Wavelength Shifts of Cladding-Mode Resonance in Corrugated Long-Period Fiber Gratings under Torsion

A finite deformation theory of elasticity and a theory of nonlinear photoelasticity are applied to describe the wavelength shifts of cladding-mode resonance in corrugated long-period fiber gratings under torsion. The deformation of fiber is found by use of the Murnaghan model of a solid elastic body. The quadratic photoelastic effect that is proportional to the second-order displacement gradient is investigated and compared with the classical photoelastic effect. The electromagnetic field in the twisted corrugated structure is presented as a superposition of circularly polarized modes of the etched fiber section. The wavelength shift is found to be proportional to the square of the twist angle. As predicted by our theory, a wavelength shift of the same nature has been found in a conventionally photoinduced long-period fiber grating.