PhotonIcs and Electromagnetics Research Symposium,
also known as Progress In Electromagnetics Research Symposium
PIERS Proceedings
Published: 2015-07-09
Exponential Regularization of EM Dyadic Green's Functions via Green's Function-induced Dirac δ-functions
By
Proceedings of 2015 Photonics & Electromagnetics Research Symposium, Prague, July 6 - 9,Page(s)1542-1547
Abstract
In a series of recently published contributions it was shown that singular or hyper- singular dyadic Green’s functions (GFs) in computational electrostatics and electromagnetics can be utilized to construct problem-specific integral representations of the Dirac δ-function, leading to parametrized smeared out δη -functions, which tend to the Dirac δ-function for the parameter η approaching 0+ . It was also shown that the constructed δη -functions can be employed to reg- ularize originating GFs associated with Poisson equation in isotropic and anisotropic dielectrics. The main result of the present paper is that the constructed δη -function is used to regularize dyadic GFs associated with Maxwell’s equations in isotropic media. The formulae arising in the formulation are all expressed in closed-form in spectral domain, allowing deep insights into the dynamics of the proposed regularization method. Complex media do not permit construction of GFs in closed form. Consequently, the integral representations for the δη -functions cannot be expressed in closed-form either. A recipe is proposed for numerically calculating δη -functions in asymptotic form. This result is claimed to present a genuine contribution to the computational physics. Applications in which near field phenomena play a role, e.g., nanoscopic and plasmonic devices will benefit from the results.
Citation
Alireza Baghai-Wadji, "Exponential Regularization of EM Dyadic Green's Functions via Green's Function-induced Dirac δ-functions," Proceedings of 2015 Photonics & Electromagnetics Research Symposium, Prague, July 6 - 9,Page(s)1542-1547
References

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