Enhanced Spin Hall effect of light in a prism-free atom-plasmon polariton system based on a three-level medium

Abstract We theoretically investigate the Photonic Spin Hall Effect (PSHE) in a prism-free four-layer structure consisting of air, a thin bimetallic film, and an effective three-level $\Lambda$ system. Driven by probe, coupling, and microwave fields in a closed-loop configuration, the atomic substrate provides dynamically controllable permittivity via electromagnetically induced transparency and coherent population trapping. Solving the steady-state Liouville–von Neumann equations and using a recursive Fresnel coefficient method, we derive the spin-dependent transverse shift of a reflected Gaussian beam. Numerical results, optimized via a genetic algorithm, show that a pure gold film with a thickness of $11.06~\text{nm}$ yields a giant PSHE displacement of $43.321~\mu\text{m}$ at an incidence angle of $46.98^\circ$, which is approximately $68.46$ times larger than the incident wavelength. Bimetallic stacks exhibit reduced performance due to deviation from optimal impedance-matching conditions. Crucially, the microwave phase enables active tuning of the magnitude and sign of the PSHE displacement. While residual thermal Doppler broadening reduces the peak displacement in a cold atomic ensemble, the shift remains robust for the optimized gold structure, underscoring the viability of the scheme under practical experimental conditions. Furthermore, evaluating the system's performance as a phase sensor reveals an exceptional spatial shift sensitivity of $S_\delta = 12674.27~\mu\mathrm{m/rad}$ and an angular sensitivity of $S_\theta = 0.64^\circ/\mathrm{rad}$ for the optimized pure gold configuration. This work establishes a compact, coupler-free platform for enhancing and controlling spin–orbit interactions in nano-photonic systems, with promising applications in high-resolution metrology and ultra-sensitive sensing.\\