Analysis of diffraction efficiency of a holographic coupler with respect to angular divergence

We present a method to optimize the Coupling efficiency between two fibers using a Holographic Coupler taking diffraction effect into account. For this we obtain expressions for field distributions at the end facet of a fiber. The results obtained by using the expression is found to be in good agreement with the finite element method in literature, the small deviation is attributed to the negligence of field in the cladding. We then use the Kogelnik theory to obtain useful formulae suitable for diffracted optical elements. The diffraction efficiency expressions are then used to predict the different parameters of Holograting so as to get maximum diffraction efficiency in a direction where the field distribution from the end facet is minimum thereby increasing the coupling efficiency.