  Cladding structures of photonic band-gap fibers often have air-holes of
non-circular shape and, typically, close-to-hexagonal air holes with curved
corners are observed. We study photonic band-gaps in such structures by aid of
a two-parameter representation of the size and curvature. For the fundamental
band-gap we find that the band-gap edges (the intersections with the air line)
shift toward shorter wavelengths when the air-filling fraction f is increased.
The band-gap also broadens and the relative band-width increases exponentially
with f^2. Comparing to recent experiments [Nature 424, 657 (2003)] we find very
good agreement.
