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The number of waveguides crossing an intersection increases with the development of complex photonic integrated circuits. Numerical simulations are presented to demonstrate that Maxwell's fish-eye (MFE) lens can be used as a multiband crossing medium. In previous designs of waveguide intersection, bends are needed before and after the intersection to adjust the crossing angle resulting in a larger footprint. The presented design incorporates the waveguide bends into the intersection which saves footprint. In this paper, 4×4 and 6×6 intersections based on ideal and graded photonic crystal (GPC) MFE lenses are investigated, where 4 and 6 waveguides intersect, respectively. The intersection based on ideal MFE lens partially covers the O, E, S, C, L, and U bands of optical communication, while the intersection based on GPC-MFE lens is optimized to cover the entire C-band. For 4×4 and 6×6 intersections based on GPC-MFE lens, crosstalk levels are below -24dB and -18dB, and the average insertion losses are 0.60dB and 0.85dB in the C-band with lenses' radii of 7×a and 10×a, respectively, where a is the lattice constant of the photonic crystal.

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 µm 2 , respectively. For both waveguide crossings, the intermodal crosstalk in the output port is lower than -22dB while the crosstalk to other ports is lower than -37dB for TE0, TE1, and TE2 modes. The insertion losses for these modes are lower than 0.5dB in a bandwidth of 415nm covering the whole optical telecommunication bands.

The Maxwell's fisheye (MFE) lens, due to its focusing properties, is an interesting candidate for implementing the crossing of multiple waveguides. The MFE lens is implemented by two different structures: concentric cylindrical multilayer and radially diverging gourd-shaped rods. Realization of the refractive index profile of the lens is achieved by controlling the thickness ratio of the alternating Si and SiO 2 layers determined by effective medium theory. Both structures are optimized to cover the entire C-band in the single mode implementation. The transmission efficiency of the ring-based structure is superior to the radial-based implementation, however, the radial-based structure almost covers the entire U-band as well. Other communication bands are partially covered in both cases. Full-wave simulations prove that the performance of multimode waveguide crossing based on the MFE lens with a radius of 2.32 m  is promising with the average insertion loss of 0.17dB and crosstalk levels below -24.2dB in the C-band for TM 0 and TM 1 modes. The multimode intersection almost covers the entire C, L, and U bands of optical communication.

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 waveguide crossing medium based on quasi-conformal transformation optics is designed and implemented on the silicon-on-insulator platform. Two approaches were taken to realize the designed lens: graded photonic crystal and varying the thickness of Si 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 3.77×3.77 µm 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 and the crosstalk of less than -72, -61, and -27 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, proposed method can be expanded to design waveguide crossings with even higher number of supporting modes by increasing the size of the lens.     J J J J J J