Ultrashort tilted-pulse-front pulses and nonparaxial tilted-phase-front beams

Electromagnetic pulses with tilted pulse fronts are instrumental in enhancing the efficiency of many light-matter interaction processes, with prominent examples including terahertz generation by optical rectification, dielectric laser acceleration, ultrafast electron imaging, and X-ray generation from free electron lasers. Here, we find closed-form expressions for tilted-pulse-front pulses that capture their exact propagation dynamics even in deeply nonparaxial and sub-single-cycle regimes. By studying the zero-bandwidth counterparts of these pulses, we further obtain classes of nondiffracting wavepackets whose phase fronts are tilted with respect to the direction of travel of the intensity peak. The intensity profiles of these nonparaxial nondiffracting wavepackets move at a constant velocity that can be much greater than or much less than the speed of light, and can even travel backward relative to the direction of phase front propagation.