Reflection factor of gradual-transition absorbers for electromagnetic and acoustic waves

Abstract
Absorbers for electromagnetic or acoustic waves are described, for which a good impedance match and low reflection factor can be achieved by providing a gradual transition of material constants into the lossy medium. The reflection factor can be calculated by means of a Riccati-differential equation. General conclusions from the WKB-perturbation method can be drawn for absorbers, the layer thickness of which is either very small or very large in comparison to the wavelength. For "thin" layers, wave energy penetrates the whole thickness of the absorber. Suitable average values of the material constants are derived to describe the performance of the panel in this case. For "thick" layers only the initial part of the panel is energized. The asymptotic expressions contain only the material constants of this part. The results are interpreted physically. Numerical solutions of the reflection factor for highly refractive panels with exponentially varying material constants are reported.

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