Extended Data Fig. 1: Microwave high-impedance waveguide characterization.

a, Schematics of the high impedance (high-Z) waveguide. The mechanical external coupling is approximately proportional to the impedance of the environment. Thus the effective impedance Zeff looking from the mechanics side into the high-Z waveguide gives us intuition on the enhanced external coupling. b, Calculated Zeff and the group delay with a free spectral range of 110 MHz and a waveguide characteristic impedance Z = 1000 Ω. c, Measured group delay of the high-Z waveguide. The coupled mechanical modes appear as sharp peaks in group delay.