# Question regarding Helmoltz equation

1. Mar 19, 2009

### 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.

2. Mar 19, 2009

### clem

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].

3. Mar 20, 2009

### maverick280857

Thanks clem.

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