Waveguide discontinuity with centered circular aperture

[EmilyRuck]

Hello!
This is the first time I write in the forum. I hope to be fully in-topic.
I'm dealing with a rectangular waveguide discontinuity: a perfect-conductor plane orthogonal to the propagation direction, with a circular aperture in the centre of the guide section. The structure is symmetrical along the x-axis and the y-axis and I drew it in the attachment, where the z axis is outgoing from the screen.
In my note the professor talked about a strange "Edge Theorem" (which we didn't demonstrate and which I can't find in any book). The Theorem says that:
- a field component which is parallel to an edge is diffracted but not folded (and so it doesn't generate any new field component);
- a field component which is orthogonal to an edge is diffracted and folded along the plane perpendicular to the edge (so it could generate a new field component).
The discontinuity is reached by the fundamental TE₁₀ mode: in my coordinate system, it has E_Y, H_X and H_Z field components.
According to the Theorem, when E_Y reaches the upper and the lower part of the circle (points A and D in the picture) it is orthogonal to the circle edge and it generates an E_Z component.
When H_Z reaches the left and the right part of the circle (points B and C in the picture) it generates H_X; similarly, in those points H_X generates H_Z.
But what about H_Y and E_X? I can't see how they are generated, but they are, because I wrote in my notes that the field becomes a 6-components field.
The only electric field component is E_Y, but when it reaches the oblique edge between A and B, it generates an E_Z again and not an E_Y! What is wrong?
Thank you anyway!
Bye,

Emily

 

[Bob S]

I don't have a copy of the article, but Hans Bethe wrote a paper during the War on microwave couplers using small holes. These later became referred to as Bethe holes. See http://prola.aps.org/abstract/PR/v66/i7-8/p163_1.
I would also look in Marcuvitz's Microwave Handbook..

 

[EmilyRuck]

I don't have a copy of the article, but Hans Bethe wrote a paper during the War on microwave couplers using small holes. These later became referred to as Bethe holes.
I would also look in Marcuvitz's Microwave Handbook..

I tried to read the article but it's not available, unfortunately. Thank you anyway for your reference! I read also the Marcuvitz's Microwave Handbook: it deals with such a discontinuity, but it considers just the equivalent circuit (an admittance) and not which field components arise from it.

Emily