  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.
