Time-resolved switching analysis of a ferroelectric liquid crystal by snapshot Mueller matrix polarimetry

TL;DR: An experimental snapshot Mueller matrix polarimeter based on wavelength polarization coding is used to get a time-resolved description of electric-field-induced fast transition within a ferroelectric liquid-crystal cell.

Abstract: An experimental snapshot Mueller matrix polarimeter based on wavelength polarization coding is used to get a time-resolved description of electric-field-induced fast transition within a ferroelectric liquid-crystal cell. The parameters extracted from experimental Mueller matrices are linked to the molecule director distribution to further determine the average trajectory and the collective behavior of these molecules while they switch over to another state.

Summary

Summary

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Figures

Fig. 4. Representation of the director end in the (Ox,Oz) plane during the up/down transition for two positions of the beam within the cell. The trajectory showed in the left is calculated from the parameters depicted in Fig.3. This representation assumes a collective movement of the directors (no depolarization). The associated error bars are for an uncertainty of 0.5°on the retardance value; r is normalized to 1.

Fig. 1. Snapshot Mueller Matrix Polarimeter in the configuration (e,e,5e,5e).

Fig. 3. Evolution of the parameters, (αR t), R(t), PD(t), εR(t)), throughout the up/down transition. The voltage switches from +15V to -15V at t = 100 µs.

Full text

HAL Id: hal-00473906
https://hal.univ-brest.fr/hal-00473906
Submitted on 16 Apr 2010
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Time-resolved switching analysis of a ferroelectric liquid
crystal by snapshot Mueller matrix polarimetry
Matthieu Dubreuil, Sylvain Rivet, Bernard Le Jeune, Laurent Dupont
To cite this version:
Matthieu Dubreuil, Sylvain Rivet, Bernard Le Jeune, Laurent Dupont. Time-resolved switching anal-
ysis of a ferroelectric liquid crystal by snapshot Mueller matrix polarimetry. Optics Letters, Optical
Society of America - OSA Publishing, 2010, 35 (7), pp.1019-1021. �hal-00473906�

1
Time-resolved switching analysis of a ferroelectric liquid
crystal by Snapshot Mueller Matrix Polarimetry
Matthieu Dubreuil
1,2
, Sylvain Rivet
1,2
, Bernard Le Jeune
1,2
and Laurent Dupont
3
1) Université Européenne de Bretagne, France
2) Université de Bretagne Occidentale, Laboratoire de Spectrométrie et Optique Laser (EA 938),
6 Avenue le Gorgeu, C.S. 93837, 29238 Brest Cedex, France
3) Telecom Bretagne, Département d’Optique (UMR CNRS 6082), Technopôle Brest-Iroise,
C.S. 83818, 29238 Brest Cedex, France
*Corresponding author: matthieu.dubreuil@univ-brest.fr
An experimental snapshot Mueller Matrix polarimeter based on wavelength
polarization coding is used to get a time-resolved description of electric field-induced fast
transition within a ferroelectric liquid crystal cell. The parameters extracted from
experimental Mueller matrices are linked to the molecule director distribution to further
determine the average trajectory and the collective behavior of these molecules while they
switch over to another state. © 2009 Optical Society of America.
OCIS codes: 120.5410, 160.3710, 230.5440, 260.5430.
Mueller matrix (MM) polarimetry is usually employed to characterize samples that show
depolarization, birefringence and dichroism. For a more complete characterization, MMs are
coupled with variables such as wavelength, space coordinates, wave vector. To our knowledge,

