The Complex Charge Paradigm: A New Approach for Designing Electromagnetic Wavepackets.

Singularities in optics famously describe a broad range of intriguing phenomena, from vortices and caustics to field divergences near point charges. The diverging fields created by point charges are conventionally seen as a mathematical peculiarity that is neither needed nor related to the description of electromagnetic beams and pulses, and other effects in modern optics. This work disrupts this viewpoint by shifting point charges into the complex plane, and showing that their singularities then give rise to propagating, divergence-free wavepackets. Specifically, point charges moving in complex space-time trajectories are shown to map existing wavepackets to corresponding complex trajectories. Tailoring the complex trajectories in this "complex charge paradigm" leads to the discovery and design of new wavepacket families, as well as unprecedented electromagnetic phenomena, such as the combination of both nondiffracting behavior and abruptly-varying behavior in a single wavepacket. As an example, the abruptly focusing X-wave-a propagation-invariant X-wave-like wavepacket with prechosen self-disruptions that enhance its peak intensity by over 200 times-is presented. This work envisions a unified method that captures all existing wavepackets as corresponding complex trajectories, creating a new design tool in modern optics and paving the way to further discoveries of electromagnetic modes and waveshaping applications.