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.
The transmission of a one-dimensional left-handed photonic crystal consisting of alternating slabs of two materials with
positive and negative refractive index respectively is investigated with the help of transfer matrix method (TTM). The
properties of defect modes of the left-handed photonic crystal were disclosed. Both the number and the location of defect modes strongly depend on the property and composition of defects. The defect modes resulted from negative
defect often appears in the zero average refractive index (ZARI) gap, while those resulted from positive defect usually
appears in the Bragg gap. The defect modes, no matter in the Bragg gap or in the ZARI gap, exhibit degeneracy and
split as the distance between the two defects decreases. Due to the coupling of the two defects, the split of defect mode
does not appear when two different kinds of defect are introduced.
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