Consequences of non-differentiable angular dispersion in optics: tilted pulse fronts versus space-time wave packets

Area of Science:

• Optics and Photonics
• Wave Packet Dynamics

Background:

• Conventional optical devices create tilted pulse fronts via differentiable angular dispersion (AD).
• Space-time wave packets exhibit intertwined spatial and temporal properties.
• The existence of non-differentiable AD, where propagation angle lacks a derivative, has been theorized.

Purpose of the Study:

• To investigate the consequences of non-differentiable angular dispersion in pulsed optical fields.
• To demonstrate the role of non-differentiable AD in achieving unique on-axis group velocities and dispersion characteristics.
• To experimentally validate the effects of non-differentiable AD.

Main Methods:

• Theoretical investigation of pulsed optical fields with non-differentiable AD.
• Analysis of group velocity and dispersion properties in free space.
• Experimental verification using a custom pulsed-beam shaper capable of arbitrary spectral profiles.

Main Results:

• Non-differentiable AD allows on-axis group velocities to deviate from the speed of light (c) in free space.
• Conventional pulsed fields in free space always exhibit an on-axis group velocity equal to c.
• Non-differentiable AD is essential for achieving normal or anomalous group-velocity dispersion while suppressing higher-order dispersion.
• Experimental results confirm the theoretical predictions regarding non-differentiable AD's effects.

Conclusions:

• Non-differentiable angular dispersion is a critical factor for controlling pulsed optical fields.
• This phenomenon enables unique control over light speed and dispersion, deviating from conventional limitations.
• Non-differentiable AD is an accessible and versatile tool for advanced optical field sculpting.