Abruptly Focusing and Defocusing Needles of Light and Closed-Form Electromagnetic Wavepackets

TL;DR

This paper introduces a novel family of electromagnetic wavepackets that can abruptly focus and defocus, overcoming traditional Fourier optics limitations, and provides the first closed-form solutions for finite-energy electromagnetic pulses with unique propagation properties.

Contribution

It presents a new class of electromagnetic wavepackets capable of abrupt focusing and defocusing, along with the first closed-form Maxwell solutions for finite-energy pulses.

Findings

Wavepackets can focus and defocus abruptly regardless of aspect ratio.

First closed-form solutions for finite-energy electromagnetic pulses.

On-axis intensity peaks travel at the speed of light despite diffraction.

Abstract

Fourier optics enforces a tradeoff between length and narrowness in electromagnetic wavepackets, so that a narrow spatial focus diffracts at a large divergence angle, and only infinitely wide beams can remain non-diffracting. We show that it is possible to bypass this tradeoff between the length and narrowness of intensity hotspots, and find a family of electromagnetic wavepackets that abruptly focus to and defocus from high-intensity regions of any aspect ratio. Such features are potentially useful in scenarios where one would like to avoid damaging the surrounding environment, for instance, to target tumors very precisely in cancer treatment, drill holes of very precise dimensions in laser machining, or trigger nonlinear processes in a well-defined region. In the process, we also construct the first closed-form solutions to Maxwell's equations for finite-energy electromagnetic pulses. These pulses also exhibit intriguing physics, with an on-axis intensity peak that always travels at the speed of light despite inherent diffraction.