Coupled Mode Theory for Surface Plasmon Polariton Waveguides

In allusion to special modes supported by surface plasmon polariton (SPP) waveguides, explicit expression for mode coupling coefficient which plays a central role in coupled mode theory is firstly redefined by adding the longitudinal electric field component. The mode coupling coefficients calculated by the proposed formula improve greatly compared with the coupled mode theory suited to conventional optical waveguides, and reasonable explanations from the point of view of physics and mathematics have been given. Afterwards, the coupling lengths, the transmission lengths, the normalized power exchanges, and the cross talk performances of adjacent parallel SPP waveguides with varying waveguide separation distances D and waveguide lengths L are investigated at telecom wavelength. The results are encouraging as they indicate that the coupled mode theory is developed in a self-consistent manner by retaining the longitudinal electric field component in the derivation and neglecting it only when the waveguides structure satisfies the weakly guiding situations. As a result, the new mode coupling coefficient formula for SPP waveguides considered in this paper is an important complement in the theory of SPP waveguides.