Negative refraction and left-handed behavior in two-dimensional photonic crystals

We systematically examine the conditions of obtaining left-handed (LH) behavior in photonic crystals. Detailed studies of the phase and group velocities as well as the phase n(p) and group n(g) refractive indices are given. The existence of negative refraction does not guarantee the existence of negative index of refraction and so LH behavior. A wedge type of experiment is suggested, which can unambiguously distinguinsh between cases of negative refraction that occur when left-handed behavior is present from cases that show negative refraction without LH behavior.