Strong Purcell effect in deep subwavelength coaxial cavity with GeSn active medium

We propose a deep subwavelength plasmonic cavity based on a metal-coated coaxial structure with Ge_0.9Sn_0.1 as the active medium. A fundamental surface plasmon polariton mode is strongly confined on the sidewall of the metal core, with the quality factor up to 5×10³ at 10 K. By reducing the cavity dimension to a few nanometers, this cavity mode shows a strong plasmon binding with the mode volume down to 8×10^-10 (λ/n)³, and significant size-dependent damping caused by the non-local optical response. The Purcell factor is achieved as high as 2×10⁹ at 10 K and 7×10⁸ at 300 K. This cavity design provides a systematic guideline of scaling down the cavity size and enhancing the Purcell factor. Our theoretical demonstration and understanding of the subwavelength plasmonic cavity represent a significant step toward the large-scale integration of on-chip lasers with a low threshold.