## 3 Waveguide Fabrication and Its Nano-Characterization  
Based on the waveguide design study and the writing range of the commercial DLW tool (NanoscribeTM GmbH photonic professional GT 3D printer located in the [PERSON] Brojde Laboratory of the Edmond J. Safra Campus, The Hebrew University of Jerusalem, Israel), we first designed a relatively simple waveguide consisting of a circular core of 2 \(\upmu\)m diameter supported by a narrow fin of width 0.3 \(\upmu\)m and height 1.5 \(\upmu\)m. To fabricate the designed waveguide structure, the optimized 3D geometry was modeled using 3D drafting software (AutoCAD Inventor) and loaded into the NanoscribeTM system software (shown in Figure 7a). The designed waveguide ran parallel to the substrate, supported by the nano-fin, with its ends curved upwards to facilitate coupling to two lensed fibers. A rectangular pedestal layer of 1 \(\upmu\)m thickness (5 \(\upmu\)m width and running along the waveguide length) was printed below to provide larger adhesion area to the substrate. The pedestal added negligible printing time to the entire U-shaped waveguide (approximately 5 min). The curved sections bent at a radius of 100 \(\upmu\)m, terminating at 45\({}^{\circ}\), and at the same time tapered out from 2 \(\upmu\)m to 4 \(\upmu\)m. Based on our simulations, this curved waveguide taper should not exhibit any significant loss. Due to the 200 \(\upmu\)m writing range limit of the system (when operating with single exposure field, i.e., without stitching), the straight waveguide section's length was only 40 \(\upmu\)m.  
Figure 6: Variation of the confinement factor inside the core with and without a fin of 1.5 \(\upmu\)m height. The designed 3D waveguide was fabricated on a glass substrate using IP-Dip photoresist, a 63\(\times\) immersion microscope objective, and the Nanoscribe 3D printer. IP-Dip is a specially formulated photoresist for Nanoscribe technology. Its refractive index is matched to the microscope objective (used to focus the laser beam), thus providing ideal focusing of the laser beam with fine lateral resolution (200 nm) of fabricated structures. A silanization process was pre-applied to the glass substrate, to enhance polymer adhesion. After laser writing, the structure was developed in PGMEA (Propylene glycol monomethyl ether acetate) for 10 min, followed by cleaning with IPA (Isopropyl Alcohol) for 2 min, and drying with Novec 7100 [27] for 1 min. We optimized the various writing parameters, such as laser power = 30 (Nanoscribe's Describe software); scanning speed = 10,000 \(\upmu\)m/s; and the distance of laser scanning hatching = 0.1 \(\upmu\)m (lateral spacing between lines) and slicing = 0.05 \(\upmu\)m (spacing between layers in the z-axis) to achieve the desired shape and size of waveguide with minimum surface roughness. The fabricated structure was characterized by using High-Resolution Scanning Electron Microscopy (HRSEM). Figure 7b shows the HRSEM image of the fabricated waveguide, which matches the designed structure (shown in Figure 7a). The cross-section of the fabricated waveguide was studied with the aid of FIB milling to directly observe the dimensional accuracy of the printing process (Figure 1d), and used to optimize the printing parameters of the waveguide and its supporting structure. The FIB analysis typically investigated several cross-sections to study longitudinal accuracy, which was reasonably good. The surface roughness of the waveguide was studied by atomic force microscopy (AFM). Figure 8a,b shows the AFM tip scanning the waveguide surface (a more intricate waveguide, described below), and its measured surface topography. The root mean square (RMS) roughness of the fabricated waveguide was ~6 nm and the spatial correlation length was 350 nm. Two parallel line profiles of the surface roughness at spacing of 400 nm further demonstrate the independent, i.e., uncorrelated, surface roughness features (Figure 8c). Surface roughness of the waveguide is likely a major source of propagation loss, which we discuss next.