| Autor: |
Pandey, Siddhant, Bharadwaj, Sathwik, Santia, M., Hodek, M., Albrecht, J. D., Ram-Mohan, L. R. |
| Předmět: |
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| Zdroj: |
Journal of Applied Physics; 2018, Vol. 124 Issue 21, pN.PAG-N.PAG, 13p, 1 Diagram, 8 Charts, 11 Graphs |
| Abstrakt: |
We show that the present approaches for the solution of Maxwell's equations in complex geometries have limitations that can be overcome through the use of C (1) -continuous Hermite interpolation polynomials. Our approach of calculating fields using the Hermite finite element method yields better accuracy by several orders of magnitude than comparable applications of the edge-based vector finite element method. We note that the vector finite element that is widely used yields pixelated solutions and ill-defined vector solutions at nodes. Our solutions have a smooth representation within and across the elements and well defined directions for the fields at the nodes. We reexamine the issue of removing spurious zero-frequency solutions. We investigate fields in an empty cubic metallic cavity and explain the level degeneracy that is larger than what is to be expected from the geometrical O h symmetry of the cube. This behavior is identified as an example of "accidental degeneracy" and is explained in detail. We show that the inclusion of a smaller dielectric cube of relative permittivity ϵ 2 within the cubic cavity leads to the removal of this accidental degeneracy so that the eigenfields have the symmetry O h. A further reduction of symmetry is obtained by allowing the dielectric function in the enclosed cube to have a linear dependence on z. The proposed method should be effective in obtaining results for scalar-vector coupled field problems such as in modeling quantum well cavity lasers and in plasmonics modeling, while allowing multi-scale physical calculations. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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