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Ground penetrating radars (GPRs) have been used extensively as a non-intrusive means for subsurface investigation. Low antenna clutter and weak antenna-ground interaction are desirable features for the detection of shallow mines. We present a finite difference time domain (FDTD) simulation of a wide band dielectric rod antenna with these desirable features. The FDTD was chosen because of its ability to handle inhomogeneous media and provide accurate results over a wide range of frequencies. The near field radiation properties of the antenna are investigated. The effectiveness of the above antenna in humanitarian demining applications is studied by analyzing the response from a position scan on anti-personal (AP) mines.