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Dielectric waveguide (DWG) interconnects frequently utilize multimode waveguides due to their low dispersion in the fundamental mode. However, these links are more vulnerable to cross-modal coupling that significantly impacts their overall performance. This study presents a technique aimed at minimizing the coupling of energy into higher-order modes within weakly coupled rectangular dielectric waveguides that are excited by a linear taper. The approach involves wrapping the waveguide with a material of a higher dielectric constant than both the core and the cladding of the waveguide. The added material significantly improves the modal confinement factor of the fundamental mode to the core, leading to a much smaller coupling to the parasitic higher-order cladding modes. The new waveguide with the additional material cladding is analyzed, and semi-analytical approximate expressions are derived to predict the mode profiles and cutoffs. Design equations are given to choose the thickness of the wrapping material. The waveguide is fabricated and compared against a similar cross-section waveguide without the additional wrapping material. Unlike the unwrapped waveguide, the group delay (GD) results of the proposed (wrapped) waveguide closely match the EM-simulated GD of the fundamental mode, confirming the significant isolation of higher-order modes. The measured GD of the proposed DWG is 50 ps/m, while the expected fundamental mode GD from EM simulations is 35 ps/m. On the contrary, the unwrapped DWG shows a measured GD of 200 ps/m with significant oscillations, while the expected fundamental mode GD from EM simulations is 25 ps/m, demonstrating that wrapping the waveguide significantly improves the GD by reducing the higher-order mode propagation.