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AbstractPropagation of light through curved graded index optical waveguides supporting an arbitrary high number of modes is investigated. The discussion is restricted to optical wave fields which are well confined within the core region and losses through radiation are neglected. Using coupled mode theory formalism, two new forms for the propagation kernel for the transverse electric (TE) wave as it travels along a curved two-dimensional waveguide are presented. One form, involving the notiondoi:10.4208/cicp.211209.200710s fatcat:g7xas77sijhxdeczexan43kd44