Fig. 1. (a) Schematic of the WDM-MDM-PDM multi-dimensional multiplexed photonic integrated circuit. (b) Schematic of the proposed multi-dimensional multiplexer, which multiplexes the first two modes of TE and TM polarizations. (c) Cross section of the adopted SOI platform.

Fig. 2. (a) The optimization procedure of the inverse design method contains adjoint optimization, binarization, and MCM. (b) The intermediate design structures generated by TO at different optimization steps. The design variable is a continuous value within the range of 0 to 1 before binarization, indicated by the “blurry boundary.” After binarization, the design variable is either 0 or 1, referring to a “sharp boundary.” (c) The iteration curve of the multi-dimensional multiplexer optimization. (d) The process of the manufacturing calibration method (MCM). (e) The structure distortion of different aperture sizes after fabrication. Yellow annotations indicate the original design. (f) Insertion losses of fabricated multiplexer with and without MCM at 1550 nm.

Fig. 3. (a)–(d) The simulated transmission spectra of the designed multi-dimensional multiplexer with and without the MCM for (a) TM1, (b) TM0, (c) TE1, and (d) TE0 modes from 1500 nm to 1600 nm. (e) The simulated mode field distributions for four mode transmission paths at 1550 nm.

Fig. 4. (a) The optical image of the fabricated MDM circuit. (b) SEM images of the back-to-back MDM multiplexer. (c)–(f) Measured transmission of the MDM circuits.

Fig. 5. The performance comparison of the experimentally demonstrated multi-dimensional multiplexer based on varying structures on the SOI platform.

Fig. 6. (a) Experimental setup for 100 Gbit/s PAM4 data transmission through the multi-dimensional photonic integrated circuit. (b) Measured BER curves versus received optical power for B2B and mode transfer paths. (c) Measured S21 response of I3-O3 and I3-O4 channels with the signal modulated on I3.

Fig. 7. (a) Measured BERs of four transmitted mode channels with 4 nm wavelength spacing. (b) Measured BERs of the I3-O3 mode channel with 0.8 nm wavelength spacing. (c) 100 Gbit/s eye diagrams of reference links and four MDM channels with different wavelength carriers.

Table 1. Properties of the Inverse-Designed Multiplexer

Table 2. Performance Comparison of Experimentally Demonstrated MDMs on SOI