  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 SiO2 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 2.23 \mu m is promising with the average insertion loss of 0.17dB and
crosstalk levels below -24.2dB in the C-band for TM0 and TM1 modes. The
multimode intersection almost covers the entire C, L, and U bands of optical
communication.
