We present the design and simulation of first-ever planar single-element solar lenses (modified hemispherical gradientindex structures) for concentrator photovoltaic applications, with high collection efficiency and liberal optical tolerance at averaged cell irradiance levels exceeding 1000 suns. These compact lens designs satisfy the severe constraints of the refractive indices of viable polymeric materials and fabrication techniques, for visible and near-infrared radiation. The planar hemispherical gradient-index lens for a far-field (solar) source is created from a near-field unit magnification spherical gradient-index lens. Our new solutions incorporate a constant-index core (crucial for manufacturability). Simulations include a polychromatic and extended sun. A sample design for an f/1.40 solar lens is provided, where planar lenses comprise a concentrator module's protective glazing, with loss-less packing due to a square lens entry allowed by the modified truncated (non-full aperture) design, without incremental optical losses.