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 (<inline-formula> <tex-math notation="LaTeX">$sIPD_{s}$ </tex-math></inline-formula>) for localized exposure to electromagnetic near-fields at frequencies from 6 to 100 GHz. The spatially averaged modulus of the complex Poynting vector (<inline-formula> <tex-math notation="LaTeX">$sIPD_{mod}$ </tex-math></inline-formula>) and spatially averaged norm of the real part of the complex Poynting vector (<inline-formula> <tex-math notation="LaTeX">$sIPD_{norm}$ </tex-math></inline-formula>) were compared using numerical approaches, where their relationships with the spatially averaged absorbed power density (<italic>sAPD</italic>) 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., <inline-formula> <tex-math notation="LaTeX">$> \lambda $ </tex-math></inline-formula>/(<inline-formula> <tex-math notation="LaTeX">$2\pi$ </tex-math></inline-formula>), 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 <inline-formula> <tex-math notation="LaTeX">$sIPD_{norm}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$sIPD_{mod}$ </tex-math></inline-formula> 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 <italic>sAPD</italic> to <inline-formula> <tex-math notation="LaTeX">$sIPD_{s}$ </tex-math></inline-formula> and those for the plane-wave normal incidence, are at most 1.4 dB and 0.9 dB for <inline-formula> <tex-math notation="LaTeX">$sIPD_{norm}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$sIPD_{mod}$ </tex-math></inline-formula>, respectively. Under the same condition, the ratios of the temperature rise to <inline-formula> <tex-math notation="LaTeX">$sIPD_{s}$ </tex-math></inline-formula> for the relatively small antennas (total dimension less than <inline-formula> <tex-math notation="LaTeX">$2\lambda$ </tex-math></inline-formula>) 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 <inline-formula> <tex-math notation="LaTeX">$sIPD_{s}$ </tex-math></inline-formula> 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.


I. INTRODUCTION
The rapid increase in the use of radio frequency (RF) transmitters in millimeter wave (MMW) bands has raised public concerns regarding human exposure to electromagnetic fields (EMFs) in a general living environment [1]- [3]. Localized temperature elevation on the human skin surface due to MMW exposure is recognized as a dominant The associate editor coordinating the review of this manuscript and approving it for publication was Zhengqing Yun . cause of adverse health effects [4]- [6]. Safety guidelines and standards have prescribed the limits for EMF exposure to prevent excessive temperature elevation on human tissues in the frequency range from 6 to 300 GHz. The International Commission on Non-Ionizing Radiation Protection (ICNIRP-2020 safety guidelines) [7] defined absorbed power density (APD) as a new metric for the basic restrictions to protect against the adverse health effects associated with superficial heating due to localized exposure. Similarly, IEEE Std C95.1 [8] specified epithelial power density as the VOLUME 9, 2021 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ metric of dosimetric reference limits (DRLs) in the frequency band.
Because the basic restrictions/DRLs are related to physical quantities inside an exposed body, which cannot be easily measured, the reference level/exposure reference levels (ERLs) have been used in the ICNIRP-2020 safety guidelines [7] and IEEE Std C95.1 [8], respectively, to serve as practical measures for safety compliance assessment [9]. In the case of local exposure for a period exceeding 6 minutes, the spatially averaged incident power density (IPD) is utilized as the metric of the reference levels/ERLs at frequencies over 6 GHz. The reference levels/ERLs of IPD for local exposure are frequency-dependent values of 275f −0.177 G and 55f −0.177 G (W/m 2 ) (f G : frequency in GHz) from 6 to 300 GHz for occupational exposure/restricted environments and general public exposure/unrestricted environments, respectively (ICNIRP-2020 safety guidelines [7], IEEE Std C95.1 [8]).
In the ICNIRP-2020 safety guidelines [7], it is recommended that APD is averaged over an area of 4 cm 2 from 6 to 300 GHz as a practical protection specification owing to its good correlation with the local maximum temperature elevation. Furthermore, for frequencies ranging from 30 to 300 GHz, it is recommended that the spatial average is reduced to approximately 1 cm 2 to account for the possibility of smaller beam exposure scenarios, where an additional constraint (twice that of 4 cm 2 ) should be imposed. For consistency with the basic restrictions/DRLs, the same averaging areas of the reference levels/ERLs are employed [7], [8].
To explain the relationship between the power densities and the resultant surface temperature elevation at MMW bands, dosimetric studies for plane-wave exposures were conducted [10]- [15]. IPD s values from RF wireless devices over 6 GHz, such as prototypes of 5G mobile antennas, have been studied in [16]- [24]. [18] and [24] reported research results including those under beam steering exposure conditions at 28 GHz, i.e., the FR2 (MMW) frequency band assigned in Japan and some other countries. These studies investigated the appropriate definitions for spatially averaged IPD s at 28 GHz, but the related discussions have not yet been extended to other frequency bands from 6 to 300 GHz.
For the compliance assessments of RF wireless devices at MMW bands, the IEC Technical Committee (TC) 106 and IEEE ICES TC34 considered the norm or normal components of the real part of the complex Poynting vector as metrics for practical near-field compliance. The comparison of these two definitions is being discussed in working groups under IEEE ICES TC95. On the other hand, the ICNIRP [7] defined IPD as the modulus of the complex Poynting vector, which includes both the real and imaginary components. This may be in consideration of the requirements associated with the determination of more conservative exposure limits for near-field exposure situations in the safety guidelines, because the imaginary component of the complex Poynting vector will be gradually increased as the distance from the antenna decreases to less than the reactive near-field boundary. Christ et al. [25] discussed the impact on the aforementioned IPD s to explain the effect of the reactive near-field using typical antennas at 1, 10, and 30 GHz. However, the relationships between the power densities and the resultant skin temperature elevation were not fully discussed in [25]. Therefore, this research attempts to investigate which of the two IPD s , namely, the modulus of the complex Poynting vector and the norm of the real part of the complex Poynting vector, is better correlated with the skin surface temperature elevation under antenna near-field exposure conditions.
In this study, we investigated the differences due to the definitions of the incident power density in detail. In particular, the relationships between each definition of the spatially averaged power density and skin temperature elevation were compared using computational approaches for different antennas and exposure conditions at frequencies from 6 to 100 GHz. Because the ICNIRP [7] specifies that the reference levels in terms of IPD are not applicable within the reactive near-field, the main purpose of this study was to understand the applicability of these two spatially averaged IPD s when approaching the boundary between the reactive and radiative antenna near-fields. FIGURE 1. Computational model: a three-dimensional four-layer skin model comprised of epidermis (i = 1), dermis (i = 2), subcutaneous fat (i = 3), and muscle (i = 4) exposed to vertically polarized antennas, (a) single dipole, (b) 1 × 4 dipole array, and (c) 4 × 4 dipole array. Fig. 1 illustrates a computational model for dosimetry analysis. A four-layer tissue model, which is composed of epidermis (i = 1), dermis (i = 2), subcutaneous fat (i = 3), and muscle (i = 4), was used to represent the skin tissue configuration in the forearm [13], [14]. The width w of the skin model and thickness of each layer, l i , are listed in Table 1. It is known that the model size used in this study is sufficiently large for temperature analysis [18]. The dielectric properties reported in [13], [26] were used.

