How to prove that TE modes cannot exist in microstrip structures

[yefj]

I kow that the modes in microstrip are TM modes.
I know that we have boundary conditions to see if the mode exists.
What boundary condtions i need to use for TE and TM?
Where do i put them in the equation bellow?
I know that for TM ,Hz=0
for TE Ez=0
How do i see that that is no TE mode in microstrip?
Thanks.

Hello, i am trying to visualise the TM TE modes in the microstrip as shown in the photos bellow.
the derivation of the TM01 mode shown bellow
by the formal definition:
the Transverse Magnetic (TM) mode, the magnetic field is transverse to the direction of propagation while the electric field is normal to the direction of propagation" transverse=paralel,the magnetic field is not paralel to the direction of propogation.So how its a TM mode based on the formal definition?
Thanks.


Thanks.
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[biff44]

If i recall, modes in microstrip are LSE modes. That is why there is frequency dispersion