Grazing-Angle Fiber-to-Waveguide Coupler

Abstract

The silicon photonics market has grown rapidly over recent decades due to the demand for high bandwidth and high data-transfer capabilities. Silicon photonics leverage well-developed semiconductor fabrication technologies to combine various photonic functionalities on the same chip. Complicated silicon photonic integrated circuits require a mass-producible packaging strategy with broadband, high coupling efficiency, and fiber-array fiber-to-chip couplers, which is a big challenge. In this paper, we propose a new approach to fiber-array fiber-to-chip couplers which have a complementary metal-oxide semiconductor-compatible silicon structure. An ultra-high numerical aperture fiber is polished at a grazing angle and positioned on a taper-in silicon waveguide. Our simulation results demonstrate a coupling efficiency of more than 90% over hundreds of nanometers and broad alignment tolerance ranges, supporting the use of a fiber array for the packaging. We anticipate that the proposed approach will be able to be used in commercialized systems and other photonic integrated circuit platforms, including those made from lithium niobate and silicon nitride.

1. Introduction

Advances in silicon photonics have enabled the miniaturization of elaborate optical components and complex circuits into a centimeter-sized chip, consuming less power and generating less heat than conventional electronic circuitry. These advantages promise energy-efficient bandwidth expansion and data transmission increases [1]. Recently, quantum photonic integrated circuits (q-PICs) have attracted significant attention in physics and quantum information science communities for potential applications, including quantum communications and quantum computing [2,3]. As losing a single photon in quantum information processing represents information loss, reducing optical loss is essential for high fidelity q-PIC technique. A significant body of research has reduced fiber-to-waveguide coupling loss caused by a large mode mismatch between the optical fiber and photonics platforms. It is, however, challenging to make a fiber-to-chip coupler satisfying broadband, high coupling efficiency, fiber-array coupling capability, and mass-producible packaging requirements simultaneously.

Butt-coupling with tapered waveguides [4,5,6,7], grating couplers [8,9,10], two-stage adiabatic evolution butt-coupling [4,11,12], coupling with adiabatically tapered fibers [13,14], coupling by 3D-fabrication [15,16], and several other coupling methods [17,18,19,20,21] could achieve more than 90% coupling efficiency with broad bandwidth, but these methods require complicated aligning systems or multiple fabrication processing steps. In [10], the packaging of a grating coupler was demonstrated using fibers whose facet was polished at a 40-degree angle with ultraviolet (UV)-cured epoxy. This coupling scheme has broad tolerance ranges, which could be satisfied with accessible mechanical positioners. However, the coupling efficiency of −12 dB per coupler is not acceptable in q-PICs. In [15], a direct laser writing (DLW) device was used to fabricate 3D-polymer vertically tapered waveguide couplers. The results indicated an approximate 1-dB insertion loss, broad bandwidth, and a versatile tolerance range of four $\mathsf{\mu }$m, but special equipment was required, which raises cost and low productivity issues. Moreover, the structure did not consider mechanical endurance for photonic packaging. In [20], sub-wavelength grating (SWG) was used for coupling with a mechanically controlled silicon prism. Simulation results showed a 0.5-dB insertion loss, 133 nm 1-dB bandwidth, and an extensive tolerance range. The prism and the coupled fiber do not require precise positional and angular accuracy, so that the cost for the setup is reasonable. Nevertheless, the coupling scheme is not suitable for fiber-array integration because of the prism alignment problem for many SWGs. Furthermore, additional loss arises at the unique taper structure mediating SWGs and the other on-chip components. In [19], a glass waveguide substrate was connected to a silicon photonic chip with SMF-28 fiber via adiabatic mode conversion and mode-matching. A 1-dB insertion loss was observed with an up to four $\mathsf{\mu }$m tolerance range on the silicon chip. The glass waveguide platform showed low loss and flexibility, such as connection pitch tuning and changing of the mode field diameter. Again, however, making glass waveguides is challenging for new market participants since a femto-second laser for 3D-printing and a well-developed technique are needed.

Here, we introduce a new coupling strategy based on adiabatic mode evolution called grazing-angle fiber coupler (GAFC). An ultra-high numerical aperture (UHNA) fiber is polished and attached to a silicon chip, having a grazing angle of 88 degrees with respect to the normal direction of the silicon chip. The silicon waveguide in this study has an inversely tapered structure without substrate removal, where the silicon thickness is 220 nm. We use a 150-nm taper tip that inversely tapers to a 450-nm wide waveguide with a half angle of the taper of $375\mathsf{\mu }\mathrm{rad}$ (77.35 arcsec). The gap between the grazing-angled fiber and waveguide structure fills with an index matching oil with a refractive index of 1.295. From numerical calculations, the maximum coupling efficiency was found to be approximately 94%, while the coupling efficiency could be more than 90% over the wavelength range from 1.5 $\mathsf{\mu }$m to 1.6 $\mathsf{\mu }$m. The geometry and parameters used in this simulation are achievable without great difficulty. The coupling efficiency at 1.55 $\mathsf{\mu }$m can be higher than 90% within an alignment tolerance of more than 40 $\mathsf{\mu }$m in the x-direction, 1.5 $\mathsf{\mu }$m in the y-direction, and 80 nm in the z-direction, indicating that this coupling method is suitable for a fiber-array coupling scheme.

