director

and x-y plane) and twist profile is shown in Figure 6, for

the total twist angle



= 90.3˚ from the upper inner sur-

face to the bottom. The pre-tilt angle on the upper sub-

strate is different from that on the bottom, which sug-

gests that ITO and aluminum coatings have different

effects on the alignment layers.

The all recorded angle-dependent reflectivity data for

each voltage were fitted to the model data produced by

the continuum theory and multilayer optical theory mod-

eling program. For all the voltages, the optical parame-

ters of the different layers used in the fitting are shown in

Table 1. The optical parameter ε = εr + iεi is complex,

where εr is the real part and εi is the imaginary part. The

parameter of aluminum refers to the result of J. R. Sam-

bles [23].

Produced by all the fits, the twist angle φ' = −17.2˚ ±

0.8˚ from the x-axis and the tilt angle θ' = 85.5˚ ± 0.5˚

from z-axis on the upper substrate; the twist angle and tilt

angle on the bottom substrate are φ = 72.5˚ ± 0.5˚ and θ =

(a)

(b)

(c)

(d)

Figure 5. Experimental data (crosses) and fitted theory

(curves) for an applied voltage of 3 V. (a) Rss, (b) Rpp, (c) Rps,

and (d) Rsp.

Z. D. ZHANG ET AL.

1590

Table 1. The optical parameters of 90˚ MTN liquid crystal cell.

Optical layers εr εi Thickness (nm)

ITO 3.24 ± 0.04 0.079 ± 0.015 32 ± 3

Alignment layers 2.025 ± 0.025 0.004 ± 0.001 38 ± 4

Liquid crystal (ε//) 2.430 ± 0.007 0.0011 ± 0.0003

Liquid crystal (ε) 2.172 ± 0.016 0.0010 ± 0.0002

(3.12 ± 0.02) × 103

Aluminum 64 ± 1 26 ± 1 30 ± 2

(a)

(b)

Figure 6. The director profile in 90˚ MTN cell at 3 V. (a)

Tilt angle; (b) Twist angle.

86.5˚ ± 0.3˚, respectively. The diagram is shown in Fig-

ure 7.

5. Conclusion

The reflective-mode 90˚ MTN liquid crystal cell has been

studied by use of the fully-leaky guided wave technique.

Figure 7. The diagram of twist angle and tilt angle on both

upper and bottom substrates.

The p or s light with different incident angles is coupled

into the cell by a pyramid, and the angle-dependent re-

flective signals are recorded. Then we used the modeling

program based on both the continuum theory and the 4 ×

4 matrix multilayer optical theory to fit the recorded data

for all the applied voltages (0 - 7 Vrms). Finally, we ob-

tained the information about the director distribution and

the parameters of different optical layers (see Table 1),

and we found that the pre-tilt angle on the upper sub-

strate is different from that on the bottom, which sug-

gests that the ITO and the aluminum coatings have dif-

ferent effects on the alignment layers.

6. Acknowledgements

This research was supported by Natural Science Founda-

tion of Hebei Province under Grant No. A2010000004,

Research Project of Hebei Education Department under

Grant No. Z2012061, and Key Subject Construction

Project of Hebei Province University. The authors thank

Professor Fuzi YANG for his helpful discussions.

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