Propagation of time-truncated Airy-type pulses in media with quadratic and cubic dispersion

TL;DR

This paper analytically studies how finite-time truncated Airy pulses propagate in media with quadratic and cubic dispersion, revealing their self-healing properties and providing an efficient mathematical approach.

Contribution

It introduces an analytical method based on superposition of exponentially truncated Airy pulses to analyze propagation with higher-order dispersion effects.

Findings

Analytical description of truncated Airy pulse propagation

Demonstration of self-healing property of truncated Airy pulses

Efficient method avoiding numerical simulations

Abstract

In this paper, we describe analytically the propagation of Airy-type pulses truncated by a finite-time aperture when second and third order dispersion effects are considered. The mathematical method presented here, based on the superposition of exponentially truncated Airy pulses, is very effective, allowing us to avoid the use of time-consuming numerical simulations. We analyze the behavior of the time truncated Ideal-Airy pulse and also the interesting case of a time truncated Airy pulse with a "defect" in its initial profile, which reveals the self-healing property of this kind of pulse solution.