Simplified treatment for radiation mode in coupled-mode analysis

In coupled-mode analysis, an approximate treatment for radiation modes in open waveguides by equivalent leaky modes in equivalent closed waveguides is presented. The equivalent closed waveguide obtained by enclosing an open waveguide with properly designed PML (perfected matched layer) terminated by PEC (perfect electric conductor) consists of a complete set of orthogonally discrete complex modes. From the solution system of the present equivalent model, a finite number of equivalent leaky modes are chosen to represent the radiation modes to be known according to the condition of phase matching in mode couplings. The coupling with radiation modes is thus treated with the same fashion as that between guided modes and greatly simplified. The equivalent principles and schemes are discussed, meanwhile the effectiveness and accuracy of this treatment is validated by the simulation results of long period fiber gratings (LPG) with an outer cladding of a high or equal refractive index.