Analytical Theory of Grating Couplers for Waveguide Sensing: A Perturbational Approach and Its Limitations

摘要

The in-coupling process for grating-coupled planar optical waveguide sensors is investigated in the case of TE waves. A simple analytical model based on the Rayleigh-Fourier method is applied together with a perturbational technique to calculate analytical expressions for the guided wave amplitudes. In addition, analytical expressions are derived for the position correction and width of the in-coupling resonant peaks. Numerical computations verify the model for shallow gratings both in terms of peak shape and position and provide the limitations for the analytical formulas.