Left-Handed-Material-like behavior revealed by arrays of dielectric cylinders

We investigate the electromagnetic propagation in two-dimensional photonic crystals, formed by parallel dielectric cylinders embedded a uniform medium. The transmission of electromagnetic waves through prism structures are calculated by the standard multiple scattering theory. The results demonstrate that in certain frequency regimes and when the propagation inside the scattering media is not considered, the transmission behavior mimics that expected for a left-handed material. Such feature may illusively lead to the conclusion that a left-handed material is fabricated and it obeys Snell's law of negative refraction. We also discuss possible ambiguities that may be involved in previous experimental evidence of left-handed materials.