  We study the field dependence of the maximum supercurrent in narrow edge-type
thin-film Josephson junctions. It is assumed that the junction extends across
thin-film strip of width W that is much less than the Pearl length; the film
thickness is much less than the London penetration depth. We calculate the
maximum supercurrent within nonlocal Josephson electrodynamics, which takes
into account the stray fields affecting tunneling currents. In the case when W
is much less than the thin-film Josephson length, the phase difference along
the junction depends only on the junction geometry and the applied field, but
is independent of the Josephson critical current density, i.e., it is
universal. Zeros of the maximum supercurrent are equidistant only in large
fields (unlike the case of junctions with bulk banks); they are spaced by a
field that is much smaller than the one of bulk junctions. Peaks of the maximum
supercurrent decrease inversely proportional to the square root of the applied
field, i.e., slower than 1/H for the bulk.
