Treatment of Inhomogeneous Dielectric Boundaries

In the case of an inhomogeneous dielectric, serving as a boundary or an intermediate layer, onesided difference operators have to be reformulated in order to circumvent possible instabilities. The key concept for these amendments, which lies on the efficient analysis of [20,23], presumes an explicit (2, 4) FDTD approach in the homogeneous areas of the computational space and 

FIGURE 2.6 (a) A 1-D interface separating two different media and the auxiliary distances d, d. (b) A vertical dielectric slab in a 2-D computational domain 

It is stressed that the stencils of (2.55) do not generate any artificial oscillations even if the interface is in very close proximity to a lattice node, guaranteeing so a uniformly bounded time-step approach. 

Should the dielectric interface be positioned at L + 1/2, i.e., at a magnetic field node, the role of Ez and Hy is reversed with the former provided by 

As a conclusive remark, it is stated that the fairly sufficient performance of (2.55)-(2.61) deteriorates with the increase of the contrast between the dielectric constants. This problem is, essentially, attributed to the faster loss of smoothness at the dielectric interface and the consequent augmentation of the dispersion error. 

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