We demonstrate adiabatically tapered fibers terminating in sub-micron tips that are clad with a higher-index material for coupling to an on-chip waveguide. This cladding enables coupling to a high-index waveguide without losing light to the buried oxide. A technique to clad the tip of the tapered fiber with a higher-index polymer is introduced. Conventional tapered waveguides and forked tapered waveguide structures are investigated for coupling from the clad fiber to the on-chip waveguide. We find the forked waveguide facilitates alignment and packaging, while the conventional taper leads to higher bandwidth. The insertion loss from a fiber through a forked coupler to a sub-micron silicon nitride waveguide is 1.1 dB and the 3 dB-bandwidth is 90 nm. The coupling loss in the packaged device is 1.3 dB. With a fiber coupled to a conventional tapered waveguide, the loss is 1.4 dB with a 3 dB bandwidth extending beyond the range of the measurement apparatus, estimated to exceed 250 nm.
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