A two-part experimental study was conducted to address the issues of supersonic fuel mixing enhancement and efficient combustor development. The first part of the study involved quantitative characterization of fuel-air mixing in a non-reacting supersonic flowfield. Two flow configurations were compared: i.) a baseline case with normal fuel injection and ii.) a case with an acoustically open cavity placed downstream of the injection in order to excite mixing. Direct measurements of local atomic fuel-air ratio were acquired using Laser Induced Breakdown Spectroscopy (LIBS), which was applied for the first time in a supersonic flowfield. Indirect measurements of fuel spreading rate were inferred from intensity gradients in time-averaged Schlieren images. The quantitative results were compared to show conclusive gains in fuel-air mixing rate for the cavity configuration. LIBS was proven as an effective diagnostic for quantifying supersonic mixing. In the second part of the study, a baseline supersonic combustor was designed, built, and tested for future comparative studies of combustion performance. The combustor featured a square cross-section and a three-dimensional expanding section, with optical access on one side. Combustor wall pressure was measured at various fuel injection conditions. Supersonic combustion was evident for some conditions, but results indicated poor combustion efficiency for all cases. This shows the need for either mixing enhancement or a redesign of the baseline conditions.