Disclosed herein are a number of dielectric pillars, arranged to form a close-packed aperiodic array, such as a Vogel spiral, where the geometries of the aperiodic array produce azimuthally isotropic scattering of luminescence within a restricted angular cone of extraction. The aperiodic array can be formed, attached or placed on a converting material, such as, phosphor, to restrict emission to within the angular cone of extraction. The phosphor could be part of a converting illumination device, such as a phosphor coated light emitting diode, or a laser activated remote phosphor converting device.