Theoretical and Numerical Investigation of the Physics of Microstructured Optical Fibres

Abstract

We describe the theory and implementation of a multipole method for calculating the modes of microstructured optical fibers (MOFs). We develop tools for exploiting results obtained through the multipole method, including a discrete Bloch transform. Using the multipole method, we study in detail the physical nature of solid core MOF modes, and establish a distinction between localized defect modes and extended modes. Defect modes, including the fundamental mode, can undergo a localization transition we identify with the mode's cutoff. We study numerically and theoretically the cutoff of the fundamental and the second mode extensively, and establish a cutoff diagram enabling us to predict with accuracy MOF properties, even for exotic MOF geometries. We study MOF dispersion and loss properties and develop unconventional MOF designs with low losses and ultra-flattened near-zero dispersion on a wide wavelength range. Using the cutoff-diagram we explain properties of these MOF designs.