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 

 of the square of the refractive index 

 . 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 

 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.