Elliptical facet cylindrical optical fiber - Mathieu equation

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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..
 

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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
 

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