“…In this paper, the lateral amorphous GeSi taper was optimized for optical coupling with the 200 nm high and 590 nm wide Ge-based FKE optical modulator; this coupling structure should be able to be adapted to other compact Ge-based devices with comparable dimensions with corresponding adjustments in taper width, height, and length. Additionally, it should be noted that although a butt coupling structure was proposed at the telecommunication wavelength of 1.31 µm for optical integration between a Si 3 N 4 waveguide and Ge/SiGe multiple quantum wells (MQWs) on Ge-rich SiGe buffer devices [32], their optical mode areas were relatively comparable, which was not the case for the Ge-on-Si device, in which a large index difference between Ge-based modulator region and Si resulted in a highly confined and much smaller optical mode in the Ge-based region, as shown Figure 1c. Regarding the amorphous taper's dimensions, its length and height were 15 µm and 200 nm, respectively, while the width at the beginning and at the end of the taper were 30 nm and 290 nm, respectively.…”