Directed diffraction without negative refraction

Using the FDTD method, we investigate the electromagnetic propagation in two-dimensional photonic crystals, formed by parallel air cylinders in a dielectric medium. The corresponding frequency band structure is computed using the standard plane-wave expansion method. It is shown that within partial bandgaps, waves tend to bend away from the forbidden directions. This phenomenon perhaps need not be explained in terms of negative refraction or `superlensing' behavior, contrast to what has been conjectured.