The consequences of non-differentiable angular dispersion in optics: Tilted pulse fronts versus space-time wave packets

TL;DR

This paper explores the effects of non-differentiable angular dispersion in pulsed optical fields, revealing its role in enabling group velocities different from c and controlling dispersion, with experimental validation.

Contribution

It demonstrates that non-differentiable angular dispersion is crucial for achieving unconventional group velocities and dispersion control in pulsed optics, expanding the understanding of angular dispersion effects.

Findings

Non-differentiable AD allows group velocities to deviate from c.

Non-differentiable AD enables anomalous or normal dispersion control.

Experimental verification using a pulsed-beam shaper confirms theoretical predictions.

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 $c$ (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.