Propagation path length variations due to bending of optical fibers

The geometric effect and material stress effects are included. Calculations are shown that put an upper limit on the expected phase shift in single mode fibers. The fractional change in propagation constant is presented. Moding effects in multimode fibers cause extraneous phase shifts of unusually high magnitude. This does not occur in single mode fibers, rendering them very insensitive to bending with a theoretical limit given by the above relation.