Theoretical method for generating regular spatiotemporal pulsed-beam with controlled transverse-spatiotemporal dispersion

Herein we theoretically report a method that generates a transverse-spatiotemporal dispersion, which is distinct from previous spatial, temporal, and longitudinal-spatiotemporal dispersions. By modulating the transverse-spatiotemporal dispersion, two not yet reported spatiotemporally structured beams, i.e., the honeycomb beam and the picket-fence beam, can be generated in the space-time domain. The generated spatiotemporally structured beams have novel and tunable periodic distributions. The transverse-spatiotemporal dispersion, spatiotemporally structured beams and their inner relationship are analyzed and introduced. We believe that this method might open a path towards new optical beams for potential applications, such as ultrafast optical fabrication and detection.