Elliptical facet cylindrical optical fiber - Mathieu equation

[Sciencestd]

Let's say I have three modes in a fiber that is elliptical cylinder shaped (cylinder with elliptical facet), as in the image below (the source:Optical Engineering, 46(4), 045003 (2007)) so what is the equations that describe these fields..

 

[Sciencestd]

Just an idea came up to my mind, I need the equations to know the evanescent field above the waveguide... do you think it is possible to fit a function like "sinc" or similar to obtain filed on the surface? if yes how one can do it