II. ANALYTICAL MODEL AND METHOD A. CONFIGURATION OF MULTI-LAYER HUMAN SKIN MODEL
For an electromagnetic near-field radiation source, single half-wavelength vertical dipole, 1 × 4 dipole array, and 4 × 4 dipole array antennas comprising half-wavelength dipoles with in-phase excitations at frequencies from 6 to 100 GHz were employed, as shown in Figs. 1 (a), (b), and (c), respectively. Each antenna was placed parallel to the surface of the skin model with vertical polarization. The separation distance from the skin surface to the antenna element was set to d (mm). In each scenario with and without skin model, the total antenna input power was normalized to an identical value.
The finite-difference time-domain (FDTD) method [27]- [32] was used to analyze the EMFs both outside and inside the skin model. The computational region was truncated by 10-layer Berenger's perfectly matched layer boundaries.

B. THERMAL PARAMETERS AND COMPUTATION
The temperature elevation in the steady state due to EMF exposure can be obtained by solving the Pennes bioheat transfer equation [29]- [37] as follows: where T and T b are the temperatures of the human tissues and blood ( • C), respectively. c is the specific heat (J/(kg • C)), and κ is the thermal conductivity (W/(m • C)). t is the time variable. M is the basal metabolism per unit volume (W/m 3 ) and B is a term associated with the blood flow in each skin tissue (W/(m 3• C)). The specific absorption rate (SAR) (W/kg), which represents the heat-generating source related to electromagnetic wave exposure [17], [29], [38], is defined as where |E(r)| is the amplitude of the induced electric field inside the skin tissue and r denotes the position vector. σ and ρ are the electrical conductivity (S/m) and mass density (kg/m 3 ), respectively. The boundary condition for the heat exchange between the air and skin tissue is given as where h, T surf , and T air denote the heat transfer coefficient (W/(m • C)), the temperature of the skin surface tissue, and that of the air, respectively. n is the normal unit vector component that represents the boundary surface.
To ensure consistency with previous works [13], [14], [39], similar parameters were used for the thermal analysis, which are listed in Table 2. The heat transfer coefficient h between the air and skin surface was set to 10 W/(m • C). The temperature at the end of the muscle was fixed at the body core temperature of 37 • C and the air temperature was 20 • C. All the other boundary conditions were set to be adiabatic.

