Cavity resonators that employ the high reflectivity of periodic arrays of dielectric layers exhibit enhanced quality factors compared with dielectric resonators. Their quality factor is limited by the exponential decay of the electric field penetrating the structure. We show that an aperiodic reflector array with dielectric layers thinner than a quarter-wave near the defect site and asymptotically approaching quarter-wave thickness distant from the site can exhibit very high quality factors. A spherical aperiodic reflector resonator consisting of nested alumina shells is simulated and shown to exhibit quality factors greater than 107 at 10GHz and room temperature.

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