Chirped optical X-shaped pulses in material media.

We analyze the properties of chirped optical X-shaped pulses propagating in material media without boundaries. We show that such ("superluminal") pulses may recover their transverse and longitudinal shapes after some propagation distance, whereas the ordinary chirped Gaussian pulses can recover their longitudinal width only (since Gaussian pulses suffer a progressive transverse spreading during their propagation). We therefore propose the use of chirped optical X-type pulses to overcome the problems of both dispersion and diffraction during pulse propagation.