Question regarding Helmoltz equation

[maverick280857]

Hi,

I have the following question regarding the Helmoltz equation in the context of a Transverse Magnetic wave in a waveguide:

$$\nabla_{t}^{2}E_z + h^2E_z = 0$$

Question: Is $h$ always real?

($\nabla^{2}_{t}$ denotes the transverse Laplacian operator)

Thanks.

 

[Meir Achuz]

In a wave guide h is almost always real. It must be real for a wave to propagate.
If the frequency is below the critical frequency, the wave is rapidly attenuated, as
exp[-(Im h)x].

 

[maverick280857]

Thanks clem.