We consider transitions of bundles of coupled optical fibre cores. Iso
lated, each core is single-moded. In the bundle, the cores touch each
other and their arrangement is gradually changed from a compact to an
elongated form. We use the method of Henry and Verbeek to calculate th
e propagation constants of bound modes during the transition. We show
that, with the parameters of the structure appropriately chosen, the n
umber of bound modes in the bundle remains approximately constant duri
ng the transition. This means that optical fibre beam transformers of
high efficiency are theoretically possible.