Structure and the Reflectionless/Refractionless Nature of Parabolic Diffusion-Wave Fields

We show the impossibility of reflection and refraction phenomena at linear diffusion-wave-field (DWF) interfaces. Instead, interfacial flux expressions are derived which involve coherent accumulation or depletion phenomena subject to an interface flux conservation principle. The conditions for reflectionless and refractionless interfaces are the parabolic nature and the concomitant Fickian constitutive relations satisfied by DWFs. Simulations show that the reflection and Snell's laws can be adequate approximations only under near-normal incidence conditions, in agreement with published experimental evidence in wide areas of biomedical, electronic, and materials physics.