Autofocusing luminal and superluminal spatiotemporally localized waves.

Highly focused space-time wavepackets in free space have already been achieved by means of suitable superpositions of nondiffracting and almost undistorted spatiotemporally localized pulses. Here, we present analytically individual autofocusing luminal and superluminal localized waves that can attain high-intensity peaks and spatiotemporal localization at prespecified positions along the path of their propagation.