Abstract-This paper reports the permanent frequency mismatch reduction of the primary wineglass modes in a planar axisymmetric resonator by strategic mass loading. The resonator consists of a set of concentric rings that are affixed to neighboring rings by a staggered system of spokes. The outer layers of spokes are targets for mass deposition. The paper develops modified ring equations that guide the mass perturbation process and despite the fact that the deposited mass and deposition locations are quantized, it is possible to systematically reduce the frequency difference of the wineglass modes to effective degeneracy such that two modes cannot be distinguished in a frequency response plot. Results on five resonators are reported with nominal wineglass modes near 14 kHz, quality factors of 50 k, and frequency mismatches exceeding 30 Hz in some cases but with post-perturbation mismatches smaller than 80 mHz. Furthermore, it is also shown that the quality factors remain unchanged.

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Abstract-This paper reports a wafer-level technique for the systematic elimination of the modal frequency difference between a nominally degenerate pair of modes in an axisymmetric resonator design. A targeted etch process is developed in which masking resist and a conformal layer are ablated at specific sites on the resonator thereby exposing the underlying silicon and enabling site-specific mass removal by SiDRIE. A model of the perturbed resonator dynamics guides the selection of the ablation sites so that the subsequent timed etch reduces the modal frequency differences by a prescribed amount. This waferlevel process is demonstrated on seven resonators whose modal frequency differences are reduced below 100 mHz from initial splits as large as 15 Hz for a pair of modes with 13.5 kHz nominal frequencies.

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We have successfully demonstrated a compact atomic frequency standard, the Chip-Scale Atomic Clock (CSAC), which achieves aggressive reductions in size and power while preserving good short-term stability. The device, based on Coherent Population Trapping (CPT), achieved volume less than 1cm 3 , power consumption below 30mW, and an Allan Deviation less than 1x10 -11 (1hour). This device incorporated a novel dual-pass reflective optical configuration based on a microstructured dualfocus optic. Compact, low-power control electronics were developed based on an injection-locked voltage controlled oscillator (VCO) circuit. This approach enabled the combined power consumption of the VCO and microcontroller-based control electronics to be kept below 15mW.