Time-reversing light pulses by adiabatic coupling modulation in coupled-resonator optical waveguides

We introduce a mechanism to time reverse short optical pulses in coupled resonator optical waveguides (CROWs) by direct modulation of the coupling coefficients between microresonators. The coupling modulation is achieved using phase modulation of a Mach-Zehnder interferometer coupler. We demonstrate that by adiabatic modulation of the coupling between resonators we can time reverse or store light pulses with bandwidths up to a few hundred GHz. The large pulse bandwidths, small device footprint, robustness with respect to resonator losses, and easy tuning process of the coupling coefficients make this method more practical than previous proposals.

Figure 1

Schematic of CROW consisting of a periodic array of optical racetrack microresonators coupled by Mach-Zehnder interferomter couplers. The MZI coupling modulation part is shown in the inset with thermo-optic phase modulation between arms.

Figure 2

Dispersion relation $\omega \left(K\right)$ of a CROW with different inter-ring amplitude couplings: $\kappa =0.1$ (red dash-dotted line), $\kappa =0.03$ (green dotted line), $\kappa =-0.03$ (blue dashed line), and $\kappa =-0.1$ (black solid line).

Figure 3

Pulse propagating through a CROW as $\kappa$ is varied from positive to negative. (a) Field intensity at 30th resonator for ${\tau }_{\text{sweep}}=2{\tau }_0$ (black curve) and ${\tau }_{\text{sweep}}={\tau }_0$ (red dash-dotted curve). Propagation as a function of time and resonator number for (b) ${\tau }_{\text{sweep}}=2{\tau }_0$ and (c) ${\tau }_{\text{sweep}}={\tau }_0$. (Note that in black and white, lower transmission appears darker and higher transmission is lighter.)

Figure 4

Storage of an optical pulse of width $0.13T$ in a lossless CROW by linear modulation of $\kappa$ from $0.2$ to 0 and then back to $0.2$. (a) Red line (first pulse from the left) shows intensity in the 10th resonator. The black line (second pulse from the left) shows the intensity in the 60th resonator without modulation of $\kappa$, while the green line (rightmost pulse) shows the intensity in the same resonator with modulation of $\kappa$ indicating a pulse storage time of $18T$. (b) Pulse propagation vs time and resonator number. All other parameters are the same as Fig. 3. (Note that in black and white, lower transmission appears darker and higher transmission is lighter.)

Figure 5

Time reversal of pulse propagation with losses for sweep time ${\tau }_{\text{sweep}}=0.4{\tau }_0$. (a) Field intensity at 6th resonator for $Q=6\times {10}^4$ (blue, lowest curve), $Q=6\times {10}^5$ (green, middle curve), and $Q=6\times {10}^6$ (red, top curve). Pulse propagation as a function of time and resonator number: (b) $Q=6\times {10}^4$ and (c) $Q=6\times {10}^5$. All other parameters are the same as Fig. 3, including $N=100$. (Note that in black and white, lower transmission appears darker and higher transmission is lighter.)

Figure 6

Time reversal of pulse propagation with losses for sweep time ${\tau }_{\text{sweep}}=0.04{\tau }_0$. (a) Field intensity at 6th resonator for $Q=6\times {10}^4$ (blue, bottom curve), $Q=6\times {10}^5$ (green, middle curve), and $Q=6\times {10}^6$ (red, top curve). The pulse widths are $0.05T$ and the solid black piecewise linear line in (a) is $\kappa \left(t\right)$. Pulse propagation as a function of time and resonator number: (b) $Q=6\times {10}^4$ and (c) $Q=6\times {10}^5$. (Note that in black and white, lower transmission appears darker and higher transmission is lighter.)