Exact Evolution of Ultrashort Hollow-Airy Pulses in the Spatiotemporal Domain

An exact analytic expression for an ultrashort hollow-Airy wave packet is presented beyond the slowly varying envelope approximation. The hollow-Airy wave packet combines the hollow-Gaussian beam in the spatial domain and the Airy pulse in the temporal domain. The spatiotemporal propagation dynamics of the ultrashort hollow-Airy pulse are analyzed by the numerical simulations. During the propagation in free space, the spatial intensity profile evolves from hollow-Gaussian to Gaussian shape; the temporal intensity profile retains Airy shape over several Rayleigh ranges. The acceleration property of the ultrashort Airy pulse is also demonstrated.