Time-spatial drift of decelerating electromagnetic pulses

Alexander G Nerukh,Dmitry A Nerukh

doi:10.1364/oe.21.017366

Alexander G Nerukh, Dmitry A Nerukh

Open Access

https://doi.org/10.1364/oe.21.017366

Copy DOI

Abstract

A time dependent electromagnetic pulse generated by a current running laterally to the direction of the pulse propagation is considered in paraxial approximation. It is shown that the pulse envelope moves in the time-spatial coordinates on the surface of a parabolic cylinder for the Airy pulse and a hyperbolic cylinder for the Gaussian. These pulses propagate in time with deceleration along the dominant propagation direction and drift uniformly in the lateral direction. The Airy pulse stops at infinity while the asymptotic velocity of the Gaussian is nonzero.

Highlights

Intensive theoretical and experimental investigations of Airy beams are motivated by their unusual features
A solution to the Schrodinger equation in the form of a non-spreading accelerating Airy wave function found by Berry and Balazs in 1979 [1] inspired Siviloglou and Christodoulides to put forward the concept of electromagnetic accelerated Airy beams [2, 3]
These seminal publications with theoretical formulations based on the paraxial approximation to the wave equation and experimental confirmation were followed by many works on the Airy beam properties, for example [4,5,6,7]

Summary

Introduction

Intensive theoretical and experimental investigations of Airy beams are motivated by their unusual features (non-diffractive propagation, accelerating motion, and self-healing). A solution to the Schrodinger equation in the form of a non-spreading accelerating Airy wave function found by Berry and Balazs in 1979 [1] inspired Siviloglou and Christodoulides to put forward the concept of electromagnetic accelerated Airy beams [2, 3] These seminal publications with theoretical formulations based on the paraxial approximation to the wave equation and experimental confirmation were followed by many works on the Airy beam properties, for example [4,5,6,7] (and citations therein). The parabolic dependence between time and the longitudinal coordinate with the leading dependence ~ eiωt is considered in a number of publications It is shown in [2] that a circular symmetric input field with the temporal behaviour according to the Airy function keeps this symmetry at later times propagating with time acceleration. We derive its solution by a rigorous method of the Green’s function that allows constructing other decelerating pulses (not Airy), the Gaussian is given as an example

The master equation

Decelerating Airy pulse

Decelerating Gaussian

Conclusions