What I really can't understand, What are the properties of a medium with refractive index less than unity? how does it effect light rays which fall on them?
It's no different than behaviour of rays that transit from matter to vacuum. In refraction, only the ratio of indices matters, not the absolute value of the phase speed of light. This is actually used in refractors for X rays.
Properties are nothing speciall really - the phase velocity is greater than the speed of light, but that's just the speed of moving maxima and minima of the field, not the speed of information (energy transfer). Why it happens? When your frequency is above the resonant frequency of some vibration mode in the medium, the mode (for instance, vibrating electrons) vibrates in such a phase that the field of the electrons amplifies the velocity of the wavecrests (they vibrate in opposite phase with the external light field) while below the resonant frequency, they are in phase (which yields large electric susceptibility - generally, the lower the frequency, the higher the susceptibility and refractive index, with a jump down at every resonance of the material (raising the frequency), with a slight "dip" just after you cross the resonance). The behaviour exactly at resonance is a bit more interesting (anomalous dispersion). That's very useful for lasing, for instance.