A “superperiodic” photonic-crystal (PhC) light-emitting diode (LED) design exhibiting high-luminance patterns is proposed for applications that require highly directive vertical light extraction. The superperiodic design employs a periodic arrangement of defective missing holes on an otherwise perfect periodic pattern of holes for the basic two-dimensional PhC structure. Avoiding the fragile semiconductor membrane structure that is popular in current PhC laser designs, the design utilizes a thick epitaxy structure with electromagnetic density-of-mode singularity. This singularity is created by the defect mode in a three-dimensional frequency versus wave vector relation within the band matched with the gain spectrum of the LED that is placed on top of the base reflector plate material. The superperiodic structure of this design is shown to provide an effective means for sharpening the vertical beam in the far field, based on discrete-Fourier transformation theory. Subsequent simulations based on the finite-difference time-domain analysis verify the effectiveness of the design principle on GaN epitaxy structures with various bottom layers.
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