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This paper presents the numerical simulation on the input impedance and beam pattern of a log-spiral antenna combined with an extended hemispherical lens. The effect of the lens on the input impedance of the antenna was studied by using HFSS (finite element method) and microwave studio CST (finite integration technique). A hybrid approach combining geometrical optics (GO) inside the lens and physical optics (PO) outside the lens was applied to calculate the far field pattern and Gaussian coupling efficiency of the integrated lens antenna. At 600 GHz the calculated maximum directivity of the hemispherical lens with an optimum extension length is about 37 dB and the corresponding Gaussian coupling efficiencies is about 76%. The off-axis performance of the integrated lens antenna was also examined.