Full Vector Complex Coupled Mode Theory for Tilted Fiber Gratings

A full vector complex coupled mode theory (CMT) for the analysis of tilted fiber gratings is presented. With the combination of the perfectly matched layer (PML) and the perfectly reflecting boundary (PRB), the continuous radiation modes are well represented by a set of discrete complex modes. Simulation of coupling to radiation modes is greatly simplified and may be treated in the same fashion as guided modes. Numerical results of the tilted fiber Bragg gratings (TFBGs) with outer-cladding index equal, lower and higher than that of the inner-cladding indicate that the complex coupled mode approach is highly effective in the simulation of couplings to cladding and radiation modes in tilted fiber gratings. The reflective TFBGs are investigated by the proposed approach in detail.