An optical device for transforming an input light distribution from an LED light source to provide an omni-directional output light distribution for solid-state lighting is disclosed. The optical device has a conical form, comprising first and second coaxial cones of different refractive index, defined by coaxial inner and outer cone surfaces, which converge from a cone base to a rounded tip at the apex. Preferably, each of the inner and outer cone surfaces comprises a plurality of conical facets defining a grating structure. The inner cone, i.e. air cavity, is directly coupled to an LED emitter area. Cone angles and spacings of conical facets, defining inner and outer gratings, are tailored to reshape a predetermined input light distribution. Apertures assist in heat dissipation. A lightweight, compact device with high transmission efficiency can be manufactured at low cost by one-step injection molding from an optical-grade polymer, such as PMMA.