Exploring the consequences of non-differentiable angular dispersion in optical fields

Diffractive and dispersive devices introduce angular dispersion (AD) into pulsed optical fields. It is commonly assumed that the propagation angle of each wavelength is differentiable with respect to wavelength. However, recently developed space-time (ST) wave packets – propagation-invariant pulsed beams whose spatial and temporal degrees of freedom are intertwined – provide evidence for the existence of ‘non-differentiable’ AD in which the derivative of the propagation angle is not defined at some wavelength. We experimentally explore the unique consequences of introducing non-differentiable AD into a pulsed optical field. Whereas traditional AD ensures luminal group velocities for pulses traveling along the optical axis, we verify that the group velocity of ST wave packets endowed with non-differentiable AD can be tuned arbitrarily. We also confirm that non-differentiable AD enables tuning the group-velocity dispersion in both the normal and anomalous regimes while simultaneously suppressing higher-order dispersion coefficients, or may be used to intentionally suppress or induce there higher-order terms. These characteristics have been realized experimentally using a universal AD synthesizer capable of producing an arbitrary AD spectral profile. These developments may lead to new applications in dispersion compensation and nonlinear optics.