On the lasing-like transmission via radiation-mode-enabled TE resonant optical tunneling in asymmetric, passive, layered media with metal

Transverse-electric (TE) resonant optical tunneling through an asymmetric, single-barrier potential system consisting of all passive materials in two-dimensional (2-D) glass/silver/TiO₂/air configuration is quantified at a silver thickness of 35 nm. Resonant tunneling occurs when the incident condition corresponds to the excitation of a radiation mode. Lasing-like transmission occurring at resonance is carefully qualified in terms of power conservation, resonance condition, and identification of the gain medium equivalent. In particular, effective gain (g_eff) and threshold gain (g_th) coefficients, both of which are strong functions of the forward reflection coefficient at the silver-TiO₂ interface, are analytically obtained and the angular span over which g_eff > g_th is further verified rigorously electromagnetically. The results show that the present configuration may be treated as a cascade of the gain equivalent (i.e. the silver film) and the TiO₂ resonator that is of Fabry-Perot type, giving rise to negative g_th when resonant tunneling occurs. The transmittance spectrum exhibiting a gain-curve-like envelope is shown to be a direct consequence of the competition of the resonator loss at the silver-TiO₂ interface and the forward tunneling probability through the silver barrier, all controlled by the effective silver barrier thickness.