Based on the exact numerical simulation and physical analysis, we have demonstrated all-angle single-beam left-handed behavior and superlens for both transverse electric and transverse magnetic modes in a two-dimensional coated photonic crystal. The imaging behaviors by two-dimensional photonic-crystal-based superlens have been investigated systematically. Good-quality images and focusing, with relative refractive index of -1, have been observed in these systems for both polarized waves. In contrast to the images in near-field region for the lowest valence band, non-near-field images, explicitly following the well-known wave-beam negative refraction law, have been demonstrated. The absorption and compensation for the losses by introducing optical gain in these systems have also been discussed. Thus, extensive applications of such a phenomenon to optical devices are anticipated.
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