Received 17 October 2024; revised 20 January 2025; accepted 29 January 2025.

Date of current version 14 March 2025.

Digital Object Identifier 10.1109/JMW.2025.3539871

# Fast In-Phantom Absorbed Power Density Evaluation at mmWaves Based on Infrared Measurements

MASSINISSA ZIANE<sup>D 1</sup>, ARTEM BORISKIN<sup>1,2</sup>, AND MAXIM ZHADOBOV<sup>D 1</sup> (Senior Member, IEEE)

(Regular Paper)

CORRESPONDING AUTHOR: Maxim Zhadobov (email: maxim.zhadobov@univ-rennes.fr).

This work was supported in part by the French National Research Program for Environmental and Occupational Health of ANSES under Grant ANSES-23-RF-03 through EXPO-5G Project; in part by Labex CominLabs under Grant ANR-10-LABX-07-01 through EM-ART and eSkin-ART Projects; in part by the European Union through European Regional Development Fund (ERDF); and in part by the Ministry of Higher Education and Research, CNRS, Brittany region, Conseils Départementaux d'Ille-et-Vilaine and Côtes d'Armor, Rennes Métropole, and Lannion Trégor Communauté, through the CPER Project CyMoCod.

**ABSTRACT** This article introduces a novel method for fast measurement of the absorbed power density (APD) induced by an electromagnetic field (EMF) emitting device operating near the human body at frequencies above 6 GHz, taking into account antenna/body interaction. The method employs an infrared (IR) thermography to remotely monitor the heat induced in a reflectivity-based skin equivalent phantom designed to reproduce the EMF scattering properties of human skin and the APD inside the human body. Such a phantom, implemented in the form of a thin planar solid dielectric structure, perturbs the device under test in a similar way as it would be perturbed by the presence of the human body, allowing the absorbed microwave energy to be effectively converted into an IR signal. The heat dynamics and the spatial temperature distribution on the phantom surface are measured by an IR camera and then converted to APD by postprocessing. To enhance the sensitivity of the method and to minimize the effect of heat conduction, spectral filtering is used. The proposed method is validated at 60 GHz using reference antennas (i.e. a cavity-fed dipole array and a pyramidal horn loaded with a slot array). The measured APD is compared with the reference APD simulated in human skin. The high accuracy and significant measurement time reduction, compared to conventional RF-based APD evaluation techniques, demonstrate a promising potential of the proposed IR-based method for fast EMF dosimetry and user exposure compliance testing of millimeter-wave (mmWave) 5 G and 6 G wireless devices.

**INDEX TERMS** Absorbed power density (APD), compliance testing, dosimetry, electromagnetic field (EMF), human exposure, millimeter waves (mmWaves), infrared (IR), near-field measurements, temperature, wireless devices, 5 G, 6 G.

## NOMENCLATURE

* **E** E-field inside the phantom.
* **g** Internal heat source associated to **E**.
* **$\bar{g}$** Integral transform of **g**.

* **PD** Power density inside the phantom.
* **$\gamma$** Attenuation of **PD** inside the phantom along z-axis.

* **$\beta$** Normalized **PD** distribution inside the phantom in xy plane.

* **$pPD$** Peak PD.

* **$pAPD$** Spatial peak APD.

* **$psAPD_{1cm^2}$** Peak spatial-average APD over an averaging area of 1 cm<fnref n="2" />.

* **$psAPD_{4cm^2}$** Peak spatial-average APD over an averaging area of 4 cm<fnref n="2" />.

* **$S_{eval}$** APD evaluation surface.

* **$T$** Temperature rise.

<footnote n="1">¹CNRS, IETR (Institut d'Electronique et des Technologies du numérique), UMR 6164, Université de Rennes, 35708 Rennes, France</footnote>

<footnote n="2">²WAVELIS, 35510 Cesson-Sevigne, France</footnote>
<table><tr><td>S<sub>meas</sub></td><td>T measurement surface.</td></tr><tr><td>T<sub>meas</sub></td><td>Measured temperature rise on S<sub>meas</sub>.</td></tr><tr><td>APD<sub>(r,s)</sub></td><td>APD reconstructed from simulated T.</td></tr><tr><td>APD<sub>(r,m)</sub></td><td>APD reconstructed from measured T.</td></tr><tr><td>APD<sub>(s)</sub></td><td>APD simulated at skin surface.</td></tr><tr><td>γ</td><td>Correlation factor.</td></tr><tr><td>Δ<sup>j</sup><sub>i</sub></td><td>Relative error on reconstructed APD.</td></tr><tr><td>Δ<sup>j</sup><sub>s</sub></td><td>Relative error on APD<sub>(r,s)</sub>.</td></tr><tr><td>Δ<sup>j</sup><sub>m</sub></td><td>Relative error on APD<sub>(r,m)</sub>.</td></tr><tr><td>d</td><td>Distance between AUT and phantom.</td></tr><tr><td>L<sub>z</sub></td><td>Phantom thickness.</td></tr><tr><td>L<sub>x</sub></td><td>Phantom size in x-axis.</td></tr><tr><td>L<sub>y</sub></td><td>Phantom size in y-axis.</td></tr><tr><td>r&#773;</td><td>Space vector.</td></tr><tr><td>u&#773;<sub>x</sub></td><td>Unit vector along x-axis.</td></tr><tr><td>u&#773;<sub>y</sub></td><td>Unit vector along y-axis.</td></tr><tr><td>u&#773;<sub>z</sub></td><td>Unit vector along z-axis.</td></tr><tr><td>ε<sub>r</sub></td><td>Permittivity.</td></tr><tr><td>σ</td><td>Conductivity.</td></tr><tr><td>η</td><td>Phantom material impedance.</td></tr><tr><td>k</td><td>Propagation constant.</td></tr><tr><td>R<sub>ph</sub></td><td>Power reflection coefficient of phantom.</td></tr><tr><td>R<sub>skin</sub></td><td>Power reflection coefficient of skin.</td></tr><tr><td>κ</td><td>Thermal conductivity.</td></tr><tr><td>c</td><td>Specific heat capacity.</td></tr><tr><td>ε<sub>N</sub></td><td>Hemispherical spectral normal emissivity.</td></tr><tr><td>h</td><td>Convective heat transfer coefficient.</td></tr><tr><td>α</td><td>Thermal diffusivity.</td></tr><tr><td>X</td><td>Eigenfunction at x-axis.</td></tr><tr><td>Y</td><td>Eigenfunction at y-axis.</td></tr><tr><td>Z</td><td>Eigenfunction at z-axis.</td></tr><tr><td>ν</td><td>Eigenvalue at x-axis.</td></tr><tr><td>υ</td><td>Eigenvalue at y-axis.</td></tr><tr><td>χ</td><td>Eigenvalue at z-axis.</td></tr><tr><td>N<sub>x</sub></td><td>Norm of eigenfunction X.</td></tr><tr><td>N<sub>y</sub></td><td>Norm of eigenfunction Y.</td></tr><tr><td>N<sub>z</sub></td><td>Norm of eigenfunction Z.</td></tr></table>

# I. INTRODUCTION

The continuous evolution of wireless technologies has led to a surge in wireless data usage, in particular due to video streaming and cloud computing. This increasing demand for high-speed ubiquitous mobile wireless communications is driving a gradual extension towards millimeter-wave (mmWave) frequencies. Forthcoming heterogeneous cellular networks are expected to exploit the FR2 bands, including frequencies around 26 GHz, 39 GHz, and 60 GHz [1], [2], [3], [4], [5].

