Slots on waveguide are cut such that it obstructs the path of the current flowing on the surface of the waveguide,so that maximum radiation occurs. Why are we not considering the field inside the waveguide to get radiated i.e the slots are cut at offset but the field keeps on decreasing as we move towards the edge of the waveguide?
The following literature may help you for waveguide slotted antenna array:
1. Book of R S Elliot, Antenna Theory & Design, Wiley
2. W. Wang et al., A broadband slotted..., IEEE Trans Antennas & Propa., vol. 54, 2006.
3. P. N. Richardson et al., Design of a ........, Microwave Journal, Jan 1988.
4. A. J. Sangster at al., Theoretical design......., IEE, Part-H, Feb. 1989.
Usually these types of antennas are based on the fundamental mode in the waveguide. If, for example, it was based on the second order mode the modal distribution must absolutely be considered when placing the slots. You would not want to place the slots where the mode has a null because the slot would not be felt. Otherwise, the placement of the slots is intended to adjust the strength of the coupling between the guided mode and the radiated field. The farther toward the outside (assuming fundamental model), the weaker the coupling and the antenna will need to be longer.
We have a PhD thesis on this at Karlsruhe Institute of Technology:
Dr.-Ing. Christian Römer
Promotion am 01.02.2008 Ref.: Prof. Dr.-Ing. W. Wiesbeck
Korr.: Prof. Dr.-Ing. W. Freude
Thema: Slotted Waveguide Structures in Phased Array Antennas
Let me know if you can not download it.
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