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The optical pulse evolution in a highly nonlinear normal dispersion increasing fiber has been considered both experimentally and theoretically. It was found that in highly nonlinear fiber with longitudinally increasing normal dispersion large spectral broadening could occur with minimal temporal instabilities. This spectral broadening impose the linear frequency modulation i.e. chirp, required for high-quality pulse compression. The pedestal-free compressed pulses have been demonstrated after de-chirping in a standard single-mode fiber with anomalous dispersion.
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Andrew A. Fotiadi, Dmitry A. Korobko, Dmitrii A. Stoliarov, Alexey A. Sysoliatin, Igor O. Zolotovskii, "Generation of wide spectrum and pedestal-free pulse compression in highly nonlinear dispersion increasing fiber," Proc. SPIE 10228, Nonlinear Optics and Applications X, 1022819 (16 May 2017); https://doi.org/10.1117/12.2265628