The increasing efficiency and adoption rate of light-emitting diodes (LEDs) for lighting is forecasted to lead to large energy savings in that sector. Intrinsic self-refrigeration, which surprisingly accompanies the emission of light from an LED, might allow the same technology to be harnessed for new applications. In the first half of this dissertation, I will discuss whether refrigeration and cooling, which also account for a large share of world energy consumption, comprise a realistic future energy application for optoelectronics. To date, electroluminescent cooling has eluded direct observation at practical power densities, since a pre-requisite for net cooling is the near-complete elimination of LED internal losses that dissipate heat. I will propose a near-ideal-efficiency LED structure, realizable with existing optoelectronic material quality and device processing capabilities, to predict the technological limits of electroluminescent refrigeration. I will show that LED-based cooling can realistically be more efficient than solid-state alternatives like thermoelectric cooling, particularly for cryogenic applications and at moderate power densities.

In the second half of this dissertation, I will discuss a new hardware accelerator for difficult combinatorial optimization problems. These problems are abundant in modern society, in the fields of operations research, artificial intelligence, chip design, financial optimization, medicine, and many others. They are difficult in that no algorithm has yet been found that solves them efficiently, but the increasing computational power of digital computers has allowed these problems to be routinely tackled. As conventional computers reach their scaling limits, however, alternative hardware architectures are being explored to accelerate computationally intensive tasks like machine learning and combinatorial optimization. Here, I will discuss the design of a new optimization machine, implemented using a network of coupled analog electrical oscillators. The machine uses an unconventional search mechanism to discover the global minimum of the Ising problem, a difficult problem that maps quickly onto other hard optimization problems. I will present the simulated performance of this machine for moderately sized problems with all-to-all connectivity and discuss its potential to scale to larger problems.