Lecture 15 Chapter IX Electrooptic Modulation of Laser Beams Highlights 1. Electrooptic (EO) Effect 3. EO Amplitude and Phase Modulations 2. EO Retardation Controlling the intensity or phase of laser beams … Propagation of laser beams in crystals with an applied electric field Index of refraction is proportional to Linear EO effect 4. High-Frequency Modulation Considerations

§9.1 Electrooptic Effect In common crystals: Birefringence Phenomenon z (optics axis) s y o ne()ne() x (n o, 0, 0) (0, -n o, 0) A B  (0, 0, n e ) Index ellipsoid ordinary extraordinary Two linear polarized modes: xyz The principal dielectric axes, along which D and E are parallel

§9.1 Electrooptic Effect In crystals with an applied E field: Electrooptic Effect However, this effect exists only in crystals that do not posses inversion symmetry For example, linear electrooptic effect is the change in the indices of the ordinary and extraordinary rays that is caused by and is proportional to an applied electric field. Rotate crystal Rotate crystal and E plates

§9.1 Electrooptic Effect I. The origin of EO Effect Don ’ t be confused with No electric field

§9.1 Electrooptic Effect Index of refraction w/o E filed Linear EO effect (Pockels Effect) Secondary EO effect (Kerr Effect) EO Effect --- the index of refraction change of media due to the applied electric field. II. The Index of Refraction Change W/O E field With E field

§9.1 Electrooptic Effect Electrooptic tensor

§9.1 Electrooptic Effect The form of EO tensor for all crystal symmetry class Table 9-1 Linear EO coefficients of some commonly used crystals Table 9-2 Be able to understand this form Be able to link these values to table 9-1

§9.1 Electrooptic Effect III. The EO effect in KH 2 PO 4 (KDP) Symmetry group: z (optics axis) y o x x y x’ y’

§9.1 Electrooptic Effect Coordinate Rotation require

§9.1 Electrooptic Effect IV. The EO effect in LiNbO 3 (LN) Symmetry group:

§9.1 Electrooptic Effect

§9.2 Electrooptic Retardation KDP crystal x x’ y’ or and The phase difference at the output plane z=l between two components is called the retardation

§9.2 Electrooptic Retardation Phase difference:

§9.2 Electrooptic Retardation Half wave voltage: Calculate the ADP crystal ’ s HWV

§9.3 Electrooptic Amplitude Modulation At  = , the polarization is rotated 90 degree, and is vertical to the original one. A polarizer after crystal can be used to control the laser beam intensity which serves as the basis of the EO amplitude modulation. At the incident plane or

§9.3 Electrooptic Amplitude Modulation Outside the crystal After polarizer

§9.3 Electrooptic Amplitude Modulation

An optical communication link using an EO modulator

§9.3 Electrooptic Amplitude Modulation An schematic configuration of EO Q-switch

§9.4 Phase Modulation of Light Amplitude modulation: by means of EO effect, phase difference convert to the polarization change, using polarizer to accomplish the intensity modulation Phase modulation: by means of EO effect, merely changes the output phase without any change of the polarization

§9.4 Phase Modulation of Light Phase modulation index

§9.5 Transverse EO Modulators Longitudinal mode of modulation: electric field is applied along the light propagation direction Transverse mode of modulation: electric field is perpendicular to the light propagation direction