Multilayer optics provides laser-plasma-coupling insight

The Herpin theorem permits the reflectance of an arbitrary medium to be reproduced with a substrate of one complex refractive index overlaid with a coating film of a second complex refractive index and an appropriate thickness. The reflectances of a variety of laser-plasma-coupling experiments can be matched with a simple and physically meaningful procedure for choosing the fitting parameters. For short-pulse experiments, s-light coupling is dominated by substrate interactions at electron densities above critical and p-light coupling is dominated by resonance at the critical density. The weak dependence of resonance absorption on damping is the result of the harmonic-oscillator resonance form. As the plasma scale length becomes vanishingly small, the reflectance is that of the Fresnel equations, but surprisingly small plasma scale lengths have dramatic effects on the p-light reflectance. Film-substrate and WKB models predict similar resonance absorption, where both models are valid approximations and both should agree with multilayer and Helmholtz wave-optics calculations. For plasma scale lengths well below a wavelength, the film-substrate and the vacuum-heating models are closely related.