Abstract
A fast integral equation approach to numerical modeling of electromagnetic wave penetration through a medium composed of discrete scatterers is described. The method utilizes a periodic extension of the fast Fourier transform-based compression of the impedance matrix. The medium is modeled as a doubly periodic slab, infinite in two lateral directions, and composed of periodicity cells. The individual periodicity cell can be filled with periodically, nearly periodically, or randomly arranged scatterers. Important advantages of the approach are as follows: (i) large-scale calculations with several million unknowns per periodic cell are possible due to the use of the compression scheme; (ii) the approach is equally applicable in a wide range of frequencies, scatterer sizes, and scatterer separations; (iii) the approach facilitates extraction of the effective material parameters and eliminates detrimental effects of boundaries associated with using a finite-size cell as a medium sample; and (iv) the approach is applicable to investigating possible traveling waves in periodic and partly disordered systems.
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Notes
- 1.
Our approach applies also to the case of scatterers covered with thin material sheets. In such problems Eq. (1) contains additional surface current components as well as terms responsible for local current–current couplings.
- 2.
The formulation applies also to the case when \(|{\bf{q}}_0|>{\rm k}\), which corresponds to propagation of a traveling (non-radiating) wave.
- 3.
Divergence of the multiple scattering series has also been observed in other computational techniques, such as the T-matrix methods, and alternative solutions are also used there.
- 4.
We also notice that, since the cross section \(\sigma _{\rm{t}} (A)\) is close to its geometrical limit 2A, even small errors may cause the computed transmission coefficient to become negative.
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Acknowledgments
We wish to acknowledge the support of the Air Force Office for Scientific Research under the contract no. FA9550-05-C-0037.
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Bleszynski, E., Bleszynski, M., Jaroszewicz, T. (2010). Rigorous Modeling of Electromagnetic Wave Interactions with Large Dense Systems of Discrete Scatterers. In: Sabath, F., Giri, D., Rachidi, F., Kaelin, A. (eds) Ultra-Wideband, Short Pulse Electromagnetics 9. Springer, New York, NY. https://doi.org/10.1007/978-0-387-77845-7_8
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