By taking the coupling between the non-neighbourhood waveguides into account, the coupling characteristic of three waveguide arrays is analysed. The strong coupling equation of three waveguides is dealt with Laplace transform and LU decomposition. The general field evolution equation is obtained by inversion of the Laplace transform. The results show that the self-imaging conditions (Talbot effect) do not satisfy in general. The theoretical predictions are in good agreement with the BPM simulations.
[1] Talbot H F 1836 Philos. Mag. 9 401 [2] Bryngdahl O 1973 J. Opt. Soc. Am. 63 416 [3] Packross B, Eschbach R and Bryngdahl O 1986 Opt.Commun. 56 394 [4] Leger J R and Swanson GJ 1990 Opt. Lett. 15 288 [5] Soldano L B and Pennings E C 1995 J. LightwaveTechnol. 13 615 [6] Robert I, Daniel A M, Demetrios N C and George I S 2005 Phys. Rev. Lett. 95 053902 [7] Nikolaos K E and Demetrios N C 2005 Opt. Commun. 246 345 [8] Compiling Group of Mathematics Manual 2004 Mathematics Manual (Beijing, Higher Education Press) chap 4 (inChinese) [9] Marcuse D 1991 Theory of Dielectric OpticalWaveguides (San Diego: Academic) chap 5 [10] Hunsperger R G 1984 Integrated Optics: Theory andTechnology 2nd edn (Berlin: Springer) chap 8 p 141