We have derived an exact large-signal theory of propagation in a dispersive fiber of an optical wave with sinusoidal amplitude and frequency modulation. This has been applied to the study of large-signal direct-modulation of semiconductor lasers. It is shown that the large-signal response can significantly deviate from the predictions of the small-signal theory. In particular, the improvement in modulation response caused by frequency-to-intensity modulation conversion in propagation that occurs with small-signal modulation is no longer achieved with large-signal modulation, which could affect systems such as dispersion supported transmission. Experimental results confirm our theory.
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