Low refractive-index-contrast Fresnel-microstructure fibre for coupling between SMF and photonic crystals

A method is described to efficiently couple light between single-mode fibre (SMF) and photonic crystals (PhCs) using a novel Fresnel-zone (FZ) MSF lens. In this study, the proposed FZ-MSF lens focuses light in a similar way to a graded-index (GRIN) rod lens, but instead of having a continuous parabolic refractive index variation, the MSF employs longitudinal FZs to focus light from SMF down to PhC dimensions, and vice-versa. Details on the equations describing the trajectory of a light ray in a medium with spatially-varying refractive index is also discussed.