A note on perfect revivals in finite waveguide arrays |
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| Authors: | Ioannis D Chremmos Nikolaos K Efremidis |
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| Institution: | 1. Department of Electronic Engineering, Xi’an University of Technology, Xi’an 710048, China;2. School of Optoelectronic Engineering, Xi’an Technological University, Xi’an 710032, China;3. Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China;1. Centro de Investigación en Ingeniería y Ciencias Aplicadas (CIICAp), Universidad Autónoma del Estado de Morelos (UAEM), Av. Universidad 1001, Col. Chamilpa, 62210 Cuernavaca, Morelos, Mexico;2. Departamento de Óptica, Instituto Nacional de Astrofísica Óptica y Electrónica, Luis Enrique Erro No. 1, A.P. 51 y 216, C.P. 72000, Tonantzintla, Puebla, Mexico;3. Universidad Autónoma de Tamaulipas, Matamoros 8 y 9, Col. Centro, C.P. 87000, CD. Victoria, Tamaulipas, Mexico;4. CREOL, The College of Optics and Photonics, University of Central Florida, 4000 Central Florida Blvd., Orlando, FL 32816, USA |
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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 utilises an inverse matrix eigenvalue 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. |
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