The compliance testing of portable wireless devices is performed to ensure the respect of the human exposure limits mainly inspired from the guidelines of the International Commission on Non-Ionizing Radiation Protection (ICNIRP) [6] and from the C95.1 standard of the Institute of Electrical and Electronics Engineers (IEEE) [7]. Below 6 GHz, the specific absorption rate (SAR) is used as the main dosimetric quantity. Due to a shallow penetration depth of the electromagnetic energy into the human body in the upper part of the microwave

spectrum [8], [9], in-tissue power density (PD), referred as the absorbed power density (APD) by ICNIRP and as the epithe-lial power density by IEEE C95.1, is employed as the main dosimetric quantity above 6 GHz. Both IEEE and ICNIRP set the limits to 10 mW/cm² for occupational environments and 2 mW/cm² for the general public. Above 6 GHz, PD is to be averaged over 4 cm² and 6 min. From 30 to 300 GHz, the PD is also to be averaged over 1 cm² and must not exceed 2 times the exposure limit for 4 cm².

SAR compliance testing is performed based on the spatial scanning of the electric field (E-field) or magnetic field (H-field) using a field probe and consequent SAR retrieval [10]. Below 6 GHz, SAR is assessed using a single probe or probe array that sense the E-field in a tissue-simulating liquid encapsulated in a container that mimics the shape of the human torso or head (referred as phantom) [11], [12], [13], [14]. Above 6 GHz, use of this method is complicated by prohibitory high losses in the near-surface tissues resulting in a strong spatial in-body PD gradient (e.g. at 60 GHz the penetration depth is about 0.5 mm), which substantially increases the uncertainty of the E-field measurement inside a lossy liquid phantom due to the tolerance of the field probe positioning and orientation.

A novel method for APD evaluation above 6 GHz based on free-space E-field measurements was introduced in [15]. In this method, a reflectivity-based phantom, represented by a thin solid structure, is employed to mimic the scattering characteristics of human skin. The partial transparency of such a phantom allows for free-space E-field measurement using a standard field probe at the opposite to the antenna under test (AUT) side of the phantom. The measured E-field is back-propagated in space to retrieve APD at the phantom surface using a plane-wave spectrum (PWS) technique.

A method for the APD reconstruction based on the E-field measurements in a tissue-simulating liquid was reported in [16]. Here, a diode-loaded probe immersed in the liquid phantom medium measures the E-field magnitude and polarization ellipse over the scanning area. The methods based on the spatial field scanning, such as those presented in [15], [16], are time consuming (typically few hours) as the E-field is scanned point-by-point over a dense spatial grid of hundreds up to thousands points with a separation resolution defined with respect to the wavelength in the host medium (free space [15] or tissue-simulating liquid [16]). Moreover, the power and/or frequency drift of AUT during point-by-point scanning may reduce the accuracy and reproducibility of results.

An alternative approach for APD assessments, based on the combination of over-the-air (OTA) measurements and full-wave electromagnetic simulations, is reported in [17]. First, E-field phasor components are measured using spherical far-field scanner over a surface encompassing the device under test (DUT). Second, equivalent electric and magnetic currents are reconstructed on a closed surface surrounding the AUT. Finally, equivalent currents on this surface are used as a source in full-wave electromagnetic simulations to compute the incident power density (IPD) at the air/skin interface of a digital human model. To account for antenna/body interactions, the AUT is replaced by a perfect electric conductor (PEC). This
allows to account, under certain assumptions, for reflection and standing wave phenomena, but neglects the impact of the proximity of the human body on the AUT (load, detuning, coupling, etc.).

It was demonstrated that modeling the source with a PEC may result in an overestimation or underestimation of APD up to 497% and down to 54.7%, respectively (for 4 × 4 patch antenna array at 60 GHz) [18]. This suggests that for accurate exposure assessment, APD should be measured in presence of a human model reproducing the reflection from the body and under conditions reproducing realistic use case scenarios.

A temperature-mediated high-resolution technique for EM PD measurement of mmWave devices was introduced in [19]. This technique employs a thin dielectric structure converting the mmWave energy into heat. The surface temperature profile recorded using an infrared (IR) camera is used to retrieve the mmWave PD distribution. Such an IR-based approach allows for non-invasive (remote), high-spatial resolution (sub-mm), and fast (several seconds to several minutes, depending on the AUT transmit power) measurement of the PD distribution. The sensitivity of the method proposed in [19] was further improved by applying the spectral frequency-domain filtering of the thermal noise using the lock-in technique [20]. This enables achieving the sensitivity sufficient for measuring PD distribution induced by low-power mmWave devices with APD below ICNIRP and IEEE C95.1 limits.

In this study, for the first time we demonstrate that the IR-based method can be employed for APD dosimetry and user safety compliance testing of low-power mmWave wireless devices operating above 6 GHz. This includes reconstruction of the APD pattern and retrieval of the spatial peak and peak spatial-average APD according to the new IEC/IEEE 63195-3/4 international standard. The method is experimentally validated for two reference antennas defined by IEC/IEEE 63195-1 international standard for validation of PD measurement systems [21].

## II. APD EVALUATION METHOD

The proposed APD measurement approach is schematically represented in Fig. 1. The AUT is placed at a distance *d* from a thin reflectivity-based phantom reproducing the reflection properties of human skin and thus perturbing the AUT in the similar way as it would be perturbed by the presence of the human body [22]. The IR signal emitted by surface *S*<sub>meas</sub> is remotely recorded by an IR camera. The intensity of the IR emission is directly proportional to the temperature at *S*<sub>meas</sub> (*T*<sub>meas</sub>) [23]. To reduce the IR noise and thus enhance the signal-to-noise ratio (SNR) and sensitivity of the method, the spectral filtering is used [20]. Finally, APD at the evaluation surface *S*<sub>eval</sub> is reconstructed from *T*<sub>meas</sub> using a parametric solution of the differential heat transfer equation.

