Abstract
For the purpose of determining the transport properties of a two dimensional array composite consisting of rotated elliptical cylinders the Laplace transform can be used to obtain rapidly convergent representations for both the field expansions and the static lattice sums. Furthermore, these representations can be used to derive interesting analytic results involving the elliptic analogue of Rayleigh’s famous conditionally convergent dipole sum.
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References
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Botten, L., C., Nicorovici, N., A., Asatryan, A., A., McPhedran, R., C., de Sterke, C., M. and Robinson, P., A. (2000). Formulation for electromagnetic scattering and propagation through grating stacks of metallic and dielectric cylinders for photonic crystal calculations. Part 2: Properties and Implementation. Journal of the Optical Society of America A
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Reuben, A.J., Yardley, J.G., McPhedran, R.C. (2001). Laplace Transform Methods and the Rayleigh Identity for an Array of Elliptical Cylinders. In: IUTAM Symposium on Mechanical and Electromagnetic Waves in Structured Media. Solid Mechanics and Its Applications, vol 91. Springer, Dordrecht. https://doi.org/10.1007/0-306-46955-3_14
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DOI: https://doi.org/10.1007/0-306-46955-3_14
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-7038-3
Online ISBN: 978-0-306-46955-8
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