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We designed a slit dipole antenna backed by an extended hemispherical silicon lens and investigated the minimum lens size in which the slit dipole antenna works as a leaky-wave antenna. The slit dipole antenna consists of a planar feeding structure, which is a center-fed and open-ended slot line. A slit dipole antenna backed by an extended hemispherical silicon lens is investigated over a frequency range from 0.2 to 0.4 THz with the center frequency at 0.3 THz. The numerical results show that the antenna gain responses exhibited an increased level of sensitivity to the lens size and increased linearly with increasing lens radius. The lens with the radius of 1.2λo is found to be the best possible minimum lens size for a slit dipole antenna on an extended hemispherical silicon lens.