Analytical Formulas for Dispersion and Effective Area in Hollow-Core Tube Lattice Fibers

Abstract

In this work, we propose analytical formulas for the estimation of dispersion properties and effective area of the fundamental mode of hollow-core inhibited coupling fibers with a microstructured cladding composed by a ring of dielectric tubes. The formulas are based on a model which has already been successfully applied to the estimation of confinement loss. The model takes into account the effects of the coupling of the fundamental core mode with the cladding modes in the context of the single-tube approximation. Effective index, group velocity dispersion, and effective area of the fundamental mode are estimated and compared with the results obtained from numerical simulations, by considering ten different fibers. The comparison shows a good accuracy of the proposed formulas, which do not require any tuning of fitting parameters. On the basis of the analysis carried out, a scaling law relating the effective area to the core radius is also given. Finally, the formulas give a good estimation of the same parameters of other Hollow-core inhibited coupling fibers, such as nested, ice-cream, and kagome fibers.

Analytical Formulas for Micro-Bending and Surface Scattering Loss Estimation in Tube Lattice Fibers

“…The condition can be re-written as λ = 2t/m n 2 d − n 2 g which is the resonant wavelength in the tube walls [11]. The approach is the same followed to obtain analytical formulas for CL [23], dispersion parameters, and effective area A ef f [27]. At frequencies approaching the highloss regions, the coupling between the FM and the cladding modes (CLMs) increases the electric field magnitude at the boundaries, and in turn this increases the EI value.…”

“…with γ = 3.5 • 10 −3 . Only the coupling with CLMs having azimuthal index µ = 1 is here considered, because they give the strongest coupling with the FM [27].…”

“…with n ef f being the FM effective index, R 0 the FM field radius, ∆β the phase constant difference between FM and LP 11 HOMs, and Φ the power spectral density (PSD) of the stochastic process describing the micro-bending. Recently, analytical formulas for the FM effective index n ef f and effective area A ef f have been proposed [27]. The effective index formula is based on Marcatili's one [24], but with an additional term ∆n ef f and an equivalent radius R co ef f :…”

“…∆n ef f takes into account the anti-crossing caused by coupling with cladding modes and R co ef f accounts for the hypocycloidal shape of the core-cladding interface. The effective area formula is based on the observation that the effective area is a function of the effective index [27]:…”

“…Black bars show the High-Loss Regions (HLRs) where PL is extremely high due to the coupling of the FM with cladding modes [26], [27]. We focus the accuracy estimation on the Transmission Bands (TBs) bounded by the HLRs.…”