Equivalent circuit of Bragg gratings and its application to Fabry-Pérot cavities

An equivalent circuit of both uniform and apodized symmetrical Bragg gratings is proposed, consisting of an ideal partially reflecting mirror placed between two wavelength-dependent uniform propagating sections. The model is simple, exact, and valid for every wavelength; it can be combined with other port-based models and is of great aid in the analysis and design of devices containing two or more Bragg gratings. As an application, the synthesis of dispersive Bragg gratings based Fabry-Pérot cavities is demonstrated. The conditions under which a Bragg-grating-based Fabry-Pérot cavity behaves exactly as an ideal dispersive Fabry-Pérot cavity are discussed. Experimental results that confirm the theoretical spectral response calculated by using the equivalent circuit are reported.