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Mode-division multiplexing (MDM) is an emerging large-capacity datacommunication technology utilizing orthogonal guiding modes as independent datastreams. One of the challenges of multimode waveguide routing in MDM systems isdecreasing the mode leakage of waveguide crossings. In this article, a squareMaxwell's fish-eye lens as waveguide crossing medium based on quasi-conformaltransformation optics is designed and implemented on the silicon-on-insulatorplatform. Two approaches were taken to realize the designed lens: gradedphotonic crystal and varying the thickness of Si slab waveguide.Three-dimensional numerical simulations show that the designed multimodewaveguide crossing has an ultrawide bandwidth from 1260 to 1675 nm with acompact footprint of only $3.77 \times 3.77 \mu m^2$. For the first threetransverse electric modes $(TE_0, TE_1, \: and \: TE_2)$, the designedwaveguide crossing exhibits an average insertion loss of 0.24, 0.55, and 0.45dB and the crosstalk of less than -72, -61, and -27 dB, and a maximum returnloss of 54, 53, and 30 dB, respectively. The designed waveguide crossingsupports low distortion pulse transmission with a high fidelity factor of0.9857. Furthermore, proposed method can be expanded to design waveguidecrossings with even higher number of supporting modes by increasing the size ofthe lens.

Multimode waveguide crossing based on square Maxwell's fisheye lens