To make an antenna out of a waveguide, you engrave a longitudinal slot (or array of slots) offset from the center because the aperture should be at a position of varying fields (eg. electric field, dominant mode with maximum at the center and zero at the edges of the lateral walls.) So the slot placement should be in-between maxima (center of the waveguide) and minima (waveguide wall) to radiate which results in E-plane beam tilt. It should be prominent in a single element and marginal in an array structure. You can avoid it by placing adjacent slots on the opposite sides from the center, as shown in the attachment.
The coupling you have shown is for slots on the broad wall of the waveguide.
Syed Muhammad Umar said he is considering slots on the narrow wall.
Vertical slots on the narrow wall of the waveguide won't radiate. To get them to radiate you either have to slant them a bit (coupling increases with angle) or put something in the waveguide to angle the fields.
If they all lean at the same angle then to be in phase or nearly in phase they have to be more than a wavelength apart, because the guide wavelength is longer than the air wavelength. This means you have grating lobes. If you don't know what grating lobes are then look them up on the internet, for example https://www.microwaves101.com/encyclopedias/grating-lobes. The way round this is to have the slots just over half a wavelength apart but tilted alternate directions so the phase reversal from the tilt cancels the phase reversal from the half-wave. You can still get grating lobes but only at very large steering angles.
But I am referring to Beam squinting problem in my array design, I wanted to know the cause of it because I have assigned the standard separation to the array
Have you taken into account that the wavelength is different in the waveguide to what it is outside?
Half-wavelength free-space spacing will result in a tilted beam because the wavelength is longer inside the guide.
It is possible that very strong coupling could also change the wavelength in the guide, but this much coupling would be unusual. Are your slots introducing reactance into the guide that is changing the guide wavelength?
If your beam is tilted along the direction of the waveguide then you have your phasing wrong, which means that the wavelength in the guide is not what you think it is, or you have calculated your separation wrongly. The slots should be a bit further apart than a free-space half wavelength, to get broadside radiation.
If you are simulating it then it is easy to measure the half-wavelength in the guide, and also to vary the frequency and see where the beam scans, and also to see if all the slots are in (alternate) phase.
Hi everyone, do you know how to get the guide wavelength in CST of a cylindrical guide with several dielectric circular layers in it? Malcolm White Syed Muhammad Umar