Effect of dispersion and nonlinearity on ultrashort optical pulse propagation in long-period fiber grating: An analytical investigation

Long-period fiber grating is widely used as an optical component in photonics communication technology. The optical pulse propagation in grating has been studied mostly numerically and some number of studies carried out experimentally. The detailed analytical investigation has not been reported due to the complexity of the mathematical equations. Here, we have investigated analytically the effect of dispersion and nonlinearity on ultrafast optical pulse propagation in long-period fiber grating and derived the expression for transmitted optical pulses because the detailed analytical investigation has not been reported by any authors. The results of the study show how grating-induced overall dispersion and nonlinearity-induced self-phase modulation (SPM) modify the shape of the ultrashort optical pulses when it's propagating through a length of the grating. The combined effects of dispersion and SPM on the optical pulse evaluation are also analyzed. From the plotted graphs it is investigated that the dispersion of the grating distorted the pulse shape whereas SPM shifts the pulse towards the higher time scale. It is also investigated that the distorted optical pulse due to dispersion is reshaped by the nonlinearity introduced in the medium due to the combined effect of dispersion and SPM. Optical pulse compression, optical limiting and pulse reshaping are also illustrated as a function of excitation intensity.