Analytic model for the complex effective index dispersion of metamaterial-cladding large-area hollow core fibers

We present a mathematical model that allows interpreting the dispersion and attenuation of modes in hollow-core fibers (HCFs) on the basis of single interface reflection, giving rise to analytic and semi-analytic expressions for the complex effective indices in the case where the core diameter is large and the guiding is based on the reflection by a thin layer. Our model includes two core-size independent reflection parameters and shows the universal inverse-cubed core diameter dependence of the modal attenuation of HCFs. It substantially reduces simulation complexity and enables large scale parameter sweeps, which we demonstrate on the example of a HCF with a highly anisotropic metallic nanowire cladding, resembling an indefinite metamaterial at high metal filling fractions. We reveal design rules that allow engineering modal discrimination and show that metamaterial HCFs can principally have low losses at mid-IR wavelengths (< 1 dB/m at 10.6 µm). Our model can be applied to a great variety of HCFs with large core diameters and can be used for advanced HCF design and performance optimization, in particular with regard to dispersion engineering and modal discrimination.