## A. EXPERIMENTAL SETUP

The experimental setup is schematically illustrated in Fig. 2(a). The AUT is fed by a tunable narrowband mmWave power generator (QuinStar, CA, USA) via WR15 rectangular

<figure><img src="image_1.png" /><figcaption>FIGURE 1. Conceptual representation of the IR-based APD measurement method.</figcaption></figure>

waveguides. A programmable power supply (R & S HMP 4040) is used to control the waveform and frequency of the input signal. The measurements are performed at 60 GHz at room temperature (20°C). The input power level set to 25 mW is monitored using an E4418B power meter (Agilent, CA, USA) through a 20 dB coupler (V752D, Hewlett Packard, CA, USA). The heat pattern and dynamics at *S*<sub>meas</sub> of the phantom are recorded by an IR camera (SC5600, FLIR Systems, OR, USA) operating in the 3.5–5.0 μm range with the thermal sensitivity of 0.02°C and spatial resolution of 640 × 512. It is located at 35 cm from the phantom (the corresponding pixel size in the measurement plane *S*<sub>meas</sub> is 0.2 mm × 0.2 mm). The measurements are performed in a closed compact anechoic chamber (internal dimensions 75 cm × 45 cm × 100 cm) that shields the set-up from parasitic EM signals, prevents multipath scattering, and minimizes environmental interference due to external heat sources and air convection around the phantom.

The lock-in technique [20] is used to filter the ambient IR noise and to mitigate the heat conduction effect, thus improving the correlation between the heat pattern and mmWave PD distribution. In this method, the amplitude of the AUT input power is modulated by a periodic waveform. The Fourier transformation is applied to the measured thermal signal to separate in spectral components of the ambient noise and low-frequency time-average heating from the useful signal (high-frequency oscillating component). Finally, the noise and low-frequency components are filtered in the spectral domain and the inverse Fourier transformation is applied to retrieve *T*<sub>meas</sub>. Measurements are performed at steady-state (reached after about 3 mins) at the lock-in frequency of 0.2 Hz.
<figure><img src="image_2.png" /><figcaption>FIGURE 2. Measurement setup and reference antennas: (a) schematic representation of the measurement setup, (b) AUT1: pyramidal horn loaded with a slot array, (c) AUT2: cavity-fed dipole array.</figcaption></figure>

The overall measurement duration is less than 5 min. The method is validated for two reference antennas [21] shown in Fig. 2(b) (pyramidal slotted horn with the aperture dimensions 23.40 mm × 18.78 mm) and Fig. 2(c) (cavity-fed dipole array with the aperture dimensions 20.0 mm × 20.0 mm).

B. REFLECTIVITY-BASED PHANTOM

A 1.2 mm-thick solid phantom (100 mm × 100 mm) is fabricated using carbon black powder and PDMS (Fig. 3(a)). The dimensions of the phantom are chosen to include the entire thermal footprint of the AUT and to avoid potential effect of boundaries. In line with [19], the PDMS and carbon powder (40%) are mixed and stirred thoroughly, then degassed under vacuum, and finally dried in an oven at 110°C. The complex permittivity of the composite phantom material at 60 GHz, measured using a coaxial-probe DAK TL2 system (SPEAG, Zurich, Switzerland), is $\epsilon_r = 12.5 - j3.6$.

The power reflection coefficient of the fabricated phantom ($R_{ph}$) and the target reference value of the Gabriel's dry skin model (semi-infinite with $\epsilon_r = 7.98 - j10.9$) ($R_{skin}$) were calculated at 60 GHz using Fresnel equations [24]. Note

that the dry skin model is used as a well-established skin model representative of practical use cases [25]. However, by adjusting the carbon concentration and/or thickness of the phantom, the power reflection coefficient can be tuned to represent, for example, wet skin properties. The deviation between $R_{ph}$ and $R_{skin}$ is 1.2% at the normal incidence and 4.7% (3.5%) for the TM (TE) polarizations near the Brewster angle (Fig. 3(b)). The reflectivity of the fabricated prototype was measured in the 57-63 GHz range using the free-space transmission method and the quasi-optical bench illustrated in Fig. 3(c) [22]. The method employs a vector network analyzer (VNA), a transmission/reflection quasi-optical setup with two focusing lenses, and two conical WR-15 horn antennas. Results in Fig. 3(d) demonstrate an excellent agreement with the maximum deviation of ~3% (within the 10% bandwidth) between the measured reflection coefficient of the phantom and the reference one of human skin.

The loading of the used AUTs (i.e., the $S_{11}$ parameter) in free space, as well as in presence of the phantom and the reference skin, is reported in Fig. 4 for the separation distance $d = 2$ mm. This distance is, among those recommended by IEC/IEEE 63195 (2 mm, 5 mm, 10 mm, and 50 mm), corresponding to the strongest reactive field. Results demonstrate that the reflectivity-based phantom reproduces the dielectric loading of the AUT by the dry skin (discrepancy < 0.5 dB for $S_{11} > -10$ dB). It is also worth mentioning that for this distance the proximity of the body results in a significant mismatch, namely 20.45 dB (from -27 dB to -6.55 dB) and 2.57 dB (from -9.57 dB to -7 dB) at 60 GHz for the slotted horn and dipole array, respectively. This mismatch is even higher at the resonance frequency of the narrow-band dipole array (15 dB). This observation highlights limitations of APD assessment methods based on free-space measurements (e.g. [17]) that do not account for antenna detuning when operate in proximity to the human body.

The following properties of the phantom material were used in the thermal analysis: the thermal conductivity $\kappa = 0.48$ Wm$^{-1}$$^\circ C^{-1}$ (measured using guarded hot disk method); the specific heat capacity $c = 1259$ Jkg$^{-1}$$^\circ C^{-1}$ (measured using the differential scanning calorimetry method) [19]; the hemispherical spectral normal emissivity $\epsilon_N = 0.94$ (measured using an IR spectrometer at 20°C in the 3.5-5 $\mu$m range); the convective heat transfer coefficient $h = 5$ W/(m$^2$$^\circ C) [26]. Note that, even if the complex permittivity of the phantom is different from that of human skin, the APD at $S_{eval}$ reproduces the one at the skin/air interface according to the energy conservation principle.

III. APD RECONSTRUCTION FROM IR MEASUREMENTS

APD at $S_{eval}$ is retrieved from temperature $T_{meas}$ recorded at $S_{meas}$. To achieve this, in Sub-section III-A the differential equation governing heat transfer in the phantom is solved to model the spatial distribution and temporal temperature dynamics inside the phantom as a function of mmWave power absorbed per unit volume. The analytical relationship between APD and $T_{meas}$ is then established in Sub-section III-B.
<figure><img src="image_3.png" /><figcaption>FIGURE 3. Reflectivity-based phantom: (a) fabricated prototype with a support; (b) deviation between the simulated power reflection coefficient of the phantom vs the target skin reference at 60 GHz; (c) quasi-optical test bench used for the phantom characterization; (d) measured power reflection coefficient of the phantom vs. the simulated one for skin at normal incidence.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>FIGURE 4. S11 at d = 2 mm: (a) slotted horn and (b) dipole array.</figcaption></figure>

Finally, the absolute APD values are derived by fitting the parametric solution of the heat transfer equation to the measured heat dynamics.

