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mathematical theory for cylindrical resonator with multi layer dielectrics inside

yefj

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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.

1724567340990.png

1724567366345.png
 

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