A function is constructed to approximate the fundamental mode field precisely in photonic crystal fibers (PCFs) using least square error criteria. Through the unconstrained nonlinear programming method, the optimum parameters of the constructed function are derived, and the optimum constructed function is found. For photonic crystal fibers, using such an optimum constructed function, small errors are brought out when approximating their fundamental mode fields regardless of d/Λ values. Furthermore, the constructed function is not only suitable for index-guiding PCFs, but also for bandgap PCFs with hollow core to some extent. Based on this constructed function, an analytic expression for the far field of the approximated fundamental mode field is deduced. Numerical results demonstrate that the analytic expression brings out small errors compared with the actual far field.
"Study of a constructed function for approximating mode field in photonic crystal fibers," Optical Engineering 51(6), 065003 (5 June 2012). https://doi.org/10.1117/1.OE.51.6.065003