Time Reversal in Dynamically Tuned Zero-Gap Periodic Systems

We show that short pulses propagating in zero-gap periodic systems can be reversed with 100% efficiency by using weak nonadiabatic tuning of the wave velocity at time scales that can be much slower than the period. Unlike previous schemes, we demonstrate reversal of broadband (few cycle) pulses with simple structures. Our scheme may thus open the way to time reversal in a variety of systems for which it was not accessible before.

Figure 1

(a) Reduced Brillouin zone plot of the band structure of a QWS PhC. The bands support pulse propagation in opposite directions (indicated by the red arrows). (b) Schematics of the frequency conversion process.

Figure 2

Geometry of the pulse propagation through the QWS PhC.

Figure 3

(a) Amplitude of an asymmetric pulse [Eq. (4); red (medium gray) line] and the associated backward wave envelope [Eq. (8); blue (dark gray) line] at the input side of the QWS as a function of time. (b) A spatiotemporal contour map of forward and backward envelopes in (a).

Figure 4

(a) Reversal of a $T_p=100\mathrm{fs}$, unit-amplitude Gaussian input pulse under a Gaussian modulation (11) as a function of the index change $\Delta$ for $n_1=3.45$, $n_2=1$, ${\lambda }_c=1550\mathrm{nm}$, and $T_{\mathrm{mod}}=10\mathrm{fs}$. Shown are numerical solutions of the wave equation [Eq. (4); blue (dark gray) dots] vs the solution of the envelope equations [Eq. (8); black circles] and the analytical solution [Eq. (12); red (medium gray) solid line]. (b) Same as (a) for $T_{\mathrm{mod}}=1\mathrm{ps}$ and $T_p=10\mathrm{ps}$.