Reflectance and Transmittance of mmWaves at the Air-Human Skin Interface (24 - 94 GHz)

This study examines the interaction between millimeter waves (mmWaves) and human skin by combining Fresnel equations with the complex Cole-Cole model for relative permittivity (ɛ*), providing a realistic representation of biological tissue. The approach is novel and has not been previously applied in this context. Analyses at 24, 35, 40, 60, 77, and 94 GHz show that reflection power at normal incidence decreases from about 48% at 24 GHz to 37% at 94 GHz due to the tissue’s frequency-dependent dielectric behaviour. The pseudo-Brewster angle, derived from complex ɛ*, identifies the condition of minimal reflection for parallel-polarized mmWaves and decreases with increasing frequency, matching theoretical expectations. At 40, 60, 80, and 100 GHz, the Cole-Cole-based pseudo-Brewster angles (76°, 75°, 74°, and 73°) and corresponding reflection coefficients (0.061, 0.054, 0.043, and 0.03) closely align with experimental reports in the literature, in the 60°-80° range. Unlike the simplified lossless model predicting zero reflection at the Brewster angle, this complex ε* approach captures realistic tissue loss and dispersion. At angles beyond the grazing-incidence threshold, most mmWave energy is reflected with negligible penetration. Since skin’s refractive index ( n ₂ > n ₁ ≈ 1), total internal reflection cannot occur. Hence, “grazing-incidence threshold” more accurately describes the observed behaviour.