Analysis for the phase-diffusion effect in a phase-shifted helical long-period fiber grating and its pre-compensation

Through analyzing the structure of the phase-shifted helical long-period fiber grating (HLPG), which is fabricated based on the thermally twisting method, we have shown that there exists a phase-diffusion effect when the thermal region is larger than the grating period itself, i.e., the inserted phase preset at particular period will be diffused to several neighboring periods, which causes a large distortion in the transmission spectrum. We have analytically proved that this kind of phase-diffusion effect can be quantified by doing the convolution between the preset phase function and the phase-diffusion function in spatial domain. According to the analytical results, we have proposed and successfully demonstrated a pre-compensation method to solve the phase diffusion effect. As an example, a phase-shifted HLPG with π phase-shift precisely inserted at middle position of the grating has been presented.