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We developed auxiliary differential equation finite-difference time-domain (ADE-FDTD) method for dispersive Drude medium, and simulated the optical part of the plasmon antenna (PA) and waveguide (WG) system for thermally assisted magnetic recording (TAMR) heads. To achieve higher efficiency without sacrificing the small spot size, our newly developed automatic computational shape optimization program was carried out for the PA designs with a variety of configurations: no recording media, with-media, with magnetic write pole, and only-PA models. The optimized designs for these cases show an enhancement of the electrical field at the PA tip compared to the initial configuration. In addition, both the PA body as well as the tip affects the performance of the guiding and focusing of the plasmon. However, the optimized detail shape and the sensitivity of the dimension are dependent upon the configuration.