TITLE:
An Analytical Framework for Frequency-Dependent Electromagnetic Power Absorption in Biological Tissues
AUTHORS:
Hongyun Wang, Shannon E. Foley, Hong Zhou
KEYWORDS:
Electromagnetic-Wave at Air-Tissue Interface, Maxwell’s Equations, Attenuation of Electromagnetic Power in Tissue
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.5,
May
28,
2026
ABSTRACT: As exposure to electromagnetic waves becomes increasingly widespread, it is important to quantify how incident fields couple into biological tissue and where absorbed energy is deposited. This work presents an analytical, physics-based framework derived from Maxwell’s equations to model the propagation of a normally incident electromagnetic plane wave within homogeneous, lossy dielectric biological tissues. Closed-form expressions for the electric and magnetic fields are derived, enabling the determination of frequency-dependent power reflectance and transmittance at the air-tissue interface, as well as the power absorption coefficient and penetration depth within the medium. Using complex relative permittivity data from the literature, we examine six tissue types across a broad frequency range (1 MHz - 100 GHz). The results demonstrate that higher water content significantly increases dielectric loss and reduces penetration depth. Conversely, low-water tissues (e.g., non-infiltrated fat) exhibit lower attenuation and deeper penetration. Frequency is shown to be a dominant driver of this behavior, with higher frequencies shifting the power budget from reflection-limited coupling toward highly superficial absorption. These findings provide a foundation basis for quantifying the heat source in assessing exposure effect and risk and in designing electromagnetic technologies.