A. THERMAL MODEL

The mmWave-induced temperature rise in the phantom is modeled in space and time by the following 3-dimentional (3D) ($\vec{r} = x \cdot \hat{u}_x + y \cdot \hat{u}_y + z \cdot \hat{u}_z$) time-dependent non-homogeneous differential heat transfer equation [26]:

$$ \frac{\partial^2 T(\vec{r}, t)}{\partial r^2} + \frac{1}{\kappa} g(\vec{r}, t) = \frac{1}{\alpha} \frac{\partial T(\vec{r}, t)}{\partial t}, \quad (1) $$

where $\alpha$, and $g(\vec{r}, t)$ are, respectively, the thermal diffusivity and the internal heat source associated with the electromagnetic field (EMF) emitted by the AUT and absorbed in the

phantom, expressed as:

$$ g(\vec{r}) = \frac{1}{2} \sigma \|E(\vec{r})\|^2, \quad (2) $$

where $\sigma$ and $E$ are, respectively, the conductivity and the absorbed E-field inside the phantom.

Adiabatic boundary conditions are used at zy plane (at $-\frac{L_x}{2}$ and at $\frac{L_x}{2}$) and the zx plane (at $-\frac{L_y}{2}$ and at $\frac{L_y}{2}$), with $L_x$ and $L_y$ being the dimensions of the phantom, and are expressed as:

$$ \frac{\partial T(x, t)}{\partial x}\bigg|_{x=\{-\frac{L_x}{2}, \frac{L_x}{2}\}} = 0, \\ \frac{\partial T(y, t)}{\partial y}\bigg|_{y=\{-\frac{L_y}{2}, \frac{L_y}{2}\}} = 0, \quad (3) $$
and convective boundary conditions at the xy plane (at z = 0 and L_z) are expressed as:

$$ \kappa \frac{\partial T(z, t)}{\partial z}\bigg|_{z=0} = h\left(T\bigg|_{z=0}\right), \quad (4) $$

$$ -\kappa \frac{\partial T(z, t)}{\partial z}\bigg|_{z=L_z} = h\left(T\bigg|_{z=L_z}\right), \quad (5) $$

where h is the convective heat transfer coefficient. The system of differential (1)–(5) is solved by separating the spatial variables x, y, and z, and then using the integral transform technique for each spatial variable [26]. The solution is expressed as:

$$ T(x, y, z, t) = \sum_m \sum_n \sum_p \frac{X(x, v_m)Y(y, v_n)Z(z, \chi_p)}{N_x(v_m)N_y(v_n)N_z(\chi_p)} e^{-\alpha \delta_{mnp}^2 t} \left[ \frac{\alpha}{\kappa} \int_{t'}^t e^{\alpha \delta_{mnp}^2 t'} \bar{g}(v_m, v_n, \chi_p, t') dt' \right]. \quad (6) $$

where X, Y, and Z are the Eigenfunctions at the x, y, and z axes, respectively, expressed as functions of the eigenvalues $v_m$, $v_n$, and $\chi_p$, respectively, as:

$$ X(x, v_m) = \cos(v_m x), \quad \text{with} \quad \sin(v_m L) = 0, \quad (7) $$

$$ Y(y, v_n) = \cos(v_n y), \quad \text{with} \quad \sin(v_n L) = 0, \quad (8) $$

$$ Z(z, \chi_p) = \chi_p \cos(\chi_p z) + H \sin(\chi_p z), \quad (9) $$

with

$$ \tan(\chi_p L) = \frac{2\chi_p H}{\chi_p^2 - H^2}, \quad H = \frac{h}{\kappa}, \quad (10) $$

$$ \text{and } \delta_{mnp}^2 = v_m^2 + v_n^2 + \chi_p^2. $$

$N_x$, $N_y$, and $N_z$ are the norms of the eigenfunctions X, Y, and Z, respectively, defined as:

$$ N_x = \begin{cases} \frac{L_x}{2}, & \text{for } v_m \neq 0, \\ L_x, & \text{for } v_m = 0, \end{cases} \quad (11) $$

$$ N_y = \begin{cases} \frac{L_y}{2}, & \text{for } v_n \neq 0, \\ L_y, & \text{for } v_n = 0, \end{cases} \quad (12) $$

$$ N_z = \frac{1}{2} \left[ \left( \chi_p^2 + H^2 \right) \left( L_z + \frac{H}{\chi_p^2 + H^2} \right) + H \right]. \quad (13) $$

$\bar{g}$ is the integral transforms of g given as:

$$ \bar{g}(v_m, v_n, \chi_p, t') = \int_0^{L_z} \int_0^{L_y} \int_0^{L_x} X(x', v_m) \quad (14) $$

$$ Y(y', v_n)Z(z', \chi_p) \times g(x', y', z', t') dx' dy' dz'. $$

## B. APD RETRIEVAL FROM MEASURED TEMPERATURE

Formula (6) gives the spatial distribution and temporal temperature dynamics inside the phantom as a function of mmWave power absorbed per unit volume g(x, y, z). Under the plane-wave equivalent approximation (PWEA) [21],

g(x, y, z) is expressed as follows:

$$ g(\vec{r}) = \sigma \left[ \mathrm{Re} \left\{ \frac{1}{\eta^*} \right\} \right]^{-1} PD(\vec{r}), \quad (15) $$

where $\eta$ is the phantom material impedance, and PD(\vec{r}) is the PD inside the phantom, which can be expressed as the product of two functions:

$$ PD(x, y, z) = \gamma(z)\beta(x, y, z), \quad (16) $$

where $\gamma(z)$ describes attenuation of the PD inside the phantom along the z-axis, and $\beta(x, y, z)$ describes the normalized PD distribution inside the phantom in a corresponding xy plane ($z = z_i$):

$$ \beta(x, y, z_i) = \frac{PD(x, y, z_i)}{\max\{PD(x, y, z_i)\}}, \quad 0 \le z_i \le L_z. \quad (17) $$

For thin phantoms, the variation of $\beta(x, y, z_i)$ along the z-axis is negligibly small (e.g., < 2.8% for the phantom introduced in Section II-B), which allows defining $\beta$ in terms of the normalized PD distribution at the surface of the phantom facing the IR camera ($z_i = L_z$):

$$ \beta(x, y, z_i) \approx \beta(x, y, L_z), \quad 0 \le z_i < L_z. \quad (18) $$

The direct proportionality between the PD and the induced initial temperature rise can be further used to redefine $\beta$ as a function of the normalized measured temperature distribution at $S_{\text{meas}}$:

$$ \beta(x, y, z_i) \approx \frac{T_{\text{meas}}(x, y, L_z)}{\max\{T_{\text{meas}}(x, y, L_z)\}}. \quad (19) $$

When lock-in is used, this remains valid both for transient temperature rise and at steady state. Use of lock-in enables mitigating the heat conduction effect, which is a bottleneck of conventional IR-based dosimetry measurements.

