Various kinds of optical near-field apertures have been proposed for higher throughput and smaller spot size. However, few studies have mentioned the readout characteristics of the recorded marks on an optical disk illuminated by a near field optical light. In this paper, we have investigated the scattering light by a two-dimensional recorded mark on a phase change disk with Finite-Difference Time-Domain (FDTD) simulations. Instead of using Recursive Convolution (RC) and Piecewise Linear Recursive Convolution (PLRC) scheme, we integrated the motion equation of free electron into conventional FDTD method to solve the electromagnetic field in the metallic materials. The validity of the proposed method is illustrated by comparing its results with those from the analytic exact solution. We analyzed the distributions of optical near-field around a two-dimensional metallic nano-aperture, and then calculated the far-field scattering pattern from a two-dimensional recorded mark on a phase change disk while it was illuminated by an optical near-field though a nanoaperture. The sum signal by a condenser lens was calculated from far-field pattern, and its relationships with the width of recorded mark and the thickness of each layer in the phase change disk were illustrated. The cross-talk between the recorded marks was also discussed.