Vector Fields and Dispersion of Fiber Cladding Modes near Crossover

We obtain exact solutions for high-order hybrid cladding modes of standard fibers, paying special attention to the case in which two hybrid cladding modes have very close propagation constants (crossover points). We calculate the mode fields, dispersion, and polarization distribution of cladding modes at crossover. We discuss the applicability of the linearly polarized modes approximation for calculating modes in this case. We show that, at the crossover points, the modes are not standard HE and EH hybrid modes but radial and azimuthal modes with field distributions resembling those of TE and TM modes. We analyze the dispersion of hybrid modes with azimuthal number equal to 1 and find crossover points in the range 0.6–1.7 μm for fibers with various V-numbers. For standard fibers, the first 23 hybrid modes have crossovers at wavelengths below 1.2 μm. Accounting for the new hybrid modes reveals the splitting of resonances in long-period fiber gratings. A linear combination of crossover modes can be used to form approximate HE and EH modes with uniform linear polarization for the HE mode and a magnetic-dipole-like field for the EH mode.