Reflections in a Pool of Mercury: An Experimental and Theoretical Study of the Interaction Between Electromagnetic Radiation and a Liquid Metal

The conclusion of Schulz and of Wilson and Rice that the low-energy absolute reflectance of liquid mercury obeys the simple Drude formula is confirmed by new measurements made at near-normal incidence in the wavelength range 0.5-30 \ensuremath{\mu}. The difficulties inherent in obtaining such data are discussed, and a precise and sensitive double-beam infrared reflectance spectrometer, constructed for the purpose of overcoming these difficulties, is described. The results described must be reconciled with recent ellipsometric studies, carried out independently at several different laboratories, in which the apparent optical constants of liquid mercury were found to be substantially higher than those predicted by the Drude theory. From an examination of the solutions of Maxwell's equations describing the interaction of electromagnetic radiation with an inhomogeneous conductor, it is shown that such anomalous optical behavior is to be expected for a liquid metal whose surface is not a geometric boundary, but a transition zone over which the properties of the system vary from those of the bulk metal to those of the contact medium. To test the plausibility of this model, a simple form for the conductivity profile across this transition zone is assumed, and the surface parameters characteristic of that profile are varied to fit the observed ellipsometric and reflectometric data. Excellent agreement between theory and experiment is found for a variety of choices of the parameters, provided that the conductivity passes through a maximum as the surface zone is traversed. It is argued that such a maximum is qualitatively consistent with the known sensitivity of the conductivity of liquid mercury to variations in the liquid structure.