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- Proving an equation in a book

Hello everyone,

I am reading some book titled: Periodic Structures: Mode-Matching Approach and Applications in Electromagnetic Engineering.

In Chapter 2, there is an equation as follows:

where
. Here the electric field is along the transverse x − y plane like the propagation vector kt.

Now it is said that if we substitute the equation above in the following equation by getting rid of H_z:

we will obtain the following:

.

When trying to prove this, I don't get the same result. It's been a long time that I am trying to prove this. Can someone please help me prove if this is true ?

Thank you very much.

I am reading some book titled: Periodic Structures: Mode-Matching Approach and Applications in Electromagnetic Engineering.

In Chapter 2, there is an equation as follows:

Now it is said that if we substitute the equation above in the following equation by getting rid of H_z:

we will obtain the following:

When trying to prove this, I don't get the same result. It's been a long time that I am trying to prove this. Can someone please help me prove if this is true ?

Thank you very much.