Abstract
In contrast with scalar modes, the vector modes of two-dimensional waveguides with separable refractive-index profiles cannot be calculated by a simple product ansatz for the fields. It is shown that a separation of the dominant field component into two factors, with each depending on only one of the two Cartesian coordinates, is accurately possible up to first order in the small relative refractive-index difference Δ for symmetric separable profiles. This allows us to calculate the modal propagation constants by decomposing the problem into two independent TE and TM planar wave equations. Birefringence is thereby included to an accuracy of first order in Δ. The minor field component can be separated to first order in Δ, if one of the two factors constituting the major field component is the fundamental mode of the parabolic profile, but cannot be separated in general. The longitudinal field components are separable to their lowest order Δ1/2 for all separable profiles.
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