Theoretical analysis of cladding-mode waveguide dispersion and its effects on the spectra of long-period fiber grating

A new method to control the free spectral range (FSR) of a long-period fiber grating (LPFG) is proposed and theoretically analyzed. As the refractive index decreases radially outward in the silica cladding by graded doping of fluorine, waveguide dispersion in the cladding modes was modified to result in the effective indexes change and subsequently the phase-matching conditions for coupling with the core mode in a LPFG. Enlargement of the FSR in a LPFG was theoretically confirmed.