Electric near-field enhancement of a sharp semi-infinite conical probe: Material and cone angle dependence

In the context of the electric near-field enhancement, we consider a simple model for the electric field near the apex of a conical probe used in scanning near-field optical microscopy for the case of real materials taking into account classical boundary conditions. To do this, we solve a transcendental algebraic equation for a parameter ν governing behavior of the electric field near the probe apex. Our results show that in the case of obtuse cones, the values of the parameter ν for real materials are not too different from those for a perfect conductor. In the case of the acute cones the parameter values can differ greatly from those for a perfect conductor. The metal (silver) probes are shown to ensure lower values of the parameter ν and, hence, the higher electric field enhancement than that of the dielectric (silicon) ones. Besides, the dependences of ν on the cone angle and the frequency are nonmonotonic, i.e., an optimal angle and frequency exist yielding the maximal near-field enhancement for both metal and dielectric probes. In addition, a possible generalization of our approach to a rounded conical probe is demonstrated. It is shown that in this case the electric near field results from the interplay between two effects, the lightning rod effect and the surface plasmon excitation.