This thesis attempts to improve on an ongoing experiment of detecting electron spin resonance (ESR) on AlGaAs/GaAs lateral quantum dots. The experiment is performed in a 2.5 Tesla magnetic field at temperatures around 100mK. A resonator cavity is used to expose the quantum dot to a perturbational microwave magnetic field pulse that induces electron spin flip transitions. The statistics for measuring the probabilities of these transitions can be improved by increasing the strength and/or the duration of the pulsed magnetic field. The drawback is that both of these improvements lead to thermal heating which diminishes the quantum nature of the dot. I used electromagnetic field calculations and simulation software to explore different resonant modes, geometries, materials, and methods of excitation and optimize the design of potential new cavities. Two cavities were built specifically to test the TM010 and TE011 cylindrical modes. Although they did not perform as well as was theoretically expected, these cavities provide a better magnetic field magnitude per heating power than the current cavity.
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