COUPLED MODE FORMULATION BY RECIPROCITY AND A VARIATIONAL PRINCIPLE.

A new coupled-mode formulation has been described by means of two methods: a generalized reciprocity relation and a variational principle. Both give the same results. Exact analytical relations governing the coupling coefficients K//a //b and K//b //a (also K//a //b and K//b //a ) and the propagation constants of individual waveguide beta //a and beta //b ( gamma //a and gamma //b ) are derived. These relations are used to show that the formulation does satisfy the reciprocity theorem and power conservation analytically. Numerical results compared with the exact solutions and a previous method which contains a slight discrepancy show that the new formulation should be very useful and self-consistent.