A complex two-dimensional hexagonal photonic crystal consisting of silicon (Si) and silica (SiO_2) cylinders embedded in the air background is proposed to achieve the effect of all-angle negative refraction imaging. Compared with normal hexagonal-lattice photonic crystals consisting of Si, the reduction of symmetry of the complex photonic crystal results in a large band gap between the second energy band and the third energy band, whereas in a normal hexagonal photonic crystal there is no gap between these two bands. Furthermore, the depressed energy band structures provide advantages to realize all-angle left-handed negative refraction similar to metamaterials. The far-field superlens imaging with an effective refractive index of -1 was demonstrated theoretically in the infrared region at the frequency of 200 THz. We also showed the far-field subwavelength resolution for imaging of two point sources with a distance of 0.66λ.
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