2
little has been done with time as variable, though a temporal monitoring of MMs could permit
the study of fast polarization dynamics and widen the scope of MM polarimetry. Such
measurements require a device allowing the acquisition of a full MM in a very short time.
The principle of the Snapshot Mueller Matrix Polarimeter (SMMP) developed by our
team and based on wavelength polarization coding [1,2] is that the polarization states are
encoded in the spectral domain through use of a broadband source and high-order retarders [3].
On condition to use a well-suited retarder-thickness configuration, the full MM of a sample is
available in a single spectrum, I(λ), measured with a dispersive detection system (spectrometer
and CCD camera). As the acquisition time only depends on the aperture time of the CCD
camera, it can be very short (about 1 µs, here). This Letter is aimed at demonstrating the
potentiality of the SMMP to give a time-resolved description of electric field-induced fast
switching in a ferroelectric liquid crystal (FLC) cell. To our knowledge, only two teams have
performed time-resolved MM polarimetry on liquid crystals [4,5]. But, the polarimeters in use
were sequential, so the MMs were reconstructed from various input and output polarization
states and multiple synchronized acquisitions. The SMMP can acquire a full MM in a single
shot.
The SMMP described in Fig. 1 is composed of a broadband source (SLD from
B&W Tek, Inc) around λ
0
= 830 nm with ∆λ = 15 nm, a linear polarizer oriented at 0°, two
calcite retarders (∆n = 0.166) of thickness e = 2.08 mm respectively oriented at 45° and 0°, two
calcite retarders of thickness 5e = 10.4 mm respectively oriented at 0° and 45°, a linear polarizer
oriented at 90°, a diffraction grating (1200 grooves/mm covering 10 nm) and a CCD camera
(512 x 512 pixels). The signal I(λ) is periodic and composed of several frequencies. With this
retarder-thickness configuration (e,e,5e,5e), 13 frequencies are generated on the analysis

3
window. The coefficients of a MM (m
ij
) are retrieved through application of a Fourier transform
to I(λ) since they are linked to the magnitudes of the Fourier peaks through relationships that
only depend on the retarder-thicknesses configuration [1]. By application of the calibration
procedures described in [2], the accuracy on the m
ij
coefficients (normalized by m
00
) is below
0.03 for measurements of well-known media (polarizer, wave-plate).
The chiral liquid crystal (LC) material under study is Felix 015/100, which has a
birefringence around 0.16 in the visible/NIR. Two glass plates with transparent ITO electrodes
and with a thin film of rubbed polyimide, produced by spin coating, are used to fabricate the cell.
Its gap, obtained by spraying of spacers, is about 1.6 µm. The cell is then filled by capillary
suction and the LC is confined between both plates in planar orientation which means that the
LC molecules are parallel to the substrate. At room temperature (25°C), this LC is in the smectic
C* phase, where the molecular layers are perpendicular to the rubbing direction. The average
orientation of molecule is specified by the unit vector
n
r
, called the director (Fig. 2). The director
is tilted by an angle θ with respect to the layer normal and in SC* bulk material, it rotates,
forming a helical structure with the axis perpendicular to the layers. However, as the LC
thickness is far below the helix pitch, and due to the planar anchoring conditions, the helical
structure is suppressed so LC exhibits ferroelectricity properties. The spontaneous polarization,
S
P
uur
, lies in the smectic layers and is perpendicular to the director. This structure is called SSFLC
(Surface-Stabilized Ferroelectric Liquid Crystal) [6]. Application of an alternative electric field,
E
ur
, to this cell (Fig. 2) makes
S
P
uur
aligns with
E
ur
and the molecules move between two stable
states (“up” and “down”). The experiments were made with the FLC cell set perpendicular to the
incident light.

