A note on perfect revivals in finite waveguide arrays

Chremmos, Ioannis and Efremidis, Nikolaos K. (2012) A note on perfect revivals in finite waveguide arrays. Optics Communications, Elsevier, 285 (21-22). pp. 4364-4367. ISSN 0030-4018

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Abstract

We propose a simple and algorithmic method for designing finite waveguide arrays capable of diffractionless transmission of arbitrary discrete beams by virtue of perfect revivals. Our approach utilizes an inverse matrix eignevalue theorem published by Hochstadt in 1974, which states that the Jacobi matrix, describing the system’s discrete evolution equations, is uniquely determined by its eigenvalues and the eigenvalues of its largest leading principal submatrix, as long as the two sets of eigenvalues interlace. It is further shown that, by arranging the two sets of eigenvalues symmetrically with respect to zero, the resulting Jacobi matrix has zero diagonal elements. Therefore, arrays with arbitrary revival lengths can be obtained by engineering only the inter-waveguide couplings.

Item Type: Article
Subjects: Q Science > QC Physics
Depositing User: Dr Ioannis Chremmos
Date Deposited: 14 Sep 2012 08:51
Last Modified: 05 May 2017 16:01
URI: http://preprints.acmac.uoc.gr/id/eprint/144

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