Multifrequency Full-Wave Simulations of Vegetation Using a Hybrid Method

Abstract

In this article, we study wave propagation in vegetation at multiple frequencies using a hybrid method. First, the multiple scattering within a single plant is captured using the high-frequency structure simulator (HFSS) for extracting the T-matrix of the plant in vector cylindrical waves (VCW). Second, the Foldy–Lax equations (FLE) are applied with the extracted T-matrices to consider the multiple scattering among different plants. The accuracy of the hybrid method is verified by comparing the scattering results from nine wheat plants with direct HFSS simulations. The hybrid method is implemented with parallel computing using a physical iterative method to perform full-wave Monte Carlo simulations of a wheat field with up to 169 plants at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L$ </tex-math></inline-formula> -, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S$ </tex-math></inline-formula> -, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$C$ </tex-math></inline-formula> -bands. The impact of the gaps and the plant structure on the microwave propagations are studied by assessing the scattered fields and the resulting nonuniform transmission at different regions. The results are compared with modeling results using the classical radiative transfer equations (RTEs), and two major differences are observed: 1) the transmission calculated from the hybrid method is much larger than that of the RTE and 2) the full-wave simulation results show much weaker frequency dependence than RTE with saturation as frequency increases.