A leached fiber bundle with the light outlet points positioned as accurately as possible is provided, in which the end faces are not completely fused together, but rather are only fused together at their contact surfaces. The interstices formed are permanently filled with adhesives with the aid of a pressure reduction. To protect the optical fibers from mechanical load, adhesives are introduced into the transition region between the fixed end region and a flexible region. This allows the leached fiber bundles to be produced more economically and also improves their service life.