Quantitative Comparison of Power Densities Related to Electromagnetic Near-Field Exposures With Safety Guidelines From 6 to 100 GHz

This paper presents a quantitative analysis of the differences between the various definitions of spatially averaged power densities ( $sIPD_{s}$ ) for localized exposure to electromagnetic near-fields at frequencies from 6 to 100 GHz. The spatially averaged modulus of the complex Poynting vector ( $sIPD_{mod}$ ) and spatially averaged norm of the real part of the complex Poynting vector ( $sIPD_{norm}$ ) were compared using numerical approaches, where their relationships with the spatially averaged absorbed power density (sAPD) and the local peak temperature elevation on skin tissue were analyzed. Our results demonstrated that outside the typical boundary of the reactive near-field, i.e., $> \lambda $ /( $2\pi$ ), which is used as a rough guide of the applicable condition for reference levels in the RF safety guidelines, but at most 10 mm from the radiation source, the maximum difference between $sIPD_{norm}$ and $sIPD_{mod}$ is smaller than 0.7 dB from 6 to 100 GHz. For the appropriate conditions recommended in the RF safety guidelines, the differences between the ratios of sAPD to $sIPD_{s}$ and those for the plane-wave normal incidence, are at most 1.4 dB and 0.9 dB for $sIPD_{norm}$ and $sIPD_{mod}$ , respectively. Under the same condition, the ratios of the temperature rise to $sIPD_{s}$ for the relatively small antennas (total dimension less than $2\lambda$ ) do not significantly exceed that for the plane-wave normal incidence, which means that the expected maximum temperature rise is lower than the temperature rise that is derived from the operational health effect threshold in terms of the temperature rise divided with the reduction factors employed in the RF safety guidelines. The above results provide suggestive evidence that the effect of the definition of $sIPD_{s}$ on the human exposure characteristics is not significant compared with those of the other factors, i.e., the antenna type (size), frequency, distance from the source, and averaging area.