NW optique physique II 1 Lecture 3 : Electrooptic effect, optical activity and basics of interference colors with wave plates • Electrooptic effect – Electrooptic effect: example of a KDP Pockels cell – Liquid crystals • Optical activity • Interference with polarized light: understanding the interference colors of birefringent plates
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NW optique physique II 1 Lecture 3 : Electrooptic effect, optical activity and basics of interference colors
with wave plates
• Electrooptic effect – Electrooptic effect: example of a KDP Pockels cell – Liquid crystals
• Optical activity
• Interference with polarized light: understanding the interference colors of birefringent plates
NW optique physique II 2
Principle
Anisotropy can be induced by external fields:
We will consider here only the effect of an electric field
Electrooptic effect
In general induced index changes are small and they require
high fields or large path lengths
However technological advances allow strong effects using low
fields (liquid crystals, electrooptic waveguides for telecoms,…)
1 – Electrooptic effect
NW optique physique II 3
• All necessary tools have been seen in the case of natural
anisotropy, we only need now to connect the characteristic
eigen indices of the material to the applied external field
• This lecture will provide a few examples of existing effects and
their applications, other courses such as « Guided and Coupled
Waves » by Jean-Michel Jonathan will go over this subject in
more details
• Numerous technological applications to these induced optical
effects
NW optique physique II 4
I. Electro-optical Effects Modification of the index ellipsoïd
We can characterize the effect of the E field by the modification
of the index ellipsoid (n in the direction of D):
Each 1/nij2 term may in general include
• terms proportional to E : Pockels effect
• and terms in E2 : Kerr effect
No linear terms in E if the medium is initially isotropic
€
x 2
nxx2 +
y 2
nyy2 +
z 2
nzz2 +
2yznyz2 +
2xznxz2 +
2xynxy2 = 1
NW optique physique II 5
The transformation of the index ellipsoïd can be calculated
from the electrooptic 3*6 matrix of the medium, according
to the following relationship:
€
1nxx
2 − 1nx
2
1nyy
2 − 1ny
2
1nzz
2 − 1nz
2
1nyz
2 − 0
1nxz
2 − 0
1nxy
2 − 0
⎛
⎝
⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟
=
r11 r12 r13
r21 r22 r23
r31 r32 r33
r41 r42 r43
r51 r52 r53
r61 r62 r63
⎛
⎝
⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟
ExEyEz
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
Pockels effect
Matrix which characterizes the
electrooptic response of the
medium
NW optique physique II 6
Example: Pockels effect in KDP (see optics labs) Electro-optic tensor Section of the index ellipsoid
Initially uniaxial with optic axis z y!
X �Applied field
E // z
€
x 2
no2 +
y 2
no2 +
z 2
ne2 + 2xyr63E = 1=
1nX2
x + y2
⎛
⎝ ⎜
⎞
⎠ ⎟
2
+1nY2
x − y2
⎛
⎝ ⎜
⎞
⎠ ⎟
2
+z 2
ne2
X Y
€
nX = no 1−12no2r63E
⎡
⎣ ⎢ ⎤
⎦ ⎥
nY = no 1+12no2r63E
⎡
⎣ ⎢ ⎤
⎦ ⎥
€
ϕ =2πλ(nY − nX )e =
2πλno3r63V
For a propagation along z
NW optique physique II 7
The direction of the new axes can also depend on
the electric field Same example of KDP but different direction of applied E
Electro-optic tensor
€
x 2
no2 +
y 2
no2 +
z 2
ne2 + 2xzr41E = 1
Applied field
E // y
z
x β and Δn ∝ E β
Section of the index ellipsoid
NW optique physique II 8
Electrooptical effect: the case of liquid crystals
V=0 V
E
α
Birefringence
Optical axis // molecules
Birefringence ↓ when α ↑ (ie V ↑)
α = 90° → no more birefringence
NW optique physique II 9
Applications of the electrooptical effect
• Modulators: polarization states or intensity
• Deflectors
• Phase shifters
• Displays
• Optical switches
Modulation frequencies can be very high, up to a few GHz (not
for liquid crystals, which are slower)
NW optique physique II 10
A linear polarization is rotated by an angle α:
• proportional to the path length through the medium
• proportional to the concentration (for a solution)
• dependent on wavelength as 1/λ2
Certain substances cause a left handed rotation (levorotatory), other a right handed rotation (dextrorotatory) with respect to the observer. A mixture with
equal concentrations (racemic) does not produce any rotation.
Examples of optically active media Cristalline quartz, used with light propagating in the direction of its optical axis
Nicotine, turpentine, camphor, sugar in solution, etc.
Microscopic origin: the atomic arrangement in the molecule is asymmetric, the
molecule is not identical to its image in a mirror (for quartz it is an asymmetry in the
crystal structure)
2 – Optical activity
NW optique physique II 11
Interpretation in terms of circular birefringence In terms of the modification induced on a polarization state, wwe can
interpret optical activity as a phase shift induced between the left handed
and right handed circular eigen polarizations :
α = (ϕR-ϕL)/2=π/λ(nR-nL)e
Note that for quartz the circular birefringence is 128 times smaller than the