We propose and optimize two designs of plasmonic lens structures, concentric grooves with a central hole (CGH) and concentric grooves with a central pillar (CGP), based on a traditional structure of concentric grooves (CG). The numerical investigation based on COMSOL Multiphysics is performed to optimize the three kinds of structures by a 355 nm radially polarized laser illumination. It is found that full-width at half maximum (FWHM) is closely related to the size of the center-position, and the field enhancement effect depends on the resonant wavelength of surface plasmon polaritons, permittivity, film thickness, and groove number. Compared to a FWHM of ( is the wavelength of the laser beam) with the conventional CG type, the combination of localized and extended surface plasmons results in CGP and CGH parameters achieving their optimal value with a much smaller spot size of and higher intensity enhancement for a variety of the aspect ratios of central pillar and hole. A focused ion beam was used to fabricate the three type nanostructures with high accuracy. The CGH type with a central hole 20.88 nm in diameter and the CGP type with a central pillar 55.45 nm in diameter have been successfully fabricated approximately to their optimization results.