Higher-order transverse modes of ultrashort isodiffracting pulses

We present a family of space-time nonseparable analytic solutions describing spatiotemporal dynamics of isodiffracting single-cycle and few-cycle pulses,with Hermite-Gaussian and Laguerre-Gaussian transverse profiles. These solutions are space-time localized wave packets propagating in free space. The transverse field profile acts as a spatially dependent filter, modifying the pulse spectrum and removing certain frequencies. The consequences of those effects in the time domain are the distortions of pulse envelope and temporal wave form and the creation of "dark pulses" at certain transverse positions. In addition, due to the space-time coupling, the instantaneous transverse field pattern changes inside the pulse, as well as with propagation distance. These higher-order mode solutions can be used to analyze reflected or scattered terahertz pulses, and to understand the wave-form distortions of terahertz signals in applications. They are also capable of modeling pulsed fields of phase locking of both transverse and longitudinal modes in total mode-locked lasers.