Generation and Enhancement of Persistent Nanoscale Magnetization in All-Dielectric Metasurfaces by Optically Injected and Localized Free Carriers

TL;DR

This work addresses dynamic control of mid‑IR metasurface resonances by optically injecting free carriers in localized hot spots, creating sharp time interfaces that scatter metasurface-guided waves. The authors develop a vectorial perturbation theory and Drude–Lorentz time-domain model to predict resonance shifts and energy partitioning during a time interface, demonstrating both blueshifts and metallization‑driven redshifts of a high‑Q metasurface resonance. They show that a rapid TI can convert MGW energy into a persistent quasistatic magnetic field localized in the hot spot, achieving efficient rectification of the AC magnetic field into a DC (quasistatic) magnetization with rectification on the order of ~82%. The results reveal that the total energy is conserved across the TI, while the MGW energy is redistributed into time-refracted/reflected waves and DC carrier dynamics, enabling giant nanoscale magnetization without external magnetic fields and offering a new platform for time-varying photonics in dielectric metasurfaces.

Abstract

Time-varying dielectric metasurfaces supporting sharp optical resonances with a non-trivial electromagnetic field distribution represent a unique platform for realizing temporal interfaces for metasurface-guided waves (MGWs). Rapidly changing metasurface resonance enables frequency conversion and temporal scattering of a concurrently propagating MGW. Using analytical methods and electromagnetic simulations, we demonstrate that localized free-carrier generation can be engineered to produce frequency-shifted, time-refracted, and reflected infrared MGWs. Furthermore, we demonstrate that such time interfaces can be utilized to generate large, highly localized quasistatic magnetic fields within the metasurfaces. The resulting nanoscale magnetization, supported by the residual circulating currents, persists after the departure of the time-scattered MGWs. We further demonstrate that the initial electromagnetic energy of the injected MGWs is partitioned between the time-reflected/refracted MGWs, residual motion of the free carriers, and a quasistatic magnetic field.

Figures (6)

