Tunable dual-band atomic mirror based on subwavelength atomic arrays under electromagnetically induced transparency

TL;DR

This work addresses the challenge of designing tunable, low-energy optical mirrors by using a two-dimensional subwavelength array of ladder-type atoms driven under electromagnetically induced transparency (EIT). Through a non-Hermitian, dipole-dipole–mediated model, the authors show the emergence of two distinct, tunable reflection bands—the dual-band atomic mirror—whose spectral positions and linewidths can be controlled by the coupling field $oldsymbol{oldsymbol{\\Omega}}_c$, detunings, dipole orientation, lattice constant $d$, and incidence geometry. The cooperative to decaying-dressed-state framework reveals two poles $oldsymbol{ riangle}_{oldsymbol{k}}$ and $oldsymbol{ abla}_{oldsymbol{k}}$ that govern the frequency shifts and radiative rates of collective modes, with strong directional coupling whose behavior depends on polarization and Brillouin-zone paths. The results further identify diffraction-order conditions and demonstrate polarization-selective functionality, enabling polarization beam-splitting and filtering across broad angular ranges, thereby offering a practical route to reconfigurable photonic elements in atomic metasurfaces without relying on Rydberg blockade. Overall, the paper delivers a concrete, tunable mechanism to realize dual-band, tunable atomic mirrors suitable for integration into all-optical networks at ultralow energy scales.

Abstract

Subwavelength atomic arrays offer a powerful platform for engineering cooperative light-matter interactions and enabling quantum metasurfaces. We demonstrate that a two-dimensional array of three-level atoms operating under electromagnetically induced transparency can function as a tunable dual-band atomic mirror, where two independently controllable reflection bands emerge from the collective optical responses mediated by dipole-dipole interactions. These resonances yield dual reflection bands with asymmetric linewidths, whose spectral positions and bandwidths can be tuned through the control-field parameters, dipole orientation, incident geometry, and lattice constant. We further identify the conditions under which additional diffraction orders emerge, which delineate the operational and tunable range of the atomic mirror via its collective-mode structure. This scheme provides a fully tunable dual-band atomic mirror operating across broad frequency and angular ranges, offering a practical and experimentally accessible pathway toward reconfigurable photonic elements in atomic-array platforms at low energy levels.

Figures (9)

• Figure 1: (a) A square atomic array positioned in the $x$-$y$ plane at $z=0$ in free space, where each atom is driven into a three-level system. (b) Schematic of two types of oblique incidence for the weak probe field with an incident angle $\theta$, where the red (blue) arrow represents incident in the $x$-$z$ ($y$-$z$) plane with a wavevector component $k'_{y}=0$ ($k'_{x}=0$). (c) Scattering of the probe field at a general incidence angle, illustrating the polarization states of the incident and scattered fields within the orthogonal polarization basis $\{\mathbf{e}_{p}^{\pm}, \mathbf{e}_{s}^{\pm}\}$, where the superscript $+$ ($-$) corresponds the transmitted (reflected) field.
• Figure 2: Band structure of the atomic array for (a) out-of-plane polarization $\hat{\wp}= \hat{\wp_{z}}$, and (b) in-plane polarization $\hat{\wp}= \hat{\wp_{x}}$. Band structure with in-plane polarization $\hat{\wp}= \hat{\wp_{x}}$ along the Bloch vector (c) $k_y=0$ path, and (d) $k_x=0$ path. The insets indicate the specific path in the first Brillouin zone. $\Gamma$, $X$ and $M$ are the symmetry points. The collective decay rate $\Gamma_{k}$ is color-coded. The shade indicates the light cone $|\mathbf{k}_{\parallel}|=\omega_{eg}/c$. The parameters are $\lambda=2\pi c/\omega_{eg}=790$ nm, $\Gamma_e=2\pi\times6$ MHz, $\Gamma_r = 2\pi \times 1.8~\text{MHz}$ and $d=0.1\lambda$.
• Figure 3: Cooperative shift $\Delta_{k}$ and collective decay rate $\Gamma_{k}$ as functions of the incident angle $\theta$, for the out-of-plane polarization $\hat{\wp}= \hat{\wp}_{z}$ in (a) and (b), for the in-plane polarization $\hat{\wp}= \hat{\wp}_{x}$ with the probe field incident in the $x$-$z$ plane in (c) and (d), and for the in-plane polarization $\hat{\wp}= \hat{\wp}_{x}$ with the probe field incident in the $y$-$z$ plane in (e) and (f). Other parameters are the same as those in Fig. \ref{['fig:2']}.
• Figure 4: (a) Real part $\mathrm{Re}\left[\chi_{\rm eff}\right]$ and (b) imaginary part $\mathrm{Im}\left[\chi_{\text{eff}}\right]$ of the effective susceptibility as functions of the probe detuning $\Delta_p$ for out-of-plane polarization $\hat{\wp} = \hat{\wp}_z$. The red solid, blue dashed, and magenta dot-dashed lines correspond to $\Omega_c = 0$, $20\Gamma_e$, and $60\Gamma_e$, respectively. (c) $\mathrm{Re}\left[\chi_{\text{eff}}\right]$ and (d) $\mathrm{Im}\left[\chi_{\text{eff}}\right]$ as functions of $\Delta_p$ for in-plane polarization $\hat{\wp} = \hat{\wp}_x$, with $\Omega_c = 20\Gamma_e$. The red solid and blue dashed lines denote probe incidence in the $x$-$z$ and $y$-$z$ planes, respectively. Here $\theta = \pi/4$, $\Delta_c = 0$, and other parameters are the same as those in Fig. \ref{['fig:2']}.
• Figure 5: (a) Reflectivity $R_{pp}$ and (b) transmissivity $T_{pp}$ as functions of the Rabi frequency $\Omega_c$ and probe detuning $\Delta_p$ with $\Delta_c = 0$. (c) Reflectivity $R_{pp}$ and (d) transmissivity $T_{pp}$ as functions of coupling detuning $\Delta_c$ and probe detuning $\Delta_p$ with $\Omega_c = 15\Gamma_e$. Here $\hat{\wp} = \hat{\wp}_z$, $\theta = \pi/4$, and other parameters are the same as those in Fig. \ref{['fig:2']}.