A modal transfer matrix method for analysis of Bragg and long-period optical fiber gratings

A new general purpose technique, the modal transfer matrix method (MTMM) is developed here to extend the study of complex optical waveguide systems beyond the capability of coupled mode theory (CMT). It is applied to overcome the numerical accuracy limitation of the finite difference beam propagation method (FDBPM) when simulating long-period gratings (LPG) and the accuracy limitation of the finite difference time domain method (FDTD) when simulating Bragg gratings. Simulation of these gratings with a broad-wavelength source using the MTMM is shown to be in agreement with analytical results based on CMT. 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 is selected to compute each element's modal transfer matrix. The elements are then combined to predict the output from the overall waveguide system. Grating parameter studies show the potential effect of combined variation in the grating amplitude, spatial wavelength, and length on the transmission spectrum. An axial strain study compared MTMM predictions of resonant source wavelength sensitivity with experimentally measured sensitivities. For the Bragg grating case, experimental and simulation sensitivities achieved agreement. Their differences were within a range of about 30% of the experimental sensitivities. For the LPG case, experimental and simulation sensitivities did not achieve agreement. The predicted sensitivities were outside the sample error tolerance for the experimental data. Contrary to the simulation predictions, the LPG experimental fibers showed little strain sensitivity. This discrepancy is attributed to both the analysis of experimental strain and to aspects of the simulation. It is expected that closer agreement will be achieved with further work.