1. Chapter 6 ELECTRO-OPTICS
Fundamentals of Photonics
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2. (1) Electro-optic Effect
refractive index( anisotropic crystal ) change with electric field
Phase or Polarization change with refractive index
Electro-optic material
Light
Electric field
Fundamentals of Photonics
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3. Fundamentals of Photonics
Possible application
controllable focal length.
Optical scanning device U 
Phase modulator U
polarizer
analyzer
Light intensity modulator U
Polarization modulation
Fundamentals of Photonics
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4. Pockels and Kerr Effects
The refractive index of an electro-optic medium is a function n(E) of the applied electric field E.
Terms higher than the third can be neglected.
Fundamentals of Photonics
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5. Fundamentals of Photonics
Pockels Effect
the third term is negligible
n(E)
r : Pockels coefficient
or the linear electro-optic
coefficient
range: to m/V n
Pockels medium or Pockels cell E
(a)
Fundamentals of Photonics
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6. Fundamentals of Photonics
Kerr Effects
the second term is negligible
n(E)
: Kerr coefficient
or the quadratic electro-optic coefficient. n
Range: to m2/V2 (for crystal)
10-22 to m2/V2 (for liquid)
Kerr medium or a Kerr cell E
(b)
Fundamentals of Photonics
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7. Fundamentals of Photonics
(2) Electro-Optics of Anisotropic Media
Crystal Optics k n2 n1 x y z nb na n3
The index ellipsoid
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8. Fundamentals of Photonics
Pockels and Kerr Effects
E = (El, E2, E3)
{rijk} : linear electro-optic (Pockels) coefficients. E
{ijkl} : quadratic electro-optic (Kerr) coefficients.
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9. Fundamentals of Photonics
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10. Fundamentals of Photonics
index ellipsoid equation
where
ij(0) is a diagonal matrix with elements l/n12, l/n22, and l/n32
principal refractive indices n1(E), n2(E), and n3(E).
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11. Fundamentals of Photonics
Trigonal 3m Crystals (LiNbO, LiTaO,…) E x y z
Optic
axis
Uniaxial crystal
n1= n2 = no, n3 = ne
Assuming : E = (0,0, E), z x y no ne
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12. Fundamentals of Photonics
Tetragonal 42m Crystal (e.g., KDP and ADP) E x y z
Optic
axis x1 x2
x’1
x’2
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13. Electra-Optic Modulators and Switches
Phase Modulators V L
define
V: half-wave voltage
Fundamentals of Photonics
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14. Fundamentals of PhotonicsV d V L V V
Longitudinal modulator
Traveling-wave
transverse modulator
Transverse modulator
d=L
several GHz
Fundamentals of Photonics
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15. Fundamentals of PhotonicsV
Input light
Modulated light
Electrodes
Cross scction E
Waveguide
integrated-optical phase modulator
Fundamentals of Photonics
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16. Fundamentals of Photonics
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17. Fundamentals of Photonics
Dynamic Wave Retarders
phase retardation
Polarization light
Fundamentals of Photonics
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18. Fundamentals of Photonics
Intensity Modulators: Use of a Phase Modulator in an interferometer V Ii Io
Branch 2
Branch 1 Vn A B C
F(V)
0.5 1
Fundamentals of Photonics
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19. Fundamentals of Photonics
Input light Ii V
Modulated light I0
An integrated-optical intensity modulator (or optical switch). A Mach-Zehnder interferometer and an electro-optic phase modulator are implemented using optical waveguides fabricated from a material such as LiNbO3
Fundamentals of Photonics
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20. Fundamentals of Photonics
Intensity Modulators: Use of a Retarder Between Crossed Polarizers Vn V B
F(V)
0.5 1 t
Polarizer s Ii Io if
linear modulation
Fundamentals of Photonics
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21. Fundamentals of Photonics
Scanners +V - q D d L a
scan resolution N
Beam angular divergence: -V q D d L a
Large V
Fundamentals of Photonics
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22. Electro-optic polarization retator
Birefringent crystal
position switch based on electro-optic phase retardation and double refraction.
Fundamentals of Photonics
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23. Fundamentals of Photonics
Directional Couplers
Waveguide 1
PI(0)
P1(0)
P2(L0)
Fibers
Waveguide 2 V
PI(0) L0
PI(z) d
P2(z)
P2(L) L0 z
(a)
power-transfer ratio
Fundamentals of Photonics
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24. Fundamentals of Photonics
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25. Fundamentals of Photonics
=2n/0 : mismatch of the propagation constants F
V0: switching voltage.
C : coupling coefficient.
Lo = /2C
Fundamentals of Photonics
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26. Fundamentals of Photonics
V0: switching voltage.
