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While dielectric resonator antennas (DRAs) offer several advantages, such as small size and high efficiency, traditional DRAs with simple geometries are usually narrow bandwidth. Much work has been done to enhance the bandwidth of DRAs. However, the geometries of these designs are usually bulky and difficult to fabricate. The paper presents a low profile eye-shaped DRA with wide bandwidth. This antenna is designed in the X-band and is excited through a narrow rectangular slot. The DRA consists of an elliptical shaped resonator which has circular cylinder embedded at its center. Two different dielectric materials are used for the elliptical cylinder and circular cylinder. A bandwidth of more than 27% is achieved. Using the embedding approach, we also propose other possible shapes for the host and the parasitic element. Simulation results are obtained. Another new feature is that the microwave substrates we use to fabricate the dielectric resonator are softer than the traditional ceramic materials. As a result, we are able to fabricate the resonators easily into any shape.