Non-Paraxial Accelerating Beams

TL;DR

This paper introduces non-paraxial accelerating electromagnetic beams that follow circular trajectories, exhibit shape-preserving bending with sub-wavelength features, and include a new family of periodic solutions, expanding the concept of Airy beams.

Contribution

It presents the first exact solutions of Maxwell's equations for non-paraxial accelerating beams, generalizing Airy beams to circular trajectories with detailed analysis.

Findings

Beams accelerate along circular paths with shape preservation.

Main lobe's Poynting vector turns over 90 degrees.

Beams are self-healing and include new periodic solutions.

Abstract

We present the spatially accelerating solutions of the Maxwell equations. Such non-paraxial beams accelerate in a circular trajectory, thus generalizing the concept of Airy beams. For both TE and TM polarizations, the beams exhibit shape-preserving bending with sub-wavelength features, and the Poynting vector of the main lobe displays a turn of more than 90 degrees. We show that these accelerating beams are self-healing, analyze their properties, and compare to the paraxial Airy beams. Finally, we present the new family of periodic accelerating beams which can be constructed from our solutions.