Deterministic time rewinding of waves in time-varying media

TL;DR

This work introduces a deterministic mechanism to rewind waves in time-varying media by engineering temporal bilayers that cancel accumulated scattering and phase, enabling complete recovery of both amplitude and phase. The authors develop a unified temporal scattering formalism applicable to electromagnetic and Dirac-wave dynamics, derive explicit time-rewinding conditions for transmission, reflection, and interband transitions, and validate these results through extensive numerical simulations for discrete and continuous modulations. The approach extends to multilayer configurations and continuous temporal profiles via invariant imbedding, showing robustness to perturbations and offering a versatile platform for temporal cloaking, secure communications, and programmable metamaterials. The findings establish a rigorous, general strategy for time-domain wave control with potential impact across photonics and quantum-inspired systems.

Abstract

Temporal modulation of material parameters offers unprecedented control over wave dynamics, enabling phenomena beyond the capabilities of static systems. Here we introduce and analyze a robust mechanism for time rewinding, whereby a temporally evolved wave is fully restored to its original state through a carefully engineered sequence of temporal modulations. In electromagnetic systems, time rewinding emerges from impedance-matched or anti-matched hierarchical bilayer structures with matched modulation durations, exploiting total transmission or reflection and reversed phase accumulation. In Dirac systems, it arises via complete interband transition driven by time-dependent vector potentials. Unlike time-reversal holography or quantum time mirrors, which produce wave echoes but only partial waveform recovery, our approach achieves deterministic and complete reconstruction of the entire wave state, including both amplitude and phase. Analytical conditions for robust amplitude and phase restoration are derived and validated through simulations of discrete and continuous modulations, demonstrating resilience to modulation complexity and temporal asymmetry. These findings establish a versatile platform for secure information retrieval, temporal cloaking, programmable metamaterials, and wave-based logic devices.

Figures (8)

• Figure 1: (a) Schematic of a temporal interface: a sudden change in material parameters induces temporal scattering, generating reflected and transmitted waves. (b) Scattering at a temporal slab: total scattering is determined by interface coefficients and phase accumulation between interfaces. (c) Temporal bilayer: impedance matching leads to total temporal transmission, while anti-matching results in total reflection. When applied sequentially with matched durations, scattering and phase effects cancel, restoring the initial wave state.
• Figure 2: Schematic illustration of time rewinding in a temporal multilayer system. Each conjugate pair—$(A, A')$, $(B, B')$, $(C, C')$, and $(D, D')$—is designed to satisfy the time-rewinding matching conditions.
• Figure 3: (a) Temporal profiles of permittivity $\epsilon(t)$ and permeability $\mu(t)$ in a simple bilayer time-varying medium, with $\tau = (ck_x)^{-1}$. (b) Formation of a temporally localized wave: the wave intensity grows exponentially in the first slab and decays in the second, due to identical refractive indices but anti-matched impedances, producing a localized peak at $t = 4\tau$.
• Figure 4: (a) Temporal profiles of permittivity $\epsilon(t)$ and permeability $\mu(t)$ in a four-layer time-varying medium, with $\tau = (ck_x)^{-1}$. (b) The electric displacement field, amplified by temporal scattering, is fully restored at $t = 9\tau$ through the time-rewinding mechanism.
• Figure 5: (a) Contour plot of a Gaussian pulse with spectral width $\sigma_k$ and central wavenumber $k_c = 10\sigma_k$, shown as a function of space and time while propagating through the temporal structure in Fig. \ref{['fig4']}(a). The pulse retraces its trajectory, demonstrating complete waveform restoration via time rewinding. The characteristic time scale is defined as $\tau = (c\sigma_k)^{-1}$. (b) Spatial profiles of the pulse at selected times. The normalized displacement field intensity is given by $|\bar{D}|^2 = |D|^2 / \int_{-\infty}^{\infty} |u(x,0)|^2 dx$.