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This paper reviews the design of some optical systems for coupling and interconnection by GRIN components. The optical systems designed with these components are based on imaging and transforming properties of such components to carry out specific functions. First of all, a brief description of light propagation through GRIN materials will be given. After that, a device to couple light by a GRIN fiber lens into fibers of different core sizes with low loss is described. The coupling efficiency as well as the coupling loss are studied versus variation of the GRIN fiber lens length and the refractive-index profile of the coupler. The design of crossover and parallel interconnects by using a GRIN planar structure will be presented. The optical analysis includes the PSF for describing the performance of the device and the SBP for estimating the numbers of channels that can be handled. The dependence of the number of channels on the wavelength of light and the transverse aperture of the planar interconnect is shown.Spherical GRIN materials: Luneburg (top) and Maxwell's fisheye (bottom) lenses.

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We present a general formulation based on the Jones-matrix theory for reciprocal nonabsorbing polarization devices, including polarization interference filters and liquid-crystal displays. The development of this formulation is based on general symmetry conditions that relate the Jones matrix when the device is illuminated from the front side and from the back side. The application to liquid-crystal displays results in a constraint of the Jones-matrix elements, which represents a generalization of the existing models that explain their modulation properties.