Chap. 8. Electro-Optic Devices - The effect of an applied electric field on the propagation of em radiation. - light modulators, spectral tunable filters, electro-optical filters, beam deflectors 8.1. Electro-Optic Light Modulators - Example as the EO modulation of light in a z-cut KDP plate (see Sec. 7.4). After traversing a distance L in the crystal, the change in phase shift due to the applied field is typically 8.1.1. Longitudinal Electro-Optic Modulation - Longitudinal case; a large acceptance area with a thin EO crystal plate. The electric field of the modulating field is parallel to the beam path of the light except near the edge of the electrodes The electrically induced phase change (or phase retardation) for the light passing through the crystal plate is proportional to EL=V (the applied voltage) provided that only the linear EO effect is taken into account.
1) Z-cut LiNbO 3 Plate: point group 3m (see Table 7.2) Let. Then,
- Since no mixed terms are involved, where The electrically induced phase change where V=applied voltage. The half-wave voltage (PM) - For a sinusoidal voltage of, the transmitted beam is phase-modulated and expressed as with and *Since no birefringence is induced by the electric field in this device geometry, there is no phase retardation between any two orthogonally polarized waves. No amplitude modulation can be achieved unless optical feedback is introduced.
2) Z-cut Cubic Crystal: GaAs, CdTe, In As, and ZnS (see Table 7.2) Let. Then, The applied electric field couples the x-polarized and y-polarized waves. The principal dielectric axes x and y are rotated around the z-axis by because of the electric field in the z-direction. - In the new principal coordinate system (x', y', z'),. Then, - If the plate is used to be as a phase modulator, the light must be polarized in either the x' or the y' direction. The induced phase change The half-wave voltage (PM) For a sinusoidal field, the modulation index (PM)
- If the plate is used to be as an amplitude modulator, a front polarizer can be aligned along the x axis so that equal amplitudes of x' and y' modes are excited. A phase retardation of is accumulated on passing through the crystal and given by and the half-wave voltage (PM) Under a sinusoidal field when a properly oriented quarter-wave plat inserted in series with the crystal, An analyzer at the output, oriented perpendicular to the front polarizer, converts the phase modulation to amplitude modulation. The transmission. For, with and the modulation depth 8.1.2. Transverse Electro-Optic Modulation - Transverse case; a long interaction length at given field strength. The modulating field is transverse to the optical beam path The electrically induced phase change (or phase retardation) for the light passing through the crystal plate is proportional to EL=VL/d with d=the separation between the electrodes provided that only the linear EO effect is taken into account.
1) LiTaO 3 Elecro-Optic Modulator: 3m point group symmetry (see Table 7.2) Let. Since the light beam is propagating in the y direction, the birefringence seen by the beam is The phase retardation for the light passing through the crystal rod is with d = the separation between electrodes
For the light polarized linearly along the z direction, the phase change induced by the applied field is. The half-wave voltage If the applied voltage is sinusoidal in time, the phase retardation is given by where = the retardation under no voltage. The modulation depth if is an odd multiple of. 2) Cubic Crystal Elecro-Optic Modulator: optically isotropic (no birefringence): m symmetry (zinc blende) group: In As, CuCl, GaAs, CdTe. *GaAs and CdTe: used for IR, 4 fold symmetry along the cube edges, <100>, <010>,.. 3 fold axes of symmetry along the cube diagonals, <111>.. The index of ellipsoid; all three variables (x, y, z) are coupled.
The eigenvalue problem:, with V in new principal axes. In the case that the electric field along the <100> direction, Then, the secular equation is given by
The new principal axes: The phase retardation The half-wave voltage
8.2. Electro-Optic Fabry-Perot Modulators - In the transverse geometry, the modulation is proportional to the interaction length L. If is the amplitude of the modulating voltage and the modulator is properly biased, the phase modulation depth, the amplitude modulation depth a large modulation depth requires a small half-wave voltage.
8.2.1. Amplitude Modulation in FP Cavity - Z-cut LiNbO 3 (LiTaO 3 ) thin plate coated with high reflectivity dielectric mirrors. The transmissivity in FP with the phase shift. Under an applied field,
- The slope of the transmission curve at the half-transmissivity point is where F = the finesse of the cavity ( ) Under, the modulation depth 8.2.2. Phase Modulation - An asymmetric FP cavity with a rear mirror reflectivity of 100% and the front mirror, a partially reflecting dielectric mirror of R < 1.0.
- The reflectivity coefficient where we took, and, - The phase shift upon reflection,, in terms of ; for. Under an applied field for the case of a Z-cut LiNbO 3 plate,. - If the EO crystal is biased such that in the absence of the modulation voltage, For small modulation voltage,
8.4. Bistable Electro-Optic Devices - Linear optical devices: with transmissivity. This linearity disappears when n depends on either the input intensity or the output intensity or both. - Optical nonlinearity: or some optical feedback in the EO crystal. 8.4.1 Bistable FP Resonator: - A small fraction of the transmitted beam is monitored by a detector whose output is proportional to the transmitted intensity and is amplified and used to drive the modulator in the resonator. The transmissivity in the resonator with. = one-half of the round-trip phase shift of light in the cavity without feedback servo, = the phase change due to the EO crystal driven by a voltage proportional to. ( = constant) Under appropriate conditions, "bistabilty", differential gain and optical limiting action are exhibited.
[Homework] Prob.# 8.5, 8.6