Download Total Internal Reflections in Liquid Crystals

Total Internal Reflections in
Liquid Crystals
Optics and Photonics
Presented in Partial Fulfillment of the
Second Midterm
Clinton Braganza
Liquid Crystal Institute, K.S.U.
4/4/2004
Reflection Coefficients
SIGMA Polarization
H
E
H
q rq
i
1
2
r
Er
qt
n1 cosq i  n2 cosq t
r12 
n1 cosq i  n2 cosq t

Reflection Coefficients

Pi Polarization
Ei
Hi
1
2
Eqri qr
Hq r
t
Ht
n2 cosq i  n1 cos qt
r12 
n2 cosq i  n1 cos qt

Et
Total Internal Reflection

SIGMA polarization
 Writing
qt explicitly using Snell’s law
r12 
 If
n12 2
n1 cosq i  n2 1 2 sin q i
n2
n12 2
n1 cosq i  n2 1 2 sin q i
n2
n1 > n2, all the incident power is
reflected if the incident angle is
greater than arcsin (n2 / n1).
TIR in Liquid Crystals:
Glass to LC.

Note that liquid crystals are birefringent,
therefore reflections will depend of the
orientation of the liquid crystal with
respect to the direction of light
propagation.
 Let us consider this liquid crystal:
ne = 1.7
no = 1.5
nglass = 1.7
 De > 0
TIR in LC’s: Orientation

We will consider the following
configurations:
 A homeotropic

With sigma and pi polarized light incident on
the cell surface
 A planar
z
y
z
y
cell
cell
– With director parallel to y-axis
 and sigma and pi polarized light incident on
the cell surface
– With director parralel to x-axis
 And sigma and pi polarized light incident on
the cell surface.
TIR in LC’s

Homeotropic Cells
E
 This
Ei, S - polarization
encounters no, therefore when the
incident angle is greater than arcsin
(no/ng) = 61.9º , all the light is reflected.
TIR in LC’s

Homeotropic Cells
Ei, P - polarization
 This
encounters
neff 
 This
ne no
ne2 cos2   no2 sin 2 
n

increase from no to ne, which is the
same as glass, therefore TIR does not
take place.
k
TIR in LC’s

Planar Cell : director parallel to y-axis
z
Ei, S - polarization
y
 Here
the electric field always encounters no,
therefore if the incident angle is greater than
the critical angle we have 100% reflectance.
TIR in LC’s

Planar Cell : director parallel to y-axis
Ei, Pi - polarization
 As
the incidence angle is increase, the
refractive index decreases from ne to no as the
electric field becomes parallel to the director,
therefore TIR happens here.
TIR in LC’s

Planar Cell : Director parallel to x-axis
Ei, S - polarization
z
y
 Here
the electric field is always parallel to ne,
therefore we do not have TIR
TIR in LC’s

Planar Cell : Director parallel to x-axis
Ei, Pi - polarization
 Here
the electric field always encounters no,
therefore TIR occurs at incident angles greater
than the critical angle.
TIR in LC’s: LC to Glass

Let us consider a different liquid crystal
 no =1.5
 ne =1.8

Therefore the critical angle is
arcsin(nglass/ne) = 70.81º
TIR in LC’s : LC to Glass

Homeotropic cell
E

Ei, S - polarization
In the liquid crystal the light encounters
no, which is less than nglass, therefore no
TIR occurs here.
TIR in LC’s : LC to Glass

Homeotropic cell
Ei, p - polarization

In the liquid crystal the light encounters
neff, which increases from no to ne.
Therefore TIR occurs.
TIR in LC’s: LC to Glass

Planar Cell: director parallel to y-axis
Ei, S - polarization
z
y
 In
the liquid crystal the light encounters no,
therefore no TIR occurs
TIR in LC’s: LC to Glass

Planar Cell: director parallel to y-axis
z
Ei, p - polarization
y
 In
the liquid crystal the light encounters neff,
which decreases to no as the incident
angle increase, therefore no TIR occurs
TIR in LC’s: LC to Glass

Planar Cell: director parallel to x-axis
Ei, S - polarization
z
y
 In
the liquid crystal the light encounters ne,
therefore TIR occurs
Ei, p - polarization
 In
the liquid crystal the light encounters no,
therefore no TIR occurs
TIR in ChLC’s: Glass to LC
 Knowing the orientation of the
liquid crystal at the boundary we
treat the planar texture as the
previous nematic cases.
Planar Texture
 Focal Conic Texture
I expect a periodic behavior here,
for example, for s- polarization:
 If director is parallel to cell
normal we have TIR
Focal Conic Texture
 if director is parallel to
polarization of light we will have
no TIR.
Some applications


Switchable fiber optic cables –too expensive
A more economical use would be for optical switches.
– Shown below is a telecom optical switch designed by Baker, that can switch
light to two different positions without changing the polarization.
ITO
ITO
Conclusions



Total internal reflection was solved by carefully
analyzing the orientation of the liquid crystal
director with respect to light propagation.
It would be nice to get a general solution for TIR
in LC’s, without first knowing the director
orientation.
For the case of cholesterics this problem would
involve studying the effect of the evanescent
wave from one chiral layer to another.
References
Yang, D-K, J. Opt. A: Pure and Appl. Opt, 5(2003)
402-408
Baker, A. P., 1998 Liquid Crystal Optical Switch
Having Reduced Crosstalk, USA Patent #
4,720,171
Xianyu, H., et al, Optics Letters, 28 10 (2003)
Boiko, Y., et al, Optics Letters, 27 19 (2002)