Simulation of optical near and far fields of dielectric apertureless scanning probes

We study apertureless field enhancing optical probes beyond the spherical approximation in a smooth transition towards up to 3 mu m long conical silicon tips. Such tips are used in apertureless scanning near field optical microscopy, which holds the promise of sub 10 nm lateral resolution. A fully three-dimensional numerical solution to the Maxwell equations is obtained with the multiple multipole method giving simultaneously both near fields and scattered far fields. The significance of focused beam excitation for work with long tips is illustrated and the relative influence of relevant length scales such as tip length, excitation wavelength, and beam waist radius is discussed. In the limit of vanishing tip apex radius, the near field grows without bounds, whereas the far field remains finite. We verify that for small apex radii the near field confinement at the tip apex, which is related to the achievable lateral resolution, scales with the inverse of the radius. We find, however, that long tips exhibit a markedly lower confinement than spherical or very short tips. Relevant for experimental studies, we demonstrate how scanning the excitation field with long conical tips can be a useful technique for mapping the focal volume. We show that the normalized near field at the tip apex is robustly tolerant against small misalignments or misorientations of illumination focus and tip apex.