Fig. 1. Thouless pumping process in an RM-modeled silicon waveguide array. (a) Schematic of the coupled-waveguide array. (b) Band structure of the TM supermodes in an array of 30 waveguides with alternating widths. The black solid lines represent the bulk bands, whereas the red and blue solid lines represent the left and right edge states when $z\in [\mathrm{0,1}/4)\cup (3/\mathrm{4,1}]$. (c) Mode profiles $(|E|)$ of the supermodes at Points IA to VIIIA (Points IB to VIIIB) on the blue (red) curve in panel (b).

Fig. 2. Mode conversions based on the topological waveguide array. (a) Schematic of the mode conversion region composed of the topological waveguide array. (b)–(d) Light propagation profiles ($|E_y|$) at 1550 nm for the (b) ${\mathrm{TM}}_0$-to-${\mathrm{TM}}_1$, (c) ${\mathrm{TM}}_0$-to-${\mathrm{TM}}_2$, and (d) ${\mathrm{TM}}_0$-to-${\mathrm{TM}}_3$ mode conversions when the ${\mathrm{TM}}_0$ mode is launched from the bottom narrow waveguide. (e)–(g) Simulated transmission spectra of different modes at the output ends of the (e) ${\mathrm{TM}}_0$-to-${\mathrm{TM}}_1$, (f) ${\mathrm{TM}}_0$-to-${\mathrm{TM}}_2$, and (g) ${\mathrm{TM}}_0$-to-${\mathrm{TM}}_3$ coupling regions in panels (b)–(d).

Fig. 3. Comparison of the topological and conventional mode-order conversions. (a)–(f) Simulated transmission of the target modes (${\mathrm{TM}}_1-{\mathrm{TM}}_3$) at 1550 nm when (a)–(c) the waveguide width deviation $\delta w$ varies from $-100$ to 200 nm, or (d)–(f) the gap distance deviation $\delta g$ varies from $-100$ to 150 nm. (g)–(i) Simulated transmission spectra of the target modes in different mode-order converters. The left, middle, and right columns of the figure correspond to the ${\mathrm{TM}}_0$-to-${\mathrm{TM}}_1$, ${\mathrm{TM}}_0$-to-${\mathrm{TM}}_2$, and ${\mathrm{TM}}_0$-to-${\mathrm{TM}}_3$ conversions, respectively.

Fig. 4. Structures of the fabricated devices. (a) Optical microscope photo of the fabricated MDM device. The correspondence between the ports and the modes is indicated in the figure. The ${\mathrm{TM}}_0$-to-${\mathrm{TM}}_1$, ${\mathrm{TM}}_0$-to-${\mathrm{TM}}_2$, and ${\mathrm{TM}}_0$-to-${\mathrm{TM}}_3$ mode conversion regions are encircled by the red, green, and blue dashed boxes, respectively. (b)–(d) SEM images of the (b) ${\mathrm{TM}}_0$-to-${\mathrm{TM}}_1$, (c) ${\mathrm{TM}}_0$-to-${\mathrm{TM}}_2$, and (d) ${\mathrm{TM}}_0$-to-${\mathrm{TM}}_3$ mode-order converters based on the topological waveguide arrays. (e)–(g) SEM images of the (e) ${\mathrm{TM}}_0$-to-${\mathrm{TM}}_1$, (f) ${\mathrm{TM}}_0$-to-${\mathrm{TM}}_2$, and (g) ${\mathrm{TM}}_0$-to-${\mathrm{TM}}_3$ mode-order converters based on the conventional ADCs.

Fig. 5. Measured transmission spectra of the four modes when the light is injected from the (a) ${\mathrm{TM}}_0$, (b) ${\mathrm{TM}}_1$, (c) ${\mathrm{TM}}_2$, and (d) ${\mathrm{TM}}_3$ input ports of the proposed topological MDM device.

Fig. 6. Measured transmission of the target modes at 1550 nm of the fabricated topological and conventional mode-division multiplexers with various fabrication errors. (a)–(c) Measured transmission of the (a) ${\mathrm{TM}}_1$, (b) ${\mathrm{TM}}_2$, and (c) ${\mathrm{TM}}_3$ modes when the waveguide width deviation $\delta w$ varies from $-90$ to 90 nm. (d)–(f) Measured transmission of the (d) ${\mathrm{TM}}_1$, (e) ${\mathrm{TM}}_2$, and (f) ${\mathrm{TM}}_3$ modes when the gap distance deviation $\delta g$ varies from $-90$ to 90 nm.

Fig. 7. High-speed data transmission experiment based on the four-channel topological MDM device. (a) Setup for the $200\text{-}\mathrm{Gb}/\mathrm{s}$ high data rate–transmission experiment. The black and orange lines represent optical and electrical links, respectively. (b) DSP algorithms for the transceivers. (c) Measured optical spectra for the 16-QAM signals at different stages. (d) BERs for the four signal channels. (e) Recovered constellations for each mode.