The Herpin theorem permits the reflectance of an arbitrary medium to b
e reproduced with a substrate of one complex refractive index overlaid
with a coating him of a second complex refractive index and an approp
riate thickness. The reflectances of a variety of laser-plasma-couplin
g experiments can be matched with a simple and physically meaningful p
rocedure for choosing the fitting parameters. For short-pulse experime
nts, s-light coupling is dominated by substrate interactions at electr
on densities above critical and p-light coupling is dominated by reson
ance at the critical density. The weak dependence of resonance absorpt
ion on damping is the result of the harmonic-oscillator resonance form
. As the plasma scale length becomes vanishingly small, the reflectanc
e is that of the Fresnel equations, but surprisingly small plasma scal
e lengths have dramatic effects on the p-light reflectance. Film-subst
rate and WKB models predict similar resonance absorption, where both m
odels are valid approximations and both should agree with multilayer a
nd Helmholtz wave-optics calculations. For plasma scale lengths well b
elow a wavelength, the film-substrate and the vacuum-heating models ar
e closely related.