The PD decay along the z-axis inside the phantom is determined using the PWEA representation [21], which yields:

$$ \gamma(z) = pPD \frac{(e^{-jzk} + e^{jk(z-2L_z)} R_{ph})}{(1 + e^{-j2L_z k} R_{ph})} \quad (20) \\ \frac{(e^{-jzk} - e^{jk(z-2L_z)} R_{ph})^*}{(1 - e^{-j2L_z k} R_{ph})^*} $$

where pPD is an unknown corresponding to the peak PD at z = 0, and k is the complex propagation constant. pPD can be determined via an iterative fitting of the measured temperature to the analytical solution (6) of the heat transfer (1).

Finally, using (16), (19), and (20), the sought absolute values of the APD(x, y) at the evaluation surface $S_{\text{eval}}$ ($z = 0$) are calculated as:

$$ \mathrm{APD}(x, y) \approx p\mathrm{PD} \frac{T_{\mathrm{meas}}(x, y, L_z)}{\max\{T_{\mathrm{meas}}(x, y, L_z)\}}, \quad (21) $$

and the spatial peak APD is calculated as:

$$ pAPD = \max\{\mathrm{APD}(x, y)\}, \quad (22) $$

while the peak spatial-average APD over an averaging area A of 1 cm² ($psAPD_{1cm^2}$) or 4 cm² ($psAPD_{4cm^2}$) is calculated
as:

$$psAPD_A = \frac{1}{A} \iint_A APD(x, y)dxdy. \quad (23)$$

In such a way, the absolute value of the APD can be obtained using (21) in addition to the normalized APD distribution that can be reconstructed from the measured temperature distribution.

By following the proposed procedure, the sought dosimetric quantities, including the spatial peak APD (22) and the peak spatial-average APD (23), can be reconstructed from a single thermal measurement.

## IV. EXPERIMENTAL VALIDATION FOR REFERENCE ANTENNAS

To validate the proposed IR-based APD evaluation method, the APD in the evaluation plane reconstructed from simulated heat patterns (APD(r,s)) and from measured heat patterns (APD(r,m)) is compared with the APD at the skin/air interface (APD(s)) simulated by solving the full-wave electromagnetic problem.

The analysis is performed for the two reference antennas (Fig. 2(b) and (c)) with an input power of 25 mW. The APD data are normalized to the free-space total radiated power (TRP) of 1 mW (0 dBm) according to the IEC/IEEE 63195 recommendation.

### A. APD DISTRIBUTION

The spatial distributions of APD(s), APD(r,s), and APD(r,m) for the reference horn antenna (Fig. 2(b)) and dipole array antenna (Fig. 2(c)) for the separation distance d = 2, 5, and 10 mm are presented in Figs. 5 and 6, respectively. The correlation coefficient (γ) is used to quantify the reconstruction and measurement accuracy:

$$\gamma = \frac{\sum_m \sum_n (G_{mn} - \bar{G})(F_{mn} - \bar{F})}{\sqrt{\sum_m \sum_n (G_{mn} - \bar{G})^2 \sum_m \sum_n (F_{mn} - \bar{F})^2}}, \quad (24)$$

where G and F are the distributions to compare, and Ḡ and F̄ are the mean values of G and F, respectively. The parameter γ is an indicator of how close the relative distributions are to each other.

The results demonstrate the correlation of 99.6% and 99% between APD(r,s) and APD(s) patterns and around 97% (±1%) and 89% (±0.5%) between APD(r,m) and APD(s) for the horn and dipole array antennas, respectively.

Figs. 5 and 6 demonstrate that the spatial distribution is well reproduced both for the main and side lobes. A decrease in the APD measurement accuracy at the peripheral region is mainly attributed to the thermal noise, estimated to be around -20 dB (Figs. 5 and 6, 1-D distributions). Advanced filtering schemes can be used to improve the SNR at the side lobes. This is out of the scope of this study and constitutes one of its perspectives.

The discrepancies between APD(r,m) and APD(s) distributions in the regions of the strong APD gradient (around y = 0 mm for the horn antenna (Fig. 5(c)) and around the local APD minimum (e.g., at y = -6 mm in Fig. 6(c)) for the

dipole array antenna) are attributed to the heat conduction effect. However, their impact on the spatial peak and peak spatial-average APD is not significant (i.e., γ > 96%). It can be further improved by increasing the lock-in frequency.

### B. SPATIAL PEAK AND PEAK SPATIAL-AVERAGE APD

The spatial peak and peak spatial-average APD(s), APD(r,s), and APD(r,m) are shown in Figs. 7 and 8 as a function of the AUT/phantom separation distance d. For both AUTs, the peak and spatial average APD values are comparable with the ICNIRP limits defined in [6]. The relative error of the reconstructed APD(r,j) (where j denotes s or m, referring respectively to APD(r,s) and APD(r,m)) is calculated as:

$$\Delta_i^j = 10 \log_{10} \frac{APD_{(r,j)}}{APD_{(s)}} \quad (25)$$

where Δi^j denotes the relative error for the pAPD, psAPD_1cm², or psAPD_4cm² (Δpeak, Δlcm², and Δ4cm², respectively).

The data for Δi^s and Δi^m are provided in Table 1. Maximum Δi^s for all d ∈ [2 - 10] mm is given in Table 2. The maximum simulated relative error for both antennas and all separation distances is within 0.49 dB and 0.06 dB for pAPD and psAPD, respectively.

A higher experimental relative error is observed for the cavity-backed slotted array antenna. Its near-field distribution comprises deep local minima with a very strong APD gradient around them, which complicates APD retrieval from measured heat locally in this region (Fig. 6(a) and (b)). This is mainly attributed to the thermal noise and heat conduction, whose impact increases in the areas with a strong APD gradient.

The maximum measured relative error on pAPD and psAPD is estimated as 0.44 dB and 0.35 dB, respectively, for the slotted horn antenna, and -0.84 dB and 0.59 dB, respectively, for the dipole array antennas.

## V. CONCLUSION

This paper introduces a novel technique for fast evaluation of the spatial peak and spatial-average APD based on IR thermography. The proposed methodology is in line with the APD assessment requirements defined in IEC/IEEE TC106 JWG11/12 TR 63572 and IEC/IEEE International Standard 63195-3/4. The method employs a thin planar solid phantom that mimics the scattering characteristics of the human skin and the AUT load by the human body, thus reproducing the antenna/body interactions and the APD at the air/skin surface.

