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A novel step-index cylindrical homogeneous lens at millimeter-wave (MMW) frequencies is designed by using the technique of parallel plates propagating the TE1 mode. The cylindrical homogeneous lens, which is sandwiched between two parallel conducting plates, has an H-shaped cross section to give the desired step-index of refraction. For a given aperture size, the focal length of the cylindrical homogeneous lens can be adjusted by changing the cross-section structural parameters rather than the dielectric material itself, which should be highlighted for cylindrical homogeneous lens for the first time. A planar linearly tapered slot antenna (LTSA) is chosen to feed the cylindrical homogeneous lens. The ray-tracing and transverse resonance methods are used to analyze and design this lens antenna at 30 GHz. Measured results of the fabricated lens antenna show good agreement with simulations. At 30 GHz, the measured 3-dB E- and H-plane beamwidths are 6.1° and 50.2°, respectively, and the first sidelobe level in the E-plane is -16.3 dB. The measured gain is 17.9 dB, corresponding to a radiation efficiency of 67.2%.