Resonant optical tunnelling in planar three-layer photonic microstructures

We present a unified analytical framework for resonant optical tunnelling in planar three-layer photonic systems embedded in a transparent dielectric medium. Using a generalized Fresnel-coefficient approach, we derive compact expressions for the transmission and show that resonant tunnelling occurs in two fundamentally different regimes, determined by the nature of the waves supported in the core layer. When the core supports propagating harmonic waves, resonances obey the conventional Fabry–Perot phase condition. By contrast, when the core supports evanescent or damped waves, resonant tunnelling arises from an amplitude-matching condition governed by the magnitude of the composite reflection coefficient. These two regimes lead to qualitatively different transmission characteristics and distinct tunnelling behaviour. Transparent systems, including ideal metals, are analysed first in order to isolate the underlying physical mechanisms. Absorption is then incorporated, showing the transition from unitary resonant tunnelling to attenuated optical tunnelling in realistic plasmonic structures. Angular–spectral transmission maps illustrate the general features of each configuration and show that resonant tunnelling may occur even when the tunnelling layer is several wavelengths thick. The results provide a consistent physical interpretation of resonant tunnelling across dielectric and metal–dielectric multilayer systems.