Lo = /2C
C : coupling coefficient. F 1
Fundamentals of Photonics
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27. Electro-optic material Transparent electrodes Photoconductive material
Spatial Light Modulators x y
Incident light
Modulated light
Transmittance T(x,y) + -
Electro-optic material x y
Write iamge IW(x,y)
Incident light
Modulated light
Transparent electrodes
Mirror
Photoconductive material
Electrically addressed
spatial light modulator
Photo-addressed spatial light modulator
Fundamentals of Photonics
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28. Pockels readout optical modulator (PROM).
BSO
Transparent electrodes
Dichroic reflector of red light
White light (blue)
Incident read light (red)
Modulated light
Polarizing beamsplitter
Pockels readout optical modulator (PROM).
Fundamentals of Photonics
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29. Fundamentals of Photonics
Electro-optics of Liquid Crystal
Electrical Properties of Nematic Liquid Crystals
Anisotropic
Uniaxial symmetry
Optics axis rotate
|| (n||, ne ) E z
 (n, no )
Fundamentals of Photonics
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30. Fundamentals of Photonics
Liquid crystal cell x y z d x y z E q
Phase modulator
Fundamentals of Photonics
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31. Fundamentals of Photonics
(V-Vc)/Vo q
Dependence of the tilt angle q on the normalized rms voltage
Dependence of the normalized retardation T/Tmax=[n(q) – n0]/(ne-no) on the normalized rms voltage when n0=1.5, for the values of △n=ne-no indicated.
Fundamentals of Photonics
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32. Fundamentals of Photonics
Nematic Liquid-Crystal Retarders and Modulators
Phase modulator
Polarization modulator
Fundamentals of Photonics
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33. Fundamentals of Photonics
Liquid- crystal cell s y x
Mirror
Polarizer
Incident light
Reflected light
Reflective light intensity modulator
=/2 (off state)
= (on state)
Fundamentals of Photonics
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34. Fundamentals of Photonics
Twisted Nematic Liquid-Crystal Modulators
Linear polarization direction rotate with liquid crystal twist direction
Fundamentals of Photonics
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35. Fundamentals of Photonicsx y
Bright s
Dark
(a)
(b)
Polarizer
Fundamentals of Photonics
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36. Fundamentals of Photonics
Liquid- crystal cell s
Mirror
Polarizer
Reflective twist nematic liquid crystal modulator, normally 45degree twisted
Fundamentals of Photonics
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37. Fundamentals of Photonics
Ferroelectric Liquid Crystals
Faster response (us, nematic: ms)
smectic-C phase q y x z
Smectic layers
90°
Surface stable Ferroelectric liquid crystal (SSFLC), only on-off state
Fundamentals of Photonics
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38. Fundamentals of Photonics
Liquid Crystals spatial light modulator
Liquid-Crystal Displays
passive devices
relatively slow
optical efficiency is limited because of polarization
the angle of view is limited
seven-bar-segment LCD
Fundamentals of Photonics
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39. Optically Addressed Spatial Light Modulators
Transparent electrodes
White light
Incident read light (red)
Modulated light
Polarizing beamsplitter
Light-locking layer
Dielectric mirror
Photoconductor
Liquid crystal
Hughes liquid-crystal light valve
Fundamentals of Photonics
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40. Fundamentals of Photonics
Photorefractive materials
light
free charge carriers
space-charge distribution
refractive index distribution
Electric field
(a)
(b)
(c)
(d)
Conduction band
Valence band x
Fe3+
Fe2+
LiNbO3
Fundamentals of Photonics
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41. Fundamentals of Photonics
Simplified theory of photorefractivity
rate of photoionization
ND : the number density of donors
ND+: the number density of ionized donors
S : the photoionization cross section.
electrons recombination rate
n(x): electrons density , R is a constant
In equilibrium,
R(x) = G(x),
Fundamentals of Photonics
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42. Fundamentals of Photonics
Electric Field
e : electron mobility
K: Boltzmann’s constant
T : temperature.
Refractive Index
Fundamentals of Photonics
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43. Fundamentals of Photonics
EXAMPLE
Incident light
If m is small
Fundamentals of Photonics
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44. Recombination at traps Refractive index grating
Fixed-charge density
E(x)
△n(x)
Free-carrier density
I(x) + -
Nonuniform light
Photoionization
Diffusion
Recombination at traps
Electric field
Refractive index grating
Response of a photorefractive material to a sinusoidal spatial light pattern
Fundamentals of Photonics
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45. Fundamentals of Photonics
Applications of the Photorefractive Effect
Wave 1 (reference)
Wave 2 (object)
Grating
Two-wave mixing: dynamic holography
Fundamentals of Photonics
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