Optical and quantum models of resonant optical tunneling effect

Resonant optical tunneling effect (ROTE) is a special phenomenon that light can fully go through the seemingly impenetrable optical structure. It is a prominent example to study the analogy of wave optics and quantum physics. Previous theoretical work mostly focused on the optical modeling of transmission spectrum using the transfer matrix method (TMM), but put little effort in the quantum model. This paper advances the optical modeling by using the finite-difference time-domain method (FDTD) to simulate the electric field distribution and by using the plane wave expansion (PWE) to predict the optical bandgap. Moreover, we present the first analytical quantum model of the ROTE and further derive a direct expression of the transmission peak positions. This expression cannot be derived by the optical models, but its predicted peak positions match the optical modeling results using the FDTD, the PWE and the TMM. This well demonstrates the merit of the quantum analogy for analyzing the optical systems. This work may inspire the transplantation of the established ideas and designs in the quantum field into the optical field to create new optical and photonic devices.