Near-field techniques for probing collective modes of anisotropic superconducting thin films

We propose the use of scattering-type scanning near-field optical microscopy (s-SNOM) to characterize the collective mode spectrum of anisotropic superconductors. To probe the dispersion of collective modes with large in-plane momenta, specifically surface plasmons and guided wave modes, we model the real-space interference patterns of modes launched by the sharp s-SNOM tip and their reflections off physical and electronic boundaries. In addition, we show that s-SNOM spectroscopy allows for a direct probe of the $c$-axis superfluid density in underdoped anisotropic superconductors with nanoscale spatial resolution.