Plasmon mode in a silver nanowire is theoretically studied when the nanowire is placed on or near a silica substrate. It is found that the substrate has much influence on the plasmon mode. For the nanowire on the substrate, the plasmon (hybrid) mode possesses not only a long propagation length but also an ultrasmall mode area. From the experimental point of view, this cavity-free structure holds a great potential to study a strong coherent interaction between the plasmon mode and single quantum system (for example, quantum dots) embedded in the substrate.
PACS numbers:The silver nanowire is a potential solution to key components in future ultra-compact electronic and photonic circuit [1][2][3] since it can confine the light in nanoscale beyond the diffraction limit. The strong confinement of light in a small area produces strong electric field intensity and dramatically changes the density of state nearby the metal surface. Therefore, the silver nanowire has been suggested to realize strong light-matter interaction, where the nanowire plays as the role of a resonator in cavity quantum electrodynamics (QED). When an optical emitter, e.g., a quantum dot (QD), is placed around the silver nanowire, its spontaneous emission can be significantly modified [4], known as the Purcell effect. As a result, single optical emitter coupling with plasmon modes of nanowire holds a great potential for broad-band cavity QED [4], single photon source [5], and sub-wavelength single photon transistor [6,7] for quantum information science.Theoretically, the plasmon mode in silver nanowire was studied as an ideal axis-symmetric mode [4], or still treated without the external influence even it was placed on a substrate [8][9][10][11][12]. However, in realistic applications, the silver nanowire is always necessary to be located on or near a substrate. For example, the nanowire on a substrate makes it convenient for manipulating assisted by the scanning near field optical microscope probe [8][9][10][11][12][13][14][15][16]. To the best of our knowledge, the influence on the plasmon mode from the substrate is still kept un-studied. Actually, the plasmon mode is very sensitive to the surrounding environment. In this Letter, we theoretically study the plasmon mode propagating along the silver nanowire near a substrate with a gap g ≥ 0. In this silver-air-substrate structure, most of the mode energy is confined around the interface between the substrate and silver nanowire. It is very different from the nanowire simply embedded in air. The benefit of the nanowire on a substrate is that the large portion of energy in the substrate reduces the mode area by a factor of 5, without significant degradation of the propagation loss.An infinite long silver nanowire with a diameter of d is near an infinite dielectric substrate with a gap of g. The cross section is shown Fig. 1(a). The surface plasmon mode propagates harmonically along the nanowire, and the electric field varies as exp(iβz − iωt), where the propagation constant β = 2πn ef f /λ is a comp...