The electrooptic effect is the modification of the refractive index by an externally applied electrostatic field. In the linear electrooptic effect, the size of the perturbation to the refractive index is directly proportional to the strength of the local electrostatic field. In OptiBPM, there are two features to model in the linear electrooptic effect; one is a general implementation of the effect for any kind of electrode shape and material, the other is aimed specifically at Lithium Niobate or other crystals with point group symmetry 3m. The general implementation was introduced in release 9.0. It follows a strategy of defining an electrode material to identify electrode position and shape the same way as dielectric materials define optical waveguide position and shape. In this approach, dielectric materials are supplied with electrostatic permittivity definition, so that the electrode potentials can be used to find the electrostatic field in the transverse plane. Once the field is found, the perturbation to the refractive index is found directly by equation [21].
The 3m point group electrooptic simulation is mainly for the specific technology of diffused waveguides in electrooptic materials like Lithium Niobate. This feature is accessed through the Electrode Region Tool found in the layout designer. This feature works independent of the general electrooptic simulation feature, it is not necessary to define electrode materials to use the Electrode Region Tool. These Lithium Niobate devices are waveguide modulators or switches that employ metallic electrodes deposited on top of optical waveguides to serve the purpose of applying the electric field. An intermediate buffer layer with a low dielectric constant is often deposited between the electrodes and the substrate to reduce the losses that are due to the metallic cover of the waveguide. The efficiency of the device depends on the overlap between the electric field and the optical field. By changing electrode parameters you can optimize the device. Usually, the electrode in this kind of electrooptic device is plated to a thickness of 2-3 microns in order to reduce its ohmic losses while the electrode width can be as small as 10 microns and the gap between electrodes is typically 5 microns. The calculation of an electric field of the coplanar electrodes in the Electrode Region of OptiBPM is based on reference [8].
OptiBPM provides the Electrodes Region tool to enter and specify one or more electrode sets. Each electrode set can have up to three electrodes, with each electrode defined by its width and applied voltage. It is also possible to adjust the separation between the electrodes, their common thickness, and to apply a buffer layer characterized by its thickness, horizontal and vertical permittivity, and refractive index. The number of the electrode sets per region is not limited.
From the electrooptic effect perspective, LiNbO3 is a trigonal crystal with the point group symmery 3m. The matrix of the electrooptic or Pockel’s coefficients for the group 3m crystals is [11]
Values of the electrooptic coefficients can be altered within the Profile Designer, however, published data are proposed as the program defaults. The crystal coordinate system (X, Y, Z) is aligned with the principal axes of the crystal. Referring to the crystal coordinates, the program offers calculations with different crystal cuts, propagation directions and the choice of the TE and TM polarization.
Notice that the (X, Y, Z) crystal system is not the same as the device layout coordinate system (x, y, z). In the layout coordinates, it is assumed that the z-direction is the propagation direction. The electrode fields are referred to the layout coordinates. The crystal cut direction in conventionally assumed as perpendicular to the crystal wafer surface. Electrode sets produce static electrical fields that can be either horizontal or vertical to the crystal surface. The optical fields, being the principal electrical component of the electromagnetic field, can oscillate horizontally (TE polarization) or vertically (TM polarization) to the surface.