Extraordinary-mode refractive-index change produced by the linear electro-optic effect in LiNbO(3) and reverse-poled LiNbO(3)

To examine aspects of an integrated photonic electric-field sensor, we calculate electro-optically induced refractive-index change in regular and reverse-poled LiNbO(3). Specifically, for y-propagating extraordinary modes, we determine how index change depends on electric-field magnitude and direction. To accomplish this, changes in index-ellipsoid shape and orientation are found by the use of a numerical eigenvalue procedure to diagonalize the impermeability tensor; then, refractive index is calculated by the use of a vector reference-frame transformation and a small perturbation approximation. A general formula is inferred from calculations for specific field directions. Electro-optic coefficients for reversepoled LiNbO(3) are obtained by application of a tensor reference-frame transformation to those of LiNbO(3). The index-calculation procedure has utility beyond the problem that is considered.