Cladding-ring-equivalent effective index method for analyzing the propagation characteristics of multi-cladding photonic crystal fibers

Cladding-ring-equivalent effective index method (CREEIM) is proposed to analyze the propagation characteristics in the multi-cladding photonic crystal fibers (MCPCFs). The effective indices and dispersions of the step index two and three-cladding structures are calculated with the Sellmeier formula. The accuracy of CREEIM is competitive to the results calculated by the multipole method (MPM). With different structure parameters, the differences between two methods are evaluated with the relative error RE of effective index and relative difference RD of dispersion. This method is also used to analyze the mode cut-off and nonlinear characteristics in the three-cladding structure PCFs by calculating the mode effective index neff instead of complex mode field distribution.