C. SPATIALLY AVERAGED INCIDENT AND ABSORBED POWER DENSITIES
For the compliance assessment of mobile terminals such as smartphones that are used in close proximity to a human body above 6 GHz, a method for evaluating sIPD s at the evaluation surface with a separation distance greater than or equal to 2 mm from any part of the device has been provided [9]. In antenna theory [40], for a short dipole antenna or an equivalent radiator, the typical boundary between the reactive and radiative near-fields is commonly considered to exist at a distance of λ/(2π ) (λ: free space wavelength) from the antenna surface. Therefore, λ/(2π ) is used as a rough guide to find the approximate boundary between the reactive and radiative antenna near-fields [7]. According to this consideration, the outer boundary can be expected to be from 8 to 0.16 mm at frequencies from 6 to 300 GHz. This suggests that at the minimum distance (2 mm) for the compliance test of a wireless device, it is possible to enter the range of the reactive near-field up to 24 GHz. Therefore, sIPD s in the antenna nearfield should be carefully handled to prevent excessive EMF exposures.
The two sIPD s used in this study are defined in the safety guidelines and standards, i.e., the spatially averaged value of the modulus of the complex Poynting vector (sIPD mod ) and the norm of the real part of the complex Poynting vector (sIPD norm ), as shown below: where E and H * denote the electric field phasor and the complex conjugate of the magnetic field phasor, respectively. The symbol A indicates the spatial average area. Eq. (4) includes all components of the complex Poynting vector with both real and imaginary parts, which is used in the ICNIRP-2020 safety guidelines [7]. Eq. (5) employs the real part of the complex Poynting vector crossing a surface of interest, as denoted by [24]. In this study, Eqs. (4) and (5) were adopted to compare their correlations with the absorbed power density and with the temperature elevation resulting from exposure to the antennas under various near-field exposure conditions. The spatially averaged absorbed power density (sAPD) crossing an area in the air to skin boundary in the direction normal to the interface represents the total power absorbed by the skin tissue [41], [42], which is expressed by the following equation, as proposed in the ICNIRP-2020 safety guidelines [7]: where ds denotes the integral variable vector whose direction is normal to the integral area A on the body surface, as shown in the coordinate of Fig. 1. Note that sAPD in Eq. (6) was averaged over the square surface area of the skin model shown in Fig. 1. The sIPD s values in Eqs. (4) and (5) were averaged over a square in free space to which the body surface space is projected [7], with the same dimension as that of the sAPD. Fig. 2 shows the ratio of sIPD norm to sIPD mod as a function of the separation distance d from antenna surface normalized with the wavelength λ in free space. The data at each frequency were calculated with d increased from 2 to 10 mm at 1 mm intervals. The spatial averaging area A of sIPD s was set to 4 and 1 cm 2 , as shown in Figs. 2 (a) and (b), respectively. In this section, emphasis is placed on the condition that sIPD norm /sIPD mod is much less than 0 dB, which results in the possible underestimation of the exposure level when sIPD norm is employed for compliance evaluation with the RF safety guidelines. For convenience, the condition of sIPD norm /sIPD mod of −1 dB or less is examined as a measure. The reason is that considering the uncertainty of the evaluation, the discussion of minute differences (numerical values near 0 dB) lacks scientific validity. In addition, a 1 dB absolute difference may not be negligible for the reduction factor of 2 (about 3 dB) that was used for deriving the basic restrictions from the operational health effect threshold in local exposure above 6 GHz in the ICNIRP-2020 safety guidelines

