Conversion of a Helical Surface Plasmon Polariton into a Spiral Surface Plasmon Polariton at the Outlet of a Metallic Nanohole

The conversion of a helical surface plasmon polariton (SPP) creeping out of a circular nanohole in a thick metal (Ag or Au) film into a spiral (Hankel type) SPP outward propagating at the film’s interface is studied theoretically. The dispersion relations of SPPs of various modes in a nanohole, calculated from a transcendental equation, show that the propagation length of an SPP of mode 1 is much larger than the other modes in a specific frequency band, which is dependent on the nanohole size. In this band, the streamlines of the Poynting vector (energy flux) of mode-1 SPP in nanohole exhibit helixes; the surface component of the energy flux is perpendicular to the phase front of the SPP. Numerical results show that, after a helical SPP tunnels through a nanohole, most of the energy flux fans out at the outlet as a dipole radiation. The spatial phase distribution of E z above the interface indicates that the transmission light carries orbital angular momentum with a topological charge of 1. Additionally, a part of the helical SPP creeping along the edge of an outlet naturally converts into a spiral (Hankel type of order 1) SPP outward propagating at the film’s interface; both SPPs have the same handedness. Moreover, the interferences of multi SPPs generating from two nanoholes and even from a two-dimensional nanohole array are also related to the spiral SPP.