A high efficiency and compact optical device comprising two or more active and resonating optical facet surfaces defined by a three-dimensional representation and configured to provide a three-dimensional device. A focal region, remote from the optical surfaces and non-contiguous therewith, is defined by two or more active optical resonant surfaces, at least one of which is self-resonant. The optical surfaces in general do not have a continuous second derivative and are defined by a piecewise continuous surface function providing radially directed facets. The optical device comprises a transparent dielectric body with its optical surfaces being formed on the surfaces of said transparent dielectric body. A light transducer may be located at a focal region to provide an energy conversion. A light source having a physical extension in space, such as an LED, may be located at the focal region to provide collimation. In some embodiments the active surfaces may be chosen to transform incident radiation into a predetermined shape and having a predetermined spatial power distribution.