If $A$ is the vector potential, the London equations imply that:
if there is no external current. This can be interpreted as an effective photon mass and so, light cannot propagate indefinitely within a superconductor. Let $\lambda = 1/\mu$ be the London penetration depth. As a thought experiment, assume we had a thin (< $\lambda$) slab of superconducting material and shined high frequency light on it. Some of the energy would be lost as heat (photons hitting atoms, etc.). The rest would ``decay" exponentially but manage to get to other side of the slab. My thoughts and chain of questions:
How would the light emerge? Would the exiting light have lower frequency but proportionally higher intensity? Would it have the same frequency and just be the surviving fraction of photons? Then, what did the photons which didn't survive decay into? Or, does the decay just mean absorption of the photons e.g. heat generation?
The $U(1)$ gauge symmetry of quantum electrodynamics is broken/hidden. How do the Feynman diagrams look inside a superconductor?