Photonic crystal waveguide crossing based on transformation optics

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.