# Phase memory preserving harmonics from abruptly autofocusing beams

## TL;DR

This paper shows that harmonics generated from abruptly auto-focusing ring-Airy beams retain the phase structure of the fundamental beam, enabling precise control of their focusing properties for applications in strong field science.

## Contribution

The study introduces the concept of phase memory in harmonics from ring-Airy beams and demonstrates their autofocusing behavior both theoretically and experimentally.

## Key findings

- Harmonics preserve the phase distribution of the fundamental beam.
- Harmonics inherit the abrupt autofocusing property.
- Harmonics' foci can coincide with the fundamental's focus under certain conditions.

## Abstract

We demonstrate both theoretically and experimentally that the harmonics from abruptly auto-focusing ring-Airy beams present a surprising property, they preserve the phase distribution of the fundamental beam. Consequently, this "phase memory" inherits to the harmonics the abrupt autofocusing behavior, while, under certain conditions, their foci coincide in space with the one of the fundamental. Experiments agree well with our theoretical estimates and detailed numerical calculations. Our findings open the way for the use of such beams and their harmonics in strong field science.