In a conventional flat plate solar cell under direct sunlight, light is received from the solar disk, but is re-emitted isotropically. This isotropic emission corresponds to a significant entropy increase in the solar cell, with a corresponding drop in efficiency. Here, using a detailed balance model, we show that limiting the emission angle of a high-quality GaAs solar cell is a feasible route to achieving power conversion efficiencies above 38% with a single junction. The highest efficiencies are predicted for a thin, light trapping cell with an ideal back reflector, though the scheme is robust to a non-ideal back reflector. Comparison with a conventional planar cell geometry illustrates that limiting emission angle in a light trapping geometry not only allows for much thinner cells, but also for significantly higher overall efficiencies with an excellent rear reflector. Finally, we present ray-tracing and detailed balance analysis of two angular coupler designs, show that significant efficiency improvements are possible with these couplers, and demonstrate initial fabrication of one coupler design.