Breaking the Limitations of Temporal Modulation via Mixed Continuity Conditions

Abstract

The conventional description of time-varying media assumes that electromagnetic fields evolve according to fixed continuity conditions during parameter jumps. Here we reveal that these conditions are not physical constraints but tunable design degrees of freedom. By developing a unified framework that treats continuity rules as engineerable parameters, we expand the scope of time-varying metamaterials and enable wave phenomena previously considered impossible. For instance, non-resonant, reflectionless wave amplification without momentum bandgaps, and reversible conversion between propagating waves and static fields for optical memory, etc. This work opens a new dimension for controlling light-matter interactions.

Figures (4)

• Figure 1: Real and imaginary parts of the time-modulated Drude dispersive medium for $J_p\omega_{p}^{-1}=\text{const.}$ continuity condition, with band gaps indicated.
• Figure 2: Analogical model for time-modulated material dispersion response. (a) Transmission line model. (b) Passive modulation of capacitance. (c) Passive modulation of inductance. (d) Practically realizable capacitance modulation circuit based on an operational amplifier. Adjusting the ratio of $R_{\mathrm b 2}$ to $R_{\mathrm b1}$ tunes the equivalent capacitance while keeping the charge constant. Meanwhile, toggling switch $K_\mathrm b$ connects $C_{\mathrm b1}$ and $C_{\mathrm b 2}$ in parallel, enabling a voltage-conserving capacitance change, and vice versa. (e) Schematic representation of the decomposition of a capacitance jump from $C_-\rightarrow C_+$ into a charge-conserving step and a voltage-conserving step.
• Figure 3: Band structure under $\omega_0$ modulation. The real parts (a) and imaginary part (b) of the energy band under traditional modulation approach, i.e., $\partial \bm P/\partial \omega_0^2 =0$. The real parts (c) and imaginary part (d) of the energy band under passive modulation approach.
• Figure 4: Simulations showing pulse spatiotemporal evolution under different continuity conditions. (a)-(d) Spatiotemporal evolution of the electric field under simultaneous modulation of permittivity $\varepsilon$ and permeability $\mu$. In all cases, $\mu_1=1.1$, $\mu_2=1$. (a) and (c) correspond to $\varepsilon_1=2.3$, $\varepsilon_2=2$ (b) and (d) correspond to increased permittivity modulation with $\varepsilon_1=3$, $\varepsilon_2=2$. Mixed continuity conditions are applied in (a) and (b), while (c) and (d) assume continuity of $\bm D$ and $\bm B$. (e) Pulse storage and retrieval enabled by temporal modulation of the plasma frequency. (f) Evolution of the matrix elements describing the scattering process with the number of modulation cycles.