Closed-form, localized wave solutions in optical fiber waveguides

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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. We present a theoretical feasibility study that shows the existence of LW solutions in optical fiber waveguides. As with the free-space case, these optical waveguide LW solutions propagate over long distances, undergoing only local variations. Four different source modulation spectra that give rise to solutions similar to focus wave modes, splash pulses, the scalar equivalent of Hillion’s spinor modes, and the modified power spectrum pulses are considered. A detailed study of the modified power spectrum pulse is performed, the practical issues regarding the source spectra are addressed, and the distances over which such LW solutions maintain their nondecaying nature are quantified.