Finite momentum Cooper plasmons in superconducting terahertz microcavities

The superconducting phase mode is a collective mode that is gapped in three-dimensional superconductors, but gapless in two-dimensional superconductors. This mode is not infrared active in the far-field, but can be probed with near-field optical measurements. We develop theory showing that the near-field nature of on-chip time domain THz spectroscopy can access this mode via superconducting microcavity resonances - which we call `Cooper plasmons'. We experimentally show spectroscopic signatures of two Cooper plasmons in a superconducting NbN film and use these Cooper plasmons to report the real and imaginary parts of the self-energy across a thermal metal-to-superconductor transition. We discuss applications of Cooper plasmons in other superconducting systems, as well as ways to avoid parasitic Cooper plasmons in superconducting circuit engineering.