Light coupling to photonic integrated circuits using optimized lensed fibers

TL;DR

Efficient light coupling between optical fibers and Si$_3$N$_4$ photonic integrated circuits is achieved by co-optimizing lensed-fiber tip shapes with inverse taper geometries. The authors model the actual lensed-fiber emission using SEM-derived hyperbolic tip profiles parameterized by $(\rho,\phi)$ and evaluate the overlap with the taper mode via the overlap integral $\eta_{ft}$, then predict the overall coupling $\eta_{sim}$ through 3D FDTD simulations, including ARDE-affected taper geometries. They validate the framework experimentally across lensed-fiber diameters $D=(2.0,3.0,4.0,5.0,6.0)\,\mu$m and multiple taper types, achieving per-facet coupling efficiencies exceeding ~0.80 in favorable configurations and demonstrating strong agreement with simulations. The results provide CMOS-foundry-ready guidelines for high-efficiency fiber-to-Si$_3$N$_4$ coupling, with significant implications for scalable photonic packaging in data centers and AI hardware.

Abstract

Efficient and reliable light coupling between optical fibers and photonic integrated circuits has arguably been the most essential issue in integrated photonics for optical interconnects, nonlinear signal conversion, neuromorphic computing, and quantum information processing. A commonly used approach is to use inverse tapers interfacing with lensed fibers, particularly for waveguides of relatively low refractive index, such as silicon nitride (Si3N4), silicon oxynitride, and lithium niobate. This approach simultaneously enables broad operation bandwidth, high coupling efficiency, and simplified fabrication. Although diverse taper designs have been invented and characterized to date, lensed fibers play equally important roles here, yet their optimization has long been underexplored. Here, we fill this gap and introduce a comprehensive co-optimization strategy that synergistically refines the geometries of the taper and the lensed fiber. By incorporating the genuine lensed fiber's shape into the simulation, we accurately capture its non-Gaussian emission profile, thereby nullifying the widely accepted approximation based on a paraxial Gaussian mode. We further characterize many lensed fibers and Si3N4 tapers of varying shapes using different fabrication processes. Our experimental and simulation results show remarkable agreement, both achieving maximum coupling efficiencies exceeding 80% per facet. Finally, we summarize the optimal choices of lensed fibers and Si3N4 tapers that can be directly deployed in modern CMOS foundries for scalable manufacturing of Si3N4 photonic integrated circuits. Our study not only contributes to light-coupling solutions but is also critical for photonic packaging and optoelectronic assemblies that are currently revolutionizing data centers and AI.

Figures (9)

• Figure 1: Principle and schematic of light coupling from the lensed fiber to the Si$_3$N$_4$ taper. a. Optical microscope image showing a lensed fiber edge-coupled to a Si$_3$N$_4$ chip, where a Si$_3$N$_4$ inverse taper is aligned to the fiber to receive light. b. Enlarged schematic of light coupling between the lensed fiber and the inverse taper. Doped fiber core, green. Si$_3$N$_4$ inverse taper, blue. Normal SiO$_2$ cladding, cyan. Light field, transparent pink. c. Simulated power distribution in logarithmic scale of the lensed fiber's focus mode. $D$, mode-field diameter. d. Principle of mode matching and overlap to calculate coupling efficiency $\eta_\text{ft}$. Accommodating one mode to the other and reducing misalignment vector $\vec{r}$ can improve $\eta_\text{ft}$. e. SEM image of a lensed fiber's tip. $\rho$, curvature radius. $\phi$, conic angle. f. Simulated light propagation profile in logarithmic scale from the lensed fiber to the taper. g. SEM image of a subtractive taper's cross-section, overlapped with its TE eigenmode in logarithmic scale. $w$, taper width. $h$, taper height or thickness. $\alpha$, the taper's sidewall angle.
• Figure 2: Imaging, modeling and simulation of different lensed fibers. a. SEM images of lensed fibers' tips with $D=(2.0, 3.0, 4.0, 5.0, 6.0)$$\mu$m. Cyan dashed curves outline the tips' hyperbolic shapes. White dashed lines mark that the tips are placed at $x=0$. b. Emission field in logarithmic scale of the lensed fibers. Blue dashed lines mark the focal planes (Foc.) of the lensed fibers' emission modes. Red dashed curves mark the divergence of the paraxial Gaussian beam (P. G. B.). c. Power distribution along the $y$ axis in the focal plane (blue dashed lines in b), for the lensed fiber’s focus mode (F. M.) and the paraxial Gaussian beam (P. G. B.) with different $D$ values. The comparison highlights discrepancy between the actual MFD extracted from the simulation and the labelled $D$. d. Calculated $\eta_\text{ft}$ for lensed fibers of different $D$ values and tapers of varying $w$, over varying longitudinal misalignment along the $x$ axis. Blue dashed lines mark the focal planes (Foc.) of the lensed fibers' emission modes. Red dashed curves mark the optimal (Opt.) coupling position for maximum $\eta_\text{ft}$. As $D$ increases, $\eta_\text{ft}$ remains high over a broader range of $x$. As $D$ decreases, the red dashed lines approach the blue dashed lines.
• Figure 3: Experimental characterization of light coupling efficiency $\eta$, misalignment tolerance, and transmission spectra. a, d. Experimentally (Exp.) characterized $\eta$ for 320-nm-thick subtractive tapers (a) and 710-nm-thick additive tapers (d) with varying $D$ and $w$ under TE or TM polarization, in comparison with simulation (Sim.) results. The error bars indicate twice the standard deviation for the three measurements of each taper with identical design parameters. The vertical range of the shaded area indicates the 95% confidence interval for $\eta$, as predicted by the Gaussian process regression modelWangj:23. b. Experimentally (Exp.) measured $\eta$ with 320-nm-thick subtractive tapers and TE polarization, for $D=3.0$$\mu$m, $w=410$ nm (yellow data, also marked with yellow dashed line in a), and $D=4.0$$\mu$m, $w=380$ nm (blue data, also marked with blue dashed line in a), in comparison with simulation (Sim.) results. c. Experimentally measured $\eta^2$ under TE polarization over the spectral range from 183 THz (1640 nm) to 203 THz (1480 nm), using $D=4.0$$\mu$m and $w=300$, 380, and 440 nm (also marked with red, blue, and green dashed lines in a). Zoom-in shows the 15-GHz-FSR FP interference pattern.
• Figure 4: SEM image processing.a. Edge extraction of the lensed fiber's tip. Left panel, gray-scale SEM image. Right panel, the corresponding edge profile obtained through sequential image processing, including $k$-means clustering, edge detection, and anomaly removal algorithms. The angles $\Theta_l$ and $\Theta_r$ define the fiber tip's geometry, representing the angles between its asymptotic lines and the $x$ axis. b. Line detection via Hough transform. This panel visualizes the transformation of the edge image (from a, right) from the image space to its corresponding Hough parameter space. The parameters $\wp$ (distance) and $\Theta$ (angle) characterize potential lines, with distinct peaks in this space indicating the most prominent linear segments. c. Geometric alignment and hyperbolic fit. The solid green curve is the best-fit hyperbolic function applied to the raw edge coordinates after rotational correction. The dashed red and blue lines represent the symmetry axes of the contour curves (raw and rotated data).
• Figure 5: Subtractive process flow and illustration of the inverse taper structure.a. Simplified Si$_3$N$_4$ subtractive process flow. b. Illustration of the inverse taper. c. SEM image of the taper's cross-section at the chip facet.