The present invention relates to light-emitting diodes (LEDs), and related components, processes, systems, and methods. In certain embodiments, an LED that provides improved optical and thermal efficiency when used in optical systems with a non-rectangular input aperture (e.g., a circular aperture) is described. In some embodiments, the emission surface of the LED and/or an emitter output aperture can be shaped (e.g., in a non-rectangular shape) such that enhanced optical and thermal efficiencies are achieved. In addition, in some embodiments, chip designs and processes that may be employed in order to produce such devices are described.