2. Simulation Geometry

Figure 1a–c illustrate the artistic, top-down, and side views of the proposed grazing-angle fiber coupling structure, respectively. A UHNA single-mode fiber (Nufern, UHNA4, East Granby, CT, USA) having an outer diameter of 125 $\mathsf{\mu }$m, core diameter of 2.2 $\mathsf{\mu }$m, and mode field diameter of 4.0 $\mathsf{\mu }$m at 1550 nm is used in this paper [22]. The refractive index of the core material is extracted from the mode field diameter calculations for various wavelengths of the data sheet of the UHNA fiber. Moreover, the simulator relates the smooth index to wavelength data by fitting the data to reduce numerical artifacts. The polishing angle of the UHNA fiber is inclined at 88 degrees with respect to the normal direction of the chip surface.

This study considers a silicon-on-insulator wafer with a 220-nm silicon top layer, 3-$\mathsf{\mu }$m buried oxide layer, and handle wafer. The strip-type silicon waveguide has an inversely tapered structure with a taper tip width of $W_{\mathrm{i}}$ and a half angle of the taper ${\theta }_{\mathrm{taper}}$, as shown in Figure 1b. The width of the final optical waveguide is assumed to be 450 nm, but the simulation is performed only near the fiber core, where light in the fiber transfers entirely to the silicon waveguide.

As shown in Figure 1c, we assume that the fiber core is in contact with the silicon taper section and the gap between the fiber and chip is filled with commercially available immersion oil whose refractive index is 1.295 [23]. In this polishing structure, the light of the optical fiber gradually approaches the silicon-tapered waveguide. The fiber core size and effective mode index decrease slowly where the fiber core is polished and touches the silicon waveguide directly, but the silicon taper cross-section and the effective mode index increase gently. Therefore, the light guided in the optical fiber core is adiabatically transmitted to the silicon waveguide. In particular, when the effective mode index and mode diameter of the fiber cross-section are very similar to those of the silicon waveguide cross-section, light coupling between the fiber and waveguide can occur without significant loss.

We performed three-dimensional finite-difference time-domain (FDTD) modeling of electromagnetic wave propagation using a commercial FDTD program (Lumerical, Inc., Vancouver, BC, Canada) to calculate the fiber-to-waveguide coupling efficiency. We consider only the fundamental transverse-electric-like (y-direction polarization) mode while light transfers from the fiber to the waveguide. The electric-field monitor located after the fiber core region measures the fundamental mode’s transmission normalized by the input power. A perfectly-matched-layer medium surrounds the simulation region to remove undesired boundary effects.

An angle of 88 degrees is selected as this condition has a high coupling efficiency and moderate silicon taper length. According to the simulation results for various incline angles, the higher the angle, the higher the coupling efficiency. The silicon taper length, touching the fiber core directly, is about 115 $\mathsf{\mu }$m, assuming the UHNA fiber’s mode field diameter is 4 $\mathsf{\mu }$m. With an angle of 89 degrees, this length becomes 230 $\mathsf{\mu }$m. A shorter taper length is preferred as the silicon taper region may have significant scattering loss. Polishing an individual optical fiber at a grazing angle may be challenging, but it becomes much easier if optical fibers are glued with a v-groove and lid and polished together.

The UHNA4 optical fiber has a different mode field diameter and numerical aperture from an SMF-28 fiber, an optical fiber used widely in optical experiments. Therefore, SMF28-to-UHNA4 splice loss can be induced. Splicing methods by optimizing arc duration, however, have been reported with 0.06 dB splice loss [24]; this splice loss can be ignored here.

3. Numerical Calculation Results

In Figure 2, the mode evolution through the suggested structure is visualized by expressing the electric field distribution profiles in three sections ((b), (c), and (d)). Figure 2a shows the entire simulation region in a two-dimensional form; the dotted lines indicate the locations of the three sections, with the electric field distribution profiles shown in Figure 2b–d. Figure 2b shows the electric field distribution profile of a Gaussian beam in a UHNA fiber whose mode field diameter is 4.0 $\mathsf{\mu }$m. Figure 2c shows the intermediate process in which light is transmitted from the optical fiber to the optical waveguide. Figure 2d shows the electric field distribution profile when light is entirely transferred to the optical waveguide.

