Quantum versus Classical Descriptions of Spontaneous Emission in Nanophotonic Cavities

Here, we demonstrate that quantum and classical descriptions generally yield different results for the spontaneous emission in nanophotonic cavities. Starting from the quantized single-mode field in a general context of dispersive and lossy cavities, we derive the expression for emission rate enhancement as well as key relevant parameters such as mode volume and quality factor. For general nanophotonic cavities, this ratio of the quantum to the classical description is typically below unity and varies with the material dispersion properties, scattering-to-absorption ratio and morphology of the cavity. Notably, the two descriptions converge for lossless, non-dispersive dielectric cavities and for noble-metal plasmonic cavities with sufficiently low scattering losses.