  Motivated by recent experimental work by Folkenberg et al. we consider the
effect of weak disorder in the air-hole lattice of small-core photonic crystal
fibers. We find that the broken symmetry leads to higher-order modes which have
generic intensity distributions resembling those found in standard fibers with
elliptical cores. This explains why recently reported experimental higher-order
mode profiles appear very different from those calculated numerically for ideal
photonic crystal fibers with inversion and six-fold rotational symmetry. The
splitting of the four higher-order modes into two groups fully correlates with
the observation that these modes have different cut-offs.
