2D FDTD programming for a lossy medium

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sansanres

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I want to build 2D grid for a lossy medium using FDTD. And I have to build a perfect conductor wire in the grid as well. Since there are two modes (TM and TE) what mode should I use in Maxwell's update equations. (Because the electric field in side the conductor is zero, I'm little confuse if I can use the TMz mode.)

Could anyone help me with this?
Thank you in advance!
 

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