Various types of holey fiber provide optical propagation. In various embodiments, for example, a large core holey fiber comprises a cladding region formed by large holes arranged in few layers. The number of layers or rows of holes about the large core can be used to coarse tune the leakage losses of the fundamental and higher modes of a signal, thereby allowing the non-fundamental modes to be substantially eliminated by leakage over a given length of fiber. Fine tuning of leakage losses can be performed by adjusting the hole dimension and/or the hole spacing to yield a desired operation with a desired leakage loss of the fundamental mode. Resulting holey fibers have a large hole dimension and spacing, and thus a large core, when compared to traditional fibers and conventional fibers that propagate a single mode. Other loss mechanisms, such as bend loss and modal spacing can be utilized for selected modes of operation of holey fibers. Other embodiments are also provided.