We consider theoretically phase locking in a simple two-dimensional Jo
sephson junction array consisting of two loops coupled via a joint lin
e transverse to the bias current. Ring inductances are supposed to be
small, and special emphasis is taken on the influence of external flux
. It is shown that in the stable oscillation regime both cells oscilla
te with a phase shift equal to pi (i.e., antiphase). This result may e
xplain the low radiation output obtained so far in two-dimensional Jos
ephson junction arrays experimentally. (C) 1996 American Institute of
Physics.