A vector boundary matching technique for efficient and accurate determination of photonic bandgaps in photonic bandgap fibers

Abstract

A vector boundary matching technique has been proposed and demonstrated for finding photonic bandgaps in photonic bandgap fibers with circular nodes. Much improved accuracy, comparing to earlier works, comes mostly from using more accurate cell boundaries for each mode at the upper and lower edges of the band of modes. It is recognized that the unit cell boundary used for finding each mode at band edges of the 2D cladding lattice is not only dependent on whether it is a mode at upper or lower band edge, but also on the azimuthal mode number and lattice arrangements. Unit cell boundaries for these modes are determined by mode symmetries which are governed by the azimuthal mode number as well as lattice arrangement due to mostly geometrical constrains. Unit cell boundaries are determined for modes at both upper and lower edges of bands of modes dominated by m = 1 and m = 2 terms in their longitudinal field Fourier-Bessel expansion series, equivalent to LP0s and LP1s modes in the approximate LP mode representations, for hexagonal lattice to illustrate the technique. The novel technique is also implemented in vector form and incorporates a transfer matrix algorithm for the consideration of nodes with arbitrary refractive index profiles. Both are desired new capabilities for further explorations of advanced new designs of photonic bandgap fibers.