Question of electro-magnetic

orthogonal te tm tem

Hello,

This a question about electromagnetic waves.
E is the electric field,
B the induction magnetic field,
k the direction of propagation,

For plane wave (TEM, Transverse EM),
E is orthogonal to k
B is orthogonal to k
E is orthogonal to B

For a Transverse Electric (TE)
E is orthogonal to k
B is NOT orthogonal to k

For a Transverse Magnetic (TM)
E is NOT orthogonal to k
B is orthogonal to k

1/ I think that for TE and TM waves, we have E orthogonal to B, right?

2/ Is there waves, where E is not orthogonal to B?

Thanks,

slvn

1) In freespace (air), yes. They are related by the intrinsic impedance.

2) No. It wouldnt satisfy maxwell equations.

Pls correct me if i'm wrong. Thanks.

Probably in medium like plasma both fields are not orthogonal

For materials that are homogeneous, a plane wave will always have

D is normal to k
B is normal to k

For isotropic and homogeneous materials, a plane will always have

E and D coplanar
H and B coplanar
E,H,k are orthogonal
All plane waves are TEM

When the material is not homogeneous such as in meta-materials or slurries, the fields can be much more complicated because there is scattering, resonances, and evanescent fields. In this case it is possible that nothing is coplanar or orthogonal.

When the permittivity is anisotroptic, E and D are no longer coplanar because the permittivity is a tensor. Similarly, H and B are no longer coplanar when the permeability is a tensor. So anisotropy can lead to the fields being noncoplanar and not orthogonal.

Some other concepts that may be helpful to you. It does not make sense to talk about TE and TM in homogeneous/isotropic materials because all plane waves are TEM. The concept of TE and TM is only useful when you are analyzing a device, waveguide, or the interface between two materials.

You will also come across TE and TM modes in waveguide analysis. Transmission line waveguides can support TEM modes of they have at least two conductors. All other waveguides that I know of only have hybrid modes that are not TEM, TE, or TM. This has to do with the geometry of fields and the magnetic fields being required to form loops. That I know of, TE and TM modes do not physically exist and are used only as an approximation to simplify the analysis. Sometimes you will hear these being called quasi-TE and quasi-TM. For sure, the longitudinal component of E or H is often extremely small and numerically you can set it to zero and still get quite accurate results. When you set Ez=0 or Hz=0, Maxwell's equations separate into TE and TM modes, but this is an approximation only. Make your teacher justify why you can set Ez or Hz equal to zero. You may find they stumble on this one. I have performed rigorous analysis of dielectric waveguides and found many times the z component is five or six orders of magnitude smaller than the transverse components.

Hope this helps!

-Tip