What Determines the Orientation of Magnetic Fields in TE Modes?

[casacasa]

I have not yet gotten any definite answer. Hope some of you can help me about this question:

We know that for the polarisation of the wave:

* TE modes (Transverse Electric) no electric field in the direction of propagation.
* TM modes (Transverse Magnetic) no magnetic field in the direction of propagation.
* TEM modes (Transverse ElectroMagnetic) no electric or magnetic field in the direction of propagation.
* Hybrid modes nonzero electric and magnetic fields in the direction of propagation.
(from wiki, sorry)

So, i call vector k is the wave vector, that means the direction of the wave; we knew that k,E,H always perpendicular each other (k_l_E, E_l_H, H_l_k) (*).
It is very clear in the case TEM, but see the case of TE for example, TE means in the direction of k, E=0 (no electric field in the direction of propagation), but, where is H?

of course H is not the same in the case TEM (in this case H in the plane _l_k to have H=0 in k direction), ----but if H wants to be perpendicular with k (*), H have to be in the plane which is perpendicular with k ---> become TEM ---> TE is not exist !? How to explane this ?

Sorry for my english and thanks.

 

[Bob S]

If you place two parallel mirrors 100 mm apart, and shine a polarized pencil laser beam at an angle such that the light beam propagates down along the mirrors by bouncing back and forth (zig-zagging) between them, the beam will propagate between the mirrors, even though the beam itself is zig-zagging. You can rotate the laser pencil, and create a light beam propagating along the mirrors with either a TE or a TM polarization. This is not a TEM beam because the laser beam is zig-zagging at an angle to the overall direction of the beam power, which is parallel to the two mirrors.

 

[Born2bwire]

The language when it comes to confined waves can be a little confusing. Technically, the wave vector k is still normal to the electric and magnetic fields. The direction of propagation that they are talking about is the guided direction. Like Bob_S stated, the actual wave is going to reflect off of the sides of the waveguide, bouncing back and forth in the x and y directions (assuming the guided axis is along z) so the net direction of propagation is the z direction. This is also seen in the solutions for the waves. What you will find is that the waves in the x and y directions are standing waves, not traveling waves. However, you can always decompose a standing wave as the superposition of two traveling waves.

Thus, you can rewrite the wave solutions for many waveguides as the summation of traveling waves. Doing so, you will see that the E and H fields are always normal to the actual wave vector. But they will not be normal to the vector of guided propagation (which is what they are referencing the transverse directions to). The TEM solution is where the true wave vector is aligned with the guided wave vector, but this solution is evanescent and so cannot create a propagating wave.