Succinct way to diagonalize the translation matrix in three dimensions

W. C. Chew, S. Koc, J. M. Song, C. C. Lu, E. Michielssen

Research output: Contribution to journalConference articlepeer-review


The translation matrix for the three dimensional Helmholtz wave equation was successfully diagonalized using an alternative and succinct method. The method reveals the relationship between the translation matrices and their representation of the translation group. A diagonalization is expected under a plane-wave basis for the representation since a plane-wave basis forms an irreducible representation for the translation group. Hence, the diagonalization of the translation matrices from the spherical harmonic representation can be viewed as a series of similarity transforms. The result can be used in the fast multimode method where multiple scattering involves interaction between multipoles.

Original languageEnglish (US)
Pages (from-to)2072-2075
Number of pages4
JournalIEEE Antennas and Propagation Society, AP-S International Symposium (Digest)
StatePublished - 1997
EventProceedings of the 1997 IEEE Antennas and Propagation Society International Symposium. Part 1 (of 4) - Montreal, Can
Duration: Jul 13 1997Jul 18 1997

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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