Surface-plasmon dispersion relation from the reflectivity of parallel-polarized light

We show that a very general method of deriving the surface-plasmon dispersion relation, ω=ω(Q), for a semi-infinite metal is to set either rₚ(qz)=∞ or rₚ(-qz)=0, where rₚ is the reflected amplitude of parallel-polarized light and qz=i(Q²-ω²c²)1/2. This method is applied to get a new formula for the dispersion in the retardation region for a surface with a continuously varying electron-density profile, and it reduces to the Harris-Griffin result in the c→∞ limit.