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Summary form only given. Nonlinear polarization rotation in optical fibers can be used to form artificial saturable absorbers, which promote passive mode locking in fiber lasers. In mode-locked lasers, care is taken to avoid strong birefringence and significant polarization-mode delays (PMD) so that the transmission in such artificial absorbers depends only on the instantaneous intensity of the incident wave. In this work we show that when the PMD is significant, the effect of nonlinear polarization rotation can be used to form a nonlinear optical derivator. The transmission of such an element is determined by the temporal structure of the input pulse; it can be adjusted to block cw background and transmit only the changes in the field. When this new nonlinear element is placed inside a laser cavity, it produces new and useful pulsed laser characteristics. Such a laser generates noiselike pulses with narrow intensity autocorrelation trace and a broad and smooth spectrum having a 3-dB bandwidth of 44 nm.