Microwave-cavity-mode optimization by background antiresonance tuning

To derive the best oscillator phase noise when implementing a high-$Q$ resonator, the resonant spectral line shape must have high contrast and symmetry. Ideally, this line shape is second order and Lorentzian; however, in a high-mode-density spectral region, low-$Q$ background spurious modes interact and distort the resonance. For a sapphire-loaded cavity resonator operating with whispering-gallery modes confined within the sapphire crystal, we show that this high contrast and symmetry can be achieved by meticulously changing the dimensions of the surrounding metallic cavity shield to tune the background low-$Q$ structures into antiresonance. This works because the high-$Q$ resonances are primarily defined by the sapphire, while the background modes are defined by the cavity shield. Alternatively, it has been shown that a similar result can be achieved by exciting the high-$Q$ resonator with a balanced microwave dipole probe in a Mach-Zehnder interferometric configuration. The probe has been constructed from two separate coaxial electric field probes symmetrically inserted into a cylindrical-cavity resonator, from opposite sides with a small gap between them, so they can behave like an active wire-dipole antenna. The power into the two separate probes may be matched with an external variable attenuator in one of the arms of the interferometer. Conversely, the phase between the two electric field probes may be changed with an external variable phase shifter, which changes the nature of the field components to which the probe couples. The probe couples to the high-$Q$ resonant modes as well as low-$Q$ background modes, which can be made resonant or antiresonant with respect to the high-$Q$ modes by changing this external phase. When the background modes are in antiresonance, the line shape of the high-$Q$ mode can be made symmetric and with higher contrast. This technique has been applied to both whispering-gallery sapphire modes, as well as hollow-cavity resonators, without changing the dimensions of the cavity.