The calculation about the positions of self-imaging in a limited number of metal waveguide arrays

We investigative the field distribution in a limited number of nanostructured metal waveguide arrays. The precise positions of self-imaging are obtained. We derive the perturbation constant and the coupling constant by perturbation approach and supermode theory in a system that contains two adjacent waveguides. The perturbation constant and the coupling constant can also be applied to the systems that contain more than two adjacent waveguides. The cases of N \(=\) 3 and N \(=\) 4 are analyzed. Our theories are verified by the finite-difference time-domain method. Numerical simulation results show a good agreement with the theoretical predictions.