Abstract
In this paper, in accordance with fully anisotropic electromagnetic materials, the duality principle is successfully validated by the fully anisotropic finite-difference time-domain (FDTD) with Bloch-Floquet periodic boundary condition (BPBC), which in theory is first effectively applied to the verification of time-domain electromagnetic computation. Starting from the conventional duality principle of isotropy, those conditions can be given without any loss term. Without loss of generality, the electromagnetic duality rules involving dielectric and magnetic lossy tensors could be obtained by combining complex extension from original real parameters. In our further research, we introduce the duality principle into the BPBC cases, then execute and validate three different fully anisotropic models by means of the FDTD method under either TE or TM modes. From highly accurate numerical point of view, we apply ourselves to a more effective verification which can forecast the reflection and transmission coefficients and detect the subsurface echoes through the duality principle.
Highlights
Since the birth of computer, numerical techniques applied in electromagnetic field, such as finite-difference time-domain (FDTD) [3] et al, have launched the real-time research and simulated the exploration of the Maxwell’s Equations in the interdisciplinary cooperation, which promotes the industry progress of modern technology and provides the powerful calculating platform for manufacturing new materials
We develop a numerical prediction of duality principle with BlochFloquet periodic boundary condition (PBC) in three-dimensional (3D) fully anisotropic FDTD, the new contributions of this work are: (a) the verification of duality principle is presented under the specific relationship with fully anisotropy; (b) the duality principles of electric and magnetic loss tensors are derived under the Bloch-Floquet PBC; (c) with the Bloch-Floquet PBC, the cross-boundary calculation is successfully validated by the duality principle, and we can capture the almost same transmission results after the radiation of the plane waves when exchanging parameters
It is further turned out that the duality principle can be applied to the Bloch-Floquet PBC with the fully anisotropic FDTD in the multi-layered cases
Summary
To master the electromagnetic propagation in free space, we concentrate much on concrete fields and signal process in the final analysis. Thanks to the hypothesis of displacement current proposed by Maxwell in symmetry relation, it foreshadows that time-varying fields can form the outward radiation which has been validated by Hertz’s experiments afterward It is not the final destination for scientists in theoretical physics. We develop a numerical prediction of duality principle with BlochFloquet PBC in three-dimensional (3D) fully anisotropic FDTD, the new contributions of this work are: (a) the verification of duality principle is presented under the specific relationship with fully anisotropy; (b) the duality principles of electric and magnetic loss tensors are derived under the Bloch-Floquet PBC; (c) with the Bloch-Floquet PBC, the cross-boundary calculation is successfully validated by the duality principle, and we can capture the almost same transmission results after the radiation of the plane waves when exchanging parameters.
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