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Bragg onion resonators with omnidirectional reflector cladding

We propose to use onion-like resonators to approximate spherically symmetric Bragg resonators. Such Bragg onion resonators have been realized in silicon based material systems. We develop an analytical theory that calculates the resonant frequencies and the quality factors of the onion cavity modes. We demonstrate that it is possible to achieve Q factors exceeding 5 x 106 in a cavity of a few microns in dimension. The onion resonators allow full control over the spontaneous emission process, which may lead to the thresholdless lasers. The onion resonators may also find many other applications in cavity quantum electrodynamics.