New insight into quasi leaky mode approximations for unified coupled-mode analysis

To facilitate the analysis of radiation mode couplings, quasi leaky mode approximations were utilized in coupled-mode analysis. The key to effectively and accurately apply this approach is how to well approximate radiation modes by the quasi leaky modes in an equivalent closed waveguide model. In this paper, the principle, applicability and accuracy of the approximations are demonstrated, and the detailed implementation is also suggested by applying a unified coupled-mode analysis to fiber gratings. First of all, based on a thorough study on the characteristics of the complex modes, for the first time, quasi leaky modes are classified into guided-mode-like inner-cladding and radiation-mode-like outer-cladding leaky modes so as to explicitly establish equivalence relationships between the discrete leaky modes and the continuous radiation modes. With this new insight, the whole analysis process especially for some of the practically tricky issues such as the criteria for developing the proper equivalent waveguide model and the subsequent mode expansion basis are better understood and easier to be dealt with for different problems where radiation modes come into play. Moreover, as essential preconditions to extend the conventional coupled mode analysis to the present unified one, the couplings between the guided core mode and a leaky mode are studied in a systematic and consistent manner. An intuitive and then a deep understanding on the roles of complex modes on mode coupling and power exchanging are thus gained for further simulations. Lastly, the transmission spectra of fiber gratings with different surrounding indices are simulated. The simulated results agree well with those obtained theoretically and experimentally in the literatures, which strongly validate the principle of quasi leaky mode approximations and its implementation on the unified coupled-mode analysis expounded in this paper.