Mode evolution and nanofocusing of grating-coupled surface plasmon polaritons on metallic tip

We present a detailed analysis on mode evolution of grating-coupled surface plasmonic polaritons (SPPs) on a conical metal tip based on the guided-wave theory. The eigenvalue equations for SPPs modes are discussed, revealing that cylindrical metal waveguides only support TM01 and HEm1 surface modes. During propagation on the metal tip, the grating-coupled SPPs are converted to HE31, HE21, HE11 and TM01 successively, and these modes are sequentially cut off except TM01. The TM01 mode further propagates with drastically increasing effective mode index and is converted to localized surface plasmons (LSPs) at the tip apex, which is responsible for plasmonic nanofocusing. The gap-mode plasmons can be excited with the focusing TM01 mode by approaching a metal substrate to the tip apex, resulting in further enhanced electric field and reduced size of the plasmonic focus.