Role of dispersion profile in controlling emission of dispersive waves by solitons inside optical fibers

When ultrashort optical pulses propagate as a soliton inside optical fibers, the presence of higher-order dispersion leads to transfer of energy from the soliton to a narrowband resonance in the form of dispersive waves (DW). The frequency of the radiation is determined by a phase-matching condition in the form of a polynomial whose coefficients depend on the numerical values of the third-and higher-order dispersion coefficients. In this paper we show that there is a striking correlation between the number of zero-dispersion points (ZDPs) and the generation of DW peaks. Detailed simulations indicate that the number of ZDPs present in a specific dispersion profile is an excellent predictor of the number of dispersive peaks created in the output pulse spectrum. A fiber with a single ZDP only has one DW peak, and a fiber with two ZDPs always exhibits dual DW peaks. Moreover, no DW can be expected in a fiber that has no zero-dispersion crossings over the entire range of wavelengths. We examine numerically dispersion profiles with as many as six ZDPs and find that this criterion always holds. Another interesting feature we notice is that, if the frequency of the ZDP is larger (smaller) than the operating frequency, DWs fall on the higher (lower) frequency side of the operating frequency. Therefore there is a possibility to generate two DW peaks on in same side (blue or red side) of the output pulse spectrum by tailoring the dispersion curve suitably.