A perturbative approach for the determination of modes in slightly elliptical waveguides

We present an approximate evaluation of the modal field distribution in an elliptical waveguide of small ellipticity in terms of modes of a circular waveguide. This with the aim of developing an approximate mode matching technique relying on the simple expressions of the field in terms of Bessel functions and avoiding the exceedingly complex modes of the elliptical waveguide, given in terms of Mathieu functions.