Fig. 2: Open cavity modes.

a Transmission properties of the cavity resonator were measured by the conductances \({g}_{{{{{{\rm{cav}}}}}}}\) and \({g}_{{{{{{\rm{loss}}}}}}}\). b Openness of the cavity region was given by \({g}_{{{{{{\rm{open}}}}}}}\) which measures the transmission in the direction transverse to the cavity (blue arrow). c Cavity transmissions \({g}_{{{{{{\rm{cav}}}}}}}\) and \({g}_{{{{{{\rm{loss}}}}}}}\) measured against \({V}_{{{{{{\rm{M}}}}}}}\) shows coinciding resonance peaks, implying the presence of circulating waves, i.e., cavity modes. The longitudinal nature of the modes can be seen by the quasiperiodicity of the conductance peaks, and hints of the transverse modes can be seen by the fine peak structures (arrows). These characteristics were observed while the cavity stayed highly open to its sides, as seen from \({g}_{{{{{{\rm{open}}}}}}}\). d The mesoscopic cavity resonator model was constructed using the Landauer–Büttiker formalism. Cavity transmission \({g}_{{{{{{\rm{cav}}}}}}}\) is given by the total transmission across both mirrors \(\left|{t}_{12}\right|^{2}\), and the openness is accounted by subunitary propagation across the mirrors (\(\left|{u}_{i}\right| < 1\)). e Changes in the mirror conductance \({g}_{i}=0.25 \sim 0.75\) led to uniform changes across the cavity spectra. A closer inspection of the circled peaks is shown in f after normalization. The model prediction for \(\left|{t}_{i}\right|^{2} = 0.25 \sim 0.75\) and \(\left|{u}_{i}\right|\,=\, 0.66\) has been plotted as solid black lines, and the prediction for \(\left|{t}_{i}\right|^{2}=0.25\) in a closed cavity (\(\left|{u}_{i}\right |=1\)) has been plotted as a dotted black line for comparison.