Abstract
We review the basis of the Rayleigh multipole method for scattering and propagation problems in photonics and phononics. The method assumes the corresponding problem for a single inclusion has been solved, and generalizes the solution to a periodic array of such inclusions. We discuss the link between the method and representations of Green’s functions involving lattice sums.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Abramowitz, M. and Stegun, I. A., editors (1972). Handbook of Mathematical Functions, pages 355–433. Dover, New York.
Glasser, M. L. and Zucker, I. J. (1980). Lattice sums. Theoretical Chemistry: Advances and Perspectives, 5:67–139.
Movchan, A. B., Nicorovici, N. A., and McPhedran, R. C. (1997). Green’s tensors and lattice sums for elastostatics and elastodynamics. Proc. R. Soc. Lond. A, 453:643–662.
Nicorovici, N. A., McPhedran, R. C., and Botten, L. C. (1995). Photonic band gaps: non-commuitng limits and the “acoustic” band. Phys. Rev. Lett., 75:1507–1510.
Perrins, W. T., McKenzie, D. R., and McPhedran, R. C. (1979). Transport properties of regular arrays of cylinders. Proc. R. Soc. Lond. A, 369:207–225.
Poulton, C. G., Botten, L. C., McPhedran, R. C., Nicorovici, N. A., and Movchan, A. B. (1999a). Boundary layers and non-commuting limits in electromagnetic scattering. SIAM J. Appl. Math. submitted.
Poulton, C. G., Movchan, A., McPhedran, R., Nicorovici, N., and Antipov, Y. A. (1999b). Eigenvalue problems for doubly periodic elastic structures and hononic band gaps. Proceedings of the Royal Society London. submitted
Strutt, J. W. (1892). On the influence of obstacles arranged in rectangular order upon the properties of a medium. Phil. Mag., 34:481–502.
Twersky, V. (1961). Elementary function representations of Schlömilch series. Arch. Rational Mech. Anal., 8:323–332.
von Ignatowsky, W. (1914). Zur Theorie der Gitter. Ann. Physik, 44:369–436.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2001 Kluwer Academic Publishers
About this paper
Cite this paper
McPhedran, R.C., Nicorovici, N.A., Botten, L.C., Movchan, A.B. (2001). Advances in the Rayleigh Multipole Method for Problems in Photonics and Phononics. 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_2
Download citation
DOI: https://doi.org/10.1007/0-306-46955-3_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-7038-3
Online ISBN: 978-0-306-46955-8
eBook Packages: Springer Book Archive