In this method, the heat dynamics at the back surface of the phantom recorded by a high-resolution IR camera is used to reconstruct the APD distribution on the evaluation surface. The multi-physics approach, combining the heat transfer equation and the PWEA technique, is employed to retrieve the spatial peak and peak spatial-average APD. The method is validated using the reference cavity-fed dipole array and slotted pyramidal horn antennas.
<figure><img src="image_5.png" /><figcaption>1D profiles along the lines (dashed white) parallel to x and y axis intersecting the peak APD</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>1D profiles along the lines (dashed white) parallel to x and y axis intersecting the peak APD</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>1D profiles along the lines (dashed white) parallel to x and y axis intersecting the peak APD</figcaption></figure>

**FIGURE 5.** APD distributions for the slotted horn antenna at (a) d = 2 mm, (b) d = 5 mm, and (c) d = 10 mm.
<figure><img src="image_8.png" /><figcaption>1D profiles along the lines (dashed white) parallel to x and y axis intersecting the peak APD</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>1D profiles along the lines (dashed white) parallel to x and y axis intersecting the peak APD</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>1D profiles along the lines (dashed white) parallel to x and y axis intersecting the peak APD</figcaption></figure>

**FIGURE 6.** APD distributions for the dipole array antenna at (a) d = 2 mm, (b) d = 5 mm, and (c) d = 10 mm.
<figure><img src="image_11.png" /><figcaption>FIGURE 7. Spatial peak APD (pAPD) and spatial average APD (psAPD) for the slotted horn reference antenna.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>FIGURE 8. Spatial peak APD (pAPD) and spatial average APD (psAPD) for the dipole array reference antenna.</figcaption></figure>

<table><caption>TABLE 1 Relative Error $\Delta_i^{(s,m)}$ (dB) for Both AUTs and Separation Distances $d = 2$ mm, 5 mm, 10 mm</caption><thead><tr><th rowspan="2">Separation distances (mm)</th><th colspan="3">Slotted horn</th><th colspan="3">Dipole array</th></tr><tr><th>Δ<sup>j</sup><sub>peak</sub></th><th>Δ<sup>j</sup><sub>1cm<sup>2</sup></sub></th><th>Δ<sup>j</sup><sub>4cm<sup>2</sup></sub></th><th>Δ<sup>j</sup><sub>peak</sub></th><th>Δ<sup>j</sup><sub>1cm<sup>2</sup></sub></th><th>Δ<sup>j</sup><sub>4cm<sup>2</sup></sub></th></tr></thead><tbody><tr><td colspan="7">APD reconstructed from simulated temperature rise (Δ<sup>s</sup><sub>i</sub>)</td></tr><tr><td>2</td><td>-0.23</td><td>0.03</td><td>0.05</td><td>-0.49</td><td>-0.01</td><td>0.01</td></tr><tr><td>5</td><td>0.05</td><td>-0.01</td><td>-0.01</td><td>-0.23</td><td>0.04</td><td>-0.04</td></tr><tr><td>10</td><td>0.08</td><td>0.02</td><td>-0.04</td><td>-0.03</td><td>0.01</td><td>-0.08</td></tr><tr><td colspan="7">APD reconstructed from measured temperature rise (Δ<sup>m</sup><sub>i</sub>)</td></tr><tr><td>2</td><td>0.37</td><td>0.22</td><td>0.35</td><td>-0.38</td><td>0.28</td><td>0.59</td></tr><tr><td>5</td><td>0.44</td><td>0.01</td><td>-0.06</td><td>-0.63</td><td>-0.15</td><td>0.42</td></tr><tr><td>10</td><td>-0.36</td><td>0.31</td><td>-0.21</td><td>-0.84</td><td>-0.26</td><td>0.22</td></tr></tbody></table>

<table><caption>TABLE 2 Maximum Relative Error max($\Delta_i^j$) (dB) in APD Reconstruction From Simulated Temperature Rise</caption><thead><tr><th rowspan="2">Separation distance (mm)<br>d</th><th colspan="3">Slotted horn</th><th colspan="3">Dipole array</th></tr><tr><th>Δ<sup>j</sup><sub>peak</sub></th><th>Δ<sup>j</sup><sub>1cm<sup>2</sup></sub></th><th>Δ<sup>j</sup><sub>4cm<sup>2</sup></sub></th><th>Δ<sup>j</sup><sub>peak</sub></th><th>Δ<sup>j</sup><sub>1cm<sup>2</sup></sub></th><th>Δ<sup>j</sup><sub>4cm<sup>2</sup></sub></th></tr></thead><tbody><tr><td>[2-10]<br>(worst case)</td><td>-0.27<br>(at 2.5 mm)</td><td>0.06<br>(at 8.4 mm)</td><td>-0.06<br>(at 9.1 mm)</td><td>-0.49<br>(at 2 mm)</td><td>0.05<br>(at 3.2 mm)</td><td>-0.01<br>(at 8.9 mm)</td></tr></tbody></table>

An excellent agreement was found between the reference APD (peak, averaged, and distribution) and the one reconstructed from simulated temperature. The maximum errors on the reconstructed spatial peak and peak spatial-average APD from the simulated heat dynamics are 0.49 dB and 0.06 dB, respectively. Very good agreement is also demonstrated between simulated APD and the one reconstructed from the IR measurements. The maximum relative errors on the reconstructed spatial peak and peak spatial-average APD are -0.84 dB and 0.59 dB, found for the dipole array antenna. The potential sources of error include those related to the AUT

(accepted power, positioning, alignment), IR measurements (noise, heat diffusion), post-processing (data sampling and averaging), and phantom (fabrication tolerance, uncertainty of electromagnetic and thermal properties characterization).

It is worth mentioning that the accuracy of the proposed method can vary for different types of antennas. For instance, the reference cavity-fed sparse dipole array antenna (Fig. 2(c)) appears more challenging for characterization than the reference horn antenna loaded with a periodic slot array (Fig. 2(b)), which is explained by higher near-field gradients associated with deep interference zeros and sharp field
intensity roll-offs that can be smoothed in thermal patterns by heat conduction. However, in most practical applications (e.g. smartphones) antenna modules are implemented in the form of conventional linear or compact 2D arrays with ~half-wavelength spacing, which translates into simpler near-field patterns with lower field gradients that can be reliably characterized with the proposed method.

