Shooting and Bouncing Rays for Sparse Particles (SBR-SP) Applied for Multiple Magnetodielectric Circular Cylinders

A numerically efficient method, called shooting and bouncing rays for sparse particles (SBR-SP), is proposed to analyze large 2-D arrays composed of magnetodielectric circular cylinders. These cylinders can be positioned anywhere on the
$xy$
plane and have various sizes and media. We employ both iterative- and closed-form versions of SBR-SP to investigate the convergence and accuracy of large cylinder arrays. A comparison with results obtained using a mode-matching technique (MMT) also reveals excellent agreement. Especially, the closed-form of SBR-SP, when Gaussian elimination is graphics processing unit (GPU)-accelerated, proves to be fast and accurate, allowing us to analyze various echowidth behaviors of an
$80 \times 80$
square array within just 71.8 s. In addition, we conduct a statistical analysis for a randomly distributed array consisting of 6400 elements focusing on mean and standard deviation. Our findings indicate that the initial shooting rays excited by the incident field strongly dominate the statistical behaviors of scattering patterns. We also compute a random
$10 \times 10$
square array comprised of lossy dielectric circular cylinders using both our method and a commercial software package. The two scattering results show favorable agreement, and we observe that our method outperforms the commercial package significantly in terms of computation speed.