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 nz ny nx

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 -

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

When Ez only,

Take LiNbO3 as an example :

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

Different index changes of TE and TM waves

Take LiNbO3 Intensity modulator Z cut TM polarization

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

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

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

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

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

+ - z z

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

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

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

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

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

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

Quantum Key Distribution (QKD) W. T. Buttler, etal. Physical Review A, Vol 57, 1998, pp. 2379-2382

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

Phase Shift (degree) Bias (V)

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

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

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

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

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

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

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

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

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

For A1(0)= A2(0) = ½ A(0),

When  = 0,

When   0,

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

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

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

Kerr effect :

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

Acoustic-optic Modulators Bragg condition:

Doppler shift Angle mismatch

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

Acoustic –optics devices Free space inter-connector Isolator

Light propagation in anisotropic crystals Optical axises o light no

Light propagation in anisotropic crystals Optical axis o light no ne

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

Light propagation in anisotropic crystals

Light propagation in anisotropic crystals ne no

Faraday rotator

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

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