This proof-of-concept study demonstrates that the proposed IR-based method enables fast, accurate, and realistic APD evaluation for compliance testing of low-power mmWave wireless devices, in line with the requirements of international exposure regulations and standards. Furthermore, this method is environment-friendly as it employs a solid reflectivity-based phantom with an extended lifetime and reduced environmental footprint compared to liquid or gel phantoms. Finally, it is based on remote non-invasive measurements, allowing for non-perturbing near-field sensing, while conventional scanning probes can locally modify the EMF distribution.

## ACKNOWLEDGMENT

The authors would like to thank F. Boutet for his kind assistance in using the quasi-optical setup for reflectivity measurements. They also acknowledge L. Cronier, C. Guitton, and X. Morvan for prototyping. They also acknowledge the Mobile & Wireless Forum (MWF) for providing the reference antennas.

## REFERENCES

[1] Huawei, "5G spectrum public policy position," 2017. [Online]. Available: https://www-file.huawei.com/-/media/corporate/pdf/public-policy/public_policy_position_5g_spectrum_2020_v2.pdf?la=en

[2] GSMA, "5G spectrum GSMA public policy position," Jun. 2022. [Online]. Available: https://www.gsma.com/spectrum/wp-content/uploads/2022/06/5G-Spectrum-Positions.pdf

[3] C. Dehos, J. L. González, A. De Domenico, D. Kténas, and L. Dussopt, "Millimeter-wave access and backhauling: The solution to the exponential data traffic increase in 5G mobile communications systems," *IEEE Commun. Mag.*, vol. 52, no. 9, pp. 88–95, Sep. 2014.

[4] MiWaveS project FP7 CORDIS European Commission. "Beyond 2020 heterogeneous wireless network with nillimeter wave small cell access and backhauling," 2014–2017. [Online]. Available: https://cordis.europa.eu/project/id/619563/fr

[5] T. Baykas et al., "IEEE 802.15.3c: The first IEEE wireless standard for data rates over 1 Gb/s," *IEEE Commun. Mag.*, vol. 49, no. 7, pp. 114–121, Jul. 2011.

[6] International Commission on Non-Ionizing Radiation Protection (IC-NIRP), "Guideliens for limiting exposure to electromagnetic fields (100kHz to 300 GHz)," *Health Phys.*, vol. 118, no. 5, pp. 483–524, May 2020.

[7] Safety Levels With Respect to Human Exposure to Electric, Magnetic, and Electromagnetic Fields, 0 Hz to 300 GHz, IEEE Standard C95.1, Aug. 2020.

[8] M. Zhadobov, N. Chahat, R. Sauleau, C. Le Quement, and Y. Le Drea, "Millimeter-wave interactions with the human body: State of knowledge and recent advances," *Int. J. Microw. Wireless Technol.*, vol. 3, no. 2, pp. 237–247, Apr. 2011.

[9] M. Zhadobov, C. Leduc, A. Guraliuc, N. Chahat, and R. Sauleau, "Antenna/human body interactions in the 60 GHz band: State of knowledge and recent advances," in *Advances in Body-Centric Wireless Communication: Applications and State-of-the-Art*, Q. H. Abbasi, M. H. Ur-Rehman, K. H. Qaraqe, and A. H. Alomainy, Eds. London, U.K.: IET, 2016, pp. 97–142.

[10] IEEE Recommended Practice for Determining the Peak Spatial-Average Specific Absorption Rate (SAR) in the Human Head From Wireless Communications Devices: Measurement Techniques, IEEE Standard 1528, Sep. 2013.

[11] B. Derat et al., "A novel technology for fast and accurate specific absorption rate measurement," in *Proc. Int. Workshop Antenna Technol.*, Karlsruhe, Germany, pp. 363–366, Mar. 2013.

[12] B. Derat, L. Aberbour, and A. Cozza, "Near-field and vector signal analysis techniques applied to specific absorption rate measurement," in *Proc. IEEE MTT-S Int. Microw. Workshop Ser. RF Wireless Technol. Biomed. Healthcare Appl.*, Taipei, Taiwan, 2015, pp. 34/35.

[13] C. Bujard, E. Neufeld, M. Douglas, J. Wiart and N. Kuster, "A Gaussian process based approach for validation of multi-variable measurement systems: application to SAR measurement systems," *IEEE Access*, vol. 12, pp. 60404–60424, Apr. 2024.

[14] S. Anwar et al., "Advanced post-processing technique to evaluate specific absorption rate (SAR) for a standard dipole antenna," in *Proc. 18th Eur. Conf. Antennas Propagation*, Glasgow, U.K., Mar. 2024, pp. 1–4.

[15] M. Ziane, A. Boriskin, C. Leconte, L. L. Coq, and M. Zhadobov, "Novel technique for in-body absorbed power density assessment based on free-space e-field measurement," *IEEE Trans. Microw. Theory Techn.*, vol. 72, no. 7, pp. 4127–4138, Jul. 2024.

[16] N. Chitnis, F. Karimi, A. Fallahi, S. Kühn, and N. Kuster, "Traceable absorbed power density assessment system in the 28 GHz band," in *BioEM2023*, Oxford, U.K., Jun. 2023.

[17] B. Derat, T. Liebig, D. Schaefer, M. Celik, and W. Simon, "Absorbed power density assessment using simulation-augmented over-the-air measurement," *IEEE Access*, vol. 12, pp. 28122–28140, 2024.

[18] M. Ziane, R. Sauleau, and M. Zhadobov, "Antenna/body coupling in the near-field at 60 GHz: Impact on the absorbed power density," *Appl. Sci.*, vol. 10, no. 21, Oct. 2020, Art. no. 7392.

[19] M. Ziane, M. Zhadobov, and R. Sauleau, "High-resolution technique for near-field power density measurement accounting for antenna/body coupling at millimeter waves," *Antennas Wireless Propag. Lett.*, vol. 20, no. 11, pp. 2151–2155, Nov. 2021.

[20] M. Ziane, A. Boriskin, and M. Zhadobov, "Near-field power density mapping of close-to-body low-power mmWave devices," *Antennas Wireless Propag. Lett.*, vol. 22, no. 10, pp. 2347–2351, Oct. 2023.

[21] Assessment of Power Density of Human Exposure to Radio Frequency Fields From Wireless Devices in Close Proximity to the Head and Body (Frequency Range of 6 GHz to 300 GHz), Standard IEC/IEEE 63195-2, May 2022.

[22] A. R. Guraliuc, M. Zhadobov, O. De Sagazan, and R. Sauleau, "Solid phantom for body-centric propagation measurements at 60 GHz," *IEEE Trans. Microw. Theory Techn.*, vol. 62, no. 6, pp. 1373–1380, Jun. 2014.

[23] FLIR, "The Ultimate infrared handbook for R&D professionals," 2015. Accessed: Feb. 24, 2025. [Online]. Available: https://www.flir.com/discover/rd-science/the-ultimate-infrared-handbook-for-rnd-professionals/

[24] D. M. Pozar, *Microwave Engineering*, 4th ed. Hoboken, NJ, USA: Wiley, 2012.

