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.