Localized wave solutions in optical fiber wavelengths

Abstract

A novel bidirectional decomposition of exact solutions to the scalar wave equation has been shown to form a natural basis for synthesizing localized wave (LW) solutions that describe localized, slowly decaying transmission of energy in free space. In this work, we demonstrate the existence of LW solutions in optical fiber waveguides operated in the linear regime. In this sense, these solutions are fundamentally different from the non-linear, soliton-based communication systems. Despite the dielectric waveguiding constraints introduced by the fiber, solutions that resemble the free-space solutions can be obtained with broad bandwidth source spectra. As with the free-space case, these optical waveguide LW solutions propagate over very long distances, undergoing only local variations. Four different source modulation spectra that give rise to solutions similar to Focus Wave Modes (FWM’s), splash pulses, the scalar equivalent of Hillion’s spinor modes and the Modified Power Spectrum (MPS) pulses are considered. A detailed study of the MPS pulse is performed, practical issues regarding source spectra are addressed, and distances over which such LW solutions maintain their non-decaying nature are quantified. Present day state-of-the-art technology is not capable of meeting requirements that will make practical implementation of LW solution-based fiber optic systems a reality. We address futuristic technology issues and briefly describe efforts that could lead to efficient LW solution-based fiber optic systems.