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We study the supercontinuum process in optical fibers numerically for a variety of dispersion profiles to investigate how a specific dispersion profile controls the emission of dispersive waves. We conclude that the number of zero-dispersion points in the dispersion profile of a fiber is an excellent predictor of the dispersive-wave peaks when it is pumped with femtosecond pulses in the anomalous dispersion regime. Our study reveals that two or more such peaks can form on the same side of the input wavelength in specially designed and practically achievable dispersion profiles. We show that dispersive waves are emitted even in the case of normal dispersion where soliton fission does not occur. We suggest that a phenomenon related to soliton spectral tunneling is responsible for this radiation. Distinct dispersive peaks may also appear when an optical pulse, launched in the normal dispersion region, later begins to …