Cavity

From MesoscopicWiki

Original version of the cavity.

Download CMI waveguide transition-bend

Circular waveguide holes are 2.515 +- .005 mm center to center. These holes are 1.5 mm in diameter. For TE11 mode this corresponds to a low-frequency cutoff of 140 GHz. The rectangular waveguide is D-band WR-6.5. There is a rectangular-circular transition built into the coupler. The holes on the mirror itself are .7mm.

Mirror radius 156 mm. Polished surface of the mirror is 145 mm in diameter. Oxygen free copper, uncoated. Approximately 1 micron accuracy with 3 nm rms roughness.

Transition made by CMI. Mirror cut and polished by SPAWR. Mounting in machined aluminium plates with invar rods.

some ideas from Weinstein's book on open resonators and waveguides

Asymptotically the mode density in a closed cavity goes like ω³, independent of the shape of the cavity. In fact

in 3-d. At high frequency, this densification of modes leads to overlap of modes, since heating losses increase like . As a result, closed cavities don't support resonance at high frequency. In 2-d this is still true. In 1-d however the modes are equally spaced in frequency. So there is no densification.

A key idea is that without radiation, you can't have high Q modes in cavities. The radiation kills most modes, effectively reducing the mode density. This allows some modes to be resonant. Another way of saying this is that, you want rays to be paraxial so that you have effectively a 1-d system. This allows you to avoid densification of modes at high frequency.

Another idea is that high-Q modes are typically associated with caustics. In effect the caustics form a boundary within the cavity, and the amplitude of the field decays exponentially away from the caustic. The diffractive changes to the geometrical optics results are standard semi-classical results. EBK quantization. Maslov asymptotics.

An important issue is why use a hemi-spherical cavity. Weinsteins says (p. 183) if you try to use 2 spherical mirrors to make a confocal cavity, the result is sensitive to minor imperfections. whereas 'these difficulties ... are eliminated if one mirror is curved and one is plane...'

Efficiency of Mode Excitation in an Open Resonator Connected to a Waveguide, I. K. Kuz'miche, Journal of radiophysics and quantum electronics, volume 46, 2003.