Difference in proof between TE and TM modes

In summary, the conversation discusses solving a system for TE modes and finding two types of solutions: symmetric and asymmetric. The solutions for TM modes are also discussed, with the difference being the addition of the dielectric constant n^2 in the eigen equations. The speaker also mentions finding insight from a resource and expresses difficulty in understanding the differences between TE and TM modes.
  • #1
GengisKhan
2
0
I'm a little confused regarding the maths of TE and TM modes.

Solving the following system for TE (which derives from Ey(x, z, t) = Em(x) = exp[i(ωt-βz)] ):
Asin(px) + Bcos(px) , -d/2 < x <d/2
Cexp(-qx), x>d/2
Dexp(qx), x<-d/2

we conclude in two types of solutions for TE modes: symmetric: ptan(pd/2) = q and asymmetric: pcot(pd/2) = -q.

What is different for the above solutions for TM? I have a hard time determining that. I think it has something to do with the dielectric constant, but I'm not quite sure.

I can elaborate on any maths you ask for. Also sorry for the quality of my post, it is my first one.
 
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  • #2
Hi, when you write the solution Ey =exp[i(\omega t - \beta z)], this is a wave traveling in the negative z direction.

If you want to break this wave as the sum of a TE mode and a TM mode, then for the TE wave, only Ez is 0. Ex, Ey, Hx, Hy, and Hz are not zero. for the TM wave, Hz is 0. Ex, Ey, Ez, Hx, Hy are not zero.

I cannot relate your question to the definitions of the TE and TM mode.

elgen
 
  • #3
Elgen, thanks for your answer! That's the very first part of the proof, I'm trying to understand beyond that.
Fortunately, I found some insight from http://ece562web.groups.et.byu.net/notes/slab_waveguide.pdf.
TM Modes solutions are found at pages 8-9. The problem is that I don't know how to reach the eigen equations, which are the same as TE's (described earlier in the .pdf), only with the dielectric constant n^2 added. If someone can briefly describe what is different from TE, I'd be grateful!
 

1. What is the difference between TE and TM modes?

The main difference between TE (Transverse Electric) and TM (Transverse Magnetic) modes is the polarization of the electric and magnetic fields. In TE mode, the electric field is perpendicular to the direction of propagation, while in TM mode, the magnetic field is perpendicular to the direction of propagation.

2. How do TE and TM modes behave in different materials?

TE and TM modes behave differently in different materials due to their different field polarizations. In a conducting material, the electric field cannot penetrate, making TE modes dominant. In a dielectric material, the magnetic field cannot penetrate, making TM modes dominant. In a perfect conductor, both TE and TM modes cannot exist.

3. Can TE and TM modes coexist in a waveguide?

Yes, TE and TM modes can coexist in a waveguide. In fact, most waveguides support both TE and TM modes simultaneously. However, the specific modes that are supported depend on the geometry and material properties of the waveguide.

4. What is the difference in propagation constants between TE and TM modes?

The propagation constant, also known as the phase constant, is the rate at which the phase of a wave changes as it propagates through a medium. In TE modes, the propagation constant is related to the electric field, while in TM modes, it is related to the magnetic field. This results in different propagation constants for TE and TM modes in the same waveguide.

5. How do TE and TM modes affect the transmission of light in optical fibers?

In optical fibers, both TE and TM modes can exist and contribute to the transmission of light. However, the specific modes that are supported depend on the fiber's core and cladding materials. This can have an impact on the transmission properties, such as the polarization sensitivity and bandwidth of the fiber.

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