The Numerical Study Of Supercontinuum Generation In Photonic Crystal Fiber

According to the ENLS equations which describe the transmission of femtosecond level laser pulse in photonic crystal fiber (PCF) , the effects of high-order nonlinearities and high-order dispersion on the supercontinuum generation in PCF are tried to explained from the angle of the study of chirp by means of mathematical and numerical computing. To take the hyperbolic-secant input pulse for example, the functions of SPM-caused chirp (self-phase modulation, SPM), ISRS-caused chirp (intra-pulse simulated Raman scattering, ISRS) and SS-caused chirp (self–steepening, SS) are resolved mathematically, and the evolutions of SS-caused chirp, TOD-caused chirp (third-order dispersion, TOD) are simulated. Also is the evolution of chirp caused by all effects above. Conclusions are as the followings.As far as the nonlinearities are concerned, the symmetrical transmission of SPM chirp leads to the symmetrical broadness of frequency-spectrum; For the ISRS chirp, the central point of chirp shifts to the trailing edge, and the absolute peak values of the negative chirps at leading edge are greater than those of positive chirp at trailing edge. So ISRS makes the spectrum center shift to long wavelength side, and red-shifted spectrum bandwidth is broader than that of blue shift. The center of SS chirp shifts to trailing edge rapidly and the whole chirp is upgrading to trailing side with propagation. In particular, Self-steepening of the pulse causes a sharp drop at the trailing part of the pulse resulting in an asymmetric broadening of the spectrum of the pulse towards the blue.For higher-order dispersions, not only in anomalous-dispersion region but also in normal-dispersion region, positive TOD-induced (Third-order dispersion, TOD) chirp develops oscillations with great amplitude in trailing edge, and for negative TOD chirp, oscillations with great amplitude are developed in leading edge, which break the spectral symmetry. FOD (Fourth-order dispersion, FOD) chirp change the shape slightly comparing with TOD chirp when FOD is considered.When all effects are considered together, for one thing, in anomalous-dispersion regime, for initial propagation, the total chirp transmits symmetrically which shows that the combination of SPM and GVD compresses pulse and higher-order solitons are formed. Because of the increase of pulse-peak power, the effects ISRS and SS make function. With further propagation, TOD effect is obvious gradually, and the combination of higher-order nonlinearities and dispersions Lead to breakup of higher-order soliton into fundamental solitons, which results in the distribution of energy and SC spectrum is formed at last. For another thing, in normal-dispersion regime,the evolutions of chirp show that, because of SPM-induced broaden pulse, the effects of ISRS and SS are slight, and TOD effect make great contribution to the spectral dissymmetry broadness. After the SPM-induced broadened spectrum enters into the anomalous-dispersion regime, higher-order nonlinearities, such as ISRS and XPM, lead to the distribution of energy and new frequencies are developed, which form SC spectrum at last.