[25] A. Boriskin, M. Ziane, M. Mafamane, S. Anwar, L. J. Foger, and M. Zhadobov, "Universal electromagnetic reference skin model for APD evaluation at 6-100 GHz," *IEEE J. Microwaves* (submitted).

[26] D. W. Hahn, *Heat Conduction*, 3rd ed. Hoboken, NJ, USA: Wiley, 2012.

<figure><img src="image_13.png" /></figure>

**MASSINISSA ZIANE** received the M.S. degree in antennas and components for telecommunications from the University of Paris-Saclay, Gif-sur-Yvette, France, in 2019, and the Ph.D. degree in bioelectromagnetics from the University of Rennes, Rennes, France, in 2022, conducted at the Institute of Electronics and Telecommunications of Rennes. Since 2022, he has been a Postdoctoral Researcher with the French National Center for Scientific Research. His research interests include electromagnetic field (EMF) and radio frequency

(RF) exposure assessment, as well as computational electromagnetics for metrology.
<figure><img src="image_14.png" /></figure>

**ARTEM V. BORISKIN (BORYSKIN)** was born in Kharkiv, Ukraine. He received the M.S. (cum laude) degree from the Kharkiv National University, Kharkiv, Ukraine, in 1999, and the Ph.D. degree from IRE NAS Ukraine, Kharkiv, in 2004. From 2004 to 2009, he was a Research Scientist and later a Senior Research Scientist with the Computational Electromagnetics Department, IRE NASU, working on advanced computational methods for solving open boundary diffraction problems with application to dielectric lens antennas

and optical components. During those years, he also had short appointments with Bilkent University, Ankara, Türkiye, IT-Warsaw, Warsaw, Poland, the George Green Institute for Electromagnetics Research, Nottingham, U.K., and IETR/CNRS Université de Rennes, Rennes, France. In 2010, he joined the Department of of Antennas and Microwave Devices, IETR/CNRS, to work on lens antennas and integrated focusing systems for mm-wave applications, as well as antenna-human body interaction in the context of user safety. In 2015, he joined the Research & Innovation Division, Technicolor R&D France, as Senior Scientist to build a new technology around his invention of nanojet-based optical components for light guiding and manipulation for augmented reality glasses and image sensor applications. This work was later extended towards opto-fluidic lab-on-a-chip devices in collaboration with Technicolor Precision BioDevices, Camarillo, CA, USA. In 2019, he joined the Wireless Communication Systems group, Mitsubishi Electric R&D Europe (MERCE), Rennes, to work on 5G/6G technologies and standardization (ETSI, 3GPP) for V2X communication and Factory automation, including time sensitive networking and integration between 3GPP/5GS and IEEE/TSN networks. In 2021, he joined SATT OV, Rennes, as Technology Maturation Expert to lead a technology maturation project built around one of his earlier inventions dedicated to electromagnetic dosimetry and user exposure compliance testing of 5G/6G wireless devices. In 2023, he returned to IETR/CNRS to pursue work in the field of electromagnetic dosimetry aimed at the development of reflectivity-based human phantoms and associated methods for fast EM dosimetry in the 6–300 GHz range. In 2025, he founded WAVELIS company for advanced research and innovation in the field of wireless and optical technologies for safe wireless future, with 5G and beyond. He has coauthored more than 100 scientific publications and more than 30 patent families granted and implemented in products. Along his career, he was the Chair of the Young Scientist Council of IRE NASU from 2004 to 2008, Founder of the OSA/OSA Student Branch from 2007 to 2010, Mentor of the IEEE/IRE Student Branch from 2008 to 2009, and Scientific Secretary of the ESF NEWFOCUS program and of the European Association EurAAP WG8 from 2010 to 2015. He was the recipient of multiple awards from IEEE in 2000, EuMA in 2004, Samsung Corp. in 2005, OSA in 2008, Government of Ukraine in 2009, and Fondation Grand Ouest in 2022. He is a member of the International Standardization Committee IEC TC106 JWG11/12.

<figure><img src="image_15.png" /></figure>

**MAXIM ZHADOBOV** (Senior Member, IEEE) received the Ph.D. and Habilitation á Diriger des Recherches degrees from the Institut d'Electronique et des Technologies du numerique (IETR), University of Rennes, Rennes, France, in 2006 and 2016, respectively. He was a Postdoctoral Researcher with the Center for Biomedical Physics, Temple University, Philadelphia, PA, USA, until 2008, and then joined the French National Center for Scientific Research (CNRS). He is currently a Senior Research Scientist with

the IETR/CNRS. Since 2017, he was in charge of the Electromagnetic Waves in Complex Media (eWAVES) research team and a Member of the Scientific Council of the IETR. He has coauthored five book chapters, 97 research papers in peer-reviewed international journals, and more than 200 contributions to conferences and workshops. His research interests include innovative biomedical applications of electromagnetic fields and associated technologies. Since 2024, he has been a Member of Board of Directors of international BioEM Society and was an elected Member of EBEA Council from 2017 to 2021. He is also a Member of IEEE TC95.4 and the President of URSI France Commission K. His review article in the *International Journal of Microwave and Wireless Technologies* was the most cited paper during 2016–2025. A paper published by his research group in 2019 is in journal Top 100 of Nature *Scientific Reports*. He is an Associate Editor for IEEE JOURNAL OF ELECTROMAGNETICS, RF AND MICROWAVES IN MEDICINE AND BIOLOGY and was the Guest Editor of several special issues, including Human Exposure in 5G and 6G Scenarios of Applied Sciences and Advanced Electromagnetic Biosensors for Medical, Environmental and Industrial Applications of Sensors. He has been involved in 31 research projects (16 as PI). He was a TPC member and/or Session Organizer at international conferences, including IMWS-Bio 2014, MobiHealth during 2015–2017, BodyNets 2016, IEEE iWEM 2017, EuMW 2019, BioEM 2019, AT-AP-RASC 2022, EUMW2022, IEEE IMBioC 2022, EUMW2022, BioEM 2023, AES 2023, and URSI AT-RASC 2024. He was the TPC Co-Chair of BioEM 2021/2020 and Member of LOC of BioEM 2025. He was on review boards of more than 15 international journals and conferences, and has been acting as an expert at research councils worldwide. He was the recipient of Brittany’s Young Scientist Award in 2010, EBEA Award for Excellence in Bioelectromagnetics in 2015, CNRS Medal in 2018, and Research & Innovation Award of Grand Ouest Foundation in 2022. Since 2010, the Ph.D. students he worked with received eight national scientific awards and six awards from the Bioelectromagnetics Society, URSI, IEEE Antennas and Propagation, and IEEE Microwave Theory and Technology Societies.