An isomorphic Fourier transform analysis of AWGs and FBGs

We present a previously unknown equivalence relationship between the spectral transfer functions of arrayed-waveguide gratings and fiber Bragg gratings (FBGs). We find that both devices can be characterized using a functionally identical Fourier transform (FT) integral; the single difference being that 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 operation of the other device.