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Zitterbewegung of optical pulses near the Dirac point inside a negative-zero-positive index metamaterial

By numerically solving Maxwell's equation with boundary conditions, we have demonstrated the optical Zitterbewegung effect by means of electromagnetic pulses propagating through a negative-zero-positive index metamaterial (NZPIM). We find that a finite pulse with frequencies near the Dirac point of the NZPIM diffuses and oscillates, and its output pulse from the finite NZPIM slab becomes an oscillating pulse with a characteristic frequency independent of the slab thickness. We further find that the oscillating properties of the optical Zitterbewegung effect are strongly dependent on the pulse parameters: such as pulse duration and pulse transverse spatial width. The physical nature of such oscillation effects is due to the interference between the upper and lower high-transmittance passbands at both sides of the Dirac point of the NZPIM slab, which is similar to the Zitterbewegung of electron wave packets.