Mode Suppression and Homogeneous Field Bandwidth Enhancement of a Tuning-Free Micro-Loop-Gap Resonator Using FR4 for Chip-Scale Rubidium Clock

We propose strategies for the design of a tuning-free micro-loop-gap resonator (mu-LGR) that provides high magnetic field homogeneity of the TE011-like mode over a broad bandwidth with a high field orientation factor (FOF). This broadband feature allows it to fulfill the FOF requirement at the precise 6.835 GHz resonance for chip-scale double-resonance (DR) rubidium (Rb) clocks without the need for any mechanical or electrical frequency tuning means. The FOF bandwidth expansion mechanism manipulates the unwanted side modes by using perturbation theory and distinct properties of the FR4 substrate characterized by an accurate method for the long-term stabilities in high temperatures. Thanks to the absence of tuning components and the usage of lossy FR4, this new mu-LGR achieves better FOF in a wide bandwidth of similar to 550 MHz and simplifies the physics package (PP) of the entire clock system. The measured S-parameters of the fabricated mu-LGR prototype and its cavity-cell assembly validate that the cell-loaded mu-LGR can operate over a 128 MHz impedance bandwidth of |S-11| < -10 dB at similar to 109 degrees C, with strong resonance at 6.83 GHz and a loaded quality factor of 12.7 which does not result in reduced signal strength but is advantageous to alleviating cavity pulling for optically detected passive DR Rb clocks. Moreover, a spectroscopic experiment of the developed chip-scale atomic clock (CSAC) based on the proposed mu-LGR verifies that the tuning-free mu-LGR can obtain a FOFexp of 0.75 at 6.835 GHz, therefore guaranteeing the atom transition to be well excited for the clock operation.