Abstract
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.
Highlights
Propagation-invariant waves form a class of growing importance and have distinct electromagnetic profiles that remain unchanged with propagation
The electromagnetic fields resulting from a charge moving in complex space-time, as opposed to real space-time, are exact, physical solutions to the source-free Maxwell’s equations
We have presented the complex charge paradigm: the use of a charge that exists in complex space-time and whose trajectory can be controlled at will to generate both existing and new families of electromagnetic wavepackets
Summary
Propagation-invariant waves form a class of growing importance and have distinct electromagnetic profiles that remain unchanged with propagation. They range description of electromagnetic beams and pulses, and other effects in modern from nondiffracting modes, such as Bessel, optics. This work disrupts this viewpoint by shifting point charges into the complex plane, and showing that their singularities give rise to propagating, divergence-free wavepackets. The abruptly focusing X-wave–a propagation-invariant X-wave-like wavepacket with prechosen displaying a host of intriguing physical phenomena like self-healing[31,32,33,34] and superluminal and subluminal travel,[35,36,37,38,39]
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