Analysis of buried parabolic index segmented channel waveguides with z-dependent profile

We analyze, to the best of our knowledge, for the first time buried parabolic index segmented channel waveguides, with high-index segments having a z-dependent refractive index variation. Using the standard ABCD ray transfer matrices for Gaussian beam propagation, we obtain the dependence of effective index, spot-size, amplitude and phase fronts of the guided modes on various waveguide parameters. Stability conditions are obtained for various cases. The analysis is used to study segmented waveguides fabricated using femtosecond laser inscription method; the experimentally observed dependence of stability on the duty cycle of segmentation is explained. ► Buried parabolic index segmented channel waveguides with high-index segments having a z-dependent refractive index variation is presented. ► Analysis is used to study segmented waveguides fabricated using femtosecond laser inscription method. ► The analysis could be used to analyze periodic segmented waveguides with other transverse dependences than infinitely extended parabolic profiles, in terms of modal spot sizes, stable regions of operation, and effective index variation with period and duty cycle of segmentation. ► The analysis offers flexibility to change the gradation parameters and refractive index function along z to realize new waveguide devices.