1) DEPENDENCE ON EXPOSURE CONDITIONS
As shown in Fig. 2, the difference between sIPD norm and sIPD mod increases monotonically with decreasing separation distance d. Many results of sIPD norm /sIPD mod are lower than −1 dB when the distance d is shorter than the typical reactive and radiative near-field boundary, i.e., d < λ/(2π ). This is because the contribution from the imaginary component of the complex Poynting vector increases markedly in the antenna reactive near-field. On the other hand, the difference between sIPD norm and sIPD mod monotonically approaches 0 dB with increasing d. At separation distances of d > λ/(2π ), sIPD norm /sIPD mod is always within −1 dB.
For the separation distances (d ≥ 2 mm) and antenna types considered in this study, sIPD norm /sIPD mod < −1 dB is only found in several cases of 6 and 10 GHz. Above 30 GHz, the results of sIPD norm /sIPD mod are within −1 dB in all cases.
Moreover, at d < λ/(2π ), the maximum variation caused by the different antenna types is 1.3 and 1.1 dB when A = 4 and 1 cm 2 , respectively. At separation distances of d > λ/(2π ), the corresponding variations reduce to 0.4 and 0.5 dB, respectively. These results indicate that at the distances (d ≥ 2 mm) and frequencies (6 to 100 GHz) assumed in this study, there is no large difference in the dependence on the antenna type for the condition that sIPD norm /sIPD mod < −1 dB.

2) DEPENDENCE ON EXPOSURE ASSESSMENT METHOD
When the different spatial averaging areas of 4 and 1 cm 2 were used, as respectively shown in Figs. 2 (a) and (b), the maximum variation between sIPD norm and sIPD mod was within 0.7 dB for the case of the single dipole at 6 GHz when d = 2 mm. At d > λ/(2π ), this difference changed to 0.4, 0.3, and 0.1 dB in the cases of the single dipole, 1×4 dipole array, and 4 × 4 dipole array, respectively, but slightly increased up to 0.7, 0.6, and 0.5 dB, respectively, at d < λ/(2π ).
Although the above-mentioned data show that the dependence on the spatial averaging area is relatively large in the antenna near-field, this conclusion is not very clear since the variation is still within 1 dB. Therefore, under the assumptions of the distance (d ≥ 2 mm) and frequency (6 to 100 GHz) in this study, it can be considered that there is no marked difference in the dependence on the spatial averaging area for the condition that sIPD norm /sIPD mod < −1 dB.

3) WORST CASE
From Fig. 2, it can be found that the lowest values of sIPD norm /sIPD mod under all conditions are −4.4 and −3.8 dB when A = 4 and 1 cm 2 , respectively, which are much lower than −1 dB. The worst condition occurs in the case of the 1 × 4 dipole array at 6 GHz when d = 2 mm.
On the other hand, Fig. 3 shows the ratio of sIPD norm to sIPD mod as a function of the separation distance d when the conditions of sIPD s specified in the ICNIRP-2020 safety guidelines were employed (d ≥ λ/(2π), A = 4 cm 2 at 6-30 GHz, whereas A = 1 cm 2 over 30 GHz). In Fig. 3, it is shown that the lowest value of sIPD norm /sIPD mod under the applicable conditions of the ICNIRP-2020 safety guidelines is within −1 dB. The worst case of −1 dB is found at d = 5 mm when using the 1 × 4 dipole array at 10 GHz.

B. COMPARISON OF POWER TRANSMISSION FOR NEAR-FIELD EXPOSURES
Figs. 4 and 5 show the ratio of sAPD to sIPD, i.e., the power transmission, normalized with that of a plane-wave normal incidence condition [14] as a function of the antenna to skin separation distance (d) normalized with λ at frequencies from 6 to 100 GHz. Similar to the condition in Fig. 2, the single dipole, 1 × 4 dipole array, and 4 × 4 dipole array antennas were considered. The square areas A for spatial averaging of 4 and 1 cm 2 are applied in Figs. 4 and 5, respectively. In this section, we focus on the condition that the normalized sAPD/sIPD is much greater than 0 dB. For similar reasons to those mentioned in Sec. III. A, a deviation of 1 dB or more is considered as a measure here.

1) DEPENDENCE ON EXPOSURE CONDITIONS
As shown in Figs. 4 and 5, the results of sAPD/sIPD norm and sAPD/sIPD mod normalized with those of plane-wave incidence increases markedly when d < λ/(2π ), where for many cases, the deviations significantly exceed 0 dB (> 1 dB). Even when d > λ/(2π ), as shown in Figs. 4 and 5, depending on the exposure conditions (antenna type, frequency) and exposure evaluation methods (sIPD definition, averaging area), the normalized sAPD/sIPD still exceeds 1 dB in several cases.
Moreover, sAPD/sIPD normalized with the plane-wave incidence increases with decreasing frequency. At frequencies of 6 and 10 GHz, the normalized sAPD/sIPD may significantly exceed 0 dB (> 1 dB). At 30 GHz and above, on the other hand, the corresponding results do not significantly exceed 0 dB. Furthermore, as shown in Figs. 4 and 5, we observed that there is no significant discrepancy in the dependence on the antenna type under the condition that the normalized sAPD/sIPD significantly exceeds 0 dB (> 1 dB) as considered in this section.
From Figs. 4 and 5, at d < λ/(2π ), the variation in the normalized sAPD/sIPD with the antenna type is relatively small (< 2 dB) compared with the variations due to the antenna-skin separation distance and frequency. When d > λ/(2π), on the other hand, the difference in the normalized sAPD/sIPD more strongly depends on the antenna type (up to 5 dB or more).

