A Mathematical Derivation of Power Penetration Depth forThinLossy Materials

Microwaves propagating through a medium of finite thickness d consist of backward as well as forward moving components as a result of internal reflections at the material boundaries. In many practical applications, e.g., when estimating the proportion of energy absorbed by a water-like dielectric material during food processing, it is usually assumed that the backward components are so small as to be negligible. In this work we use mathematical analysis to show firstly that serious errors could result from a neglect of the backward components when d is less than (500 , the nominal skin-depth of the material. Secondly it is found that the coefficients of reflection, absorption and transmission of energy all exhibit strong oscillatory behaviors in the thickness domain, a feature the implications of which we believe have never been fully appreciated. Thirdly, the current definition of the skin-depth, or its associated power penetration depth, is found to give rise to non-unique results when one tries to apply it to describe a material which is thinner than 2 (L. In the case of the power penetration depth, by considering power absorption instead of decay within the material, a definition applicable to materials of any thickness can be derived. This is equivalent to the older definition in the limit as thickness tends to infinity.