Uneven ground plane dimensions under patch antenna

Hello all,
I've made an antenna in which th ground plane under it on one side is much shorter than the ground plane on the other side as a result of which, I'm getting side lobe that i suspect is because of reflection from the extended ground plane on the other side.

Has anybody seen a phenomenon like this and if yes, how can one control it? Would an absorber over the ground plane on the larger ground plane side help at all?

Thanks,
Ananth.