A rotationally symmetric all-dielectric lens antenna is designed by defining the phase function inside the dielectric directly via a closed-form series formula. The refractive index of the lens is modified using state of the art optical path rescaling to keep the refractive index within practical values. The lens optimization is done using the genetic algorithm in MATLAB, where each case is evaluated by conducting linked ray tracing and fullwave electromagnetic simulation in COMSOL. A lens prototype is shown to provide a directivity enhancement of 5.1 dB compared to the optimal conical horn antenna, an improvement of 2 dB compared to the Luneburg lens, and an improvement of 3.8 dB compared to a reference graded index lens. All the examined cases shared a similar length of 5???? for the center frequency of 10 GHz. The prototype lens antenna has a maximum refractive index of 2.1, a reflection coefficient of −22 dB, and a side-lobe level of −25 dB at the center frequency of 10 GHz. The lens’ performance is consistent in the 9–11 GHz band supported by the standard circular waveguide. The results from a prototype with a discretized refractive index simulated in CST Studio Suite are in excellent agreement with the ones with a continuous refractive index profile simulated in COMSOL.

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