Analysis of Kerr type nonlinear single-mode triangular index fiber directional coupler by a simple method

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We present the coupling characteristics of directional coupler comprising two identical single-mode triangular index fibers both in the presence and the absence of Kerr nonlinearity. Triangular index fibers of some typical V numbers are chosen for our investigation. Our analysis is based on the simple series expression for the fundamental modal field for triangular index fiber developed by Chebyshev technique. Analytical expression of the coupling length in the absence as well as in the presence of Kerr nonlinearity is prescribed. Using the said expression of coupling length, we apply a method of iteration to evaluate the said coupling parameter in the presence of Kerr nonlinearity. We also show that our results match excellently with the exact results obtainable by rigorous finite-element technique. The execution of our formalism requires little computation. Thus our simple but accurate formalism to study the triangular index directional coupler will prove a suitable alternative to the existing rigorous methods in the field of nonlinear optics. This user-friendly method will prove beneficial to the scientists and technologists working in the field of nonlinear optics.