Analytic Solutions for the Spectral Responses of RCA-Grating-Based Waveguide Devices

Analytic solutions (ASs) for the spectral responses of waveguide devices with raised-cosine-apodized (RCA) gratings are presented. The waveguide devices include short- and long-period RCA-gratings, RCA-grating-based interferometers as Fabry–Perot, Mach–Zehnder and Michelson interferometers. The calculations based on the analytic solutions are demonstrated and compared with those based on the transfer matrix (TM) method preferred, which has confirmed that the AS-based analysis is with enough accuracy and several thousands times the efficiency of the TM method.