In the absence of electrode fields the refractive index ellipsoid, or indicatrix, is of the following form:

Optical BPM - Equation 19

where no , ne  are the ordinary and extraordinary refractive indices, respectively.

Under the influence of an electric field the index ellipsoid is deformed in space:

Optical BPM - Equation 20

In different cases of the cut, the propagation and polarization, and the electrode field direction, different electrooptic coefficients rij  are used in the simulation program. Table 4 is the reference table to help you in entering your electrooptic coefficients. The mixed coupling terms in the index ellipsoid were ignored. The change in the corresponding refractive index can be approximated as

Optical BPM - Equation 21

where EH , EV , rH , and rV  are the electric fields in horizontal and vertical directions and the corresponding electro optic coefficients, respectively, and i denotes either ordinary or extraordinary refractive index. Notice that whether the electrode field is considered horizontal or vertical depends on the electrode configuration, voltage and the waveguide position. Intuitively, you can assume that the electrostatic field lines between electrodes follow patterns familiar from electrostatics. For example, if you place one of the electrodes right on the top of the waveguide, it will likely produce the static field that is vertical in the waveguide.

TE

TM

Crystal CutPropagation

Direction

Horizontal

Electrode Field

Vertical

Electrode Field

Horizontal

Electrode Field

Vertical

Electrode Field

XYr330r130
YXr330r13r22
ZXr22r130r33
ZY0r130r33
YZ0–r220r22
XZr220–r220

Table 4