Unified Approach for Coupling to Cladding and Radiation Modes in Fiber Bragg and Long-Period Gratings

Couplings of core mode to guided cladding and unguided radiation modes in fiber Bragg and long-period gratings are investigated by a unified approach based on complex mode matching method (CMMM). With the combination of the perfectly matched layer (PML) and the perfectly reflecting boundary (PRB), the continuous radiation modes can be well represented by a set of discrete complex modes so that simulation of coupling to radiation modes is greatly simplified and may be treated in the same fashion as guided modes. Numerical results of fiber Bragg and long-period gratings with refractive index of the outer cladding lower, equal, and higher than that of the inner cladding indicate that the unified approach is highly effective in the simulation of couplings to cladding and radiation modes.