4
The parameters issued from experimental MMs (M) were extracted by the Lu and
Chipman decomposition [7], which consists in assuming that the medium under study is
composed successively of a diattenuator, M
D
, a retarder, M
R
, and a depolarizer, M
∆
, so that
R D
M M M M
∆
= . For a FLC cell in normal incidence, no diattenuation is expected, and the values
obtained are only associated to the experimental noise. In that case, the parameters used for the
characterization are the depolarization index, P
D
, the retardance, R, the fast axis-orientation, α
R
,
and -ellipticity, ε
R
[8]. They are linked to the director-orientation and -distribution in the FLC
cell. The orientation of the fast axis, α
R
, is equal to the apparent angle, θ
app
(Fig. 2). It represents
the angle between the projection of the director on the (O
x
,O
y
) plane and the smectic layer
normal (O
y
axis). The retardance, R, is linked to the angle, χ, by the following relationships:
0
2 ( )
n d
R
π χ
λ
∆
=
[ ] [ ]
2 2 2 2
( )
e o
o
e o
n n
n n
n Cos n Sin
χ
χ χ
∆ = −
+
(1)
where n
o
is the ordinary index of the FLC, and n
e
is the extraordinary one. As R gives insight into
the director position in the (O
y
,O
z
) plane, the knowledge of θ
app
and χ is sufficient to describe
n
r
in a 3-D system on condition to assume a homogeneous distribution of the latter within the light
beam. The last two parameters characterize the homogeneity of the director distribution. The
ellipticity of the FLC cell-associated retarder appears when the distribution of the director
orientation is non-homogeneous in the O
z
direction (twist). Indeed, if one considers a succession,
in the O
z
direction, of thin layers of thickness, ξ, composed of molecules with an orientation, ψ
i
,
the resulting MM is
( , )
Z R i
M M
ξ ψ
=
∏
, where M
R
is the MM of a linear retarder of thickness,
ξ
,
and fast axis orientation,
ψ
i
. If
ψ
i
is varying across the total thickness, d, M
z
will be an elliptic
retarder. Ellipticity gives thus insight into the homogeneity of the director orientation along the
cell thickness. The depolarization index, P
D
, is equal to 1 for an elliptic retarder. If one now

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Time-resolved switching analysis of a ferroelectric liquid crystal by snapshot mueller matrix polarimetry" ?

HAL this paper is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. 

Q2. What is the principle of the Snapshot Mueller Matrix Polarimeter?

The principle of the Snapshot Mueller Matrix Polarimeter (SMMP) developed by ourteam and based on wavelength polarization coding [1,2] is that the polarization states are encoded in the spectral domain through use of a broadband source and high-order retarders [3]. 

Q3. What is the LC confined between the plates?

The cell is then filled by capillary suction and the LC is confined between both plates in planar orientation which means that the LC molecules are parallel to the substrate. 

Q4. What are the parameters used for the characterization of the FLC cell?

In that case, the parameters used for the characterization are the depolarization index, PD, the retardance, R, the fast axis-orientation, αR, and -ellipticity, εR [8]. 

Q5. What is the direction of the director?

The director is tilted by an angle θ with respect to the layer normal and in SC* bulk material, it rotates, forming a helical structure with the axis perpendicular to the layers. 

Q6. What was the MM obtained from the FLC cell?

A square voltage between ± 15 V at 30 Hz was applied to the FLC cell to investigate thedynamics of switching between the up and the down states. 

Q7. Why is the R behavior more complex?

Analysis of εR behavior at the transition is more complex because of the non homogeneity of the director distribution in the (Ox,Oy) plane. 

Q8. What is the focus of the research?

On-going researches are focused on the development of a more detailed model of the director distribution within the cell to further quantify ellipticity and depolarization. 

Q9. What is the corresponding coefficient of a MM?

The coefficients of a MM (mij) are retrieved through application of a Fourier transform to I(λ) since they are linked to the magnitudes of the Fourier peaks through relationships that only depend on the retarder-thicknesses configuration [1]. 

Q10. What is the accuracy of the mij coefficients?

By application of the calibration procedures described in [2], the accuracy on the mij coefficients (normalized by m00) is below 0.03 for measurements of well-known media (polarizer, wave-plate). 

Q11. What is the MM of a linear retarder of thickness?

if one considers a succession, in the Oz direction, of thin layers of thickness, ξ, composed of molecules with an orientation, ψi, the resulting MM is ( , )Z R iM M ξ ψ= ∏ , where MR is the MM of a linear retarder of thickness, ξ,and fast axis orientation, ψi. 

Q12. What is the smectic phase of the LC?

At room temperature (25°C), this LC is in the smectic C* phase, where the molecular layers are perpendicular to the rubbing direction.