The consequences of non-differentiable angular dispersion in optics: Tilted pulse fronts versus space-time wave packets
arXiv:2109.07039 · doi:10.1364/OE.442950
Abstract
Conventional diffractive and dispersive devices introduce angular dispersion (AD) into pulsed optical fields thus producing so-called 'tilted pulse fronts'. Naturally, it is always assumed that the functional form of the wavelength-dependent propagation angle associated with AD is differentiable with respect to wavelength. Recent developments in the study of space-time wave packets -- pulsed beams in which the spatial and temporal degrees of freedom are inextricably intertwined -- have pointed to the existence of non-differentiable AD: field configurations in which the propagation angle does not possess a derivative at some wavelength. Here we investigate the consequences of introducing non-differentiable AD into a pulsed field and show that it is the crucial ingredient required to realize group velocities that deviate from (the speed of light in vacuum) along the propagation axis in free space. In contrast, the on-axis phase and group velocities are always equal in conventional scenarios. Furthermore, we show that non-differentiable AD is needed for realizing anomalous or normal group-velocity dispersion along the propagation axis, while simultaneously suppressing all higher-order dispersion terms. These and several other consequences of non-differentiable AD are verified experimentally using a pulsed-beam shaper capable of introducing AD with arbitrary spectral profile. Rather than being an exotic phenomenon, non-differentiable AD is an accessible, robust, and versatile resource for sculpting pulsed optical fields.
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