A structure is provided that includes an aperiodic dielectric stack. The structure may include a substrate, a device disposed over the substrate, and a first dielectric stack disposed between the substrate and the device. The first dielectric stack includes a plurality of layers comprising a first dielectric material, wherein at least two of the layers comprising a first dielectric material have substantially different thicknesses, as well as a plurality of layers comprising a second dielectric material. The average outcoupling efficiency into air of the device over a bandwidth of at least 300 nm may be at least 40% greater than that of an otherwise identical device disposed in a structure without the first dielectric stack.