Long wavelength behavior of the fundamental mode in microstructured optical fibers

Abstract

Using a novel computational method, the fundamental mode in index-guided microstructured optical fibers with genuinely infinite cladding is studied. It is shown that this mode has no cut-off, although its area grows rapidly when the wavelength crosses a transition region. The results are compared with those for w-fibers, for which qualitatively similar results are obtained.

Accurate Defect Mode Modelling in Photonic Crystals Using the Generalised Fictitious Source Superposition Method

“…In such cases, the computational requirements of modelling a sufficiently large structure can be overwhelming or lead to inaccurate results. To handle problems of this type, we have developed an exact theory [2] known as the fictitious source superposition (FSS) method for computing defect modes in a genuinely infinite 2D lattice and have applied it to the study of the long-wavelength behaviour [3] of microstructured optical fibres (MOFs). Not only does our approach handle MOFs with an infinite cladding, but also it is computationally more efficient than other techniques when the size of the structure becomes large.…”

“…Not only does our approach handle MOFs with an infinite cladding, but also it is computationally more efficient than other techniques when the size of the structure becomes large. While our original treatment [2] of the FSS method was a useful tool that helped resolve the controversy about the existence of a cutoff of the fundamental mode in a MOF [3], it was restricted to modelling only simple defects, i.e., a single defect in a single row of scatterers. The purpose of this paper is to extend the theory to accommodate arbitrary defects comprising compound defects (i.e., with a multiplicity of cylinders removed or modified) in multiple rows of an infinite photonic crystal [4].…”

Rigorous sufficient conditions for index-guided modes in microstructured dielectric waveguides

“…First, even if ∆ε is strictly non-negative, is there a guided mode at every wavelength, or is there the possibility of e.g. a long-wavelength cutoff (as was initially suggested in holey fibers [15], but was later contradicted by more careful numerical calculations [16])? Second, what if ∆ε is not strictly non-negative, i.e.…”

Exact modelling of generalised defect modes in photonic crystal structures

“…In order to deal with this class of problems, we developed an exact theory [2], known as the fictitious source superposition (FSS) method, for computing defect modes in an infinite 2D lattice, applying it to the study of the long-wavelength behaviour of PC fibres (PCFs) [3], and demonstrating unambiguously that the fundamental mode was never cut off. While our original implementation [2] was a useful tool, it is nevertheless limited to handling only simple (single cylinder) defects.…”