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Electro-optic effect:

Electro-optic effect:. Kerr effect. Pockels effect. Linear electro-optic effect:. When no E applied,. Refractive indices on principle axes. Refractive index ellipsoid:. When no electric field applied,. Refractive index ellipsoid. n z. n y. n x. Refractive index ellipsoid:. Generally,.

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Electro-optic effect:

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  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 5 4 3 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. 2379-2382

  23. Receiver: Bob QKD Links Transmitter: Alice QKD Links Receiver: Bob Integrated QKD Receiver

  24. Phase Shift (degree) Bias (V)

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

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

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

  28. TM-pass waveguide Polarizer TM input TE input

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

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

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

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

  33. For A1(0)= A2(0) = ½ A(0),

  34. When  = 0,

  35. When   0,

  36. B A + V0 Z0 VL Vg(t) Vi ZL l z = - l z = 0 - V0 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: - ZL Z0   = + ZL Z0

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

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

  39. Kerr effect :

  40. Applicationsof Kerr effect : • Self-phase modulation • Self-Focusing

  41. Acoustic-optic Modulators • Bragg condition:

  42. Doppler shift Angle mismatch

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

  44. Acoustic –optics devices • Free space inter-connector • Isolator

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

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

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