Understanding formation of photonic bandgap edge for maximum propagation angle in all-solid photonic bandgap fibers

Abstract

We propose a simple formula that gives the effective refractive index of the first-order photonic bandgap (PBG) edge for the maximum propagation angle, which corresponds to the PBG floor in all-solid photonic bandgap fibers (PBGFs). In particular, based on an antiresonant reflecting optical waveguide (ARROW) theory incorporating a phase relation between resonant modes in low-index regions for perpendicular direction of the light propagation, we show that the effective index of the PBG edge at a wavelength does not depend on the diameter and refractive index of high-index rods, and is largely determined only by the pitch when normalized rod diameters are small. In other words, it has a constant value for the structural parameters with which the PBG emerges at the same wavelength normalized by the pitch. Moreover, the source of rod-diameter and refractive-index dependences on the condition for the formation of the PBG edge is demonstrated when the diameter and the refractive index of high-index rods are effectively large. Finally, the validity of the proposed simple formula, which can be applied for any structural parameters, is verified with the vectorial solver based on the finite-element method (FEM).