## 2 Materials and Methods
### Exposure Scenarios  
To analyze variations of TPD in the skin-equivalent model due to the presence of a radiating structure, seven scenarios of increasing complexity are considered (Figure 1). Scenarios 1-4 are considered to determine the fundamental limits of TPD variations for a plane-wave excitation. In scenarios 5 and 6, we model the radiation pattern of antennas neglecting the impact of the phantom and a perfect electric conductor (PEC) on the antenna performances. Finally, antennas placed close to the skin-equivalent model are considered in scenario 7. These scenarios are detailed hereafter.  
* Scenario 1: Plane-wave incident from free space onto a semi-infinite flat skin-equivalent model (Figure 1a).  
Normal incidence is considered to represent the worst-case exposure scenario with maximum TPD [20]. Due to a shallow penetration depth at mmWs (\(<\)1 mm), the interaction with the human body is mainly limited to skin. As a consequence, a homogenous skin-equivalent layer is used as a model [21,22]. The dielectric properties of skin-equivalent model are those of dry skin at 60 GHz (\(\varepsilon=7.98-\mathrm{j}10.90\)); they were extracted from [23]. For completeness, we also provide in the paper the main results for a wet skin model (\(\varepsilon=10.22-\mathrm{j}11.83\)[23]).  
* Scenario 2: Scenario 1 adding a perfect electric conductor (PEC) parallel to the skin model (Figure 1b).  
The total transmitted field (\(\mathbf{E}_{\mathrm{Total}}\), \(\mathrm{TP}_{\mathrm{Total}}\)) is equal to the superposition of the transmitted field from direct incidence (\(\mathbf{E}_{\mathrm{Direct}}\), \(\mathrm{TP}_{\mathrm{Direct}}\)) and the scattered field resulting from multiple reflections at the PEC/skin-model interface es (\(\mathbf{E}_{\mathrm{R}}\), \(\mathrm{TP}_{\mathrm{R}}\)).  
* Scenario 3: Scenario 1 with free-space losses (i.e., the amplitude of the plane-wave is attenuated in free space) (Figure 1c).  
The amplitude of the electric field radiated by an infinitesimal dipole decreases as 1/d in the far-field, where d is the distance between the source and the observation point. Hence, we assume in this scenario that the amplitude of the incident E-field decreases with an attenuation function \(\mathrm{f}(\mathrm{d})=1/\mathrm{d}\).  
* Scenario 4: Scenario 2 with free-space losses (Figure 1d).
* Scenario 5: Scenario 1 with an antenna equivalent source replacing the plane-wave illumination (Figure 1e).  
The antenna equivalent source is defined as a combination of equivalent electric and magnetic currents flowing on a closed surface surrounding the antenna (dashed line in Figure 1e) generating the same electromagnetic field as the antenna in free space.  
* Scenario 6: Scenario 2 with the antenna equivalent source replacing the plane-wave illumination (Figure 1f).  
Figure 1: Schematic representation of considered exposure scenarios: (**a**) scenario 1; (**b**) scenario 2; (**c**) scenario 3; (**d**) scenario 4; (**e**) scenario 5; (**f**) scenario 6; (**g**) scenario 7. PEC: perfect electric conductor.  
* Scenario 7: Realistic antennas placed in the vicinity of the skin model (Figure 1g).  
The source main beam is directed towards the phantom representing the worst-case exposure scenario. Several sources have been considered: single patch antenna (SPA) and patch antenna array (PAA) with 4, 8, or 16 (\(2\times 2\) PAA, \(2\times 4\) PAA, and \(4\times 4\) PAA, respectively) radiating elements, inspired from [10; 24] (Figures 2 and 3) and matched to 50 \(\Omega\) in free-space at 60 GHz. All results are provided for an antenna input power of 10 mW.