Comparison of a new modal transfer matrix method with coupled-mode theory for simulation of long-period grating fiber sensors

The modal transfer matrix method (MTMM) is a new general- purpose technique developed by the authors as an alternative to coupled mode theory (CMT) to study complex optical waveguide systems. It is applied here to overcome the numerical accuracy limitation of the beam propagation method (BPM) when simulating long-period gratings (LPG). Simulation of a LPG optical fiber sensor with a broad-wavelength source using the MTMM is compared with analytical results based on CMT. A simple grating parameter study shows that both methods are in agreement, indicating that the MTMM is a promising method of analysis. In addition, the results reveal the potential effect of combined variation in grating amplitude, spatial wavelength, and length on sensor performance. By discretizing the waveguide into small elements, the MTMM reduces the problem domain size and makes use of proven electromagnetic numerical simulation methods. An appropriate numerical method, in this case the BPM, is selected to compute each element's modal transfer matrix. The elements are then combined to predict the output from the overall waveguide system.