Enhanced empirical relations for higher-order dispersions modeling in holey fibers

In this paper, a set of enhanced empirical relations is introduced to enhance the design process of silica-based photonic crystal fibers (PCFs). These relations, which apply to the U parameter and higher-order dispersions, depend solely on the air hole diameter and wavelength. The accuracy of these relations is rigorously validated by comparing them with results obtained from the finite-difference time-domain (FDTD) method. This approach offers a computationally efficient alternative to conventional methods, eliminating the need for extensive numerical simulations, time-consuming design processes, and complex coding. As a result, it enables a simplified and rapid evaluation of the fundamental properties and dispersion characteristics of PCFs, making it a powerful tool for dispersion engineering in various nonlinear applications. Moreover, the method not only improves computational efficiency but also accelerates the design and optimization processes, offering significant advantages over traditional simulation-based approaches.