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. 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 a HCF with indefinite metamaterial cladding. We reveal design rules that allow engineering modal discrimination and show that metamaterial HCFs can have low losses at mid-IR wavelengths (< 1 dB/m at 10.6 um). 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.