2) DEPENDENCE ON EXPOSURE ASSESSMENT METHOD
In Figs. 4 and 5, it is shown that there is no marked difference in the conditions under which the normalized sAPD/sIPD significantly exceeds 0 dB (> 1 dB) between the definitions of the incident power density. The normalized sAPD/sIPD norm from plane-wave normal incidence is slightly higher than that of sAPD/sIPD mod . At d < λ/(2π ), the variation in the normalized sAPD/sIPD due to the difference in the definition of sIPD is relatively large (up to 3 to 4 dB). When the separation distance d > λ/(2π ), the corresponding variation reduces to less than 1 dB.
On the other hand, there is no obvious difference in the conditions under which the normalized sAPD/sIPD significantly exceeds 0 dB (> 1 dB) between the spatial averaging areas.

3) WORST CASE
The ratio of sAPD to sIPD as a function of the separation distance d under the applicable conditions of sIPD s specified in the ICNIRP-2020 safety guidelines (d ≥ λ/(2π), A = 4 cm 2 at 6-30 GHz, whereas A = 1 cm 2 over 30 GHz) is shown in Fig. 6. In Fig. 6, the highest deviations of the normalized sAPD/sIPD under all the conditions are over 3 to 6 dB, which significantly exceed 0 dB (> 1 dB).
Considering the conditions of sIPD s specified in the ICNIRP-2020 safety guidelines (d ≥ λ/(2π), A = 4 cm 2 at 6-30 GHz, whereas A = 1 cm 2 over 30 GHz), as shown in Fig. 6, the highest deviations of the normalized sAPD/sIPD norm in comparison with that under plane-wave FIGURE 5. Ratios of spatially averaged absorbed to incident power densities for the dipole and dipole array antennas at frequencies from 6 to 100 GHz. The ratios are normalized with those of plane-wave normal incidence. The antenna-skin separation distances d of 2, 5, and 10 mm are normalized with the wavelength at each frequency. The averaging area is A = 1 cm 2 : (a) sAPD/sIPD norm , (b) sAPD/sIPD mod . exposure slightly exceed 0 dB (at most 1.4 dB). For the case of the normalized sAPD/sIPD mod , the highest deviations do not significantly exceed 0 dB (at most 0.9 dB).

C. COMPARISON OF HEATING FACTORS FOR NEAR-FIELD EXPOSURES
Considering the impact of the definitions of sIPD s on the skin surface temperature elevation to be used for setting the RF safety guidelines, the frequency characteristics of the heating factors of sIPD s were investigated in this section. Figs. 7 and 8 show the heating factor of sIPD s normalized with that under plane-wave normal incidence conditions [14] as a function of the antenna-skin separation distance d normalized with λ at frequencies from 6 to 100 GHz. The data at each frequency were calculated when d was set at 2, 5, and 10 mm.
The heating factor (•C/(W/m 2 )) is defined as the ratio of the local peak temperature elevation ( T peak ) at the skin surface to the spatially averaged power density [32]. This metric was employed to estimate the local peak temperature elevation due to MMW exposure as per the safety guidelines [7]. Here, we focus on the condition that the normalized T peak /sIPD is significantly higher than 0 dB, where a deviation of 1 dB or more is considered as being significant, which is the same measure as that employed in the above subsections.

1) DEPENDENCE ON EXPOSURE CONDITIONS
In Figs. 7 and 8, the results of T peak /sIPD normalized with those of the plane-wave normal incidence markedly increase when d < λ/(2π ), where for many cases, the deviation significantly exceeds 0 dB (> 1 dB). When d > λ/(2π ), depending on the exposure conditions (antenna type, frequency) and exposure evaluation methods (sIPD definition, averaging area), the normalized T peak /sIPD still exceeds 1 dB in certain cases.
The T peak /sIPD profiles fluctuate with the separation distance d, which tends to be minimal near d = λ/(2π ) and maximal close to d = 0.1λ and d = λ. Moreover, T peak /sIPD normalized with that of the plane-wave incidence greatly exceeds 0 dB (> 1 dB) in the entire frequency band from 6 to 100 GHz examined in this study. Furthermore, due to the different antenna types, a large discrepancy is observed under the condition that the normalized T peak /sIPD significantly exceeds 0 dB (> 1 dB), as described below. For the case of the single dipole, the normalized T peak /sIPD significantly exceeds 0 dB (> 1 dB) only at frequencies of 60 and 100 GHz at d = 2 or 5 mm. In Figs. 7 and 8, at d < λ/(2π ), the variation in the normalized T peak /sIPD among the different antenna types is relatively large (up to 11 dB). When d > λ/(2π ), on the other hand, the difference in the normalized T peak /sIPD among the antenna types is relatively small (< 6 dB).

