1. Electro-optic effect:
Kerr effect
Pockels effect
Linear electro-optic effect:
When no E applied,
Refractive indices on principle axes

2. Refractive index ellipsoid:
When no electric field applied,
Refractive index ellipsoid nz ny nx

3. Refractive index ellipsoid:
Generally,
 is a 3x3 tensor,  = -1 or  = -1
When electric field applied,
3x3x3 tensor, 27 components
No EO effect for crystal with central symmetry, why?
Why? + z z z x x y y y x x z y -

4. j
i = 1 2 3 1 6 5 1 2 6 2 4 3 5 4 3

5. When Ez only,

6. Take LiNbO3 as an example :

7. Take LiNbO3 as an example:
Z cut
TM polarization
TE polarization

8. Different index changes of TE and TM waves

9. Take LiNbO3 Intensity modulator
Z cut
TM polarization

10. Take LiNbO3 Intensity modulator
Z cut
TM polarization
Linear region
Frequency double region

11. Operating characteristics
Modulation depth
Bandwidth: the highest frequency the modulator can operate, R and C
Insertion loss (dB):

12. Power consumption: P/f, f: bandwidth
for a channel waveguide, assuming the E filed is uniform,
C ~ 0.4pF
Take LiNbO3 as an example:
P/f ~ 2µW/MHz

13. Power consumption: P/f, f: bandwidth
for a bulk EO modulators, assuming the E filed is uniform, z
C ~ 3pF
Take LiNbO3 as an example:
P/f ~ 2W/MHz

14. Phase modulator:
Phase shift due to the applied voltage:
Examples:

15. + - z z

16. Polarization modulator:x y
Phase shift due to the applied voltage:

17. Polarization modulator:W x y Ax  Ay
Phase difference due to the applied voltage:

18. Polarization modulator: Phase difference due to the applied voltage:W x y Ax Ax
When  = /2,   Ay Ay Ax Ax
When  = ,    Ay Ay

19. TE-TM converter:
Phase Shift (degree)
Bias (V)

20. Quantum Key Distribution (QKD)
Bennett and Brassard 1984 protocol
Proc. IEEE Int. Conf. Computers, Systems and Signal Processing, 1984, pp. 175–179.
Single photon
JUSTIN MULLINS, IEEE SPECTRUM, p. 40, May 2002

21. Quantum Key Distribution (QKD)
Bennett and Brassard 1984 protocol
Proc. IEEE Int. Conf. Computers, Systems and Signal Processing, 1984, pp. 175–179.
JUSTIN MULLINS, IEEE SPECTRUM, p. 40, May 2002

22. Quantum Key Distribution (QKD)
W. T. Buttler, etal. Physical Review A, Vol 57, 1998, pp

23. Integrated QKD Receiver
Transmitter: Alice
Receiver: Bob
QKD Links
Input photon polarization states
Detection polarization basis
Final polarization
states
Si single photon detector signal TE
Linear
Circular
TE & TM x TM 1
Circular – left-hand
Circular – right-hand

24. Phase Shift (degree)
Bias (V)

25. Input photon polarization states Applied voltage
Detection polarization basis
Final polarization states
detected signal TE
Linear V
Circular x TM 1
Circular – left-hand
Circular – right-hand

26. EO Polymer poling
Poling of polymer materials, contact poling and corona poling:

27. Uniform poling voltage
Heating/Cooling block
Buffer Layer
EO polymer
Electrode
Needle V
Heating/Cooling block V
Buffer Layer
Film
Poling Electrode
Advantages:
Lower voltage ~ 800V
Good film quality
Uniform poling voltage
Easy control of poling voltage
Select poling area

28. I-V curve during poling:
Poling voltage : 900V
EO coefficient ~ 22pm/V

29. TM-pass waveguide Polarizer
Before poling
After poling
n (TE)
1.594
1.591
n (TM)
1.598
TM input
TE input

30. Directional coupler: 1 3 For A1(0) = A1, A2(0) =0 A1(z) A2(z)
Un-connected port 4

31. Directional coupler: 1 3 For A1(0) = A1, A2(0) =0 A1(z) A2(z)
Un-connected port 4

32. 1 3
A1(z)
A2(z)
Un-connected port 4
For A1(0) = A1, A2(0) =0

33. Directional coupler: 1 3 For A1(0) = A1, A2(0) =0 A1(z) A2(z)
Un-connected port 4

34. For A1(0)= A2(0) = ½ A(0),

38. When  = 0,

39. When   0,

40. Traveling-wave electrodes:1 3
For A1(0) = A1, A2(0) =0
A1(z)
A2(z)
Un-connected port 4
For high-speed electrode using transmission lines:
Vg(t) VL A
z = 0 B l ZL
z = - l Z0 Vi - V0 + ZL - Z0
  = ZL + Z0

41. Standing waves for impedance mismatching:
Vg(t) VL A
z = 0 B l ZL
z = - l Z0 Vi - V0 + ZL - Z0
  = ZL + Z0
|V(z)|
2|V0| + -
-3/4
-/2
-/4
Standing waves
Cancelled

42. Traveling waves for impedance matching:
Vg(t) VL A
z = 0 B l ZL
z = - l Z0 Vi - V0 + ZL - Z0
  = ZL + Z0
traveling waves
|V(z)|
|V0| + -
-3/4
-/2
-/4

43. Kerr effect :

44. Applications of Kerr effect :
Self-phase modulation
Self-Focusing

45. Acoustic-optic Modulators
Bragg condition:

46. Doppler shift
Angle mismatch

47. Acoustic –optics devices
Modulator
Bandwidth:
Beam Scanner
Number of resolvable spots:

48. Acoustic –optics devices
Free space inter-connector
Isolator

49. Light propagation in anisotropic crystals
Optical axises
o light no

50. Light propagation in anisotropic crystals
Optical axis
o light no ne

51. Light propagation in anisotropic crystals
Optical axis
Polarization beam splitter no ne

52. Light propagation in anisotropic crystals

53. Light propagation in anisotropic crystals
ne no

54. Faraday rotator

55. Fiber–optics devices
Coupler
FC/APC
FC/PC
SC/PC
SC/APC

56. Circulator