Then, we calculate the effective index evolution over the simulation region, including the fiber, tapered silicon waveguide, and index matching oil. The effective index varies adiabatically sufficiently slowly along the axis parallel to the silicon inverse taper, as seen in Figure 3a. The calculated value of the effective index is in a range between ${\mathrm{SiO}}_2$ cladding and the effective index of the inverse taper. In addition, Figure 3b shows the coupling efficiencies for various taper tip widths and taper angles around the proposed structure when all other simulation parameters are fixed. The coupling efficiencies are evaluated at 1550 nm. The maximum modal coupling efficiency at 1550 nm can be achieved for $W_{\mathrm{i}}=150\mathrm{nm}$ and ${\theta }_{\mathrm{taper}}=375\mathsf{\mu }\mathrm{rad}$. Therefore, we determine the taper tip and angle for calculating the coupling efficiency spectrum.

As seen in Figure 4, the taper with $W_{\mathrm{i}}=150\mathrm{nm}$ and ${\theta }_{\mathrm{taper}}=375\mathsf{\mu }\mathrm{rad}$ shows the best coupling efficiency of about 94.7%, occurring at 1535 nm. It appears to have a width of 245 nm for 0.5-dB bandwidth (green dotted line) with a bandwidth center located at 1507.5 nm. A negligibly small amount of light reflects into the fiber core and most light loss results from bouncing off of the polished fiber facet. Therefore, we can achieve a highly efficient broadband fiber-to-waveguide coupling method.

Last, we test the robustness of our method for alignment tolerance. The influence of the position deviation of x, y, and z-axis on the coupling efficiency is calculated and shown in Figure 5. The curves of 0.7511 represent a 1-dB tolerance line compared to the perfect transmission value (94.56%). The initial core center position is set to $x=2\mathsf{\mu }\mathrm{m}/\sin \left(2^{\circ }\right)$ from the taper tip, $y=z=0$, and we repeat the simulation while varying an individual position parameter and fixing the rest. In Figure 5a, there is no significant induced loss by the x-axis displacement. Note that the typical core-clad concentricity is ±0.5 $\mathsf{\mu }$m, raising by ±14.4 $\mathsf{\mu }$m the core position deviation along the x-axis. This core position deviation will induce negligible loss variance when using more than one fiber. The coupling efficiency result of the y-axis displacement is worse than the x-axis deviation because of the narrow mode field diameter, as seen in Figure 5b. Nevertheless, the y-axis tolerance is 1.5 $\mathsf{\mu }$m, indicating robustness against the core-clad concentricity. Lastly, the coupling efficiency exhibits the most severe loss change on the z-axis variance as the coupling coefficient between the core and taper changes significantly, as seen in Figure 5c. In this case, the variance results from the surface roughness of the wafer or the polished fiber. The surface roughness of a commercial wafer is already in the few nanometers range; hence, wafer roughness can be neglected. Moreover, the fiber surface roughness could be reduced to tens of nanometers using a well-established fiber polishing method [25]. In sum, all the tolerance ranges of the proposed structure exceed common fiber core-clad concentricity and surface roughness. This result does not consider position drift induced by the curing adhesive; however, the adhesive in the proposed structure occupies the area between the fiber and wafer surface. As in [17], the adhesive shrinkage pulls the fiber position toward the wafer surface, which may improve the coupling efficiency.

4. Discussion

UHNA fibers are commercially available but must be customized to make such a grazing-angle fiber. Grinding an individual fiber at any angle is challenging due to the flexibility of an optical fiber. Here, we suggest using a fiber-array block instead of an individual fiber when grinding fibers. Figure 6 illustrates a grazing-angle fiber-array block and inverse tapers for coupling multi-ports. Individual fibers could be maintained to achieve their optimal positions with appropriate positioning systems. Therefore, the grazing-angle fiber coupling method can be used for fiber-array fiber-to-chip couplers.

Regarding fiber-end-face processing, there are many commercialized items available for polishing fiber, such as lapping films, ferrules, jigs, etc. In addition, many fiber-array block suppliers offer angle shift polishing, changing of the type of fiber, and substrate replacement, which are needed to realize and modify GAFC. Further, we expect the GAFC method to be adapted in various PIC platforms, such as lithium niobate on insulator (LNOI) or silicon nitrides on insulator (SiNOI). In the future, the GAFC coupling scheme could be produced in PIC business laboratories with specialized machinery and services.

5. Conclusions

The coupling structure presented here has $W_{\mathrm{i}}=150\mathrm{nm}$ and ${\theta }_{\mathrm{taper}}=375\mathsf{\mu }\mathrm{rad}$ inversed taper with fully etched 220 nm Si and fiber with two degrees inclination to the center axis. This coupler attains 94% coupling efficiency with a 0.5-dB wavelength bandwidth of 245 nm and 1-dB tolerance ranges of 40 $\mathsf{\mu }$m x-axis, 1.5 $\mathsf{\mu }$m y-axis, and 80 nm z-axis. The processes for making the silicon tapers are complementary-metal-oxide-semiconductor-compatible. We propose use of the fiber-array block for polishing grazing-angle optical fibers. The tolerance bounds are beyond the typical fiber core-clad concentricity and polishing roughness, enabling use of the fiber-array block for mass-production.