Mode-division multiplexing (MDM) is an emerging large-capacity data communication technology utilizing orthogonal guiding modes as independent data streams. One of the challenges of multimode waveguide routing in MDM systems is decreasing the mode leakage of waveguide crossings. In this article, a square Maxwell’s fish-eye lens as a waveguide crossing medium based on quasiconformal transformation optics is designed and implemented on a silicon-on-insulator platform. Two approaches were taken to realize the designed lens: graded photonic crystal and varying the thickness of the silicon slab waveguide. Three-dimensional numerical simulations show that the designed multimode waveguide crossing has an ultrawide bandwidth from 1260 to 1675 nm with a compact footprint of only $3.77\times 3.77{\mathrm{\mu m}}^2$. For the first three transverse electric modes (TE0, TE1, and TE2), the designed waveguide crossing exhibits an average insertion loss of 0.24, 0.55, and 0.45 dB; a crosstalk of less than $-72$, $-61$, and $-27\mathrm{dB}$; and a maximum return loss of 54, 53, and 30 dB, respectively. The designed waveguide crossing supports low-distortion pulse transmission with a high fidelity factor of 0.9857. Furthermore, the proposed method can be expanded to design waveguide crossings with an even higher number of supporting modes by increasing the size of the lens.

Multimode waveguide crossings are crucial components for novel mode-division-multiplexing systems. One of the challenges of multimode waveguide routing in MDM systems is decreasing the inter-mode crosstalk and mode leakage of waveguide crossings. In this work, we present the intersections of three and four waveguides based on polygonal Maxwell’s fisheye lens via transformation optics. The designed lenses are implemented by mapping their refractive index to the thickness of guiding Si layer. The three-dimensional finite-difference time-domain simulations are used to evaluate the performance of the proposed 3 × 3 and 4 × 4 crossings. The footprint of the 3 × 3 and 4 × 4 waveguide star crossings are 18.6 × 18.6 and 27.5 × 27.5 μ m ² , respectively. For both waveguide crossings, the intermodal crosstalk in the output port is lower than −22 dB while the crosstalk to other ports is lower than −37 dB for TE ₀ , TE ₁ , and TE ₂ modes. The insertion losses for these modes are lower than 0.5 dB in a bandwidth of 415 nm covering the whole optical telecommunication bands.

Reducing the bending radius of low-index-contrast waveguides is essential in reducing the size of the integrated optical components. A polymeric multimode waveguide bend is presented based on the Eaton lens. Ray-tracing calculations are utilized to truncate the Eaton lens in order to improve the performance of the bend. The truncation of the lens decreases the footprint of the bend as well. A designed waveguide bend with a radius of 18.4 μm is implemented by a concentric cylindrical multilayer structure. Average bend losses of 0.69 and 0.87 dB are achieved for the ${\mathrm{TM}}_0$ and ${\mathrm{TM}}_1$ modes, respectively, in the C-band of optical communication. The bend loss is lower than 1 dB in a bandwidth of 1520–1675 nm for both modes.