A light-emitting diode includes a first semiconductor region of one of p- or n-conductivity types, a second semiconductor region of the other one of p- or n-conductivity types, forming a p-n junction with the first semiconductor region, and a quantum well layer at the p-n junction between the first and second semiconductor regions. A hyperbolic metamaterial structure is provided in the second semiconductor region. The hyperbolic metamaterial structure is coupled to the quantum well layer for extracting light from the quantum well layer. The hyperbolic metamaterial structure may be patterned to provide an array of nanoantennas to apodize the emitted beam, and to control the polarization state of the emitted beam.