Nonreciprocity and Faraday Rotation at Time Interfaces

Nonreciprocity is critically important in modern wave technologies, yet its general principles and practical implementations continue to raise intense research interest, in particular in the context of broken reciprocity based on spatiotemporal modulation. Abrupt changes in time of the electromagnetic properties of a material have also been shown to replace spatial boundaries, supporting highly unusual wave-matter interactions in so-called time metamaterials. Here, we introduce nonreciprocity for temporal boundaries, demonstrating Faraday polarization rotation in a magnetoplasma with material properties abruptly switched in time. Our findings open new opportunities for time metamaterials, yielding new avenues for nonreciprocity with broad applicability for wave engineering.

Figure 1

(a) Angular frequencies ${\omega }_l^{\pm }$ (in units of $k_z{c}_0$) of forward waves in a magnetoplasma as a function of ${\omega }_c$ (in units of $k_z{c}_0$) when ${\omega }_p=0.8k_z{c}_0$ (solid lines) and ${\omega }_p=0.535k_z{c}_0$ (dashed lines). (b) Schematic of a temporal magnetoplasma slab.

Figure 2

(a) Time-dependent evolution of the nonzero components (in units of $\mathrm{V}/\mathrm{m}$) of the electric field $\overrightarrow{E}$, normalized magnetic field ${\eta }_0\overrightarrow{H}$ and plasma current density $\overrightarrow{J}/({\epsilon }_0{\omega }_{\mathrm{inc}})$ at $z=0$ in the case of excitation with a circularly polarized wave propagating in a medium that switches abruptly at time $t=0$ from free space to a magnetoplasma with ${\widehat{\omega }}_p=0.8$, ${\widehat{\omega }}_c=0.5$ [see colored backgrounds]. Analytical and FDTD results are indicated by solid lines and symbols, respectively. (b) Snapshot of FDTD simulations for $E_x(z,t)$ versus $z$ (in units of $2\pi /k_z$) at $t=33.46T_{\mathrm{inc}}$, when one forward wave (green arrow) and two backward waves (blue and red arrows) are clearly seen. Throughout our study, a small uniform time-independent loss $\gamma ={10}^{-5}{\omega }_{\mathrm{inc}}$ is assumed, and ${\omega }_{\mathrm{inc}}/(2\pi )=1\mathrm{GHz}$.

Figure 3

(a) ${\log }_{10}\mathrm{\Delta }$ as a function of the normalized plasma frequency ${\widehat{\omega }}_p$ of the temporal magnetoplasma slab in Fig. 1 and its thickness $\mathrm{\Delta }t$ (in units of $T_{\mathrm{inc}}$). (b) Time-dependent evolution of the electric field components at $z=0$ in the case of left (upper panel) and right incidence (lower panel) for the demonstration of a perfect 45° Faraday rotator occurring at ${\widehat{\omega }}_p\approx 0.535$ and $\mathrm{\Delta }t/T_{\mathrm{inc}}\approx 1.28$, consistent with the minimum in panel (a). The theoretical results (solid and dashed lines) have been verified by FDTD simulations (symbols), and the colored backgrounds indicate time-varied material properties. For both subfigures, ${\widehat{\omega }}_c=0.7$.