Eigenvalue and field equations of three-layered uniaxial fibers and their applications to the characteristics of long-period fiber gratings with applied axial strain.

By using the Debye potentials, the exact eigenvalue equations and the corresponding field distributions of the core and cladding modes for three-layered, radially stratified, and dielectric uniaxial optical fibers are derived completely; the modes include TE, TM, and hybrid HE/EH modes. The strain characteristics of long-period fiber gratings' (LPFGs') with applied axial strain are investigated theoretically by studying three-layered uniaxial optical fibers. When uniform axial strain is applied to fiber, the core, and inner and outer cladding become uniaxial crystal optically; that is, the optical axes are parallel to the fiber's axis. Analytic expressions of the strain sensitivities of LPFGs are derived. The analysis reveals that the strain sensitivities of LPFGs based on various cladding modes, including the shift value and direction of the resonance wavelength, differ greatly.