Manipulation of Airy Beams in Dynamic Parabolic Potentials

Abstract

The propagation of finite energy Airy beams in dynamic parabolic potentials, including uniformly moving, accelerating, and oscillating potentials, is investigated. The propagation trajectories of Airy beams are strongly affected by the dynamic potentials, but the periodic inversion of the beam remains invariant. The results may broaden the potential applications of Airy beams, and also enlighten ideas on Airy beam manipulation in nonlinear regimes.

Dynamic Optical Vortex Trajectory Guided by the Symmetric Pearcey Gaussian Vortex Beam in the Uniformly Moving Parabolic Potential

“…Different forms of the dynamic functions m(z) will result in the beam propagation of different trajectories, such as uniformly moving parabolic potential, accelerating parabolic potential, and oscillating parabolic potential. [22] If m(z) = 0, the dynamic parabolic potential case turns into the static parabolic potential situation. [24] To find out the solution of Equation (1), we change the dynamic potential into a static potential so that we can obtain the solution easily.…”

“…The uniformly moving parabolic potential, one kind of the dynamic potential, implies the potential will change uniformly with the enhancement of the propagation distance and affect the evolution of the optical beam, acting as an "external force" to stretch or suppress the beam during propagation. [22,23] In contrast to the beam propagates in the static potential, [24,25] the force from the dynamic potential is more flexible, and more parameters can control the accelerating trajectory. That means the beam can follow a pre-designed trajectory by configuring the refractive index of the medium.…”

Controlling the Trajectory of Swallowtail Gaussian Beams in Dynamic Parabolic Potentials

“…In the paraxial approximation, the propagation of the beams in the dynamic parabolic potential is described by the (1+1)D dimensionless Schrödinger equation [ 23,24 ] $$$$\begin{equation} 2i \frac{\partial \varphi (x, z)}{\partial z}+\frac{\partial ^2 \varphi (x, z)}{\partial x^2}-\alpha ^2[x-f(z)]^2 \varphi (x, z)=0 \end{equation}$$$$where φ is the beam envelope, α is the parabolic potential depth, x and z are the normalized transverse coordinate and propagation distance respectively. Assuming a medium with a parabolic potential, the refractive index can be expressed as $$n^{2}(r)=n_{0}^{2}(1-\alpha ^{2} r^{2})$$, where $$\alpha =(n_{0}^{2}-n_{1}^{2})^{1 / 2} /(n_{0} r_{1})$$.…”

“…[15] The photonic potential refers to an external potential that can effectively modify the dynamic behavior of the beam, which is based on the refractive index distribution of the medium. Various potential models, such as linear, [16][17][18][19][20] parabolic, [20][21][22] and general dynamic potentials [23,24] have been proposed by researchers to manipulate the acceleration trajectory of the beam. Regarding the parabolic potential, researchers have examined the propagation dynamics of different types of beams, [25][26][27][28] revealing some unique and intriguing characteristics during the propagation process, such as periodic inversion and focusing, as well as self-induced Fourier transformation.…”

Reflection and Refraction of an Airy Pulse at a Moving Temporal Boundary

“…The Airy pulse is a new type of wave packet that has been investigated extensively. [21][22][23][24][25][26][27] It has three novel characteristics: such as self-acceleration, resulting from a varying group velocity; [28,29] self-healing ability, which allows it to withstand the severity of perturbations; [24] and dispersion-free propagation. Airy pulses are often truncated to be of finite energy to enable them to be realized physically.…”