Dual Abruptly Focus of Modulated Circular Airy Beams

Jinggui Zhang,Jun He

doi:10.1109/jphot.2017.2655015

Abstract

In this paper, we propose a new kind of circular Airy beam whose spectrum is imposed an initial quadratic phase modulation (QPM). Unlike common abruptly autofocusing beams, we find that such modulated circular Airy beams (MCAB) at image plane, i.e., initial plane, may be morphed into conventional Airy patterns or Bessel-like patterns in spatial regime, depending on the magnitude of QPM. We further investigate the propagation characteristics of the MCAB both analytically and numerically. It is found that the focal intensity, as well as the size of focal spot, do not change with the QPM, but the latter greatly affects the focal trajectory and the focal position of MCAB. In particular, we show that, for the case of Airy pattern, MCAB will exhibit a dual abruptly focusing behaviors having the same focal intensity as well as size of focal spot, where there is one focus behind the image plane, and the another one is in front of it. On the other hand, for the case of Bessel-like pattern, the dual abruptly foci are simultaneously observed behind the image plane for positive QPM but in front of it for negative QPM, thus leading to the formation of an elegant optical bottle with paraboloidal shape. Such novel dual focusing behaviors are expected to be applied in the field of optical trapping and particle acceleration.

Highlights

The original research to the theoretical concept of circular Airy beams was reported by Efremidis and Christodoulides in 2011 [1], followed soon after by their first experimental observation [2]
We have presented a theoretical investigation on the propagation characteristics of modulated circular Airy beams (MCAB) both numerically and analytically
The results of our analysis show that such modulated circular Airy beams at image plane may be morphed into conventional Airy patterns or Bessel-like patterns in spatial regime, depending on the magnitude of quadratic phase modulation (QPM)

Summary

Introduction

The original research to the theoretical concept of circular Airy beams was reported by Efremidis and Christodoulides in 2011 [1], followed soon after by their first experimental observation [2]. An optical beam can be generated or controlled either directly in the spatial regime or indirectly in the Fourier regime For the latter, engineering optical beams in spectral regime has been found to highlight some potential applications for generating and manipulating different families of specific laser beams, such as the reduced-side lobe Airy beams [14], curved Bessel beams that follows desired paths [15], and nonlinear curved beams [16]. In [20] Zhang et al introduced an initial QPM into an Airy pulse in spectral regime, showing how to control the shedding solitons in optical fibers Motivated by these foregoing researches, in this paper, we propose a new kind of MCABs based upon the Hankel transform. Numerous novel and intriguing behaviors will be found in our investigations

Theories of Modulated Circular Airy Beam

Analytical Analysis

Numerical Analysis

Conclusion