2) DEPENDENCE ON EXPOSURE ASSESSMENT METHOD
In Figs. 7 and 8, there is no large difference in the conditions under which the normalized T peak /sIPD significantly exceeds 0 dB (> 1 dB) between the definitions of sIPD s . The normalized T peak /sIPD norm from plane-wave incidence is higher than that of T peak /sIPD mod . At d < λ/(2π ), the variation in the normalized T peak /sIPD due to the difference in the definition of sIPD is relatively large (up to 3 to 4 dB). At d > λ/(2π), the corresponding variation reduces to < 1 dB.
At d < λ/(2π ), there is no clear difference in the conditions under which the normalized T peak /sIPD significantly exceeds 0 dB (> 1 dB) between the spatial averaging areas. When d > λ/(2π ), however, the dependence on the spatial averaging area under the considered conditions is observed. In particular, when the spatial averaging area of A = 4 cm 2 is employed, the normalized T peak /sIPD exceeds 0 dB (> 1 dB) in many cases, and this tendency is noteworthy for the array antennas. In Figs. 7 and 8, the normalized T peak /sIPD values with the averaging area of A = 4 cm 2 are relatively higher than those with A = 1 cm 2 . In addition, it can be observed that the variations in the normalized T peak /sIPD due to the difference in the spatial averaging area at d < λ/(2π) (up to 2.4 to 3.8 dB) are relatively smaller than those at d > λ/(2π ) (up to 4.4 to 5.8 dB). Fig. 9 shows the heating factor of sIPD s normalized with that of plane-wave normal incidence as a function of the separation distance d under the applicable conditions of sIPD s specified in the ICNIRP-2020 safety guidelines (d ≥ λ/(2π ), A = 4 cm 2 at 6-30 GHz, whereas A = 1 cm 2 over 30 GHz).

3) WORST CASE
As shown in Fig. 9, although the maximum value of the normalized T peak /sIPD norm is smaller than the highest deviation under all the exposure scenarios, it may still significantly exceed 0 dB in some cases, e.g., 3.5 dB for the 4 × 4 dipole array at 30 GHz when A = 4 cm 2 .

IV. DISCUSSION
In the previous section, the computational results were compared to clarify the relationships between A) sIPD norm VOLUME 9, 2021 and sIPD mod , B) sAPD/sIPD norm and sAPD/sIPD mod , and C) T peak /sIPD norm and T peak /sIPD mod using the fourlayer skin model exposed to various antennas at near-fields. We will next further discuss our results in terms of these three relationships.

FIGURE 7.
Heating factors of sIPD s for the dipole and dipole array antennas at frequencies from 6 to 100 GHz at the antenna-skin separation distances d of 2, 5, and 10 mm normalized with the wavelength in free space at each frequency when the averaging area is A = 4 cm 2 : (a) T peak /sIPD norm , (b) T peak /sIPD mod .

A. DISCUSSION ON sIPD norm /sIPD mod
It was shown that sIPD norm /sIPD mod is highly dependent on the distance normalized with the wavelength. The difference between sIPD norm and sIPD mod decreases monotonically with decreasing distance from the antenna and may be much lower than 0 dB (< −1 dB). At d < λ/(2π ), the absolute difference between sIPD mod and sIPD norm is up to 4.4 dB. This finding indicates that at the antenna near-field, sIPD norm may underestimate the reference level of sIPD mod as the metric specified in the ICNIRP-2020 safety guidelines [7]. These results correspond well with the conclusion reported in [25]. However, in the applicable range of sIPD s specified in the RF safety guidelines (d ≥ λ/(2π)), as shown in Fig. 3, the lowest value of sIPD norm /sIPD mod is within −1 dB. This value is not significant compared with the uncertainty due to the thickness and dielectric constants of body parts (about 1 dB) reported in [13] and the reduction factor of 2 (about 3 dB) for the exposure limits considered in the guidelines [7]. Therefore, the impact of underestimating sIPD mod by using sIPD norm on the exposure compliance assessment is not significant for the conditions assumed in this study.

