  The absolute instruments like the Maxwell's fisheye (MFE) lens with
aberration-free imaging properties have found interesting applications such as
waveguide crossing. The flat wavefront of an optical wave in the waveguide does
not match with the circular wavefront of the circular MFE lens at its edge,
hence, we design and study the performance of a square MFE lens as photonic
crystal waveguide crossing medium. We also have truncated the square MFE lens
to a cross-shaped lens to squeeze it inside the crossing waveguides, therefore,
practically no extra footprint is consumed by the truncated MFE lens. The
numerical simulations show that graded photonic crystal-based implementation of
the truncated MFE lens provides a bandwidth of 186 nm covering the entire S-
and C-bands and partially covering the E- and L-bands of optical communication.
The crosstalk levels are lower than -18 dB while the average insertion loss is
0.32 dB in the C-band.
