The field distribution in a finite number of nanostructured metal waveguide arrays

We investigative the field distribution in nanostructured metal waveguide arrays. Firstly, we analyze a simple discrete system containing two adjacent metallic waveguides (N=2). The propagation constants β1 and β2 can be calculated by a rigorous field analysis approach. According to the supermode theory of conventional dielectric waveguide arrays, we can also obtain the expressions of propagation constants. So we can obtain the coupling constant and the perturbation constant of the expressions in the supermode theory. Next, we consider a system that contains five adjacent metal waveguides (N=5). The propagation constants and the wavefunctions of the supermodes can be obtained according to the coupling constant, the perturbation constant, and the supermode theory. The incident light is located at the input of the 4st waveguide. The initial excited field can be expressed as a sum of supermodes. The total field is formed by the superposition of supermodes. The variation of field amplitude with propagation distance is obtained and can predict the precise positions of the field distribution. To demonstrate the analytical results, we numerically simulate the field distribution in the waveguides (N=5) constructed with silver by the finite-difference time-domain method. The numerical simulation results show a good agreement with theoretical expectations.