In this paper, we develop and present a complete analytical method to analyze the spectral response of a non-uniform multimode fiber Bragg grating assisted devices supporting a few modes. We present the analytical solution while taking into account the two forward and two backward propagating even or odd normal modes of the grating using the matrix method of multimode coupled grating assisted coupler, for sensing application. Earlier, these types of numerical technique based analysis were presented by other researchers, but no one seems to present a complete analytical solution for the given case. The present analytical analysis can simulate a single mode to multimode coupled sensing waveguide devices based on non-uniform grating assisted operation in a coupled structure. The potential applications of our findings will be mostly in sensing devices.
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