With only 2 elements in the microphone array, i was getting a polar plot resembling a figure-eight pattern sideways close to 20 kHz. I didn't like that, so I tried an experiment where I doubled the array to 4 microphones, arranged in a square. This improved the pattern — it now has a, uh, dentoid (tooth-like) pattern close to 20 kHz, and the sideways Bode plot is very interesting — it cuts the high end by 6 dB. I think that's going to improve the perceived directivity.