Nanoantennas are efficient devices exhibiting large confined electric field enhancements. So far, they have been extensively researched mainly in the receiving mode, which means that the illuminating field is essentially a plane wave. In this article, we consider the problem of designing an efficient and highly directive transmitting nanoantenna where the system is energized by a nonplane wave field, a subwavelength laser excitation. The main objective of this article is to establish through an accurate computational model a basic understanding of how a dipole-type radiator can be made to resonate with such complex nonplane-wave type of near-field illumination. Including short-wavelength components allowed us to achieve a 200-nm spot radius, which is a quarter of its incident wavelength (800 nm). Near- and far-field antenna quantities are introduced and calculated using an efficient full-wave finite-element method-based multiphysics solver. A nanoscale optical antenna is then presented with optimized dimensions and material settings. Various design data and insights are also discussed in connection with issues such as how to define efficiency and determine whether the system is radiating properly.