  Optical fibers containing multiple cores are being developed towards capacity
enhancement in space-division multiplexed optical communication networks. In
many cases, the fibers are designed for negligible direct coupling of optical
power among the cores. The cores remain, however, embedded in a single,
mechanically-unified cladding. Elastic (or acoustic) modes supported by the
fiber cladding geometry are in overlap with multiple cores. Acoustic waves may
be stimulated by light in any core through electrostriction. Once excited, the
acoustic waves may induce photo-elastic perturbations to optical waves in other
cores as well. Such opto-mechanical coupling gives rise to inter-core
cross-phase modulation effects, even when direct optical crosstalk is very
weak. The cross-phase modulation spectrum reaches hundreds of megahertz
frequencies. It may consist of discrete and narrow peaks, or may become
quasi-continuous, depending on the geometric layout. The magnitude of the
effect at the resonance frequencies is comparable with that of intra-core
cross-phase modulation due to Kerr nonlinearity. Two potential applications are
demonstrated: single-frequency opto-electronic oscillators that do not require
radio-frequency electrical filters, and point-sensing of liquids outside the
cladding of multi-core fibers, where light cannot reach.
