Interacting Ring-Airy Beams in Nonlinear Media

Abstract

Finite-energy Airy optical beams were first observed in 2007 [1], followed by much research on these freely-accelerating, non-diffracting beams [2]–[4]. Several variants of the original Airy beam have since been studied, one of which is a radially-symmetric version known as the ring-Airy beam (RAB); this beam has several intriguing properties, such as the ability to strongly autofocus [4]. The form of the ring-Airy beam is\begin{equation*}u(x,y,z = 0) = A\cdot{\text{Ai}}\left( {{r_0} - \sqrt {{x^2} + {y^2}} } \right)\exp \left( {a\left( {{r_0} - \sqrt {{x^2} + {y^2}} } \right)} \right),\tag{1}\end{equation*}with Ai the Airy function, a a decay parameter, A the amplitude of the field, and r <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> a radial parameter controlling the form of the field [3]. It has already been revealed that a single RAB exhibits interesting dynamics in a Kerr medium [2], including a low-intensity region and a double focus – the position of the former being controllable by altering the degree of the medium’s nonlocality. These features have been argued to be potentially useful for optical trapping [2].