Fig. 1. (a) Schematic diagram of a grating outcoupler. (b) Gaussian beam profile with a 100 µm beam waist. (c) Spatially varying coupling strength at the 100 µm beam waist profile.

Fig. 2. (a) Spatially varying coupling strength for mirroring. (b) Pitch as a function of the duty cycle that satisfies the Bragg condition. The inset shows a schematic of a unit cell in a grating coupler. (c) Calculated parameters of grating pitch and etching width as functions of propagation distance. (d) Near-field power distribution of the grating outcoupler.

Fig. 3. (a) Processing of the grating outcoupler. Optical micrographs of the (b) grating outcoupler, (c) edge coupler, and (d) multimode interference coupler. (e) Confocal micrograph of the grating.

Fig. 4. (a) Optical image of the beam emitted by the grating outcoupler. (b) Intensity profile of the beam along the length of the grating with a Gaussian fit. (c) Intensity profile of the beam orthogonal to the grating with a Gaussian Fit. (d) Optical images of the beam taken at different heights above the chip. (e) Relationship between beam spot position and height with linear fit. (f) Relationship between beam spot size and height along the length of the grating and orthogonal to the grating with linear fit.

Fig. 5. (a) Schematic of on-chip laser cooling beam delivery used to generate free-space beams for the 3D MOT. (b) Optical image of the chip emitting beam at 6 mm height. (c) Optical images of the beam taken at different heights above the chip.