FIGURE 8.
Heating factors of sIPD s for the dipole and dipole array antennas at frequencies from 6 to 100 GHz at the antenna-skin separation distances d of 2, 5, and 10 mm normalized with the wavelength in free space at each frequency when the averaging area is A = 1 cm 2 : (a) T peak /sIPD norm , (b) T peak /sIPD mod .
It is also noted that the ICNIRP-2020 safety guidelines use d = λ/(2π ) as a rough guide of the boundary between the reactive and radiative near-fields, which means that more appropriate boundary conditions should be used for individual antennas. Therefore, we examined other reactive nearfield boundary conditions, as described below: 1. For a linear dipole antenna, the boundary condition is slightly extended from λ/(2π ) to 0.62 D 3 /λ [40], e.g., the distance for a half-wavelength dipole is 0.22λ, where D denotes the antenna length. 2. For a linear/planar array antenna, the boundary between the reactive and radiative near-field regions is related to the antenna's geometrical size, but it can be approximated to λ when the maximum dimension of the antenna is less than 2.5λ [43]. From the above consideration, we apply the boundary conditions of d < 0.62 D 3 /λ for the single dipole antenna and d < λ for the 1 × 4 and 4 × 4 dipole array antennas. It is shown that when employing the above individual reactive near-field boundary conditions, the lowest sIPD norm /sIPD mod is −0.5 dB under the conditions of applying the guidelines. Therefore, the underestimation of sIPD mod by sIPD norm can be further improved when using more appropriate boundary conditions between the reactive and radiative antenna nearfields.

B. DISCUSSION ON THE NORMALIZED sAPD/sIPD
The ratio of sAPD to sIPD normalized with that of the planewave incidence is also highly dependent on the distance normalized with the wavelength. The ratio of sAPD to sIPD markedly increases (above 1 dB) with decreasing antennaskin separation distance d in several cases. This indicates that in the vicinity of the antenna, even if sIPD is lower than the reference level, sAPD can exceed the basic restrictions. However, from the results in Sec. III. B, we observed that the maximum deviations of the ratios of sAPD to sIPD for the near-fields from those of plane-wave normal incidence are 1.4 dB and 0.9 dB for sIPD norm and sIPD mod , respectively. These observations are in reasonable agreement with those in [25], where a deviation of about 2 dB (1.6 times) from the plane-wave equivalent transmission at distances d > λ/(2π ) is reported. Consequently, in consideration of the uncertainty evaluation reported in [13] and the reduction factor of 2 (about 3 dB) for the exposure limits used in safety guidelines [7], the impact of this degree of deviation is not significant.
On the other hand, when the reactive near-field boundary conditions for individual antennas in the discussion of sIPD norm /sIPD mod are employed, both sAPD/sIPD norm and sAPD/sIPD mod are less than 0 dB under the applicable conditions specified in the safety guidelines. Therefore, the underestimation of sAPD can also be ignored when using appropriate boundary conditions of the reactive near-field.

