Although the concept of an artificial compound eye has been discussed in the literature, its optical arrangement has never been widely adopted for optical design. A design is presented for a tunable gradient-index microlens array, believed to be new, induced electro-optically inside a cylindrical shell. The transparent electrodes on the both sides of the shell are positioned such that the electrodes on the opposite side compensate the phase delay from the electrodes on the front side for a normally incident plane wave, thus suppressing the intrinsic electrode diffraction for the device without applied voltage. The original technique of the electric field calculation was developed to analyze the induced refractive index inside the shell for two types of electro-optic (EO) ceramics: with linear and with quadratic EO effects. For the linear effect it was shown that for given EO coefficients, electric field strength and intrinsic refractive index, the electrode number should exceed a certain amount to make the focal distance less than the cylinder radius. The quadratic effect provides higher sensitivity to the type of the diffracted wave polarization. It was shown how the quadratic coefficient ratio R_(12)/R_(11) affects the focal-length difference between TE and TM light polarization.
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