Abstract
In this paper, we designed Maxwell's fish-eye lens in a square shape from a conformal mapping and constructed it into a waveguide and a photonic crystal. We studied the unidirectional self-imaging effect from both geometric optics and wave optics. Ray tracing and full-wave simulations were performed to validate this effect. Specifically, the designed waveguide is of a finite width while having the same imaging properties as the ideal infinite waveguide---the Mikaelian lens, the refractive index profile of which is 1/cosh ($x$) [Mikaelian and Prokhorov, Prog. Opt. 17, 279 (1980)].
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