An isomorphic Fourier transform analysis of AWGs and FBGs

We present a previously unknown equivalence relationship between the spectr al transfer functions of arrayed-waveguide gratings and fiber Bragg grating s (FBGs). We find that both devices can be characterized using a functional ly identical Fourier transform (FT) integral; the single difference being t hat the FT lies within a simple hyperbolic function for the FBG case. Thus, the mode of operation of one device informs and yields insights into the o peration of the other device.