In this paper, we use electromagnetic homogenization techniques to model the effective permittivity of graded ellipsoidal particles, with relevance to applications in biomedicine. Using the electrostatic approximation, we analyze a single graded ellipsoid and a suspension of randomly oriented ellipsoidal particles. Analytical results for graded and isotropic particles, individually or in a suspension, demonstrate variations in effective permittivity depending on the particle grading profile, aspect ratio, and volume fraction of particles to the surrounding medium. These findings enable more accurate predictions of their functional performance, such as their electromagnetic absorption, and provide insight into the electromagnetic behavior of such particles in biomedical applications.

We study TE-wave propagation in a circular waveguide with a graded transition from a lossy right-handed material (RHM) filling the left-hand half of the waveguide to the impedance-matched lossy left-handed material (LHM) filling the right-hand half of the waveguide. We obtain exact analytical solutions to Maxwell's equations and perform corresponding numerical simulations in COMSOL. An excellent agreement is obtained between the numerical simulations and analytical results. The presented method can model smooth realistic material transitions, where the interface width is an additional degree of freedom in the design of practical RHM-LHM interfaces.