The effect of the ▿n2term on the modes of an optical square-law medium

Solutions of the mode problem of an optical waveguide with a square-law medium are usually based on the scalar wave equation. An exact derivation of the wave equation from Maxwell's equations results in an additional term containing the gradient
\nablan^{2}
of the square of the refractive index
n
. It is the purpose of this correspondence to evaluate the change of the propagation constants of the modes of the square-law medium that is caused by the
\nablan^{2}
term. We find that the change is significant only for TM modes of low order, but insignificant for all other modes of a dielectric slab with parabolic index distribution.