Supercell lattice method for photonic crystal fibers

Abstract

A supercell lattice method, believed to be novel, deduced from the plane-wave expansion method and the localized basis function method, is presented for analyzing photonic crystal fibers (PCFs). The electric field is decomposed by use of Hermite-Gaussian functions, and the dielectric constant of PCFs missing a central air hole is considered as the sum of two virtual different periodic dielectric structures of perfect photonic crystals (PCs). The structures of both virtual PCs are expanded in cosine functions. From the wave equation and the orthonormality of the Hermite-Gaussian functions, the propagation characteristics of the PCFs, such as the mode field distribution, the effective area, and the dispersion property, are obtained. The accuracy of the novel method is demonstrated as we obtain the same results when the dielectric constant is split into two virtual ideal PCs in different ways.

Photonic Crystal Fibers

“…The supercell lattice method is a combination of PWE and LBF methods [17]. The electric field is decomposed by use of Hermite-Gaussian functions.…”

Birefringence Analysis of Photonic-Bandgap Fibers Using the Hexagonal Yee's Cell

“…Similarly, the elimination of and from (2) using (4) and the corresponding equation for leads to (6) As detailed in Section III, (5) and (6) and the equivalent expressions for the other field components, for all grid points in a particular computational window, can be written in a matrix form. The eigenvalues and eigenvectors of this matrix yield the modes' effective indexes and their field profiles.…”

“…To implement sub-pixel averaging scheme, we need to modify (5), (6), and the corresponding equations for other transverse fields, so that they account for an anisotropic dielectric with such a permittivity tensor. Note that (3) and (4), which are derived from the discretization of (independent of refractive index), remain unchanged.…”

“…Either the set of (5), (6), and their equivalents for other transverse fields (isotropic case, no averaging) or the set of (5), (12) and their equivalents (pixel-averaged expressions), can be written in a general matrix form:…”

“…In order to most accurately describe the modal properties of a photonic-bandgap fiber, the grid should have the same symmetry as the fiber. It has been shown [4], [6], [10], [16], [20] that for a fiber with symmetry, failing to use a grid with this symmetry leads to substantial numerical birefringence.…”