Efficient and reliable light coupling between optical fibers and photonic integrated circuits is essential for optical interconnects, nonlinear signal conversion, neuromorphic computing, and quantum information processing. A standard approach involves interfacing inverse tapers with lensed fibers, particularly for waveguides with a moderate refractive index, such as silicon nitride ($\mathrm{Si}$${}_3$$\mathrm{N}$${}_4$), silicon oxynitride, and lithium niobate. While this method offers broad bandwidth and high coupling efficiency, prior research has predominantly focused on taper design, largely neglecting the optimization of the lensed fiber itself. Here, we fill this gap and present a comprehensive co-optimization strategy that synergistically refines the geometries of both the taper and the lensed fiber. By incorporating the genuine shape of the lensed fiber into the simulation, we accurately capture the non-Gaussian emission profile, demonstrating the limitations of the widely used paraxial Gaussian approximation. We characterize a wide range of lensed fibers and $\mathrm{Si}$${}_3$$\mathrm{N}$${}_4$ tapers fabricated via different processes, observing remarkable agreement between experiment and simulation with maximum coupling efficiencies exceeding 80% per facet. Finally, we establish design guidelines for lensed fibers and $\mathrm{Si}$${}_3$$\mathrm{N}$${}_4$ tapers compatible with modern CMOS foundries for scalable manufacturing of $\mathrm{Si}$${}_3$$\mathrm{N}$${}_4$ photonic integrated circuits. These findings provide a scalable solution for photonic packaging and optoelectronic assembly, essential for advancing data-center and artificial-intelligence (AI) hardware infrastructure.

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• Integrated optics
• Spatial profiles of optical beams
• Lenses
• Optical fibers
• Semiconductor compounds
• Waveguides
• Finite-difference time-domain method
• Scanning electron microscopy