Fig. 1. (a) 3-D schematic of the fiber to Si waveguide free-form coupler. The Si nonlinear inverse taper, deep trench, and reflector sections are annotated. The design methodology of the free-form coupler is guided by the Fermat’s principle. 3-D FDTD simulations of (b) forward-propagating light wave exiting from the Si waveguide inverse taper, (c) forward-propagating light wave from the fiber, and (d) co-propagation of back-propagated light wave from the fiber and forward-propagating light from the waveguide taper. The white arrows illustrate the phase accumulated by the light wave as it propagates. The yellow arrows indicate the light sources in the different simulations, and corresponding propagation directions.

Fig. 2. (a) TE-mode electric field distribution in the xy plane of light waves exiting from 170 and 480 nm wide waveguides at 1550 nm wavelength. The full width at half-maximum divergence angles are marked. The electric field intensity of the light waves in the xy and xz planes as (b) fundamental TE mode and (c) fundamental TM mode propagate along the nonlinear inverse taper. The respective electric field distributions (yz plane) at both facets of the taper are shown. (d) Spectral dependence of the total insertion loss of the taper.

Fig. 3. (a) Cross-sectional illustration of the designed free-form coupler, where the constituent components are illustrated and critical dimensions are labeled. (b) False-colored SEM image of the fabricated free-form coupler. The two slabs (short and thick, and long and thin) extending toward the waveguide are visual aids to quickly gauge alignment accuracy in and out of plane; they do not perform any optical function. (c) Simulated spectral performance of the designed free-form coupler for the case of TE and TM waveguide polarizations. Electric field intensity (xy plane) as the light wave is coupled between the fiber and the Si waveguide through the coupler for the case of (d) fundamental TE and (e) TM polarization. The electric field (xz plane) evolution of the optical mode as it is reflected normally from the Si waveguide and propagates toward the fiber facet is shown for different y positions. The optical modes at the taper, reflector, and fiber output are also illustrated.

Fig. 4. Computed fiber misalignment tolerance in the (a) xz plane and (b) y direction. (c) Computed excess loss in coupling efficiency of the reflector as a result of printing misalignments with respect to the waveguide facet. Simulated for TE polarization at 1550 nm.

Fig. 5. (a) Micrograph showing fiber-coupled (SMF-28) red laser light (630 nm) into a Si waveguide via the free-form couplers. (b) Measured spectral performance of the 3-D free-form coupler pertaining to the fundamental TE and TM modes.

Fig. 6. (a) Measured fiber misalignment tolerance in the xz plane measured using a piezoelectric actuator with a step size of 500 nm. The contour traces the 1 dB alignment tolerance. (b) Measured excess loss as a function of output fiber misalignment in the y direction.

Fig. 7. (a) Measured spectra for two Si waveguides with different configurations of light coupling: grating-to-reflector and grating-to-grating. (b) Measured total insertion loss of a Si waveguide terminated with two free-form couplers as-fabricated and after annealing at 250°C for 10 min.

Fig. 8. Potential photonic packaging solution involving the free-form coupler, enabling packaging with (a) individual fibers and (b) fiber arrays. A mechanical alignment feature is printed onto the chip, with a stopper to prevent collision of the fiber (array) with the reflector surface. The fiber (array) is guided by the alignment structure and brought down onto the chip, until it rests onto the stopper. The optical assembly can then be bonded with optical epoxy as is conventionally done for grating couplers.

Fig. 9. (a) Atomic force micrograph of the top surface of a printed cube. The striations observed come as a result of the discrete lines exposed during the printing process. The root mean square roughness of the masked area is 17.6 nm. (b) Simulation on the effect of shrinkage on coupling efficiency of the free-form reflector. A uniform 5% shrinkage was applied.

Fig. 10. Optical performance of a photonic link comprised a free-form reflector and a grating coupler as input/output devices, before (red) and after (blue) exposure to ∼470  mW of continuous-wave laser emission centered at 1550 nm for 1 h continuously. It can be deduced that little to no change occurred, indicating the compatibility of the reflectors with high-power applications.