Terahertz-wave scattering in tissues: Examining the limits of the applicability of effective-medium theory

Terahertz (THz) technology offers a variety of applications in medical spectroscopy and imaging. In such applications, tissues are commonly assumed to be optically homogeneous at the THz-wavelength scale, while the THz-wave-tissue interactions are described (in a simplified manner) within the effective medium theory (EMT). Meanwhile, recent studies of tissues from human, animal, and plants involving emerging modalities of superresolution (beyond the Abbe diffraction limit) THz microscopy, have found tissue inhomogeneities with dimensions comparable to the THz wavelength (approximately lambda), which can lead to THz-wave scattering effects. This poses a problem of studying an interplay between the THz-wave absorption and the scattering phenomena in soft turbid tissues. To mitigate this challenge, in this paper, a tissue-mimicking phantom is developed that has the form of a gelatin slab, as a highly absorbing hydrated matrix, into which silicon dioxide (SiO2) microparticles are embedded, with their lower refractive index and loss and subwavelength or mesoscale diameters. The analytical methods of Lorenz-Mie scattering theory have predicted a nonisotropic differential extinction cross section for such scatterers, which results in the non-Rayleigh scattering regime and casts doubt on the applicability of EMT for such tissues. Surprisingly, we have found theoretically, using the radiative transfer theory (RTT), and confirmed experimentally, using THz pulsed spectroscopy, that the effective optical properties of the proposed phantom are still determined by EMT over wide ranges of the diameters (d <= 0.47 lambda) and volume fractions (f(v)<= 0.2) of the scatterers. This effect was attributed to the strong THz-wave loss in a host medium and, therefore, should be general for a variety of soft tissues in the THz range. Thus, our findings hopefully broaden the applicability of EMT for describing the interactions between THz radiation and soft turbid tissues.