• Figure 1: a. Schematic of a metasurface comprising rectangular semiconductor blocks periodically arranged on an infrared-transparent substrate. Red spots: cylindrical region where free carriers are generated by a laser pump. Inset: metasurface transmission spectra for normally incident $x$-polarized mid-infrared light. b. Electric field (arrows) and its intensity $|\mathbf{E}|^2$ (color-coded) distribution at the magnetic dipolar (MD: top) and electric (ED: bottom) dipolar resonances. The field is shown in the $x-z$ plane drawn through the middle of a meta-atom. c. Same as b for the ED resonance, but in the $x-z$ meta-atom mid-plane. d. Schematic for the perturbative calculation of the resonance frequency shift produced by free-carrier generation inside the hot-spot cylinder with radius $\mathrm{r_{hs}}$ using annular rings (shown in green). Materials: germanium (Ge, $\mathrm{n_{Ge} \approx 3.98}$Amotchkina2020) for meta-atoms, calcium fluoride (CaF$_2$, $\mathrm{n_{CaF_2} \approx 1.4}$Malitson1963) for the substrate. Geometric parameters: $p_x=1.94\ \mu \mathrm{m},\ p_y=2.04\ \mu \mathrm{m}$, $w_x \times w_y \times h$: $0.87\ \mu \mathrm{m} \times 1.54\ \mu \mathrm{m} \times 0.6\ \mu \mathrm{m}$, and $\mathrm{r_{hs}}=200\ \mathrm{nm}$.
• Figure 2: $\bf{a.}$ Metasurface transmission as a function of hot spot free carrier density ($\mathrm{N_e}(\mathbf{r},\mathrm{t})$) for normally incident x-polarized light. $\bf{b.}$ Intensity $\mathrm{|E|^2}$ enhancement (color), and $\mathbf{E}$ (black cones) of the ED resonance in the meta-atom's x-y and x-z mid-planes for $\lambda_{\mathrm{pert}}= 3.81\ \mu\mathrm{m},\ \mathrm{N_e^{pert}}=1.6\times 10^{19}\ \mathrm{cm}^{-3}$ (blue star) and $\lambda_{\mathrm{PEC}}=4.5\ \mu\mathrm{m},\ \mathrm{N_e^{PEC}}=9.4\times 10^{20}\ \mathrm{cm}^{-3}$ (red star) $\bf{c.}$ The black curve shows the metasurface transmission spectrum before FC generation ($\mathrm{N_e^{i}}=0$), while the blue (red) curve shows the spectrum when the carrier density is increased to $\mathrm{N_e^{pert}}$ ($\mathrm{N_e^{PEC}}$). The stars and dashed lines serve as guides to the eye.
• Figure 3: $\bf{a.}$ Setup used for TI simulations where the shaded red region shows the cylindrical hot spots of radius 200 nm inside each meta-atom. Probe points are located in the substrate (green circles). MGW is launched using a dipole array (red arrows) separated by $d_x=\pi/2\mathrm{k_x}$ and at a height $d_y=\lambda_0/4$ above the metasurface; the length of the arrows represents the magnitude of the dipole moment. Inset: Pump pulse (red) and dipolar excitation (blue) intensity and the temporal variation of hot spot FC density (black dashed). $\bf{b.}$ Dispersion plot of the ED mode for hot spot FC density, $\mathrm{N_e^i=0\ cm^{-3}}$ (black circles) and $\mathrm{N_e^{PEC}=9.4\times10^{20}\ cm^{-3}}$ (red circles); the green shaded region indicates the spectrum of the dipolar excitation. Red dashed arrow: redshifting of the ED mode when the hot spot FC density is increased from $\mathrm{N_e^i\ to \ N_e^{PEC}}$. $\bf{c}.$$\mathrm{H_y}$ field profile of the ED mode (in the x-z midplane) before (top) and after (bottom) the TI; the black cones indicate the FC current density in the hot spot.
• Figure 4: $\bf{a.}$ Normalized $\mathrm{H_y}$ profile in the x-z mid-plane of the simulation domain on the left (right) shows the MGW propagating with group velocity $\mathrm{v^i_g \approx 0.007c}$ ($\mathrm{v^{PEC}_g \approx 0.009c}$) without a TI (with a TI) at t=4955 fs; the rectangular region inside each meta-atom represents the cylindrical hot spot of radius 200 nm. $\bf{b.}$$\mathrm{|FT(E_x)|^2}$ recorded at the two probe locations after the TI for the two cases: without a TI where $\mathrm{N^{(2)}_e}=\mathrm{N^{i}_e=0\ cm^{-3}}$ throughout (black dashed (bold) line at Probe A (B)), and with a TI where $\mathrm{N^{(2)}_e=N^{PEC}_e=9.4\times10^{20}\ cm^{-3}}$ after the TI (red dashed (bold) line at Probe A (B)). $\bf{c.}$ Time evolution of the contributions ($\mathrm{E_1}$: blue line, $\mathrm{E_2}$: red line) to the total energy ($\mathrm{E_{Total}}$: black line).
• Figure 5: $\bf{a.}$ Normalized $\mathrm{H_y}$ profile in the y-z mid-plane of the meta-atom marked using a light green star in Fig. \ref{['Fig4']}a, at 2905 fs, 3000 fs, and 3105 fs; the yellow cones represent the magnetic field lines $\bf{b.}$ Time evolution of FC density and its temporal derivative. $\bf{c.}$ Time evolution of the QS mode at three consecutive time steps separated by $\Delta \mathrm{t}=5\ \mathrm{fs}$ in the x-z midplane of the same meta-atom; the black cones indicate the FC current density in the hot spot. The rectangular region inside the meta-atom in all plots represents the cylindrical hot spot of radius 200 nm. The light green star shows the meta-atom where we show the magnetic field in Fig. \ref{['Fig5']}.