C. DISCUSSION ON THE NORMALIZED T peak /sIPD
The ratio of T peak to sIPD normalized with that of planewave incidence is highly dependent on the separation distance normalized with the wavelength and the utilized antenna type. The normalized T peak /sIPD significantly exceeds 0 dB (>1 dB) in some cases. This indicates that even if sIPD is lower than the reference level, T peak may exceed the exposure level derived from the operational health effect threshold with the reduction factors employed in the RF safety guidelines, e.g., 0.5 • C in a general public environment. Similar to the discussion of sAPD/sIPD, the ratio of T peak to sIPD for plane-wave incidence exposures was used as the rationale for setting the basic restriction (sAPD) and reference levels (sIPD) derived from sAPD in the safety guidelines. Thus, if the normalized T peak /sIPD significantly exceeds 0 dB (>1 dB), then T peak may exceed the exposure level considering the operational health effect threshold with the reduction factors.
From the results in Sec. III. C, we observed that the highest deviations of the ratios of T peak to sIPD for sIPD norm and sIPD mod from those of plane-wave normal incidence under the applicable conditions of sIPD s specified in the guidelines are 3.5 dB and 3.3 dB, respectively. These values are comparable to the uncertainty reported in [13] and the reduction factor considered in the safety guidelines [7]. Therefore, the impact of underestimating T peak by sIPD norm and sIPD mod (and perhaps sAPD) on the safety compliance assessment may not be negligible.
When the reactive near-field boundary conditions for the individual antennas are applied, the maximum deviations of the normalized T peak /sIPD norm and T peak /sIPD mod under the applicable conditions of sIPD s specified in the safety guidelines are still significant, i.e., 3.2 dB and 3.1 dB, respectively. Therefore, it may not be possible to improve the underestimation of T peak by using more appropriate reactive near-field boundary conditions.
In the ICNIRP-2020 safety guidelines, the spatial averaging area of 1 cm 2 is applied above 30 GHz but not at 30 GHz. Because an ideal beam can be focused within one wavelength, the beam width of the antenna may be narrow compared with 4 cm 2 (2 cm × 2 cm) at or below 30 GHz. Therefore, it may be necessary to employ the averaging area of 1 cm 2 at lower frequencies (for example, above 15 GHz where the wavelength is 2 cm). It is shown that when applying the spatial averaging area of 1 cm 2 at 30 GHz (4 cm 2 so far) in addition to the reactive near-field boundary conditions of the individual antennas, the highest normalized T peak /sIPD norm and T peak /sIPD mod reduce to 1.7 and 1.6 dB, respectively. Therefore, the impact of underestimating T peak may be reduced when employing the spatial averaging area of 1 cm 2 at frequencies of 30 GHz or lower. This suggests that a suitable area for spatial averaging lies in the range between 1 and 4 cm 2 , as pointed out in [35].
Furthermore, we only observed a normalized T peak /sIPD of over 3 dB under the applicable conditions in the current RF safety guidelines in the case of 4 × 4 dipole arrays. For the other antennas with smaller dimensions, the highest values under the applicable conditions in the current RF safety guidelines were 1.5 to 1.6 dB for the cases of T peak /sIPD norm and T peak /sIPD mod . Note that 4 × 4 antenna arrays are relatively large and may not be suitable for installation in the existing 5G user equipment operating at 28 GHz. Thus, the current guidelines may still protect a human body from EMF exposure from 5G terminals mounted with an ordinary four-element array antenna.

V. CONCLUSION
In this study, we investigated the spatially averaged power densities for localized exposure to EMFs at MMW frequencies. Two spatially averaged sIPD s in the safety guidelines and standards, i.e., sIPD norm and sIPD mod , were compared via a computational evaluation approach. Their relationships with each other, sAPD, and the local peak temperature elevation at the skin surface were analyzed using three types of antennas at distances of 2 to 10 mm from the skin surface at frequencies ranging from 6 to 100 GHz.
The investigations demonstrated that outside the typical boundary of the reactive near-field, i.e., > λ/(2π ), 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 antennas, the maximum difference between sIPD norm and sIPD mod is at most 0.7 dB. For the appropriate conditions recommended in the RF safety guidelines, the differences between the ratios of sAPD to sIPD and the ratio for the normal incidence of plane-wave exposures are at most 1.4 dB and 0.9 dB for sIPD norm and sIPD mod , respectively. Furthermore, we found that for the appropriate conditions recommended in the RF safety guidelines, the heating factors of sIPD s for the relatively small antennas (i.e., the dipole and 1 × 4 dipole array, for both of which the total dimension is smaller than 2λ) do not significantly exceed those for the plane-wave normal incidence, which means that the expected maximum temperature elevation is lower than the operational health effect threshold in terms of the temperature elevation with the reduction factors employed in the RF safety guidelines. It is, however, shown that for the other cases with the large antenna (4 × 4 dipole array, whose total dimension is larger than 2λ), the ratios can increase up to 3.5 dB and 3.3 dB for sIPD norm and sIPD mod , respectively, from those for the planewave normal incidence.
These 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 other factors, such as the antenna type (size), frequency, distance from the radiation source, and spatial averaging area. The findings of this study are useful for discussing the appropriate definition of sIPD s for the safety guidelines and their compliance procedures in cases of near-field exposure conditions above 6 GHz. She is currently with the National Institute of Information and Communications Technology, Tokyo, where she is involved in research on biomedical electromagnetic compatibility.
Dr. Wake is a member of the Institute of Electronics, Information and Communication Engineers, the Institute of Electrical Engineers, Japan, and the Bioelectromagnetics Society. She was a recipient of the 1999 International Scientific Radio Union Young Scientist Award.
TERUO ONISHI (Member, IEEE) received the B.S. degree in physics from Tokyo University of Science, Tokyo, Japan, in 1987, and the Ph.D. degree from the Graduate School of Science and Technology, Chiba University, Chiba, Japan, in 2005.
He was with Toyo Communication Equipment Company, Ltd., Kanagawa, Japan, and Nippon Ericsson K.K., Tokyo. From 1990 to 1992, he was with Hokkaido University, Sapporo, Japan, where he was involved in the finite-difference time-domain (FDTD) analysis for solving electromagnetic problems. He