Something to be clarified about EM Wave: TE, TM and TEM

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In electromagnetic (EM) wave theory, Transverse Electric (TE) waves have a zero electric field component in the direction of propagation (E_z = 0), but both E_x and E_y can be non-zero. The assertion that E_y must also be zero in TE waves is incorrect; both E_x and E_y can exist simultaneously. For Transverse Magnetic (TM) waves, the magnetic field component in the direction of propagation (H_z) is zero, while for Transverse Electromagnetic (TEM) waves, both E_z and H_z are zero. To clarify these concepts, consulting undergraduate-level textbooks on optics or electrodynamics, such as Griffiths or Hecht, is recommended. Understanding these distinctions is essential for further study in the field.
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I have been reading different articles about EM wave modes,
it is said that in TE waves the E_z is zero, similarly for TM H_z is zero, and TEM both E_z and H_z are zero.

How about the E_x and E_y in TE wave?
Someone said E_y is also zero and only E_x exists in TE...is this true? Is it possible that I overlooked some assumptions made?
Or actually the fact is, for TE, both E_x and E_y are NON-zero; only E_z is zero?

I know this is a simple question but I do hope to confirm it earlier and proceed with my study, thanks for your kind attention.:smile:
 
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Please go through a textbook of UG level optics or electrodynamics & then in your problem specify what x,y,z directions mean.
You may refer Griffiths (electrodynamics), Hecht/ Ajay Ghatak (optics).
 
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