  The imaging properties of the Maxwell's fisheye (MFE) lens makes it a viable
candidate to implement power coupling between different types of waveguides. A
coupler based on the MFE lens is designed to couple a square lattice photonic
crystal to a triangular lattice one. The MFE lens is implemented as ring-based
multilayer and graded photonic crystal (GPC) structures. The performance of the
ring-based MFE lens is better than the GPC-based one in the C-band of optical
communication. The proposed ring-based MFE coupler has a footprint of
$3.62\times 3.62\mu m$ and covers the entire C and U bands. The S and L bands
are partially covered. The average insertion loss of 0.1dB and the maximum
return loss of -11dB in the C-band is achieved.
