Light coupling to photonic integrated circuits using optimized lensed fibers

Technical Summary: Light Coupling to Photonic Integrated Circuits Using Optimized Lensed Fibers

Problem Statement
Efficient and reliable light coupling between optical fibers and photonic integrated circuits (PICs) remains a critical bottleneck in integrated photonics, particularly for applications in optical interconnects, nonlinear signal conversion, neuromorphic computing, and quantum information processing. While inverse tapers interfacing with lensed fibers are a standard approach for low-refractive-index waveguides (e.g., silicon nitride, Si$_3$N$_4$), existing optimization strategies have largely focused on the taper design while neglecting the lensed fiber itself. Furthermore, conventional numerical simulations typically approximate the lensed fiber's emission as a paraxial Gaussian mode. This approximation fails to account for the sub-wavelength structures at the fiber tip, which generate non-Gaussian, non-axial emission profiles with strong evanescent fields, leading to inaccuracies in predicting coupling efficiency and hindering the development of robust optimization strategies.

Methodology
The authors introduce a comprehensive co-optimization strategy that synergistically refines the geometries of both the Si$_3$N$_4$ inverse taper and the lensed fiber. The methodology involves three primary components:

1. Accurate Fiber Modeling: Instead of relying on vendor-provided Mode Field Diameter (MFD) values derived from far-field divergence angles (which assume a Gaussian beam), the authors performed Scanning Electron Microscope (SEM) imaging of commercial lensed fiber tips. They extracted the physical profiles and fitted them to a hyperbolic form defined by curvature radius ($\rho$) and conic angle ($\phi$). These genuine geometric parameters were then incorporated into 3D Finite-Difference Time-Domain (FDTD) simulations to capture the true, non-Gaussian emission profiles.
2. Taper Fabrication and Characterization: The study utilized Si$_3$N$_4$ inverse tapers fabricated via two distinct processes: a subtractive process (constant thickness, varying width) and an additive process (varying thickness and width due to aspect-ratio-dependent etch effects). Tapers with varying widths ($w$) and thicknesses ($h$) were characterized.
3. Co-Optimization and Validation: The authors calculated the overlap integral ($\eta_{ft}$) between the simulated fiber mode and the taper mode to determine coupling efficiency ($\eta$) as a function of longitudinal misalignment ($\vec{r}$) and taper width. These simulations were validated against experimental measurements of coupling efficiency, misalignment tolerance, and transmission spectra across a broad spectral range (1480 nm to 1640 nm) for both TE and TM polarizations.

Key Results

• Deviation from Gaussian Approximation: The study demonstrated that the actual MFD ($D_s$) extracted from simulations of the genuine fiber shape differs significantly from the labeled MFD ($D$) provided by vendors. For example, a fiber labeled with $D=6.0$ $\mu$m exhibited a simulated $D_s$ of 5.0 $\mu$m. This discrepancy confirms that the paraxial Gaussian approximation is insufficient for accurate coupling prediction.
• High Coupling Efficiency: The co-optimized designs achieved maximum coupling efficiencies exceeding 80% per facet. Specifically, for 320-nm-thick subtractive tapers, the optimal configuration using a $D=4.0$ $\mu$m fiber and a taper width of $w=380$ nm yielded an experimental efficiency of 80% (TE polarization) and 80% (TM polarization).
• Misalignment Tolerance: The results indicate that lensed fibers with larger MFDs ($D$) provide broader tolerance to longitudinal misalignment ($\Delta x$). For instance, a $D=6.0$ $\mu$m fiber offered a $\Delta x$ tolerance of approximately 14.8 $\mu$m, compared to 4.6 $\mu$m for a $D=2.0$ $\mu$m fiber.
• Spectral Performance: Over a spectral range of 1480 nm to 1640 nm, the optimal configuration maintained coupling efficiencies above 77% with only 3% variation.
• Simulation-Experiment Agreement: The experimental data showed remarkable agreement with the 3D FDTD simulation results, not only in global trends but also in absolute amplitude, validating the accuracy of the non-Gaussian modeling approach.

Significance and Claims
The paper claims that by filling the gap in lensed fiber optimization and moving beyond the Gaussian approximation, it provides a reliable, scalable solution for light coupling in Si$_3$N$_4$ PICs. The authors summarize specific optimal choices of lensed fibers and Si$_3$N$_4$ tapers that can be directly deployed in modern CMOS foundries. They assert that this work is critical for photonic packaging and optoelectronic assemblies, which are essential for the advancement of data centers and AI, in addition to its direct contributions to quantum information processing and neuromorphic computing. The study emphasizes that accurate modeling of the fiber tip is as crucial as the taper design for achieving high-efficiency, broadband coupling.