A New Method For Coupled-Wave Theory Of Directional Couplers

With the development of optical-fiber communications, the optical-fiber directional couplers are particularly demanded. The design is required more and more with the development of technology. So the weak coupling theory is newly appraised. And a more rigorous one is developed, which is very innovational and can instruct the couplers development. In this paper, base on the weak coupling theory, the improved coupled-mode theory has simple mathematics format and is of great physical significance are developed, which can embody the science' continuity and innovation.Firstly, when the distance between the cores is small enough, we suppose the original fibers' modes remain unchanged but the overlap integral S is large between the evanescent fields of two fibers. Based on the Maxwell Equation, the coupled-modes theory with non-orthogonal fibers' modes at the coupling zone is analyzed. Then the coupling equations and the simple formulas of the output powers are obtained, which are compared with those from the weak coupling theory.Secondly, an improved coupled-mode theory is presented. In this theory, the local orthogonal modes are introduced in terms of a unitary transformation to the original fibers' non-orthogonal modes, in which the overlap integral S between the evanescent electromagnetic fields of two fibers is considered as parameter. Then a couple of coupling mode equations of local modes and the analytical solutions to these equations can be obtained. The zero-order term in these solutions are in accordance with those deduced from the weak coupling theory.