Permanent, photoinduced refractive-index gratings written along the longitudinal axis of germanium-doped, two-mode, elliptical-core fibers are found to affect the differential phase modulation between the co-propagating LP₀₁ and LP₁₁ even modes. The modal beat length of a two-mode fiber grating is found to vary inversely with strain induced to the fiber and leads to a new type of weighted optical fiber sensor whose sensitivity varies as a function of length along the structure to which it is attached or embedded. A weighting function is imparted to the fiber sensor by way of a chirped, two-mode grating written into the core, the chirp adopting the shape of a specific vibration-mode amplitude. This novel type of spatially-weighted, distributed fiber sensor is shown experimentally to function as an efficient vibration-mode filter by enhancing either the first or second mode of a thin, one dimensional cantilever beam. These results support future applications of spatially-weighted/ distributed optical fiber sensors for the evaluation and control of vibrating structures. / Master of Science