Nonlocal coupling effects on single-photon transmission in a one-dimensional waveguide interacted with a side optical cavity

The nonlocal coupling effect between a one-dimensional waveguide (1DW) and a side optical cavity (SOC) is studied. We first find the real-space Hamiltonian of the nonlocal-coupling system of the 1DW and SOC, and then derive out an equation determining the energy of the hybridization state between the 1DW and SOC modes and an analytic formula for the single-photon transmission. Through them, we recognize that the single-photon transmission-dip position can be changed by adjusting the SOC size and the coupling strength between the 1DW and SOC. The transmission spectra strongly depends on the nonlocal-coupling function between the 1DW and SOC, and holds an asymmetry line shape. At last, we simulate the asymmetry of the single-photon transmission by a gold-based waveguide coupled with a rectangular SOC.