Closed-form expressions for nonparaxial accelerating beams with pre-engineered trajectories

TL;DR

This paper introduces a real-space method to generate nonparaxial accelerating beams with arbitrary convex trajectories, providing closed-form phase expressions and enabling control over intensity profiles along the caustic.

Contribution

It presents the first closed-form solutions for power-law and exponential trajectories in nonparaxial accelerating beams with arbitrary convex paths.

Findings

Closed-form phase expressions for various trajectories

First-time derivation of power-law and exponential trajectories

Ability to tailor intensity profiles along the caustic

Abstract

In this letter, we propose a general real-space method for the generation of nonparaxial accelerating beams with arbitrary predefined convex trajectories. Our results lead to closed-form expressions for the required phase at the input plane. We present such closed-form results for a variety of caustic curves: besides circular, elliptic, and parabolic, we find for the first time general power-law and exponential trajectories. Furthermore, by changing the initial amplitude we can design different intensity profiles along the caustic.