Quantum model for waveguide transverse coupling

In variation calculus, the Fermat’ s theory is similar to the Hamilton’ s theory except that Hamilton’ s theory uses time as the independent variable to achieve minimum of a function while Fermat’ s theory uses space as the independent variable1. That is one of the essential differences between dynamics and optics. When time coordinate t in dynamics is substituted by space coordinate z, and generalized momentum is introduced, optics is obviously similar to dynamics. Thus, we can use corresponding quantum mechanics methods to handle similar phenomena in optics. First, in this paper, the concept of potential energy of Hamilton operator is introduced. Based on this, the law of energy minimization of a system, which is composed of two parallel waveguide, is used to deal with the transverse coupling between them. A more understandable result is gotten and the comparison between the results of classical electromagnetic methods is discussed.