Dynamics of anomalous ultrashort pulse splitting in nonlinear metamaterials

In this paper, we in detail investigate the dynamic behavior of pulse splitting in metamaterials (MMs) with a Kerr nonlinear polarization, focusing on the anomalous propagation properties associating with the unique and engineerable electromagnetic properties of such materials. The numerical results show that, the pulse symmetric splitting in MMs will occur for the case of defocusing nonlinearity with anomalous dispersion due to the negative refractive index; while it will appear for the case of focusing nonlinearity with normal dispersion in ordinary materials. Moreover, our further analysis shows that, like the case in ordinary materials, the inclusion of self-steepening (SS) effect with positive value gives rise to the asymmetry between the leading and trailing pulses, but the relative magnitudes of the two peaks are reversed, namely, the leading pulse is higher than the trailing pulse. However, the negative SS does opposition.