A write head includes a near-field transducer near a media-facing surface of the write head. The write head includes a waveguide having a core with a first side disposed proximate to the near-field transducer. The core overlaps the near-field transducer at a substrate-parallel plane. The core includes one of a step or a taper on a second side facing away from the first side. The step or the taper causes a reduced thickness of the core normal to the substrate-parallel plane. The write head includes a cladding layer that encompassing the second side of the core and that fills in the step or the taper.