mathematical theory for cylindrical resonator with multi layer dielectrics inside

[yefj]

Hello , I have simulated a cylindrical resonator as shown below.
I have put teflon cylinder inside epsilon=2.1 and saphire epsilon=9.4.
Is there a way i Could see how mathematickly this multi layer structure changes the magnetic and electric fields of the modes?
Thanks.

 

[FvM]

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