Microscopic calculation of electromagnetic fields in refraction at a jellium-vacuum interface

For a long-wavelength electromagnetic wave of frequency ω, incident on a jellium-vacuum interface, the spatial dependence of the vector potential, →A(→r;ω), is evaluated in the surface region. A simple integral equation is derived which relates →A(→r;ω) to the jellium nonlocal conductivity tensor ↔σ(→r;→r,ω); numerical calculations based on this equation are reported, in which the random-phase approximation to ↔σ(→r;→r,ω) was used---the required single-electron wave functions were evaluated via the self-consistent surface-barrier potentials of Lang and Kohn. Families of graphs of →A(→r;ω) are presented, for fixed bulk electron concentration as a function of frequency and for fixed ωₚω (where ωₚ is the plasma frequency) as a function of bulk electron concentration. The sensitivity of →A(→r;ω) to the shape of the surface potential barrier, at fixed ω and bulk electron concentration, is also explored. The use of the results obtained for →A(→r;ω) is proposed for the calculation of refraction effects in surface photoemission and in reflection spectroscopy.